Philosophy: Everything You Need to Know


Here I will be laying out the main ideas of some of history’s most important philosophers. These will be extremely brief, simplified explanations of some of the big ideas for each of these philosophers. This should not be construed as a replacement or substitute for a deeper reading on these philosophers.


As I said, these summaries will be very brief. Entire books could (and have been) written by, and about, each and every one of these philosophers and their various ideas. There have been numerous ways of interpreting, and refuting, practically every word I’ll be writing here. As such, it’s important to keep in mind that what will be written here is not the definitive or settled consensus, though I have tried to stay within the sort of “orthodox” interpretation on all these things. The point of this post is to be a resource for (A) seeing the historical development of thought and (B) getting a general sense of what each of these thinkers was about.

In the name of brevity, there will be minimal biographical information provided for each of these philosophers, aside from the best known dates of birth and death. Even though historical context is important, this is meant to be a quick overview of main concepts.

Most of what will be here is western philosophy, which is European, American, and some Middle Eastern. I am likely not qualified to speak on much eastern philosophy (assuming I’m even qualified to speak on western philosophy), so entries on East Asian, South Asian, and African philosophy will be minimal, covering only a few of the most towering figures in those areas.

Also note that this will be a progressive entry, where I will update and add to it over time, so what you see is likely not the final form, and there will likely be empty entries (names without any information for them). Feel free to leave comments asking for clarifications or with suggestions for further additions. Without further ado, lets get into it.

Ancient to Medieval Philosophy

The ancients (mostly Greek) and the medieval scholastics (mostly European and Arabic) can perhaps be broadly thought of as the pre-scientific philosophers. Their concerns (speaking very generally) tended to be more metaphysical and their approach tended to be deferential to their predecessors. Notable exceptions were people like Socrates, Plato, and Aristotle in the west and Lao Tzu, Siddhartha Gautama, and Confucius in the east (hence why they are such towering figures). The pre-Socratics were original thinkers as well, but they suffer from having so little known about them (much of it coming from sources like Aristotle, who was looking to refute them).


Orpheus (said to have lived several generations before Homer): a Thracian bard, legendary musician and prophet in ancient Greek religion. He was also a renowned poet and, according to the legend, travelled with Jason and the Argonauts in search of the Golden Fleece, and even descended into the Underworld of Hades to recover his lost wife Eurydice. Many Greeks believed Orpheus to be a real person, but others (like Aristotle) believed he was just a legend.

  1. Orphism: religious beliefs and practices originating in the ancient Greek and Hellenistic world, associated with literature ascribed to the mythical poet Orpheus, who descended into the Greek underworld and returned. Orphics revered Dionysus (who once descended into the Underworld and returned) and Persephone (who annually descended into the Underworld for a season and then returned). Orphism has been described as a reform of the earlier Dionysian religion, involving a re-interpretation or re-reading of the myth of Dionysus and a re-ordering of Hesiod‘s Theogony, based in part on pre-Socratic philosophy.

Homer (8th or 9th century): legendary author to whom the authorship of the Iliad and the Odyssey (the two epic poems that are the foundational works of ancient Greek literature) is attributed. He is regarded as one of the greatest and most influential authors of all time.

Thales of Miletus (624 B.C.E. – 548 B.C.E.): Water.

  1. “That from which is everything that exists and from which it first becomes and into which it is rendered at last, its substance remaining under it, but transforming in qualities, that they say is the element and principle of things that are. …For it is necessary that there be some nature (φύσις), either one or more than one, from which become the other things of the object being saved… Thales the founder of this type of philosophy says that it is water.” -Aristotle speaking on Thales
  2. Thales’ Theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.

Anaximander of Miletus (610 B.C.E. – 546 B.C.E.): Apeiron.

  1. Claimed that nature is ruled by laws, just like human societies, and anything that disturbs the balance of nature does not last long.
  2. Anaximander explains how the four elements of ancient physics (air, earth, water and fire) are formed, and how Earth and terrestrial beings are formed through their interactions. Unlike other Pre-Socratics, he never defines this principle precisely, and it has generally been understood (e.g., by Aristotle and by Saint Augustine) as a sort of primal chaos. According to him, the Universe originates in the separation of opposites in the primordial matter Apeiron (“that which is limitless”). It embraces the opposites of hot and cold, wet and dry, and directs the movement of things; an entire host of shapes and differences then grow that are found in “all the worlds” (for he believed there were many).

Anaximenes of Miletus (586 B.C.E. – 526 B.C.E.): Ancient Greek, Ionian Pre-Socratic philosopher from Miletus in Asia Minor, active in the latter half of the 6th century BC. The details of his life are obscure because none of his work has been preserved. Air as the arche, with more condensed air made for colder, denser objects and more rarefied air made for hotter, lighter objects.

Xenophanes of Colophon (570 B.C.E. – 475 B.C.E.): Greek philosopher, theologian, poet, and critic of Homer from Ionia who traveled throughout the Greek-speaking world in early Classical Antiquity. As a poet, Xenophanes was known for his critical style, writing poems that are considered among the first satires.

  1. Water and Earth: Xenophanes concluded from his examination of fossils of sea creatures that were found above land that water once must have covered all of the Earth’s surface. He used this evidence to conclude that the cosmic principle of the universe was a tide flowing in and out between wet and dry, or earth (γῆ) and water (ὕδωρ). These two extreme states would alternate between one another, and with the alternation human life would become extinct, then regenerate (or vice versa depending on the dominant form).
  2. Reincarnation: These two extreme states (wet and dry) would alternate between one another, and with the alternation human life would become extinct, then regenerate (or vice versa depending on the dominant form).

Pythagoras of Samos (570 B.C.E. – 495 B.C.E.): Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Namesake of the Pythagorean Theorem.

Lao Tzu (ca. 571 B.C.E.): alternatively Laozi or Lao-Tze. Author of the Tao Te Ching and founder of Taoism (Daoism). The existence of Laozi is somewhat mythical, with much of Taoism actually coming from a later philosopher Zhuangzi (aka Zhuang Zhou) who lived between 369 B.C.E. and 286 B.C.E. As with much of eastern philosophy, I am quite unqualified to speak on it, so I am going to leave some links that do a better job of explaining it than I could (text is all copied and pasted from the linked article).

  1. Laozi: “The name “Laozi” is best taken to mean “Old (lao) Master (zi),” and Laozi the ancient philosopher is said to have written a short book, which has come to be called simply the Laozi, after its putative author, a common practice in early China.”
  2. Daoism: “Daoism is an umbrella that covers a range of similarly motivated doctrines. The term “Daoism” is also associated with assorted naturalistic or mystical religions.”
  3. Religious Daoism: “Even if the term “religious Daoism” is accepted, it is not clear which entity it should define, and different scholars might explain its meaning in different ways. Should “religion” include all of Daoism except for its “philosophy”? This would probably exclude the views of the Daode jing (Book of the Way and Its Virtue; §1.1 below), which Daoists have seen as an integral part—in fact, as the source—of their tradition. Omitting these views would be something like writing a survey of Christianity that intentionally neglects to consider the thought and works of the theologians. Should “religion” only include communal ritual with the related pantheons of gods, on the one hand, and the priestly and monastic institutions, on the other? If so, an article on “religious Daoism” would exclude meditation, alchemy, and other individual practices that Daoists—including those who did not practice them—have seen as major components of their tradition.”
  4. Neo-Daoism: “The term “Neo-Daoism” (or “Neo-Taoism”) seeks to capture the focal development in early medieval Chinese philosophy, roughly from the third to the sixth century C.E. Chinese sources generally identify this development as Xuanxue, or “Learning (xue) in the Profound (xuan).””
  5. Metaphysics in Chinese Philosophy: “[W]hile European metaphysics has tended to center on problems of reconciliation (how ontologically distinct things can interact), Chinese metaphysics has been more concerned with problems of distinction. The most central problems are around the status of individualized things, the relationship between the patterns of nature and specifically human values, and how to understand the ultimate ground of the world in a way that avoids either reification or nihilism. These become problems precisely because of the underlying assumptions of holism and change.”

The following videos are a great introduction to Daoism:

Siddhartha Gautama (ca. 563 B.C.E. – ca 483 B.C.E.): an ascetic and a religious teacher of South Asia who lived in the latter half of the first millennium BCE. He is the founder of Buddhism and revered by Buddhists as an enlightened being whose teachings sought a path to freedom from ignorance, craving, rebirth and suffering. Probably the broadest teachings common to Buddhism are the Four Noble Truths and the Noble Eight-Fold Path, which I will explicate below:

  1. Four Noble Truths (source): this is all just copy-pasted from the Wikipedia article
    1. dukkha (suffering, incapable of satisfying, painful) is an innate characteristic of existence in the realm of samsara;
    2. samudaya (origin, arising, combination; ’cause’): together with dukkha arises taṇhā (“craving, desire or attachment, lit. “thirst”);
    3. nirodha (cessation, ending, confinement): dukkha can be ended or contained by the renouncement or letting go of this taṇhā; the confinement of tanha releases the excessive bind of dukkha;
    4. magga (path, Noble Eightfold Path) is the path leading to the confinement of tanha and dukkha
  2. The Noble Eight-Fold Path (source): this is all just copy-pasted from the Wikipedia article
    1. Right Resolve or Intention: the giving up of home and adopting the life of a religious mendicant in order to follow the path; this concept aims at peaceful renunciation, into an environment of non-sensuality, non-ill-will (to loving kindness), away from cruelty (to compassion). Such an environment aids contemplation of impermanence, suffering, and non-Self.
    2. Right Speech: no lying, no rude speech, no telling one person what another says about him to cause discord or harm their relationship.
    3. Right Conduct or Action: no killing or injuring, no taking what is not given, no sexual misconduct, no material desires.
    4. Right Livelihood: no trading in weapons, living beings, meat, liquor, and poisons.
    5. Right Effort: preventing the arising of unwholesome states, and generating wholesome states, the bojjhagā (Seven Factors of Awakening). This includes indriya-samvara, “guarding the sense-doors”, restraint of the sense faculties.
    6. Right Mindfulness (sati; Satipatthana; Sampajañña): “retention”, being mindful of the dhammas (“teachings”, “elements”) that are beneficial to the Buddhist path. In the vipassana movement, sati is interpreted as “bare attention”: never be absent minded, being conscious of what one is doing; this encourages the awareness of the impermanence of body, feeling and mind, as well as to experience the five aggregates (skandhas), the five hindrances, the four True Realities and seven factors of awakening.
    7. Right samadhi (passaddhi; ekaggata; sampasadana): practicing four stages of dhyāna (“meditation”), which includes samadhi proper in the second stage, and reinforces the development of the bojjhagā, culminating into upekkha (equanimity) and mindfulness. In the Theravada tradition and the vipassana movement, this is interpreted as ekaggata, concentration or one-pointedness of the mind, and supplemented with vipassana meditation, which aims at insight.
    8. Right View: our actions have consequences, death is not the end, and our actions and beliefs have consequences after death. The Buddha followed and taught a successful path out of this world and the other world (heaven and underworld/hell). Later on, right view came to explicitly include karma and rebirth, and the importance of the Four Noble Truths, when “insight” became central to Buddhist soteriology.

I am quite unqualified to speak on Buddhism with any authority. I will link to some great articles on Buddhism and offer some videos.

  1. The Buddha: “teachings, preserved in texts known as the Nikāyas or Āgamas, concern the quest for liberation from suffering. While the ultimate aim of the Buddha’s teachings is thus to help individuals attain the good life, his analysis of the source of suffering centrally involves claims concerning the nature of persons, as well as how we acquire knowledge about the world and our place in it. These teachings formed the basis of a philosophical tradition that developed and defended a variety of sophisticated theories in metaphysics and epistemology.”
  2. Mind in Indian Buddhism:
  3. Ethics in Indian and Tibetan Buddhism
  4. Nāgārjuna (ca 150–250 CE): “the most important Buddhist philosopher after the historical Buddha himself and one of the most original and influential thinkers in the history of Indian philosophy. His philosophy of the “middle way” (madhyamaka) based around the central notion of “emptiness” (śūnyatā) influenced the Indian philosophical debate for a thousand years after his death”
  5. Abhidharma: ” [the method of] Abhidharma is to be contrasted with Sūtrānta, the system of the Buddha’s discourses (Skt., sūtras, Pali, suttas). Unlike the earlier Buddhist discourses that are colloquial in nature, the Abhidharma method presents the Buddha’s teachings in technical terms that are carefully defined to ensure analytical exactitude. In content, Abhidharma is distinctive in its efforts to provide the theoretical counterpart to the Buddhist practice of meditation and, more broadly, a systematic account of sentient experience.”
  6. Japanese Zen Buddhism: “aims at the perfection of personhood. To this end, sitting meditation called “za-zen” is employed as a foundational method of prāxis across the different schools of this Buddha-Way—which is not an ideology, but a way of living. Through za-zen the Zen practitioner attempts to embody non-discriminatory wisdom vis-à-vis the meditational experience known as “satori” (enlightenment). A process of discovering wisdom culminates, among other things, in the experiential apprehension of the equality of all thing-events.”

I could never do a better job of explaining Buddhism than the following videos:

Confucius (September 28, 551 B.C.E. – April 11, 479 B.C.E.): real name Kǒng Fūzǐ. Confucius was a Chinese philosopher and politician of the Spring and Autumn period who is traditionally considered the paragon of Chinese sages. Confucius’s teachings and philosophy underpin East Asian culture and society, remaining influential across China and East Asia to this day.

  1. Analects (from Wikipedia): It is believed to have been written during the Warring States period (475–221 BC), and it achieved its final form during the mid-Han dynasty (206 BC–220 AD). By the early Han dynasty the Analects was considered merely a “commentary” on the Five Classics, but the status of the Analects grew to be one of the central texts of Confucianism by the end of that dynasty. The Five Classics are the following:
    1. I Ching or Classic of Change or Book of Changes.
    2. Classic of Poetry or Book of Songs is the earliest anthology of Chinese poems and songs.
    3. Book of Documents or Book of History Compilation of speeches of major figures and records of events in ancient times embodies the political vision and addresses the kingly way in terms of the ethical foundation for humane government.
    4. Book of Rites describes the social forms, administration, and ceremonial rites of the Zhou Dynasty.
    5. Spring and Autumn Annals chronicles the period to which it gives its name, Spring and Autumn period (771–476 BCE) and these events emphasise the significance of collective memory for communal self-identification, for reanimating the old is the best way to attain the new.

Again, I defer to the following videos (made by the same person as the ones above on Buddha).

Sun Tzu (544 B.C.E. – 496 B.C.E.): Chinese military general, strategist, philosopher, and writer who lived during the Eastern Zhou period. Sun Tzu is traditionally credited as the author of The Art of War, an influential work of military strategy that has affected both Western and East Asian philosophy and military thinking.

Heraclitus of Ephesus (535 B.C.E. – 475 B.C.E.): Fire.

  1. Everything changes: “Everything changes and nothing remains still … and … you cannot step twice into the same stream.”
  2. If objects are new from moment to moment so that one can never touch the same object twice, then each object must dissolve and be generated continually momentarily and an object is a harmony between a building up and a tearing down. Heraclitus calls the oppositional processes ἔρις (eris), “strife”, and hypothesizes that the apparently stable state, δίκη (dikê), or “justice”, is a harmony of strife.

Parmenides of Elea (Born c. 515 B.C.E.): The Parmenidean One.

  1. The every-day perception of reality of the physical world is mistaken, and that the reality of the world is ‘One Being’ – an unchanging, ungenerated, indestructible whole.
  2. He argued that movement was impossible because it requires moving into “the void”, and Parmenides identified “the void” with nothing, and therefore (by definition) it does not exist.

Anaxagoras (510 B.C.E. – 428 B.C.E.): Disagreed with Parmenides.

  1. Described the world as a mixture of primary imperishable ingredients, where material variation was never caused by an absolute presence of a particular ingredient, but rather by its relative preponderance over the other ingredients; in his words, “each one is… most manifestly those things of which there are the most in it”.
  2. He introduced the concept of Nous (Cosmic Mind) as an ordering force, which moved and separated out the original mixture, which was homogeneous, or nearly so.

Empedocles of Acagras (494 B.C.E. – 434 B.C.E.): Fire, Air, Water, Earth.

  1. The four elements are eternal and unchanging, but are brought together and separated by Love and Strife. As the best and original state, there was a time when the pure elements and the two powers co-existed in a condition of rest and inertness in the form of a sphere. The elements existed together in their purity, without mixture and separation, and the uniting power of Love predominated in the sphere: the separating power of Strife guarded the extreme edges of the sphere. Since that time, strife gained more sway and the bond which kept the pure elementary substances together in the sphere was dissolved.
  2. He was a firm believer in Orphic mysteries, as well as a scientific thinker and a precursor of physics.
    • Like Pythagoras, Empedocles believed in the transmigration of the soul, that souls can be reincarnated between humans, animals and even plants.

Leucippus (5th Century B.C.E.): Atomist – pre-Socratic Greek philosopher who has been credited as the first philosopher to develop a theory of atomism. Leucippus’ reputation, even in antiquity, was obscured by the reputation of his much more famous pupil, Democritus, who is also credited with the first development of atomic theory.

Democritus (460 B.C.E. – 370 B.C.E.): Atomist – Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. None of his work has survived.

Protagoras of Abdera (490 B.C.E. – 420 B.C.E.): pre-Socratic Greek philosopher and rhetorical theorist. He is numbered as one of the sophists by Plato. In his dialogue Protagoras, Plato credits him with inventing the role of the professional sophist.

The Big Three

Socrates (470 B.C.E. – 399 B.C.E.):

  1. Socrates does not have a lot of philsophy of his own that has been passed down to posterity since he never wrote anything himself. All we know about him comes from second hand accounts. That being said, probably the main thing attributed to him is the so-called Socratic method, which is interrogating a person’s presuppositions with questions that expose where a person’s beliefs are contradictory. This is often thought to be a precursor of Hegelian/Marxian dialectical logic.

Plato (428 B.C.E. – 348 B.C.E.):

  1. Platonic Forms or Ideas are one of Plato’s largest contributions to philosophy. This is the notion that all the physical objects that we come in contact with are deviations from a perfect version of themselves. There is a realm of Forms, for instance, where there is the perfect Tree, and all the trees that you ever come in contact with are imperfect approximations of this. This is true as well of more abstract things, such as perfect Justice and perfect Love.
  2. Because we are exposed to imperfect versions of things like Justice and Love, it takes the great mind of a philosopher to glimpse the perfect Forms of these things. This is where the famous allegory of the cave comes in. Plato asks us to consider people chained in a cave, only able to see shadows cast on the wall in front of them. All they have ever known are the shadows, and so this is their whole world. Then one of these people becomes freed and walks out of the cave to see the real world for the first time. If that person were to go back down and tell his fellows about the world above, they would likely think the escapee mad, yet the escapee is someone who knows more truth than them. Someone who has glimpsed the perfect Forms is like the person who has left the cave – a philosopher.
  3. It’s from this that Plato’s Republic is based, where we have philosopher kings at the top, since they have glimpsed the Forms and therefore have much greater knowledge than everyone else. Plato splits his ideal Republic into a hierarchy of three strata:
    1. Philosopher Kings or Guardians: wise rulers who live communally
    2. Auxiliaries: soldiers and police
    3. Craftsman: the bulk of the population who carry out all the labor jobs
  4. This Republic is a type of aristocracy, which Plato thought the best form of government. The other ones he thought, in descending order of desirability, are the levels that each such government will degenerate into over time; it is the wise philosopher kings of an aristocracy that must prevent this. The following are the other types:
    1. Timocracy: essentially a government where the Auxiliaries have taken over. Plato thought that Sparta, with its warrior rulers, was a Timocracy. This is more favorable than Oligarchy because the soldiers are at least high-minded and honorable people.
    2. Oligarchy: rule by a small number of rich and influential people. This is better than democracy, Plato thinks, because at least such people would be more enlightened than the masses.
    3. Democracy: rule by the masses.
    4. Tyranny: when the most vicious and ruthless people among the masses take power and rule by terror and violence.

Aristotle (384 B.C.E. – 322 B.C.E.): Aristotle is probably the most important philosopher in western philosophy. His shadow still hangs over just about everything in western philosophy, whether someone is using his ideas or attempting to refute or subvert them. It would not even be that much of an exaggeration to argue that until perhaps the 1800’s that all of philosophy was just extensions, footnotes, and commentaries on Aristotle.

  1. Categories: the ten ways that Aristotle said are the ways in which something can be described. The first one is of primary importance and the other nine are secondary substances (called predicates in modern parlance). They are the following (source):
    • (1) substance,
    • (2) quantity,
    • (3) quality,
    • (4) relation,
    • (5) where,
    • (6) when,
    • (7) being-in-a-position,
    • (8) possessing,
    • (9) doing or
    • (10) undergoing something or being affected by something
  2. Substance and Predicates (secondary substances): a substance is what something is, and is that which other things are predicated of. For instance, Alice is a substance, and human is a predicate. Thus, we can make the proposition “Alice is human” where human has been predicated of Alice.
  3. Essential and Accidental Properties: an essential property is one that a thing has to have in order to be what it is, whereas an accidental property is one that the object has only contingently. In other words, if the object ceased to have that property, it would remain the object that it is. For instance, a cup is something that has to be able to contain things, and so something like a hoola-hoop is not a cup because it lacks this essential property of being able to contain things. Having a handle, on the other hand, is an accidental property, since a cup can either have a handle or not have a handle.
  4. Four Causes
    1. Material Cause: what the object is made out of
    2. Formal Cause: the form or structure of the object
    3. Efficient Cause: how the object came to be. Also our modern day kind of cause, such as the billiard ball picture, where a ball contacts another one and causes it to move
    4. Final Cause: the purpose of the object, i.e., what the object was made for (it’s functionality)
  5. Logic
    1. We’ll begin with the laws of thought. While these were never expressed in this way by Aristotle, the medieval scholastic philosophers were able to identify these three, sometimes four, so-called laws of thought in Aristotle’s logic
      • Law of identity: things are identical with themselves
        • A = A
      • Law of non-contradiction: a proposition and its negation cannot both be true
        • not (A and not-A)
      • Law of excluded middle: either A must be true or not-A must be true
        • either A or not-A
      • Law of sufficient reason (disputable): everything must have a cause
    2. Now we will look at propositions and syllogisms. We’ll begin with Aristotle’s table of oppositions:
Aristotle logic square of opposition
Aristotle’s square of opposition (source)
Aristotle square of opposition categorical syllogism
Same as above, but shown with the A, E, I, and O designations.
  • Is & Are: these are what are called copulae, which link the subject and predicate. They are essentially words that broadly mean “to be”. We might say that “S is P” means something like “S being P” or “P = the way of being for S” or to get even worse in our grammar “S be’s P”
    • The ‘A’ proposition, the universal affirmative: ‘every S is a P’
      • In logic, if there is only 1 thing in the category, then that 1 thing is exhaustive and therefore counts as all. In other words, to say that “Socrates is P” is like saying “all of Socrates is P” since referring to Socrates exhausts everything in the category of “Socrates” (assuming we know by context that our referent is Socrates, the well-known Greek philosopher, that we’re talking about, but getting into how we fix our reference will bring us too far afield at this point).
    • The ‘E’ proposition, the universal negative: ‘no S are P’
    • The ‘I’ proposition, the particular affirmative: ‘some S are P’
      • In logic, the word some means any amount that isn’t zero or all. It could be read as “at least one S are/is P”
    • The ‘O’ proposition, the particular negative: ‘some S are not P’
  • Contradictory propositions possess opposite truth-values.
  • Contrary propositions cannot both be true.
  • The relationship of subalternation results when the truth of a universal proposition, “the superaltern,” requires the truth of a second particular proposition, “the subaltern.”
  • Subcontrary propositions cannot both be false.
  • Syllogisms: there are two premises of the above A, E, I, or O forms. If the syllogism is valid, then the conclusion is guaranteed if the premises are true. If the syllogism is sound, then the premises are true and the syllogism is valid, and so the conclusion is both true and guaranteed. All valid syllogisms must have at least one universal premise. A syllogism takes the following form:
      • Major premise
      • Minor premise
      • Conclusion
    • Syllogism Example:
      • All S is P
      • X is S
      • ∴ X is P
  • Moods: with the four types of proposition and three propositional positions (major premise, minor premise, and conclusion) there are 256 possible syllogisms. There are, however, only 24 valid syllogisms, which are often divided into four “figures” based on the placement of the minor premise and are the following (parenthetical ones are known as weakened moods and derive particular conclusions from two universal “all” or “none” premises):
    • First figure: AAA, EAE, AII, EIO, (AAI), (EAO).
    • Second figure: AEE, EAE, AOO, EIO, (AEO), (EAO).
    • Third figure: AAI, EAO, AII, EIO, IAI, OAO.
    • Fourth figure: AAI, AEE, EAO, EIO, IAI, (AEO).

Aristotle was a rare genius who touched on just about every intellectual, scholarly topic. He was a biologist, performing many animal disections and mapping the anatomy of humans and numerous animals (many, famously, sent back by his pupil, Alexander the Great, during his conquest). Indeed, Aristotle’s anatomical work was used for over a millenium after his work.

In philosophy he also theorized about ethics, epistemology, aesthetics, politics, and numerous other areas. I will cover these in more detail in future edits of this post. For now it will suffice to say that his virtue ethics, with the golden mean, is still important in modern ethics. He also came up with the notions of eudaimonia and catharsis, which are still popular in ethics and aesthetics respectively. Needless to say, the works of Aristotle can fill (and has filled) a great many volumes.

Ancient (323 B.C.E. – 400 C.E.)

Antisthenes (445 B.C.E. – 365 B.C.E.): Cynicism.

Mencius (372 B.C.E. – 289 B.C.E.): born Mèng Kē; or Mèngzǐ was a Chinese Confucian philosopher who has often been described as the “second Sage”, that is, after only Confucius himself. He is part of Confucius’ fourth generation of disciples. Mencius inherited Confucius’ ideology and developed it further.

Euclid of Alexandria (fl. Ca. 300 B.C.E.): Mathematician.

Zeno of Citium (332 B.C.E. – 262 B.C.E.): Early Stoicism.

Epicurus (341 B.C.E. – 270 B.C.E.): Epicureanism.

Nāgasena (ca 150 B.C.E.): the interlocutor in the Milinda Pañha

Marcus Tullius Cicero (106 B.C.E. – 7 December 43 B.C.E.): Orator and Philosopher.

Seneca the Younger (4 B.C.E. – 65 C.E.): Late Stoicism.

Jesus (Christ) of Nazareth (4 B.C.E. – 30 C.E.): Apocalyptic Jewish Prophet and Christian Messiah.

Paul of Tarsus (5 B.C.E. – 64 C.E.): Jewish Apostle of Christ and Christian Evangelist.

  1. Author of at least seven of the thirteen Pauline Epistles (Galatians, Romans, 1 Corinthians, 2 Corinthians, Philemon, Philippians, 1 Thessalonians), while three of the epistles in Paul’s name are widely seen as pseudepigraphic (1 Timothy, 2 Timothy, and Titus). Three others (2 Thessalonians, Ephesians and Colossians) are widely debated.

Epictetus (ca. 135 C.E.): Late Stoicism.

Marcus Aurelius (April 26, 121 C.E. – March 17, 180 C.E.): Late Stoicism.

Tertullian (155 C.E. – 240 C.E.): Christian Apologist and Theologian.

  1. Called “the father of Latin Christianity” and “the founder of Western theology.”

Origen of Alexandria (184 C.E. – 253 C.E.): Christian Apologist and Theologian.

  1. His treatise On the First Principles (230 C.E.) systematically laid out the principles of Christian theology and became the foundation for later theological writings.

Plotinus (204 C.E. – 270 C.E.): Neoplatonist.

Porphyry of Tyre (234 C.E. – 305 C.E.): Neoplatonist.

Council of Nicaea (325 C.E.): Its main accomplishments were settlement of the Christological issue of the divine nature of God the Son and his relationship to God the Father, the construction of the first part of the Nicene Creed, establishing uniform observance of the date of Easter, and promulgation of early canon law.

First Council of Constantinople (381 C.E.): repudiated Arianism and Macedonianism, declared that Christ is “born of the Father before all time”, revised the Nicene Creed in regard to the Holy Spirit (procession from the Father).

Augustine of Hippo (November 13, 354 C.E. – August 28, 430 C.E.): Christian Theologian. One of the most influential Christian philosophers, he is still often considered an authority on many issues important to the faith.

  1. Epistemology: Augustine was a Platonist when it came to knowledge. For Plato, knowledge of the forms came from our prior acquaintance with them before life – the knowledge was already buried deep within ourselves, recoverable through the use of reason. Augustine thought that knowledge came through personal intellectual insight. But, the possibility of such an insight was conditioned on God.
    • Augustine actually came up with a formulation of Descartes’s “I think therefore I am” a millennium earlier. Wanting to stave off skepticism, Augustine came up with the following indubitable sources of knowledge (source):
      1. the certainty of self-referential knowledge (the wise person “knows wisdom”, Contra Academicos 3.6; the Academic skeptic “knows” the Stoic criterion of truth, ib. 3.18–21);
      2. the certainty of private or subjective knowledge (I am certain that something appears white to me even if I am ignorant whether it is really white, ib. 3.26);
      3. the certainty of formal, logical or mathematical, structures (ib. 3.24–29), knowledge of which is possible independently of the mental state of the knower, whereas the reliability of sense impressions differs according as we are awake or dreaming, sane or insane.
  2. The Soul: the immortality of the soul can be proven, according to Augustine, though his proof is not a very good one. He says that “since truth is both eternal and in the soul as its subject, it follows that soul, the subject of truth, is eternal too” and says “that soul is immortal because of the inalienable causal presence of God (= Truth) in it” (source). What is interesting, however, is that even though Augustine thought the soul was incorporeal and could persist outside the body, he thought that the soul preferred to be embodied and that the soul would be reunited with the body at the end of time (this was pretty typical back then as most Christians and Jews of the time thought that the final kingdom of God would be here on earth).
  3. Grace and Original Sin: probably the biggest impact that Augustine has on modern Christianity, however, are his concepts of Grace and Original Sin. The latter says that all humans are born with original sin, a sinful nature that they are born with instead of due to something they have done. Indeed, it is this original sin that makes it impossible for humans to do any good at all. All humans, therefore, deserve punishment. But, due to the Grace of God through Christ, which restores humanity’s ability to do good works, some humans will be saved. I say some because Augustine was a proponent of predestination, i.e., that some people were “elected” by God prior to their creation to be saved from the damnation that all humans deserve. This is fine, according to Augustine, because, as I said, he thought all humans deserved eternal damnation, so it is actually a demonstration of God’s grace to save even a handful of them.
  4. City of God: according to Augustine, history is driven by the celestial battle of good vs. evil. The Catholic church (the eponymous City of God) fights on the side of good against evil. Therefore, any government that aligns itself with the Catholic church is fighting on the side of good. This book was written in response to the 410 C.E. sack of Rome by the Visigoths, which was blamed by some on Rome’s abandoning its old Pagan religion. Augustine disagreed, saying that Rome’s success was due to aligning with the Catholic church and making Christianity the religion of the Empire. Furthermore, the success of Rome would continue in the afterlife, which was much more important than the goings-on of the physical world.

Council of Chalcedon (451 C.E.): Its most important achievement was to issue the Chalcedonian Definition, stating that Jesus is “perfect both in deity and in humanness; this selfsame one is also actually God and actually man” (Dyophysitism). The council’s judgments and definitions regarding the divine marked a significant turning point in the Christological debates.

Late Antiquity (400 C.E. – 800 C.E.)

Pseudo-Dionysius the Areopagite (Late 400’s C.E. – Early 500’s C.E.): Christian Theologian.

Boëthius (477 C.E. – 524 C.E.): Christian Theologian.

  1. God’s prescience of the future is not a contradiction with free will because for humans, future events are contingent (the outcome is not fixed) but from God’s point of view as an eternal being, they are.
    • God’s eternity ‘is the complete, simultaneous, and perfect possession of unending life.’ The past, present, and future are all experienced as the present from God’s point of view. Freedom happens in the present, therefore freedom is conserved even if God is present to our future.

Proclus Lycaeus (February 8, 412 C.E. – April 17, 485 C.E.): Pagan Neoplatonist Philosopher.

Muhammad (570 C.E. – June 8, 632 C.E.): Prophet of Islam.

Third Council of Constantinople (680/681): Condemned monoenergism and monothelitism as heretical and defined Jesus Christ as having two energies and two wills (divine and human).

Medieval (800 C.E. – 1600 C.E.)

Al-Kindī (801 C.E. – 873 C.E.): Islamic Theologian.

Al-Fārābī (872 C.E. – 950 C.E.): Islamic Theologian.

  1. Ten levels of intelligence, emanating from God, the First Cause, down the concentric spheres to the lowest intelligence, the Agent Intellect (has no sphere of its own), which bestows form to matter and lets humans understand universals.
    1. Plotinian emanational cosmology.
    2. God’s principle activity is self-contemplation. This thinking “overflows” into the second intellect and so on down to the physical world.
  2. Ethics: based on Plato’s Republic. The rulers should be philosophers/imams who have gained access to the Agent Intellect (rather than Plato’s philosopher kings who have gained access to the Ideas).

John Scotus Eriugena (815 C.E. – 877 C.E.):

Al-Ash’ari (874 C.E. – 936 C.E.): Islamic Theologian.

Ibn Sina aka Avicenna (980 C.E. – 1037 C.E.): Persian Islamic Theologian.

  1. Realist in terms of universals: particular things have a nature that we base our concepts on. For example, a horse has some nature – it’s horseness – and I base my conception of horse on that nature. But the nature – the horseness – is not a thing; it is not a subject for predication, such that the question of whether ‘horseness’ is one or not one is incoherent (solving the problem of having one thing (the universal) be fully present in multiple things (the particulars)).
  2. Accepts Al-Fārābī’s Plotinian emanational cosmology.

Catholic-Orthodox Christian Schism (1054 C.E.)

  1. Filioque: It is not in the original text of the Creed, attributed to the First Council of Constantinople (381), the second ecumenical council, which says that the Holy Spirit proceeds “from the Father”, without additions of any kind, such as “and the Son” or “alone”. In the late 6th century, some Latin Churches added the words “and from the Son” (Filioque) to the description of the procession of the Holy Spirit, in what many Eastern Orthodox Christians have at a later stage argued is a violation of Canon VII of the Council of Ephesus, since the words were not included in the text by either the First Council of Nicaea or that of Constantinople. This was incorporated into the liturgical practice of Rome in 1014, but was rejected by Eastern Christianity.
  2. Papal supremacy and rejection of Pentarchy
  3. Roman Catholic unleavened bread because it is what Jews would have had at the last supper; Eastern Orthodox leavened bread because it doesn’t matter what Jesus actually had.

Saint Anselm of Canterbury (1033 C.E. – 1109 C.E.): Christian Theologian.

  1. His biggest claim to fame is probably his ontological argument for the existence of God. It goes like this:
    1. By definition, God is a being than which none greater can be imagined.
    2. A being that necessarily exists in reality is greater than a being that does not necessarily exist.
    3. Thus, by definition, if God exists as an idea in the mind but does not necessarily exist in reality, then we can imagine something that is greater than God.
    4. But we cannot imagine something that is greater than God.
    5. Thus, if God exists in the mind as an idea, then God necessarily exists in reality.
    6. God exists in the mind as an idea.
    7. Therefore, God necessarily exists in reality.

Al-Ghazālī (1058 C.E. – 1111 C.E.): Sufi Islamic Kalam Theologian.

Peter Abelard (1079 C.E. – 1142 C.E.): Christian Theologian.

  1. First to defend nominalism (as opposed to realism) in regards to the question of universals: he said that universals are nothing but words, not actual things. Words ‘nominate’ (refer to) things in the world while also ‘signifying’ things by producing the concept in a person’s mind. Universal words do not nominate universal things but nominate all the particular things which fall under them – universals nominate how particulars come together (e.g., under the status of ‘horse’).

Gilbert of Poitiers (1085 C.E. – 1154 C.E.): Christian Theologian.

Ibn Tufayl (1105 C.E. – 1185 C.E.): Andalusian Sufi Muslim Polymath.

Ibn Rušd aka Averroes (1126 C.E. – 1198 C.E.): Andalusian Islamic Theologian.

  1. A single possible intellect for all humans: that which individuates things is bodily, but the possible intellect is not bodily, so it must be unindividuated. Therefore, there is only one intellect shared by all humans. That’s why when person A and person B learn astronomy, they learn the same
    • The object is to the sense organ what the imaginative form of the universal is to the possible intellect; the Agent Intellect is analogous to the light shining on the object. The imaginative form of the universal is mine even if the possible intellect is shared by all humans, therefore we do not all share the same thoughts.
  2. Rejects Al-Fārābī’s Plotinian emanational cosmology. There is a First Mover and intelligences which move the celestial spheres, but only because they desire for the most perfect being. The Agent Intellect does not give forms to the physical (sublunar) world, but is used only for rendering universals in the possible intellect.

Moses ben Maimonides (1135 C.E. – 1204 C.E.): Sephardic Jewish Theologian.

  1. God’s prescience: uses negative theology. When we talk about God, we can’t apply the human meanings of words used to describe Him (human language is used equivocally when talking about God). That means when we say God ‘knows’ contingent future events, we don’t actually understand what that means as it pertains to God.

Shahāb ad-Dīn” Yahya ibn Habash Suhrawardī (1154 C.E. – 1191 C.E.): Persian Islamic Theologian.

Fakhr al-Dīn al-Rāzī (1150 C.E. – 1210 C.E.): Persian Sunni Islamic Theologian.

Ibn Arabi (July 26, 1165 C.E. – November 16, 1240 C.E.): Andalusian Islamic Theologian.

Saint Thomas Aquinas (1225 C.E. – March 7, 1274 C.E.): Christian Theologian.

  1. If Aquinas had one lasting impact on western philosophy, it would be in popularizing Aristotle in European philosophy and theology. Prior to Aquinas, the European philosophers were much more Platonic in their ethos, while the Arabic philosophers were more Aristotelian. Aquinas was deeply Aristotelian, offering incisive commentaries on Aristotle’s works and adopting much or Aristotle’s philosophy into his own. With Aristotle’s more worldly philosophy, this made what is called natural theology a much more prominent part of the European Christian tradition.
  2. The second thing that Aquinas is most known for are his “Five Ways” which are five arguments for the existence of God. I will give a brief overview of these five arguments here.
    • (1) Unmoved Mover: a movement (whether in the usual sense of a moving object or as a movement from potentiality to actuality) must be moved by something else. Since there cannot be an infinite regress, there must be an unmoved mover. God is that unmoved mover.
    • (2) First Cause: nothing can cause itself, because then it would have to have been prior to itself, which is a contradiction. That means everything has a cause external to it. But again there cannot be an infinite regress, so there must be something that was not cause, i.e., a first cause. God is that first cause.
    • (3) Contingency: if it is possible for something to exist, then it is also possible for it not to exist. But if everything was contingent (merely possible instead of necessary) then nothing would exist. Therefore there must be something that exists necessarily. God is that necessary thing.
    • (4) Degree: things like love, justice, mercy, holiness, and so on all exist to different degrees in the things that exist. But, just like in a room full of people with varying degrees of height, one of them must be the tallest. Therefore there must be something that has the most of all those things (love, justice, etc.). God is that which has the highest degree of all those things.
    • (5) Final Cause: the world proceeds by regular, reliable, and predictable laws. Since matter has no intelligence of its own, it could not have given itself this regularity on its own. Therefore there must be an intelligence that gave matter its reliable nature. God is that intelligence.
  3. Aquinas rejects Averroes’s idea of the Agent Intellect. Says it’s like an eye (the Agent Intellect) looking at a colored (imaginative universal) wall (the possible intellect) and the colored wall somehow seeing the color. Says instead that the human soul is itself intellective and is the substantial form of the human body; intellectual reasoning, unlike perceiving or imagining, requires no bodily organ and therefore the soul can exist independent of the body.
  4. Accepts Boëthius’s view of God’s prescience.

Dante Alighieri (1265 C.E. – 1321 C.E.): Italian Poet. He wasn’t a philosopher per se, but his depctions of Heaven, Hell, and Purgatory have been extremely influential as to our conceptions of them.

John Duns Scotus (1266 C.E. – 1308 C.E.): Christian Theologian.

  1. Agreed with Avicenna on universals, but altered it somewhat. Said there are two sorts of unity: numerical unity and singularity (which is less than numerical). Horses have the same singular horseness, but this horseness is not numerically the same – in the same way that any white thing (not just a single white thing) is the opposite in color to a single black thing. It is a things haecceity – it’s thisness – that individuates things, ‘contracting’ the common nature into an individual.
  2. For God’s prescience: God knows all the possible ways the entire existence of humankind could be, but he wills only one of them. God was free in that he could have willed existence to be otherwise, but is providential in that he does not change what he has

William of Ockham (1287 C.E. – 1347 C.E.): Christian Theologian.

  1. Rejected Duns Scotus’s realism on universals (though he never read Abelard’s works). If A = horse1, B = horseness, and C = horse2, then A = B and C = B must mean that A = C and it’s absurd for horse1 = horse2.
  2. Accepted Duns Scotus’s view on God’s prescience.

Levi ben Gershon aka Gersonides (1288 C.E. – 1344 C.E.): French Jewish philosopher.

  1. God’s prescience: rejects Maimonides negative theology. If words applied to God don’t have the same meaning as when applied otherwise, anything can be applied to God by just saying the meaning is different for God.
    • Gersonides says God does not know particular events, but knows their providential order. God knows the reason for events, but not the particular outcome: using their intellects, humans can turn away from divine providence.
      • This was rejected by Gersonides’s contemporaries and successors since it contradicts God’s perfection by limiting God’s knowledge and providence.

Martin Luther (November 10, 1483 C.E. – February 18, 1546): German theologian

  1. Famous for his 1517 C.E. ninety-five theses that sparked the protestant reformation. These theses famously called the Catholic church out for indulgences (paying the Catholic church in order to have punishment for sins reduced) and for arguing that salvation comes through a personal relationship with God instead of through the Sacraments of Penance.
  2. Another of his lasting influences is the printing of the Bible into German. It was previously almost exclusively printed in Latin, which few people could read. Printing the Bible in a more common language made it available for many more people to read (and interpret) on their own. Making it so people did not have to go through the Catholic church to read and interpret the Bible rivals the ninety-five theses in importance.

Nicolaus Copernicus (February 19, 1473 C.E. – May 24, 1543 C.E.): Polish Renaissance polymath, mathematician, and astronomer

  1. Most famous for coming up with the heliocentric model of the universe. This de-centering of the earth also famously demonstrated that humans were not as special as they once thought. This has come to be called the Copernican Principle, where a scientific hypothesis is supposed to avoid privileging humans in any special way.

Niccolò Machiavelli (May 3, 1469 C.E. – June 21, 1527 C.E.): Italian philosopher

Pietro Pomponazzi (September 16, 1462 C.E. – May 18, 1525 C.E.): Italian philosopher.

  1. Criticizes Aquinas’s view of the soul – how can intellective soul be form of the body and still live independently of it? How can they be individuated if individuation is by matter?
    1. Says the soul does not survive human death – no reward or punishment. Being virtuous ought to be for virtue itself, not a reward after death, which makes it less virtuous.
    2. Though he defends his position, he accepts Aquinas’s view of immortality anyway – reason cannot answer the question, so one must turn to faith.

John Calvin (Jean Cauvin) (July 10, 1509 C.E. – May 27, 1564): French theologian, pastor, and reformer in Geneva.

  1. Sensus Divinitatis (“sense of divinity”): “That there exists in the human mind and indeed by natural instinct, some sense of Deity [sensus divinitatis], we hold to be beyond dispute, since God himself, to prevent any man from pretending ignorance, has endued all men with some idea of his Godhead…. …this is not a doctrine which is first learned at school, but one as to which every man is, from the womb, his own master; one which nature herself allows no individual to forget.”
  2. Famous for his focus on predestination, which says that there are a certain number of people who are God’s elect. These elect are people who will go to heaven. Being elect is not something you can earn or lose, but is something you were predestined with.

The Moderns

This section will things from Descartes to Immanuel Kant and then up to some of the important 19th century thinkers, like Karl Marx. As usual, making these kinds of demarcations can be somewhat arbitrary, but it’s useful for getting an understanding of the evolution of thought. Modern philosophy is often said to begin with Descartes, where philosophy transcended scholasticism, which was characterized by a sort of religious adherence to the ancients, whose wisdom was thought to be sacred. It was Descartes who wanted to move past the slavish adherence to Plato and especially Aristotle, though even most of these thinkers (including Descartes) didn’t move past most of the Platonic/Aristotelian presuppositions.

Early Modern (1600 C.E. – 1800 C.E.)

Descartes (March 31, 1596 C.E. – February 11, 1650 C.E.): French philosopher.

  1. Methodological Doubt: Descartes is famous for his extreme skepticism, which is somewhat ironic since what he had set out to do was try to find indubitable certainty. He thought that to do this he needed to doubt every possible thing that he could in order to find those things that could not possibly be doubted. From there, in a foundationalist epistemological formulation, he would be able to erect all the rest of knowledge on those indubitable, self-evident foundations.
  2. You can think about it this way: if A and B are undoubtable, self-evident propositions, then they are certain knowledge. Now, if C, D, and E all are not self-evident, but indubitably follow from A and B, then I can be absolutely confident in C, D, and E as well. And then if F, G, H, I, and J all indubitably follow from some combination of A, B, C, D, and E, then I can be absolutely certain of those as well. And in this fashion, all knowledge can be regained with absolute certainty.
  3. Evil Demon/Genius/Genie (depending on your translation): Descartes began by considering that even those things that seem obvious can be doubted. That I am seeing my computer screen in front of me can be doubted because it is not logically impossible that some evil demon is fooling me (in modern times, we often propose that we might be a brain in a vat or living in a simulation). My memories can be doubted because this evil demon may have implanted false memories in me. Everything can be doubted… except the fact that I am doubting. And if I am doubting, that means I am thinking. And if I am thinking, that means I must exist. Hence, Descarte’s famous “Cogito ergo Sum” – I think, therefore I am.
  4. Descartes then proves to himself the existence of God using a formulation of the ontological argument. With certainty that God exists, and that God, being benevolent, would not fool him the way his evil demon would, Descartes then feels assured that the world exists.
  5. Mind-Body Dualism: according to Descartes, the mind can doubt the existence of the body, but it cannot doubt its own existence. This means that the mind and body are separate substances. There is the immaterial mind (or soul) and the material body. He conjuctured that the immaterial soul could interact with the body through the pineal gland.

Francis Bacon (January 22, 1561 C.E. – April 9, 1626 C.E.): English philosopher. His works are seen as contributing to the scientific method and remained influential through the later stages of the scientific revolution.

Galileo Galilei (February 15, 1564 C.E. – January 8, 1642 C.E.): Italian astronomer and physicist

Thomas Hobbes (April 5, 1588 C.E. – December 4, 1679 C.E.): English philosopher

  1. State of Nature: a war of all against all, where life is nasty, brutish, and short.
  2. Leviathan

John Locke (August 29, 1632 C.E. – October 28, 1704 C.E.): English philosopher

In what follows, quotes are all from Locke, except where stated otherwise. My main source for this has been The Cambridge Companion to Locke, edited by Vere Chappel.

  1. Representational Theory: Locke posited Ideas as the representation of what someone is thinking about. He says in his Essay Concerning Human Understanding: “[Idea] being the Term which, I think, serves best to stand for whatsoever is the Object of the Understanding when a Man thinks, I have used it to express whatever is meant by Phantasm, Notion, Species, or whatever it is, which the Mind can be employ’d about in thinking.” And “whatsoever the Mind perceives in it self, or is the immediate object of Perception, Thought, or Understanding, that I call Idea.” This tells us that for Locke, the idea is a representation in the mind – they are the immediate objects of thought which mediate between objects in the world and our perceptions of them. This produces what critics call a “veil” between the perceiver and an external world, where we don’t have direct perception of the object, but instead must go through the intermediate step of the Idea.
    • Locke makes distinctions between simple and complex ideas, particular and general ideas, concrete and abstract ideas, adequate and inadequate ideas. The main one is that of simple and complex Ideas, which I’ll define further.
      • Simple Ideas: Locke says of simple Ideas that “being…in itself uncompounded, contains in it nothing but one uniform Appearance, or Conception in the Mind, and is not distinguishable into different Ideas.” In other words, there is no differentiation within a simple Idea, such as containing two different colors. Locke gives as examples of simple Ideas “Yellow, White, Heat, Cold, Soft, Hard, Bitter, Sweet” for sensations, but he also gives examples of “ideas of reflection” which are “Perception, Thinking, Doubting, Believing, Reasoning, Knowing, Willing, and all the different actings of our own Minds.” These two things, experience and reflection, are the only two sources of simple ideas for Locke, which is why he is considered an empiricist.
      • Complex Ideas: compositions of simple Ideas, where, for instance, an apple is a composition of color, shape, size, taste, rigidity, and so on. These complex ideas actually inhere in the object, they are not put together by the mind, and so perceiving them is a passive process. However, the mind can take simple Ideas that it has experienced in the past and “compound” them into complex ideas in the imagination.
        • Complex Ideas can be of two kinds: mixed and realtional. The former would be like our example of the apple, which mixes a bunch of simple Ideas together into a single object. Relational would be like the complex Idea of seeing multiple apples and perceiving the relations they share with one another (spatial, but also how each appears in comparison with the others – redder, larger, smoother, etc.)
  2. Primary and Secondary Qualities: Locke was a proponent of the corpuscular theory of matter, where all matter is composed of indivisible corpuscles, championed by his friend, the famos chemist Robert Boyle. While Boyle defended the division of primary and secondary qualities by appealing to his corpuscular theory, Locke took a more philosophical approach.
    • Primary Qualities: Locke says that primary qualities are “utterly inseperable from the Body [object], in what estate soever it be” and are “such as in all the alterations and changes it [the object] suffers, all the force can be used on it, it constantly keeps” and are “such as Sense constantly finds in every particle of Matter, which has bulk enough to be perceived, and the Mind finds inseperable from every particle of Matter, though less than to make it self singly be perceived by our Senses.”
      • Primary Qualities include: solidity, extension (being spatial), figure (shape), motion or rest, number, situation, bulk, texture, and motion of parts.
    • Secondary Qualities: secondary qualites are “nothing in the Objects themselves, but Powers to produce various Sensations in us by their primary Qualities, i.e. by the Bulk, FIgure, Texture, and Motion of their insensible parts.”
      • Secondary Qualities include: colors, sounds, tastes, smells, heat and cold.
  3. Language: Locke understood the shortcomings of language and how it can lead to miscommunication. Much of this results from the fact that our concepts of things are not “real” universals that exist in nature, but are ways that we have classified things. In other words, only particulars exist in the world, that there is no such thing as a general object. This means that the sounds we utter, which are abstracted from the particulars (we don’t use a proper name for every insect, leaf, or chair we come in contact with), are connected with certain Ideas is conventional and not because of something inherent in the Ideas (objects) themselves. We therefore can’t assume that words have the same meaning for ourselves as they do for others. Locke doesn’t seem to have a better solution to this conundrum that all of us in a sense have our own private language than to counsel that we should be careful to accord our definitions with the common use of language.
  4. Knowledge: one thing that Locke is known for is his notion that humans are a blank slate or tabula rasa. This means that we are not born furnished with knowledge, but must acquire it through experience. There are things, however, once we have the knowledge through experience, we can produce further knowledge through the combination of such experiential knowledge. For instance, one can know that the number 24 is an even number without having experienced 24 as an even number; but one has to have, through experience, learned the concepts of number and evenness.
  5. Treatises on Government (using the Stanford Encyclopedia entries on Locke in general and on Locke’s political philosophy as my sources): Locke wanted to come up with what a legitimate government ought to be in order to determine what illegitimate governments are, as they would be deviations from the good government.
    • State of Nature: Locke takes a rosier view of this than Hobbes, seeing it as a state of equality. He does, however, think there are inherent problems, such as the fact that people must take enforcement of the “law of nature” into their own hands. They will likely see slights agains themselves as greater infringements than they are and therefore mete out disproportionate punishments (in other words, Locke could see that it would generate an honor culture). Furthermore, when people began needing to live in much larger communities, there were more chances for such confronations, and therefore people agreed (social contract) to abide by a civil government.
    • Private Property: for Locke, we come into private property through self-ownership. But he says that the advent of money produced conditions of inequality, which gave rise to crime. It is therefore the role of a legitimate government to protect private property.
    • Social Contract: everyone gives tacit consent to be governed by the state by virtue of the fact that they use the fruits of the state – we use the roads and infrastructure that the state has provided. This agreement cannot be revoked, since that would make civil society impossible (someone could revoke their consent, commit a murder, then reinstate their consent; if everyone decided to revoke their consent whenever the state did something people didn’t like, it would undermine the authority of the state). We are thus obligated to obey the laws set down by the state.
    • Separation of Powers: Locke actually makes the separation into the legislative, the executive, and foreign relations (what he calls federative power). The separation of the judicial branch from the legislative and executive is actually given by Montesquieu, who is discussed below. The judicial interpretation of laws, for Locke, is something inherent in both the legislative and executive branches. The roles of these three branches are as follows:
      • Legislative: to make the laws
      • Executive: to enact and enforce the laws
      • Federative: adjuticate international disputes
  6. Religious Tolerance: (source: Wikipedia)
    1. earthly judges, the state in particular, and human beings generally, cannot dependably evaluate the truth-claims of competing religious standpoints;
    2. even if they could, enforcing a single ‘true religion’ would not have the desired effect, because belief cannot be compelled by violence;
    3. coercing religious uniformity would lead to more social disorder than allowing diversity.

Baruch Spinoza (November 24, 1632 C.E. – February 21, 1677 C.E.): Dutch philosopher of Portuguese Sephardic Jewish origin

  1. Substance: “that which is in itself and is conceived through itself”
  2. God: “a substance consisting of infinite attributes, each of which expresses eternal and infinite essence”

Nicolas Malebranche (August 6, 1638 C.E. – October 13, 1715 C.E.): French philosopher who sought to synthesize the thought of St. Augustine and Descartes, in order to demonstrate the active role of God in every aspect of the world.

Isaac Newton (January 4, 1643 C.E. – March 31, 1727 C.E.): English mathematician and physicist. His most famous work is in the independent formulation of the infinitesmal calculus (along with Leibniz, which led Newton to hate Leibniz), his universal law of gravitation, and his Opticks. Going into each of these areas is more a matter of science than philosophy. For our purposes in this post, it is most important to know what affect Newton’s work had on philosophy. This was primarily in the notion of the mechanical, clockwork universe. Philosophers who came after Newton’s discoveries were often concerned with refuting the mechanical, clockwork view of the universe, wanting to rescue notions of free will. Indeed, Kant thought of his project as deconstructing knowledge in order to rescue free will.

Gottfried Wilhelm Leibniz (July 1, 1646 C.E. – November 14, 1716 C.E.): German philosopher and mathematician. His work in mathematics, which includes independently inventing the infinitesimal calculus at the same time as Newton (which led to a venomous rivalry between the two) and binary arithmetic, were groundbreaking. He also dabbled in numerous other areas of scholarship. However, in this post I am going to focus more on his philosophical work.

  1. Leibniz asserts in the Monadology §§31–32, “Our reasonings are based on two great principles, that of contradiction… [and] that of sufficient reason” (G II 612/AG 217). To these two great principles could be added four more: the Principle of the Best, the Predicate-in-Notion Principle, the Principle of the Identity of Indiscernibles, and the Principle of Continuity. (source)
  2. Principle of the Best or the Best of All Possible Worlds: Leibniz makes the following argument in his Discourse on Metaphysics:
      • God has the idea of infinitely many universes.
      • Only one of these universes can actually exist.
      • God’s choices are subject to the principle of sufficient reason, that is, God has reason to choose one thing or another.
      • God is good.
      • Therefore, the universe that God chose to exist is the best of all possible worlds
    • Humans, however, have free will, and this is why the world isn’t a perfect paradise. All God does is make actual the world that has the highest possible good.
  3. Predicate-in-Notion Principle: this is the idea that the predicate is “contained within” the subject. For a proposition “S is P” the predicate P is contained within the subject S. More concretely, when we say, for instance, that “rock is hard” we are saying that the concept of hardness is contained within the concept of rock. Leibniz thought this true for what Kant would call a priori analytic (definitional) and a posteriori synthetic (empirically discovered) propositions. Kant will disagree with this.
  4. Principle of Contradiction: “a proposition cannot be true and false at the same time, and that therefore A is A [law of identity] and cannot be not A [law of contradiction]” (G VI 355/AG 321) (source)
  5. Principle of Sufficient Reason: everything that happens, it happens for a reason (because of some cause). Anyone with enough information will be able to answer the question of why something is the case. Or put differently in the following way (source):
    • A simple formulation of the principle is as follows:
    • (1) For every fact F, there must be a sufficient reason why F is the case.
    • The term “fact” in the above formulation is not intended to express any commitment to an ontology of facts. Still, if one wishes to avoid such connotations, the principle can be formulated more schematically:
    • (2) For every x, there is a y such that y is the sufficient reason for x (formally: ∀xyRyx [where “Rxy” denotes the binary relation of providing a sufficient reason]).
      • See the Analytic Philosophy section of this post for an explanation of the formal logical symbols.
  6. Principle of Indiscernibles or the Principle of the Identity of Indiscernibles (PII): if two objects S1 and S2 share all the same predicates P1, P2, P3, … Pn then those two objects are identical, i.e., S1 = S2. In other words, if two things share all properties, they are identical, or (∀F)(FxFy) → x = y.
    • Leibniz clarifies, however: “although time and place (i.e., the relations to what lies outside) do distinguish for us things which we could not easily tell apart by reference to themselves alone, things are nevertheless distinguishable in themselves. Thus, although diversity in things is accompanied by diversity of time or place, time and place do not constitute the core of identity and diversity, because they [sc. different times and places] impress different states upon the thing. To which it can be added that it is by means of things that we must distinguish one time or place from another, rather than vice versa.”
  7. Principle of Continuity: changes do not occur suddenly, but must pass through intermediate stages. This is important for the idea that nothing could just begin moving immediately and on its own.
  8. Complete Individual Concept: a subject contains all of its predicates eternally. Leibniz says in his Discourse on Metaphysics:
    • “…we can say that the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed.”
    • “God, seeing Alexander [the Great]’s individual notion or haecceity, sees in it at the same time the basis and reason for all the predicates which can be said truly of him.”
  9. Substances: Leibniz says the following about substances in the Aristotelian sense (source):
    • (1) No two substances can resemble each other completely and be distinct. (PII)
    • (2) A substance can only begin in creation and end in annihilation.
    • (3) A substance is not divisible.
    • (4) One substance cannot be constructed from two.
    • (5) The number of substances does not naturally increase and decrease.
    • (6) Every substance is like a complete world and like a mirror of God or of the whole universe, which each expresses in its own way.
      • This is where his monadology comes from.
  10. Monadology: a monad is a simple, indivisible substance. Monads make up everything, including souls and rational minds. The monads can be said to be God’s thoughts, since God has perfect knowledge of the monads and can perceive reality from the point of view of every monad. As such, the monads are continually being created at every moment “…by continual fulgurations of the Divinity.” Objects are infinitely divisible and gain their properties from the properties of the infinitesimal components. Furthermore, monads do not actually interact, but move out of a preestablished harmony.

Christian Wolff (January 24, 1679 C.E. – April 9, 1754 C.E.): German philosopher, thought to be the most important in the time between Leibniz and Kant. Leibniz and Wolff are two philosophers who are extremely influential for Kant, as a reading of Wolff’s philosophy will reveal. Important as well for writing his philosophy in German rather than Latin, making German into a language for philosophy. He was a prolific writer, so much of his philosophy will not be discussed here.

  1. Rationalism: heavy focus on the a priori, the Principle of Contradiction (PC), and the Principle of Sufficient Reason (PSR).
  2. Ontology: Being is something if it is possible, which is the case if all the predicates are non-contradictory. A “possible object” is one that is non-contradictory, and a “possible concept” is one that corresponds with a possible object.
    • “Nothing” is a concept that doesn’t refer to any thing and is therefore contradictory.
    • Existence is, for Wolff, a predicate that makes a possible thing actual.
    • The philosopher is then tasked with determining the sufficient reason for why something is possible.
      • “In §56 of his Ontologia, [Wolff] writes: “By sufficient reason we understand that from which it is understood why something is [or can be]”. Unlike Leibniz who essentially restricts the notion of sufficient reason to “contingent truths of fact”, Wolff considers the notion to have a much broader scope of application to include the set of all possible objects and what Leibniz calls “necessary truths of reason”. The idea that everything has a sufficient reason is presented formally by Wolff as the principle of sufficient reason.” (source)
  3. Cosmology: the study of the “world-whole” in general. The world is an extended-composite of extended-composites.
    • Atoms: “unextended points of force” without internal motion but are in a constant state of change. Unlike Leibniz’s monads, the “simples” or atoms for Wolff can interact and influence one another.
    • Corpuscles: composites of Atoms, they are extended and take up space. They are still too small to be seen, but they are what determines the mechanical properties of an object.
    • Bodies: this is the level of appearances. It is a composite of composites, i.e., a composite of Corpuscles, which are composites of Atoms. The actual properties of Bodies, however, are secondary characteristics, which are mind-dependent. Wolff says that even Locke’s primary qualities, such as extension, are mind-dependent – space, according to Wolff, is just the way for the mind to organize things outside itself (this notion was very influential on Kant).
  4. Psychology (Soul): Wolff innovated the notion of a separation between empirical psychology and rational psychology. The former is the observation of our mind (introspection) and the latter is reasoning about the mind.
    • Empirical Psychology: concerned with the following four things (source):
      1. the initial consideration of the human soul in an attempt to arrive at an initial definition; the consideration of the soul’s
      2. cognitive faculty and
      3. appetitive faculty; and
      4. a consideration of what can be known of the soul’s relation to the body through experience.
    • Rational Psychology: concerned with determined the independence of the soul (from the body) and the immortality of the soul
  5. Natural Theology: “the science of those things that are possible through God.” It is broadly concerned with proving the existence of God and determining the nature of God (what attributes God possesses).
    • Proofs of God: Wolff uses versions of the cosmological and the ontological arguments.
    • God’s Nature: independent (not of the world), necessary (eternal and non-composite), possesses intellect (to represent all possible worlds) and will (to make a possible world actual), is perfectly free (his sufficient reason to do anything is in himself), wise (uses perfect means to actualize the world), and good.
  6. Practical Philosophy: humans must strive for the perfection that exists in our essence; yet, this perfection is not dependent on God’s commands (though it is compatible with them). When we take action that brings us closer to perfection, this results in pleasure; actions that bring us further from perfection cause pain. This consequentialist aspect to Wolff’s ethics is something that Kant will reject.

Montesquieu (January 18, 1689 C.E. – February 10, 1755 C.E.): French political philosopher. Full name is Baron de Montesquieu, Charles-Louis de Secondat.

  1. The Spirit of the Laws (all the follows uses the Stanford Encyclopedia entry on Montesquieu as my source): Montesquieu says that laws should conform to the nature of the peoples to whom the laws are applied: laws should be formed in accord with “the people for whom they are framed…, to the nature and principle of each government, … to the climate of each country, to the quality of its soil, to its situation and extent, to the principal occupation of the natives, whether husbandmen, huntsmen or shepherds: they should have relation to the degree of liberty which the constitution will bear; to the religion of the inhabitants, to their inclinations, riches, numbers, commerce, manners, and customs. In fine, they have relations to each other, as also to their origin, to the intent of the legislator, and to the order of things on which they are established; in all of which different lights they ought to be considered”
    1. The different kinds of governments are republican, monarchic, and despotic. Republican can be either democratic or aristocratic. The difference between monarchic and despotic is essentially the rule of law, where a monarch is bound by laws and a despot rules arbitrarily and by decree. He saw Protestantism as best for republics, Catholicism for monarchies, and Islam for despotisms.
    2. Liberty and Separation of Powers: Montesquieu essentially abided by the dictum that liberty ends only where another’s begins – a person should be allowed to do as they please so long as it doesn’t infringe on the rights of another. This liberty is, however, always under threat by the government, which is run by people who will seek to infringe on people’s liberties. The government must therefore have a system of checks and balances, which is achieved through the separation of powers. For Montesquieu, this was the separation into the legislative, executive, and judicial branches.
    3. Commerce: Montesquieu thought that commerce, rather than conquest or colonialism, was the best way for a country to enrich itself.
    4. Religion: Montesquieu was a proponent of religious tolerance and the separation of religion and state. Religion was personal, meant for the betterment of the individual, while the state was for the betterment of society. Therefore, the laws should “require from the several religions, not only that they shall not embroil the state, but that they shall not raise disturbances among themselves.”

Voltaire (November 21, 1694 C.E. – May 30, 1778 C.E.): French writer, historian, and philosopher; real name is François-Marie Arouet.

  1. He was a deist and a critic of organized religion.

George Berkeley (March 12, 1685 C.E. – January 14, 1753 C.E.): Irish philosopher

  1. Idealism

Francis Hutcheson (August 8, 1694 C.E. – August 8, 1746 C.E.): Scottish philosopher born in Ulster to a family of Scottish Presbyterians who became known as one of the founding fathers of the Scottish Enlightenment.

David Hume (April 26, 1711 C.E. – August 25, 1776 C.E.): Scottish philosopher. Hume saw as his project to “reject every system … however subtle or ingenious, which is not founded on fact and observation.” He is thus known as the quintessential empiricist. What follows uses the Stanford Encyclopedia entry on Hume as the main source.

  1. The Mind:
    • Perceptions: all mental content. It is broken down into Impressions and Ideas.
      • Impressions: include sensations as well as desires, passions, and emotions. These are the ways that an experience feels in the moment. These can be broken down further into Original Impressions and Impressions of Reflection.
        • Original Impressions: the actual data from the five senses.
        • Impressions of Reflection: the way that such data makes us feel.
      • Ideas: “the faint images of these [impressions] in thinking and reasoning”. This is then recalling impressions in memory. These are therefore mental objects and are not the way an impression actually feels or appears.
    • Percaptions (both Impressions and Ideas) can be either simple or complex, in basically the same way that Locke formulated these notions. Impressions, according to Hume, are more “forceful” than Ideas (more vibrant or vivacious) – the memory of how something tasted isn’t as “forceful” as actually having the direct experience of tasting it. Furthermore, Ideas are only ever copies of Impressions (Hume’s so-called Copy Principle). Ideas, however, can be manipulated and conjoined with one another in our imagination, which is often done in predictable ways due to Hume’s Principle of Association, which says “There is a secret tie or union among particular ideas, which causes the mind to conjoin them more frequently, and makes the one, upon its appearance, introduce the other.”
  2. Cause-and-Effect: Hume distinguished between what he called the “relations of ideas” and “matters of fact” which roughly correspond to the Kantian notion of a priori analytic and a posteriori synthetic – the former are truths that can be determined by the definitions of concepts (e.g., that the angles in a triangle add up to 180 degrees is known by virtue of the definition of a triangle) while the latter are truths that must be determined through experience (e.g., that Mount Everest is the tallest mountain in the world). Hume argues that cause-and-effect are matters of fact and not relations of ideas, since a cause is different from its effect – there is nothing in the effect that logically implies its particular cause, which means we cannot reason about causality a priori. We therefore only come up with cause-effect relationships through induction from prior experience. This is only done by “custom” and not by reason: “whenever the repetition of any particular act or operation produces a propensity to renew the same act or operation … we always say, that this propensity is the effect of Custom.”
  3. Moral Philosophy: Hume was a moral sentimentalist, which essentially means that the content of our morals is derived from experience, where we have either a good or bad sentiment toward different actions we see people take. From these experiences of good and bad sentiments associated with these actions, we come to conclusions, through induction, about which actions are morally good an which actions are morally bad.

Thomas Reid (May 7, 1710 C.E. – October 7, 1796 C.E.): Scottish philosopher

  1. Often said to be David Hume’s biggest philosophical critic.

Jean-Jacques Rousseau (June 28, 1712 C.E. – July 2, 1778 C.E.): Genevan philosopher

  1. Romanticism

Denis Diderot (October 5, 1713 C.E. – July 31, 1784 C.E.): French philosopher

  1. Co-founder of Encyclopedia, or a Systematic Dictionary of the Sciences, Arts, and Crafts with Jean-Baptiste le Rond d’Alembert. Usually just known as the Encyclopédie, it was a watershed achievement during the Enlightenment. It was meant to be a repository of knowledge (sort of like what Wikipedia is now) so that anyone could have access to information.
  2. He is known for his religious skepticism. Indeed, the Encyclopédie was banned by both the Catholic church and the French government. Many see the Encyclopédie as an inspiration for the French revolution.

Alexander Gottlieb Baumgarten (July 17, 1714 C.E. – May, 1762 C.E.): German philosopher and brother of Siegmund Jakob Baumgarten. Known most for his pioneering work in aesthetics, and is even credited with changing the meaning of the word aesthetics to being the study of good and bad art.

Siegmund Jakob Baumgarten (March 14, 1706 C.E. – July 4, 1757 C.E.): German theologian and brother of Alexander Gottlieb Baumgarten.

Adam Smith (June, 1723 C.E. – July 17, 1790 C.E.): Scottish economist

  1. Invisible hand of the market.

Edmund Burke (January 12, 1729 C.E. – July 9, 1797): Irish-British statesman and philosopher

  1. Realist and pragmatist in politics.

Moses Mendelssohn (September 6, 1729 C.E. – January 4, 1786 C.E.): Jewish German philosopher.

  1. Thinks that mathematics and metaphysics are closely related. The differences are the following (source):
    1. first, metaphysics’ greater reliance upon arbitrary signs (signs that do not essentially coincide with what is signified);
    2. second, the holistic content of metaphysics (no quality can be defined without an adequate insight into the others); and
    3. third, metaphysics’ need to establish the actual existence of what corresponds to the analyzed concepts
  2. Idealism, Materialism, Dualism: Mendelssohn thought that the disagreements between these schools of thought were mostly linguistic (i.e., because of the reliance upon arbitrary signs). He appeared to lean more toward idealism, and thought that God needed to be proven to exist in order to have certainty of an external world. Mendelssohn does this with a cosmological argument (appealing to the principle of sufficient reason) an a version of the ontological argument.
    • Mendelssohn’s ontological argument (adapted from here): Non-existent things are either impossible or possible. If it’s impossible, then it must be contradictory. If it is possible, then its intrinsic properties are insufficient to determine its existence, and so depends on something external. If God doesn’t exist, then it’s either because the idea of God is impossible or because it’s possible (contingent) but not actual. Since contingency means it is dependent and being independent is greater than dependence, it contradicts the essence of a perfect being for that being to be contingent. Thus, the idea of a perfect being can’t be the idea of something merely possible. But the idea of a perfect being also doesn’t contain determinations that must be affirmed and denied at the same time. In other words, the idea is not impossible. And so Mendelssohn concludes that God exists from the consideration that the idea of God cannot be the idea of something nonexistent.
  3. Rational Psychology: Mendelssohn gives an account of the simplicity (not composite, since its character is unifying) and immortality of the human soul.
    • “We would be able neither to remember nor to reflect nor to compare nor to think, indeed, we would not even be the person who we were a moment ago, if our concepts were divided among many and were not to be encountered somewhere together, combined in the most precise ways they can. We must, therefore, assume at least one substance that combines all concepts of the component parts…. There is, therefore, in our body at least one sole substance that is not extended, not composed, but instead is simple, has a power of presentation, and unites all our concepts, desires, and inclinations in itself” (Phädon (2007), pp. 119f (translation slightly altered)/Gesammelte Schriften, 3/1, pp. 96f). (source)
  4. Ethics: there are major premises that are general maxims (that can be proven with mathematical rigor) for how to act, and then minor premises that are the particular situation one is faced with. Thus, ethics is a kind of syllogism that looks like the following:
      1. If presented with situation A, then do B
      2. Situation A is presented
      3. Therefore, do B
    • Imperfect applications of this syllogism is what causes people to have differing views on what is good and bad. Once a person has sufficient insight into the general maxims, they would know how to be perfectly moral.
    • The maxims that Mendelssohn comes up with are the following (source): “Summing up these three proofs, Mendelssohn lists three basic maxims that lead to the same conclusion. Whether we (1) consider what is common to all human inclinations, (2) recognize ourselves as entities endowed with free wills, or (3) acknowledge that we are God’s creation, “all three maxims lead to the common conclusion: perfect yourself and others.””

Friedrich Heinrich Jacobi (January 25, 1743 C.E. – March 10, 1819 C.E.):

Johann Gottfried Herder (August 25, 1744 C.E. – December 18, 1803 C.E.)

Immanuel Kant (April 22, 1724 C.E. – February 12, 1804 C.E.): German philosopher

  1. Intuition: the way that objects appear to us. You can maybe think about it like the stage on which our representations of the world are experienced.
  2. Understanding: the application of concepts to the objects in our intuition.
  3. Transcendental Deduction: taking the way things are as a given and then attempting to deduce what conditions must hold in order for the way things are to be possible.
  4. Transcendental Aesthetic: this is the part of Kant’s Critique of Pure Reason where he discusses the form of our intuition. He says that our intuitions always occur in space and in time. Indeed, it’s impossible to have an intuition that is not spacial and temporal. Everything we experience is extended in space and occurs as a series in time.
  5. Transcendental Analytic: this is the part of Kant’s Critique of Pure Reason where he lays out the general concepts for the possibility of experience. These concepts, called the categories of understanding, take the form of judgements, which are the forms of propositions in an Aristotelian sense.
  6. Phenomena and Noumena: the former is the world as it is experienced by people where the latter is the world of things in-themselves. In the realm of experience, the Phenomena, the sorts of things that we understand, like cause-and-effect, hold true. For things in-themselves, the Noumena, we cannot know whether this is the case or not.
  7. Transcendental Dialectic: this is the part of Kant’s Critique of Pure Reason where he shows that, in light of his discussion in the Transcendental Aesthetic and the Transcendental Analytic, reason itself is constrained. Past philosophers have attempted to go beyond what our faculty of reason is capable of to describe things in-themselves.
  8. Categorical Imperative

You can learn more about Immanuel Kant from my video series covering his work:

(Post)-Kantian and German Idealist (1750 C.E. – 1850 C.E.)

Salomon Maimon (1753 C.E. – November 22, 1800 C.E.): Lithuanian Jewish philosopher

Karl Leonhard Reinhold (October 26, 1757 C.E. – April 10, 1823 C.E.): Austrian-German philosopher

  1. He was a big fan of Kant’s work, but thought that Kant left his work incomplete. And so, like many of the “post-Kantian” philosophers, he set out to fix and complete Kant’s critical philosophy. To do this he began his project of what came to be called (by himself) “Elementary Philosophy”.
  2. Elementary Philosophy: what is philosophy and how is it possible? It is to establish “universally valid” propositions that are understandable and agreed upon by everyone. Furthermore, these propositions must be systematic (consistent and complete), able to logically connect to one another. He therefore saw it as one of his tasks to systematize Kant’s philosophy.
  3. To systematize, Reinhold thought that philosophy needed to be foundationalist – able to be derived from first principles, i.e., all propositions can be derived from the basic axioms in a mathematical way (although Reinhold’s conception of derivation is somewhat unclear). He therefore sought to discover the (self-evident) first principle (hence why his philosophy is elementary).
  4. From the Stanford Encyclopedia of Philosophy: “What then is the “first principle” of the Elementary Philosophy? It is the “Principle of Consciousness,” namely, the proposition that “in consciousness, the subject distinguishes the representation from the subject and the object and relates the representation to both” (Beyträge I, p. 167). In this proposition, the term “representation” [Vorstellung] designates whatever we are directly conscious of whenever we are conscious of anything whatsoever; the term “subject” designates the one who “is conscious” of whatever one is conscious of (the “conscious subject” or “subject of consciousness”); and the term “object” designates that “of which” the representation is a representation (the intentional object of consciousness, that to which the representation “refers”).”
  5. From this Reinhold goes on to show “that space, time, the twelve categories, and the three forms of the ideas are originally nothing but properties of mere representations” (Fundament, pp. 72–73)
  6. Both Fichte and Schelling were greatly influenced by Reinhold’s Elementary Philosophy

Johann Gottlieb Fichte (May 19, 1762 C.E.January 29, 1814 C.E.): German philosopher. Can perhaps be thought of as the bridge between the so-called “post-Kantians” and the German idealists (Schelling was a student of Fichte’s)

  1. Wissenschaftslehre (Theory of Scientific Knowledge): Fichte, having read both Kant and Reinhold, thinks he knows what is even more fundamental than Reinhold’s Principle of Consciousness. He saw that there were two competing and mutually exclusive (both cannot be true and neither can refute the other) possible starting points:
      1. Selfhood (Free Will): leads to idealism
      2. Thinghood (Necessity): leads to dogmatism (Cartesian style rationalism)
    1. Fichte thought the former stronger than the latter, since it allows an explanation of the experience of objects, whereas the latter cannot be used to deduce the possibility of experience. One’s own free will, however, has to be taken as a brute fact, according to Fichte – it has to be presupposed, since it cannot be proven philosophically.
    2. The first principle then, according to Fichte, is “the I posits itself as self-positing.”
        • “To posit” (setzen) means “to be aware of,” “to reflect upon,” or “to be conscious of”; it does not mean “to create” (source)
        • “In Fichte’s technical terminology, the original unity of self-consciousness is to be understood as both an action and as the product of the same: as a Tathandlung or “fact/act,” a unity that is presupposed by and contained within every fact and every act of empirical consciousness, though it never appears as such therein.” (source)
        • From this first principle, Fichte says a transcendental deduction of what conditions must hold in order for the “self-positing I” to be possible must be completed.
      • Anstoß: the “I” posits itself as unlimited and absolute, but discovers that it is in fact limited (it cannot determine, for instance, why sensations have the sensation that they do; this is not something the “I” has control over). This limitation, however, is posited by the “I” which therefore divides the “I” against itself. This tension leads to our conscious experience. The Anstoß is thus a condition of the possibility of experience.
  2. System of Ethics: (source) – divided into three sections
      1. “The deduction of the principle of morality” gives the transcendental reconstruction of the moral law and freedom as a necessary condition for the thinking ‘I.’
      2. “The deduction of the reality and applicability of the principle of morality” explains how the concept derived in in the first part can have an effect in the world.
      3. “The systematic application of the principle of morality, or ethics in the narrower sense,” presents a system of duties derived from the first and second parts.
    • Tries to make connection between Kant’s moral law and Kant’s theory of subjectivity, and between theoretical and practical reason. Fichte claims that the moral law is the condition for being a self-conscious entity, saying that thinking is practical insofar as it must construct itself as a thinking being under the moral law. We therefore have to think of ourselves as necessarily under the moral law.
  3. Foundations of Natural Right
    • Relation of Right: recognition of others as conscious, rational beings
    • Sphere of Freedom: people must be free from outside forces
    • Original Right: a person must be considered as a cause and not an effect. This means that to treat someone as an effect is to use coercion against them, which is immoral.

Jakob Friedrich Fries (August 23, 1773 C.E. – August 10, 1843 C.E.): German philosopher and mathematician

  1. In his 1807 work The New or Anthropological Critique of Reason, he wanted to find out how Kant’s critical method and transcendental deduction provides knowledge. To do this, he Fries was prepared to use empirical psychology methods.
    1. “Fries said the critical method provides knowledge by a regressive analysis which begins with the empirical facts of consciousness; thus, the, critical method leads to empirical, not metaphysical, knowledge. … Fries maintained that we come to know the a priori forms in our thought only as a matter of experience.” (source)
    2. “The basis of Fries’s critical method – its first step – was self-observation. Through a careful phenomenology of the mind Fries hoped not only to determine the various types of knowledge, but also to describe and classify the general types of mental processes which constitute mental life. He viewed the establishment of an adequate theory of the mind as a necessary preliminary to a critical analysis of the innate forms of the mind.” (source)

Gottlob Ernst Schulze (August 23, 1761 C.E. – January 14, 1833 C.E.): German philosopher

Friedrich Wilhelm Joseph Schelling (January 27, 1775 C.E. – August 20, 1854 C.E.): German philosopher

Georg Wilhelm Friedrich Hegel (August 27, 1770 C.E. – November 14, 1831 C.E.): German philosopher

  1. Most known for his dialectical method.

Middle Modern (1800 C.E. – 1920ish C.E.)

Jeremy Bentham (February 15, 1748 C.E. – June 6, 1832 C.E.): English philosopher, jurist, and social reformer regarded as the founder of modern utilitarianism. Bentham defined as the “fundamental axiom” of his philosophy the principle that “it is the greatest happiness of the greatest number that is the measure of right and wrong.”

David Ricardo (April 18, 1772 C.E. – September 11, 1823 C.E.): British political economist

Auguste Comte (January 19, 1798 C.E. – September 5, 1857 C.E.): French philosopher and writer who formulated the doctrine of positivism. He is often regarded as the first philosopher of science in the modern sense of the term.

Harriet Martineau (June 12, 1802 C.E. – June 27, 1876 C.E.): English social theorist often seen as the first female sociologist.

Charles Darwin (February 12, 1809 C.E. – April 19, 1882 C.E.): British scientist who formulated the theory of evolution by natural selection. Click the links below for my explications of Darwin’s theory.

  1. Natural Selection
  2. Evidence
  3. Higher Concepts

John Stuart Mill (May 20, 1806 C.E. – May 8, 1873 C.E.): English philosopher, political economist, Member of Parliament and civil servant. One of the most influential thinkers in the history of classical liberalism, he contributed widely to social theory, political theory, and political economy.

Ludwig Feuerbach (July 28, 1804 C.E. – September 13, 1872 C.E.): German anthropologist and philosopher who was very critical of Christianity.

Karl Marx (May 5, 1818 C.E. – March 14, 1883 C.E.): frequently worked with Friedrich Engels, making their philosophies difficult to disentangle from one another. Many things that are considered Marxist, such as the stages of dialectical materialism, were never written about by Marx personally, but are claimed by Engels (who outlived Marx) to have been part of Marx’s thought.

  1. Means of Production: the machines and natural resources needed to produce finished commodities.
  2. Use Value vs. Exchange Value: the former is the value that something has because of its function while the latter is the value that it has on the market. The exchange value is how we can say that x amount of A [which I’ll represent as A(x)] and y amount of B [which I’ll represent as B(y)] have equal value (perhaps x amount of copper and y amount of cabbage). We can thus say that A(x) = B(y). But, since, for instance, cabbage is perishable, there must be a way of making an exchange at different points in time, which is where money comes in; we can then say that A(x) = $ = B(y). That allows the cabbage farmer to sell the cabbage for money before they perish and then use that money at a different time to purchase the copper.
    • Marx named the difference between the two (Use Value and Exchange Value) a contradiction, since the Use Value is qualitative while the Exchange Value is quantitative. Because of this contradiction, since capitalists produce commodities only for their Exchange Value and not their Use Value, the capitalists will produce commodities that have only the bare minimum use value in order to maximize profits (by producing more at a larger scale), leaving us with suboptimal commodities.
    • Contradiction: Marx often uses the word contradiction when writing about capitalism, saying that there are inherent contradictions, such as between Use Value and Exchange Value. This is often misconstrued as the kind of contradiction talked about in formal logic (where A and not-A cannot both be the case at the same time). This is misleading, however, since the contradiction is actually meant more like an inconsistency.
    • Labor Theory of Value: the value of something comes from the difficulty of attaining or producing that thing.
  3. Surplus Value: the difference between the value of the commodity as a function of the labor needed to produce the commodity and the amount the laborer is paid. This difference becomes profit for the capitalist, who did zero work to produce the commodity, and therefore profits off the surplus value that the commodity possesses.
  4. Wage Labor: the notion that workers must work for subsistence – a worker gets paid, then has to spend that money on essentials to live, which then means they must continue working in order to get paid again, maintaining a vicious cycle.
  5. Crises: the ability to exchange commodities at different points in time untethers those commodities from each other. For instance, a person sells so many cabbages for a certain amount of money and then a week later uses that money to buy copper, the net exchange is cabbage for copper, but these events are separated in time. During that time, many things could have happened, including the devaluing of currency, inflation, theft, and so on. Money also makes it possible for people to take loans and credit, wherein interest rates can change or an inability to pay back loans for a variety of reasons can lead to default.
    • For Marx, a crisis happens when too many commodities are produced than can be sold (since the capitalist will always be expanding (infinite growth) in order to gain a competitive edge and maximize profits), but nobody will be willing to lower the prices since the first firm to do so might jump the gun and lose money. This will force firms to default on loans and go out of business. This results in job loss for the workers, who will then be left destitute and desperate.
    • Marx predicted that such crises will grow worse and worse in the future, leading to a revolt by the workers that will usher in a dictatorship of the proletariat.
  6. Commodity Fetishism: production and exchange is a relationship among things rather than people.
  7. Alienation: the worker produces commodities that do not benefit themselves in any way, alienating them from the fruits of their labor. Likewise, the division of labor, and competition for employment, has alienated the workers from each other.
  8. Ideology: those ideas that are used by the bourgeois to justify the current social relations. They are meant to make people think that the way things are (with a small number of capitalists and a majority of workers doing wage labor) is normal, natural, and necessary.
  9. Dictatorship of the Proletariat: the workers seize the means of production and take control of the state. This is often conflated with Leninist/Maoist notions that there is a dictator who has to pull their (usually agrarian/feudal) society into the communist future. But for Marx it is actually more literal in that, under socialism (the next step after capitalism) the society is run by the proletariat. Marx predicts that after a while, this dictatorship will become obsolete and the proletariat will dissolve the state away and bring society into a stateless, classless communism.

20th Century Until Now

For this part, which covers roughly the twentieth century until now, I am going to break it down by the various schools of thought. This is also going to have many, many more people who are left out, since the number of notable philosophers has exploded, and so I will focus mainly on those names big enough that even people outside of philosophy may have heard of them.

Critical Theory

W. E. B. du Bois (February 23, 1868 C.E. – August 27, 1963 C.E.): William Edward Burghardt Du Bois was involved in the creation of the NAACP (National Association for the Advancement of Colored People). He is highly regarded as a black scholar who worked during the Jim Crow era and was instrumental in the scholarly work of the black experience in the United States.

  1. The Souls of Black Folk: Du Bois’s most famous work, where he developed the idea of the double consciousness
    • Double Consciousness: the way black Americans experience living in the world. Is is living with the consciousness of a black person and as a person living in world created by (and for) white people. It’s a double consciousness of how black people view themselves and of how the world views them.
      • “One ever feels his twoness,—an American, a Negro; two souls, two thoughts, two unreconciled strivings; two warring ideals in one dark body, whose dogged strength alone keeps it from being torn asunder. The History of the American Negro is the history of this strive-this longing to attain self-conscious manhood, to merge his double self into a better and truer self. He simply wishes to make it possible for a man to be both a Negro and an American, without being cursed and spit upon by his fellows, without having the doors of Opportunity closed roughly in his face.”

György Lukács (April 13, 1885 C.E. – June 4, 1971 C.E.): Hungarian Marxist philosopher, literary historian, critic, and aesthetician. He was one of the founders of Western Marxism, an interpretive tradition that departed from the Marxist ideological orthodoxy of the Soviet Union. He was Hungarian Minister of Culture of the government of the short-lived Hungarian Soviet Republic (March–August 1919). He preached about the “destruction of the oppressing classes” using the violence of the state

  1. Hungarian Soviet Republic: I have heard the story in a number of places that György Lukács, as the Minister of Culture, had intentionally exposed children to deviant sexual material. I’ve even heard that he tried to force kids into sex transition (boys becoming girls and girls becoming boys). I don’t know if this is true or not, as most of the sources that mention this are people and organizations who have an axe to grind against LGBT issues. The leftist website Jacobin does mention that “The Commissariat established a sex education program aimed at schoolchildren — the first of its kind in deeply Christian Hungary” but doesn’t say anything more. This Daily Mail article does claim that György Lukács’s Marxist ideology sought to destroy “old values” but doesn’t confirm that György Lukács was exposing children to sexually deviant material.
    • From the Daily Mail article: “While the book [Michael Löwy’s Georg Lukacs: From Romanticism to Bolshevism] quotes extensively from Lukacs and is well sourced it does not include a direct admission from Lukacs that he was attempting to demoralise Christian society with his education program. This charge seems to stem from the observation of a Yugoslav professor, Victor Zitta. Mr Audritt quotes Michael Lowy, quoting Victor Zitta: “The bourgeois fury and indignation at Lukacs’s profoundly subversive cultural policy has recently found echo in the writings of one Victor Zitta. Portraying Lukacs as a ‘fanatic… bent on destroying the established social order’, Zitta argues that education became ‘something perverse’ under Lukacs’s guidance: ‘Special lectures were organised in school and literature printed and distributed to “instruct” children about free love, about the nature of sexual intercourse, about the archaic nature of the bourgeois family codes, about the outdatedness of monogamy, and the irrelevance of religion which deprives man of all pleasure. Children urged thus to reject and deride paternal authority and the authority of the church, and to ignore precepts of morality’.”
  2. False Consciousness: the lower class is unaware of their own oppression due to the ideology (in the Marxist sense) essentially brainwashing them into thinking their lot in life is natural and normal. The kind of happiness that people experience in capitalism (e.g., consumption of commodities) is not a real kind of happiness, but one that results from their false consciousness about how society ought to be.
  3. Reification: the process of making things that are not real seem real, such as the capitalist class divisions. Basically the way that the ideology of the dominant ruling class is made so as to seem like it is natural, normal, and necessary.

Antonio Gramsci (January 22, 1891 C.E. – April 27, 1937 C.E.): Italian Marxist philosopher, journalist, linguist, writer, and politician. He wrote on philosophy, political theory, sociology, history, and linguistics.

  1. Cultural Hegemony: the dominant ruling class owns the means of cultural production and get to decide what the “correct” beliefs, values, norms, and social mores are.

Theodor Adorno (September 11, 1903 C.E. August 6, 1969): German philosopher, sociologist, psychologist, musicologist, and composer known for his critical theory of society.

  1. Negative Dialectics:

Max Horkheimer (February 14, 1895 C.E. July 7, 1973 C.E.): German philosopher and sociologist who was famous for his work in critical theory as a member of the Frankfurt School of social research.

  1. Traditional and Critical Theory:
  2. Dialectic of Enlightenment:

Herbert Marcuse (July 19, 1898 C.E. July 29, 1979 C.E.): German-American philosopher, sociologist, and political theorist, associated with the Frankfurt School of critical theory.

  1. An Essay on Liberation: people need to have psychopathologies induced in them that make them unable to tolerate liberalism in order for people to take on a “new sensibility,” meaning that they see anything and everything through the lens of Critical Theory. This is why all Critical Theories are said to be negative insofar as they do not submit a vision of their Utopia, but say that Utopia will be what is left standing once liberalism has been completely razed to the ground.
  2. Repressive Tolerance: repression is tolerable if it is done by the left.

Derrick Bell (November 6, 1930 C.E. October 5, 2011 C.E.): American lawyer, professor, and civil rights activist. Bell worked for first the U.S. Justice Department, then the NAACP Legal Defense Fund, where he supervised over 300 school desegregation cases in Mississippi.

  1. Interest Convergence Thesis: This is the idea that the only time the dominant group (white people) would ever give anything like rights to other races (especially black people) is if it was in their own interest to do so. In other words, the interests of the non-white people who will “benefit” from some policy must converge with the interests of the white dominant class. I put scare quotes around “benefit” because a part of this doctrine is that the non-whites don’t truly benefit, since when the white interests are upheld it is only ever at the cost of the non-whites (it is zero sum). Indeed, Derrick Bell came up with the interest-convergence thesis when he argued that Brown vs. Board of Education case that led to school integration was done for white interests (like, for instance, stemming the tide of Marxism) and only succeeded (as far as black people are concerned) in making racism more hidden.

Richard Delgado (October 6, 1939 C.E. Present): American legal scholar who teaches civil rights and critical race theory at the University of Alabama School of Law. He has written and co-authored numerous articles and books, many with his wife, Jean Stefancic

Jean Stefancic (January 14, 1940 C.E. Present): American legal academic, Professor and Clement Research Affiliate at the University of Alabama. She has written numerous books with her husband Richard Delgado.

Angela Davis (January 26, 1944 C.E. Present): American political activist, philosopher, academic, scholar, and author.

Cornel West (June 2, 1953 C.E. Present): American philosopher, political activist, social critic, actor, and public intellectual. The grandson of a Baptist minister, West focuses on the role of race, gender, and class in American society and the means by which people act and react to their “radical conditionedness”.

Judith Butler (February 24, 1956 C.E. Present): American philosopher and gender theorist whose work has influenced political philosophy, ethics, and the fields of third-wave feminism, queer theory, and literary theory.

Kimberlé Crenshaw (May 5, 1959 C.E. Present): American civil rights advocate and a leading scholar of critical race theory. She is a professor at the UCLA School of Law and Columbia Law School, where she specializes in race and gender issues.


Arthur Schopenhauer (February 22, 1788 C.E. September 21, 1860 C.E.): German philosopher. He is best known for his 1818 work The World as Will and Representation, which characterizes the phenomenal world as the product of a blind noumenal will.

Søren Kierkegaard (May 5, 1813 C.E. November 11, 1855 C.E.): Danish theologian, philosopher, poet, social critic, and religious author who is widely considered to be the first existentialist philosopher.

  1. Leap of Faith:

Friedrich Nietzsche (October 15, 1844 C.E. August 25, 1900 C.E.): German philosopher, cultural critic and philologist whose work has exerted a profound influence on modern intellectual history. He began his career as a classical philologist before turning to philosophy.

  1. God is Dead:
  2. Will to Power:

Edmund Husserl (April 8, 1859 C.E. – April 27, 1938 C.E.): German philosopher and mathematician who established the school of phenomenology. In his early work, he elaborated critiques of historicism and of psychologism in logic based on analyses of intentionality.

Martin Heidegger (September 26, 1889 C.E. May 26, 1976 C.E.): German philosopher who is best known for contributions to phenomenology, hermeneutics, and existentialism. He is among the most important and influential philosophers of the 20th century.

Jean-Paul Sartre (June 21, 1905 C.E. April 15, 1980 C.E.): One of the key figures in the philosophy of Existentialism, a French playwright, novelist, screenwriter, political activist, biographer, and literary critic, as well as a leading figure in 20th-century French philosophy and Marxism.

  1. Being and Nothingness:
  2. Existentialism is Humanism

Simone de Beauvoir (January 9, 1908 C.E. April 14, 1986 C.E.): French existentialist philosopher, writer, social theorist, and feminist activist.

Albert Camus (November 7, 1913 C.E. January 4, 1960 C.E.): Algerian-born French philosopher, author, and journalist. He was awarded the 1957 Nobel Prize in Literature at the age of 44, the second-youngest recipient in history. His works include The Stranger, The Plague, The Myth of Sisyphus, The Fall, and The Rebel.

  1. The Myth of Sisyphus:


Michel Foucault (October 15, 1926 C.E. June 25, 1984 C.E.): French philosopher, historian of ideas, writer, political activist, and literary critic. Foucault’s theories primarily address the relationship between power and knowledge, and how they are used as a form of social control through societal institutions.

Jean-Francois Lyotard (August 10, 1924 C.E.  April 21, 1998 C.E.): French philosopher, sociologist, and literary theorist. His interdisciplinary discourse spans such topics as epistemology and communication, the human body, modern art and postmodern art, literature and critical theory, music, film, time and memory, space, the city and landscape, the sublime, and the relation between aesthetics and politics. He is best known for his articulation of postmodernism after the late 1970s and the analysis of the impact of postmodernity on the human condition.

Jacques Derrida (July 15, 1930 C.E. October 2004 C.E.): Algerian-born French philosopher best known for developing a form of semiotic analysis known as deconstruction, which he analyzed in numerous texts, and developed in the context of phenomenology. He is one of the major figures associated with post-structuralism and postmodern philosophy.

Jean Baudrillard (July 27, 1929 C.E. March 6, 2007 C.E.): French sociologist, philosopher and cultural theorist. He is best known for his analyses of media, contemporary culture, and technological communication, as well as his formulation of concepts such as simulation and hyperreality.

Henri Bergson (October 18, 1859 C.E. January 4, 1941 C.E.): for both Bergson and Deleuze, and to some extent Jaspers, I didn’t have a good school of thought to place them. An argument could be made that they were existentialist, an argument could be made that they were analytic, and an argument could be made that they were postmodern. And so, I just had to make a decision, which ended up being here at the bottom of the postmodern school of thought.

Gilles Deleuze (January 18, 1925 C.E. November 4, 1995 C.E.): French philosopher who, from the early 1950s until his death in 1995, wrote on philosophy, literature, film, and fine art. His most popular works were the two volumes of Capitalism and Schizophrenia: Anti-Oedipus and A Thousand Plateaus, both co-written with psychoanalyst Félix Guattari.

Karl Jaspers (February 23, 1883 C.E. February 26, 1969 C.E.): German-Swiss psychiatrist and philosopher who had a strong influence on modern theology, psychiatry, and philosophy.

Structuralism and Semiotics

Ferdinand de Saussure (November 26, 1857 C.E. February 22, 1913 C.E.): Swiss linguist, semiotician and philosopher.

  1. Semiotics: To give an oversimplified description, semiotics is a theory in linguistics (sometimes also called semiology, and is most often associated with the structuralism of Claude Lévi-Strauss), most famously explicated by Ferdinand de Saussure and Charles Sanders Peirce. In broad strokes, semiotics says that language is structural in that it is dependent on the rest of the language for its meaning (a single word doesn’t have any intrinsic meaning outside the context of the rest of a language; in other words, it is holistic). Saussure puts it like this: “Language is a system of interdependent terms in which the value of each term results solely from the simultaneous presence of the others … concepts are purely differential and defined not by their positive content but negatively by their relations with the other terms of the system.”
  2. Semiotics is also known for its signifier and signified (the “sound-image” and “concept” respectively) distinction, where the former is the “symbol” (usually meaning words, though depending on the scholar it can be interpreted more broadly) and the signified is what the signifier points to (it is the meaning of the signifier, i.e., the concept). Notably what is missing in the signifier and signified (particularly in Saussurean semiotics) is the physical referent “out there” in the real world; all we have is the “symbol” or “sound-image” and the concept, or the way that the “sound-image” is understood. Whether Saussure thought a language could be understood without referent at all or whether he was simply bracketing reference for methodological purposes is a point of debate, but Storm takes the interpretation that Saussure was methodologically bracketing reference in order to study the structure of language itself.
  3. In Saussurean semiotics, the signifiers tend to be words belonging only to humans. Biosemiotics brings in signifiers (and the corresponding signified) from plants, animals, and other non-linguistic sources. It is now well-attested that many animal species use vocalizations and gestures to communicate. Additionally, organisms like ants use pheromones, bees use a kind of “dance”, and plants communicate through chemicals as well.

Charles Sanders Peirce (September 10, 1839 C.E. April 19, 1914 C.E.): American philosopher, logician, mathematician and scientist who is sometimes known as “the father of pragmatism”.

Claude Lévi-Strauss (November 28, 1908 C.E. October 30, 2009 C.E.): French anthropologist and ethnologist whose work was key in the development of the theories of structuralism and structural anthropology.

Roland Barthes (November 12, 1915 C.E. – March 26, 1980): French literary theorist, essayist, philosopher, critic, and semiotician. His work engaged in the analysis of a variety of sign systems, mainly derived from Western popular culture.

Julia Kristeva (June 24, 1941 C.E. Present): Bulgarian-French philosopher, literary critic, semiotician, psychoanalyst, feminist, and, most recently, novelist. Her sizeable body of work includes books and essays which address intertextuality, the semiotic, and abjection, in the fields of linguistics, literary theory and criticism, psychoanalysis, biography and autobiography, political and cultural analysis, art and art history. She is prominent in structuralist and poststructuralist thought. 

Analytical Philosophy

Preface: analytical philosophy concerns itself with symbolic formal logic, which ends up having a lot of crossover with mathematics. Indeed, late 19th and early 20th century logic was motivated by attempting to make logic as rigorous and axiomatic as math had become throughout the 19th century. As such, many of the people here will actually be mathematicians whose contributions might seem only tangential to philosophy. But, there is an old adage among mathematicians and analytical philosophers that every mathematician has to be half a philosopher and every philosopher has to be half a mathematician.

Another consequence of this mixture of math and philosophy is that a symbolic language has been invented for logic. Here I will give some definitions for a few of these symbols, since they will pop up here and there during this explication.

  • is the universal quantifier. It can be read as “for all…”
    • ∀x can be read as “for all x” which means it is talking about all of the things that x can stand for
    • Sometimes parentheses are used instead, where (x) is the same as ∀x
    • If you see ∀xPx it means “for all x such that x is P”
  • is the existential quantifier. It can be read as “there exists a…”
    • ∃x can be read as “there exists an x…”
    • ∃xPx can be read as “there exists an x such that x is P”
  • is the material implication. It’s basically the symbol for if-then statements, where x→y means “if x, then y”. Sometimes you will see ⊃ used instead of →
  • means if and only if, which is sometimes written as “iff” and sometimes the symbols ⟷ or ⇔ are used. This means that A≡B can be read as “A if and only if B” and is true only if both A and B are true or if A and B are false.
  • ¬ and ˜ are both used as a negation. If you see ¬P that can be read as “not P” (e.g., where if P meant “blue” then ¬P would mean “not blue”)
  • and & are both used for the conjunction “and” so if you see A∧B that means “A and B”
  • and + are both used for the disjunction “or” so if you see A∨B that means “A or B or both” (since it is the inclusive or, it means “either A or B or both A and B”)
  • { } brackets are used to denote a set. So if you see {a, b, c} that means the set that contains the elements a, b, and c.
  • means element of. If you see a∈M it means that “a is an element of the set M”
  • means the union of two or more sets. If you se AB that means “the union of sets A and B” which means all of the elements in both A and B as well as any elements that overlap.
  • means the intersection of two or more sets. If you see AB that means “the intersection of sets A and B” which means only the elements of A and B that overlap.
  • is the subset symbol. If you see AB that means “A is a subset of B” Alternatively, ⊄ means not a subset.
  • Ø is the empty set such that Ø = {}
  • \ the backslash is used for a set difference. So if you see A\B it means that set of all members of A that are not members of B
    • If you see AB that means the set of all elements that are only a member of A or of B. This is called the symmetric difference.
  • × is the Cartesian product, which takes all the ordered pairs of two sets. So if you see A×B it means a set whose members are pairs composed of every member of A paired with a member of B. For instance, if we have A = {a, b, c} and B = {d, e, f} then A×B = {(a,d), (a,e), (a,f), (b,d), (b,e), (b,f), (c,d), (c,e), (c,f)} where (_,_) are ordered pairs.
  • P(A) is the power set of A, which is usually written with a fancy letter P. A power set is just every combination of elements in a set, including the empty set and the entire set itself. For instance, if A = {a, b, c} then P(A) = {Ø, a, b, c, {a, b}, {a, c}, {b, c}, {a, b, c}}

Augustus De Morgan (June 27, 1806 C.E. March 18, 1871 C.E.): British mathematician and logician

  1. De Morgan’s Laws:
    • The negation of a disjunction is the conjunction of the negations
      • not-(A or B) = not-A and not-B
    • The negation of a conjunction is the disjunction of the negations
      • not-(A and B) = not-A or not-B
  2. Upgrade to Aristotle: the introduction of quantification (differentiate between most and some)
    1. (copied from Wikipedia): The followers of Aristotle say that from two particular propositions such as Some M’s are A’s, and Some M’s are B’s nothing follows of necessity about the relation of the A’s and B’s. But they go further and say in order that any relation about the A’s and B’s may follow of necessity, the middle term must be taken universally in one of the premises. De Morgan pointed out that from Most M’s are A’s and Most M’s are B’s it follows of necessity that some A’s are B’s and he formulated the numerically definite syllogism which puts this principle in exact quantitative form. Suppose that the number of the M’s is m, of the M’s that are A’s is a, and of the M’s that are B’s is b; then there are at least ( a + b − m ) A’s that are B’s. Suppose that the number of souls on board a steamer was 1000, that 500 were in the saloon, and 700 were lost. It follows of necessity, that at least 700 + 500 – 1000, that is, 200, saloon passengers were lost. This single principle suffices to prove the validity of all the Aristotelian moods. It is therefore a fundamental principle in necessary reasoning. 
  3. Mathematical Induction
    • Proof by Induction: First step is to prove the base case for n = 0 without assuming any knowledge of other cases. The second step is the induction step, proving that if the statement holds for any given case n = k, then it must also hold for the next case n = k + 1

George Boole (November 2, 1815 C.E. December 8, 1864 C.E.): English mathematician, philosopher, and logician. There is dispute about whether Boole or De Morgan is the originator of the predicate quantifier.

  1. In his book Mathematical Analysis of Logic, Boole wanted to make logic more mathematical. To do this he showed how algebraic properties like the distributive and commutative properties apply to classes.
    • xy = the intersection of class x and class y
    • Distributive: x(u + v) = the intersection of x with the disjoint classes u and v
    • Commutative: xy = yx meaning that the intersection order doesn’t matter
    • Idempotent law:

      • From this we know that x =
      • We can then use Boole’s algebra with integer coefficients and x,y = {0,1}
      • It’s from this that Boolean algebra can be derived. There is a lot to go into with it that will take this far down the rabbit hole. I recommend the Stanford Encyclopedia entry on Boole if you want more detail. The take-home message, however, is that this helped generalize logic and make it more algorithmic.
  2. Generalization of Aristotelian Logic: augmenting Aristotle’s four types of categorical propositions by allowing the subject and/or predicate to be of the form not-.

    • Conversion by Limitation: All is , therefore Some is – Boole found Aristotelian classification defective since it didn’t treat contraries, such as not-, the same footing as named classes , etc. For example, Boole converted No is into All is not-, and All X is Y into All not-Y is not-X
  3. In his other book, The Laws of Thought, Boole set out to correct and clarify some of the mistakes from the previous book while also bringing in concepts from probability theory.

Karl Weierstrass (October 31, 1815 C.E. February 19, 1897 C.E.): German mathematician often cited as the “father of modern analysis”

  1. Pioneer in the mathematical field of real analysis, coming up with the δ-ε method of showing continuity (a requirement for being able to do algebra on a function is that it is continuous).
    • The function f(x) is continuous at x = x0 if for all ε > 0 there exists a δ > 0 such that for every x in the domain of f(x): if |x – x0| < δ then |f(x) – f(x0)| < ε
  2. You can get a sense of Weierstrass’s contribution by how many theorems contain his name.
  3. One way that this is important for philosophy is when it comes to things like functional analysis, which is where set theory and topology are given more mathematical rigor. Sets in particular take on great importance in analytical philosophy.

Richard Dedekind (October 6, 1831 C.E. February 12, 1916 C.E.): German mathematician who made important contributions to number theory, abstract algebra, and the axiomatic foundations of arithmetic

  1. He gave a rigorous definition of rational and irrational real numbers. The former is any real number that can be expressed as the division of two integers {n,m} of the form n/m. The latter cannot be expressed this way. Examples of irrational numbers are π, e, 2, and so on (there are uncountably infinite irrational numbers).

Giuseppe Peano (August 27, 1858 C.E. April 20, 1932 C.E.): Italian mathematician

Georg Cantor (March 3, 1845 C.E. January 6, 1918 C.E.):

Gottlob Frege (November 8, 1848 C.E. July 26, 1925 C.E.): while others above made great leaps forward in logic from the Aristotelian form in which it had stagnated until the 19th century, it was Frege who really brought it all together and kicked off the logic renaissance of the 20th century. Frege had wanted to make logic as rigorous as mathematics, and while he is largely considered to have failed in that regard, he mage great leaps forward in how logic is done, as well as motivating the largely formal, symbolic way that logic is now done.

  1. Propositions as Functions: Frege thought of propositions as a kind of function. A proposition is something of the form “S is P” where S is a subject, P a predicate, and “is” the copula joining them. Frege came up with the idea of sort of emptying S out and making the subject position a variable so that it was more like “X is P” where X can take on multiple “values” (subjects) for the same predicate, where the output is either “True” or “False”. By this, it means that “X is P” is sort of like a mathematical function f(x) where x can range over multiple values (e.g., all the real numbers) such that when x = a then f(x) = f(a) and when x = b then f(x) = f(b). In the same way, the “X is P” can range over every possible subject, and then output “True” when it is actually the case that the subject being substituted in for X is, in fact, P, and “False” when the subject is not P.
    1. Some examples of “X is P” where P = blue
      1. X = the sky “[the sky] is blue = True”
      2. X = a tree “[a tree] is blue = False”
      3. X = a horse “[a tree] is blue = False”
      4. X = a sapphire “[a sapphire] is blue = True”
      5. And so on for every object in existence
  2. Sense and Reference (On Sense and Reference”, Frege 1892): a problem arose for Frege: when we assign a specific subject to our proposition, how do we know that what we are referring to is the same thing? For instance, when I say the name Socrates when I make the proposition “Socrates is a Philosopher from ancient Greece” how do I know that the name “Socrates” refers to the same thing for anyone who reads the proposition? Or, more famously, when I talk about the morning star (phosphorous) and the evening star (hesperus), to what am I referring? It turns out that the actual object to which I refer is the same in both cases, namely the planet Venus. So, according to Frege, the reference for Socrates is the actual man who had lived; for both phosphorous and hesperus, they both refer to the actual planet Venus.
    • There still seems to be something missing, though. For one person, the name Socrates means something, but for another it has a different meaning. Same with the morning star and the evening star. They both have a different sense. And this is what Frege meant by sense. To simplify things, it essentially means the sort of subjective concept of the thing being referred to. The morning star has a different subjective meaning than the evening star, even if they both refer to the same thing, objectively speaking.
  3. Extension (On Concept and Object, Frege 1892 and The Foundations of Arithmetic, Frege 1884): these are the objects that a concept points to, i.e., the referents of a concept. All of the subjects, which are real things in the word, that make “X is P” true, are the extension of that set. Thus, the elements of a set can be fined as the objects that make “X is P = True” be the case.
    • Frege also had the notion of intensionality, though without calling it that. Intensionality is the meaning or definition of a concept. Frege said that the predicate in “X is P” pointed to the concept. What he meant by this wasn’t 100% clear, since he often talked about the concept having an objective existence (even with his doctrine of sense, he refused to think of this as being subjective, even though I described it that way above as a simplification – Frege had a real aversion of psychologizing things).

Bertrand Russell (May 18, 1872 C.E. February 2, 1970 C.E.): British philosopher and activist. While most of what I will discuss here has to do with Russell’s philosophy, it’s important to point out that much of his time was devoted to activism, whether his pacifism, his atheism, or his nuclear disarmament stance. Indeed, a lot of accounts of Russell’s contributions to analytical philosophy focus on his very early career, particularly his work with Alfred North Whitehead on Principia Mathematica (PM), his 1905 paper On Denoting, and his 1908 paper Mathematical Logic as Based on the Theory of Types. I will focus mainly on these three things (for now, though I will add more in future edits of this post).

  1. Russell’s Paradox: if Bertrand Russell is famous for anything besides his atheism (that seems to be how the internet likes to remember him), it’s for his eponymous paradox. This has to do with a letter he sent to Gottlob Frege, who had been working on the foundations of arithmetic, came up with his “basic laws“, of which “basic law V” had a paradox that Russell spotted.
    • Basic Law V (source): the extension of the concept is identical to the extension of the concept if and only if all and only the objects that fall under fall under (i.e., if and only if the concepts and are materially equivalent). In more modern guise, Frege’s Basic Law V asserts that the set of s is identical to the set of s if and only if and are materially equivalent:

      • The Law of Extensions asserts that an object is a member of the extension of a concept if and only if it falls under that concept:
      • Principle of Extensionality asserts that if two extensions have the same members, they are identical:
      • The Paradox: being an x that is the extension of some concept which x doesn’t fall under
    • The paradox can be stated in plain English: the set of all sets that don’t contain themselves. If the set doesn’t contain itself, then it is a set that doesn’t contain itself, and therefore must be contained within itself, but then it cannot be contained within itself. Or, the popularized version that Russell used: a barber that own shaves those who do not shave themselves.
  2. Principia Mathematica: this is a dense set of books filled with lots of fancy notation. Few people have probably ever read through the entire thing. Thankfully, Russell put out a much shortened version later on that condenses everything: Introduction to Mathematical Philosophy. It essentially attempts to ground arithmetic in axiomatic set theory (or, more precisely, Russell’s Type Theory).
  3. Logical Atomism (adapted from here): philosophy is “logical atomism”, both metaphysically and methodologically. The former means that the world consists of a many independently existing things that have internal qualities and external relations. All truths are dependent on atomic facts, which are simples with qualities or multiple simples standing in relation to one another. The methodology is that of analysis, where we define complex notions using the simples. Through this we could come to a language that only has words for these simples, their properties, and their relations.
  4. On Denoting: again, as a sort of response to Frege, Russell put forth his theory of denotation. This is a theory of how to fix a reference (i.e., how to determine that X in the proposition “X is P” is actually referring to the correct and universally agreed upon subject). It basically says that the reference is fixed to a description, where the name of something is a sort of placeholder for a complete description of that thing. For instance, when someone says the name “Alexander the Great” they are using a shorthand for “the Macedonian son of Philip II and Olympias, born in 356 B.C.E., tutored by Aristotle, reigned as king of Macedon from 336 B.C.E. until his death in 323 B.C.E., conqueror of Persia and Egypt, etc.”
  5. Type Theory: to try getting around his own eponymous paradox, Russell came up with his theory of types, which essentially tried to make a hierarchy of sets wherein a set can only contain elements that are below it within the hierarchy. The base of this hierarchy would be specific, concrete objects. Those objects can then be grouped together into a set. We then have a second order of things, which are sets composed of specific, concrete objects as their elements. These sets cannot contain each other, i.e., the set of all chairs cannot contain the set of all possums as an element. But, these sets can then be grouped together into a higher third order set. For instance, the set of all squirrels and the set of all leopards can be grouped together into the higher order set of all mammals. This can continue on ad infinitum. This makes it so that a set cannot contain itself (since a set would be at the same level as itself and therefore could not contain itself).
    • Russell’s theory of types is largely thought to be a failure, at least as far as being rigorous. Some of the axioms (like the axiom of reducibility) are disputed, and it is sometimes charged with being arbitrary (why should it be that sets at a certain “level” can’t contain other sets at that level? This is just taken axiomatically and goes unjustified).

Ernst Zermelo (July 27, 1871 C.E. May 21, 1953 C.E.): German logician and mathematician. With Abraham Fraenkel he helped come up with Zermelo–Fraenkel set theory. Abraham Fraenkel (February 17, 1891 C.E. October 15, 1965 C.E.): German-born Israeli mathematician. With Ernst Zermelo he helped come up with Zermelo–Fraenkel set theory. I am putting these two together because it is going to be their work on set theory that I discuss here. I will lay out the axioms of Zermelo-Fraenkel set theory, from which all the rest of set theory (and perhaps even arithmetic and all the rest of math) can be derived.

  • Axiom of extensionality: Two sets are equal (are the same set) if they have the same elements.
    • ∀x∀y[∀z(z∈x⇔z∈y)→x=y]
  • Axiom of regularity: Every non-empty set x contains a member y such that x and y are disjoint sets.
    • ∀x[∃a(a∈x)→∃y(y∈x∧¬∃z(z∈y∧z∈x))]
  • Axiom schema of specification: Given any set A, there is a set B (a subset of A) such that, given any set x, x is a member of B if and only if x is a member of A and φ holds for x
    • φ is a formula, which is essentially any string of symbols that you can ask the question “is φ true?”
    • let ϕ be any formula in the language of ZFC with all free variables among x , z ,w1 , … ,wn (y is not free in ϕ). Then:
      • ∀z∀w1∀w2∀w3…∀wn∃y∀x[x∈y⇔((x∈z)∧ϕ)]
  • Axiom of pairing: If x and y are sets, then there exists a set which contains x and y as elements.
    • ∀x∀y∃z((x∈z)∧(y∈z))
  • Axiom of union: For any set of sets F there is a set A containing every element that is a member of some member of F.
    • For example, the set of sets F = {{1, 2}, {2, 3}, {3, 4}} then A is a set that contains only the elements of those “internal” sets such that A = {1, 2, 3, 4}
    • ∪F = {x∈A : ∃Y(x∈Y∧Y∈F}
  • Axiom schema of replacement: The image of a set under any definable function will also fall inside a set.
    • For example, if we have a function on the real numbers F(x) = 2x, then the image F(x) at 2 [which is in the original set] is F(2) = 2(2) = 4 [which is in the image of the set]. There will be a corresponding image for each member of the real numbers, and those images are also a set.
    • ∀A∀w1∀w2∀w3…∀wn[∀x(x∈A→∃!yϕ)→∃B∀x(x∈A→∃y(y∈B∧ϕ))]
  • Axiom of infinity: In words, there is a set I (the set which is postulated to be infinite), such that the empty set is in I, and such that whenever any x is a member of I, the set formed by taking the union of x with its singleton {x} is also a member of I. Such a set is sometimes called an inductive set.
    • This is essentially the successor notation:
      • 0 = Ø = {}
      • 1 = Ø∪{Ø} = {}∪{Ø} = {{}}
      • 2 = 1∪{1} = {Ø}∪{1} = {0, 1} = {{}, {{}}}
      • And so on up to infinity
  • Axiom of power set: For any set x, there is a set y that contains every subset of x.
    • ∀x∃y∀z[z⊆x→z∈y]
  • Well-ordering theorem: For any set X, there is a binary relation R which well-orders X. This means R is a linear order on X such that every nonempty subset of X has a member which is minimal under R.
    • An example of a well-ordered set are the natural numbers, which are well ordered by the binary relation ≤
    • ∀X∃R(R well-orders X)

Rudolf Carnap (May 18, 1891 C.E. September 14, 1970 C.E.): German philosopher best known for being an originator of what is known as logical positivism (sometimes logical empiricism) and being a prominent member of the so-called Vienna Circle.

  1. Logical Positivism: the logical positivist movement was broadly concerned with making philosophy more scientific. This came with a strong skepticism of metaphysics, which the logical positivists thought was nonsense. This was because such metaphysical claims could not be verified, where the logical positivists held strong to verificationism, which said that only statements that can be empirically verified (or are an analytic tautology) are meaningful. In Kantian terms, the logical positivists thought that only a priori analytical statements and a posteriori synthetic statements were meaningful, where the former are essentially tautologies meant to clarify language while the latter were empirical statements that could at least in principle be verified.
    • A priori analytical statements are those that do not need to be empirically verified because it is expressing a definition, or the predicate is contained within the subject, or the subject and predicate are synonyms. For instance “bachelors are unmarried men” is essentially tautological, since the words “unmarried men” is synonymous with “bachelors” and so one could substitute it so that it says “bachelors are bachelors.”
    • A posteriori synthetic statements are propositions that have to be verified in order to determine if it is true. For instance “seawater has a salinity of between 31 g/kg and 38 g/kg” does not have the predicate “salinity between 31 g/kg and 38 g/kg” contained in the subject “seawater”. Instead, a person has to actually go out in the real world and discover this fact.
  2. Conceptual Engineering: for Carnap, our concepts are not things that exist out in the real world, but are things that we make up about the world – they are voluntaristic. Since all we can know about the world is what can be empirically verified, and the existence of such concepts cannot be empirically verified, then they don’t actually exist, except as useful tools to help us do science. They are what Carnap called explications or rational reconstructions.
    • Frameworks: logical object languages can be engineered with rules of logical inference. These formal languages can be applied to the sciences, where empirical facts are used to interpret the purely syntactical formal symbols of the language. The formal language itself, however, is without any semantic interpretation on its own.
    • For Carnap’s discussion of this, see his The Logical Structure of the World and Pseudoproblems in Philosophy (often called the Aufbau, where aufbau is a German word often translated as construction) and The Logical Syntax of Language.
    • Principle of Tolerance: this is the idea that no formal, syntactical framework is intrinsically better than any other. The most we could say is that one is more useful for a specific purpose than another might be. This gets at Carnap’s distinction between internal and external questions, where the former are questions that can be asked within a framework and the latter are questions that can be asked about a framework (for instance, how useful is this framework for what we’re trying to do?). What one cannot ask, however, is whether the framework is “true” in some more metaphysical sense, i.e., whether the concepts used within the framework correspond to actually existing things out there in the real world (e.g., are “quantum fields” something that actually exist in some ontological sense?).
  3. In future edits of this post I will discuss Carnap’s “On Inductive Logic“, Meaning and Necessity, and “Empiricism, Semantics, and Ontology“.

Alfred Tarski (January 14, 1901 C.E. October 26, 1983 C.E.): Polish-American logician and mathematician. A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.

  1. Truth: in philosophy, one of the main things Tarski is known for is his investigation into the concept of truth in formal languages. His book The Concept of Truth in Formalized Languages (1935), and his papers The Semantic Conception of Truth (1944) and “Turth and Proof” (1969) are his best known works on this problem.
  2. Object Language and Metalanguage (source): when we talk about a language (with language being understood as a formal logic), the language we are using is the Metalanguage and the language we are talking about is the Object Language. We can call the former M and the latter L. The role of M, which can use notions from set theory, is to give definitions in L and to say whether a statement in L is true or not (by saying S “is true of L” where S is some sentence said in L). Anyone you can say in L also needs to be able to be said in M (M should contain a “copy” of L). The  definition of True in M has to be in terms of the other expressions in M, dependent on the syntax, set theory, and the notions expressible in L, but not semantic notions such as ‘denote’ or ‘mean’ (unless the object language happened to contain these notions).

    • Formal Correctness: a sentence is formally correct if it has the form “for all x, True(x) if and only if ϕ(x)” and True never occurs in ϕ
    • Material Adequacy: a sentence in L is true if “ϕ(S) if and only if ψ” which can essentially be translated as “[sentence S] if and only if (sentence S)” where the square brakets is saying the sentence, but in the object language, where the parantheses is saying the sentence in the metalanguage. For example, “[the sky is blue] if and only if (the sky is blue)” which is kind of like saying “the sentence [the sky is blue] is true if and only if it is actually the case that the sky is blue.”
  3. Truth Definitions: Tarski gives four such definitions. One way would be to simply list every sentence in a language and label the true ones as true and the false ones as false. I will go through the other three in more detail.
    • Satisfaction: when something satisfies a formula in the object language. This is a sort of Fregean view, where we can think of a formula “F” as a kind of function that we can input things into and have it give the output of either True (if x satisfies F) or False (if x failes to satisfy F). This satisfaction definition of truth allows it to remain purely syntactical, since actually putting in an object for “x” would make it semantical. And so we get the following (source):
      • The assignment a satisfies the formula ‘F and G’ if and only if a satisfies F and a satisfies G
      • The assignment a satisfies the formula ‘For all x, G’ if and only if for every individual i, if b is the assignment that assigns i to the variable x and is otherwise exactly like a, then b satisfies G
    • Compositionality: this is a semantic notion of truth, where the meanings of the words in a sentence are sufficient to determine the truth of the sentence.
    • Quantifier Elimination: Theorem. If the domain A [the set of all of the objects in the object language L] is infinite, then a sentence S of the [object] language L is correct in A if and only if S is deducible from [the set of true facts in the object language L] T and the sentences saying that the number of elements of A is not any finite number.

      • The kinds of “facts” included in T would be things like “‘x is the empty set’ (viz. x every class)” and “‘x is an atom’ (viz. x is not empty, but every subclass of x not equal to x is empty)”
      • The proof is a bit too long for our purposes, but you can read it here.

John von Neumann (December 28, 1903 C.E. February 8, 1957 C.E.): Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was the rare kind of genius who seems to have had a hand in just about everything in 20th century mathematics. Wikipedia lists the following: “Von Neumann made major contributions to many fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory and general equilibrium theory), computing (Von Neumann architecture, linear programming, numerical meteorology, scientific computing, self-replicating machines, stochastic computing), and statistics. He was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis, and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer.” While there isn’t something I could point to as a direct contribution to philosophy from von Neumann, many of the areas in which he worked are extremely important to philosophy, and so he is worth mentioning just because of how much what he has accomplished influences philosophy.

Frank Ramsey (February 22, 1903 C.E. January 19, 1930): British philosopher, mathematician, and economist. Personal friend of Ludwig Wittgenstein. His withering criticisms of both Wittgenstein’s Tractatus Logico-Philosophicus and Russell & Whitehead’s Principia Mathematica led Wittgenstein to largely abandon his work (leading to his later work, the Philosophical Investigations) and showed how Russell’s Theory of Types ran into too many problems to remain workable.

  1. You can read Ramsey’s most influential papers in this PDF of the book edited by D. H. Mellor.
  2. “Universals”: Ramsey points out that the subject-predicate style of logic is merely a holdover from language and isn’t necessarily the logical way that propositions must be structured. For instance, the sentences “Socrates is wise” and “wisdom is a characteristic of Socrates” both express the same thought, but in the former Socrates is the subject and wisdom is the predicate while in the latter wisdom is the subject and Socrates is the predicate. Which one is subject and which one is predicate is therefore not a logical distinction, but merely a linguistic one that depends on which thing (Socrates or wisdom) we want to emphasize.
  3. “Facts and Propositions”:

Kurt Gödel (April 28, 1906 C.E. January 14, 1978 C.E.): obviously most known for his incompleteness theorems. You can read the paper here, but it’s fairly technical. The video below does a great job of explaining both the motivation behind the incompleteness theorems and explaining what it means.

Ludwig Wittgenstein (April 26, 1889 C.E. April 29, 1951 C.E.): both the continental philosophers (postmodernists, Marxists, critical theorists) and the analytical philosophers like to claim Wittgenstein as their own. He may or may not have started it, but he codified the linguistic turn taken by both. Since the publication of the Tractatus Logico-Philosophicus in 1921/1922, both the continental and analytical philosophers have examined the role of language in philosophy, the former concerned with how language shapes people and society, the latter with how it applies to logic and epistemology.

W. V. O. Quine (June 25, 1908 C.E. December 25, 2000 C.E.): American philosopher and logician in the analytic tradition, recognized as “one of the most influential philosophers of the twentieth century”

Karl Popper (July 28, 1902 C.E. September 17, 1994 C.E.): Austrian-British philosopher, academic and social commentator. One of the 20th century’s most influential philosophers of science, Popper is known for his rejection of the classical inductivist views on the scientific method in favor of empirical falsification.

Donald Davidson (March 6, 1917 C.E. August 30, 2003 C.E.): American philosopher who worked extensively in philosophy of mind, philosophy of language, and action theory.

John Rawls (February 21, 1921 C.E. November 24, 2002 C.E.): American moral and political philosopher in the liberal tradition.

Hilary Putnam (July 31, 1926 C.E. March 13, 2016 C.E.): American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century. He made significant contributions to philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science.

Wilfrid Sellars (May 20, 1912 C.E. July 2, 1989 C.E.): American philosopher and prominent developer of critical realism.

John Searle (July 31, 1932 C.E. Present): American philosopher widely noted for contributions to the philosophy of language, philosophy of mind, and social philosophy.

Thomas Nagel (July 4, 1937 C.E. Present): American philosopher working in legal philosophy, political philosophy, and ethics.

Ned Block (1942 C.E. Present): American philosopher working in philosophy of mind who has made important contributions to the understanding of consciousness and the philosophy of cognitive science.

Saul Kripke (November 13, 1940 C.E. Present): American philosopher and logician in the analytic tradition. He has been a central figure in a number of fields related to mathematical logic, modal logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and recursion theory.

  1. You can read a lot of his papers here:

Alvin Plantinga (November 15, 1932 C.E. Present): American analytic philosopher who works primarily in the fields of philosophy of religion, epistemology, and logic. Much of his work is in Christian apologetics, using logic and analytical philosophy to defend theism in general and Christianity in particular.

  1. You can read a lot of his papers here:

Peter van Inwagen (September 21, 1942 C.E. Present): American analytic philosopher working in areas of metaphysics, philosophy of religion, and philosophy of action.

  1. You can read a lot of his papers here:

Daniel Dennett (March 28, 1942 C.E. Present): American philosopher, writer, and cognitive scientist whose research centers on the philosophy of mind, philosophy of science, and philosophy of biology, particularly as those fields relate to evolutionary biology and cognitive science.

Douglas Hofstadter (February 15, 1945 C.E. Present): American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics.

David Chalmers (April 20, 1966 C.E. – Present): Australian philosopher and cognitive scientist specializing in the areas of philosophy of mind and philosophy of language.

  1. I’ve discussed his book Reality+: Virtual Worlds and the Problems of Philosophy in my review and his book The Conscious Mind: In Search of a Fundamental Theory in this post.

Islamist Thinkers

Muhammad ibn Abd al-Wahhab (1703 C.E. June 22, 1792 C.E.): Islamic scholar, religious leader, reformer, activist, and theologian from Najd in central Arabia

  1. Founder of the Sunni fundamentalist Wahhabi movement.

Jamal al-Din al-Afghani (1838 C.E. March 9, 1897 C.E.): Afghan political activist and Islamic ideologist

Muhammad Rasheed Rida (September 23, 1865 C.E. August 22, 1935 C.E.): Lebanese Islamic scholar, reformer, theologian and revivalist

Hassan al-Banna (October 14, 1906 C.E. – assassinated February 12, 1949 C.E.): Egyptian schoolteacher and imam

  1. Best known for founding the Muslim Brotherhood

Sayyid Qutb (October 9, 1906 C.E. August 29, 1966 C.E.): Egyptian author, educator, Islamic scholar, theorist, revolutionary, poet, and a leading member of the Egyptian Muslim Brotherhood

Abul A’la Maududi (September 25, 1903 C.E. September 22, 1979 C.E.): Indian Islamic scholar, Islamist ideologue, Muslim philosopher, jurist, historian, and journalist

Mohammed Omar Mujahid (1960 C.E. April 23, 2013 C.E.): Afghan religious scholar, partisan fighter and political leader. Often called just Mullah Omar

  1. Founder of the Taliban and served as its first leader
  2. Founded the Islamic Emirate of Afghanistan in 1996

Political, Economic, and Sociological Theorists

Max Weber (April 21, 1864 C.E. June 14, 1920 C.E.): German sociologist, historian, jurist, and political economist regarded as among the most important theorists of the development of modern Western society. Husband of Marianne Weber.

Marianne Weber (August 2, 1870 C.E. March 12, 1954 C.E.): German sociologist, women’s rights activist and the wife of Max Weber.

Georg Simmel (March 1, 1858 C.E. September 28, 1918): German sociologist, philosopher, and critic. Simmel was influential in the field of sociology.

Émile Durkheim (April 15, 1858 C.E. November 15, 1917 C.E.): French sociologist.

Ferdinand Tönnies (July 26, 1855 C.E. April 9, 1936 C.E.): German sociologist, economist, and philosopher.

  1. Gemeinschaft and Gesellschaft

Frédéric Bastiat (June 30, 1801 C.E. December 24, 1850 C.E.): French economist, writer and a prominent member of the French Liberal School.

Ludwig von Mises (September 29, 1881 C.E. October 10, 1973 C.E.): Austrian School economist, historian, logician, and sociologist.

John Maynard Keynes (): British economist

Friedrich Hayek (May 8, 1899 C.E. March 23, 1992 C.E.): Austrian economist, legal theorist, and philosopher.

Milton Friedman (July 31, 1912 C.E. November 16, 2006 C.E.): American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the complexity of stabilization policy.

Joseph Schumpeter (February 8, 1883 C.E. January 8, 1950 C.E.): Austrian-born political economist.

Ayn Rand (February 2, 1905 C.E. March 6, 1982 C.E.): Alice O’Connor, better known by her pen name Ayn Rand, was a Russian-born American writer and philosopher. She is known for her fiction and for developing a philosophical system she named Objectivism.

Robert Nozick (November 16, 1938 C.E. January 23, 2002 C.E.): American philosopher.

Leo Strauss (September 20, 1899 C.E. October 18, 1973 C.E.): Jewish German-American political philosopher and classicist who specialized in classical political philosophy.

Carl Schmitt (July 11, 1888 C.E. April 7, 1985 C.E.): German jurist, political theorist, and prominent member of the Nazi Party.

Hannah Arendt (October 14, 1906 C.E. December 4, 1975): Political philosopher, author, and Holocaust survivor.

Jürgen Habermas (June 18, 1929 C.E. Present): German philosopher and sociologist in the tradition of critical theory and pragmatism.

Simone Weil (February 3, 1909 C.E. August 24, 1943 C.E.): French philosopher, mystic, and political activist.

Pierre Bourdieu (August 1, 1930 C.E. January 23, 2002 C.E.): French sociologist and public intellectual. Bourdieu’s contributions to the sociology of education, the theory of sociology, and sociology of aesthetics have achieved wide influence in several related academic fields.

Alain Badiou (January 17, 1937 C.E. Present): French philosopher.

Noam Chomsky (December 7, 1928 C.E. Present): American linguist, philosopher, cognitive scientist, historical essayist, social critic, and political activist.

Thomas Sowell (June 30, 1930 C.E. Present): American economist, historian, and social theorist.

Francis Fukuyama (October 27, 1952 – Present): Yoshihiro Francis Fukuyama is an American political scientist, political economist, and writer.

Slavoj Žižek (March 21, 1949 – Present): Slovenian philosopher, cultural critic, and psychoanalytic researcher.

Renata Salecl (January 9, 1962 C.E. – Present): Slovene philosopher, sociologist and legal theorist.

Ayaan Hirsi Ali (November 13, 1969 C.E. – Present): Somali-born Dutch-American activist, feminist, author, scholar and former politician.

Maajid Nawaz (November 2, 1977 C.E. – Present): Maajid Usman Nawaz is a British activist and radio presenter. He was the founding chairman of Quilliam, a counter-extremism think tank that sought to challenge the narratives of Islamist extremists.

Jordan Peterson (June 12, 1962 C.E. – Present): Canadian clinical psychologist, YouTube personality, author, and a professor emeritus at the University of Toronto.

Sam Harris (April 9, 1967 C.E. – Present): American philosopher, neuroscientist, author, and podcast host. His work touches on a wide range of topics, including rationality, religion, ethics, free will, neuroscience, meditation, psychedelics, philosophy of mind, politics, terrorism, and artificial intelligence.

  1. The Moral Landscape:
  2. Determinism: