Sense, Reference, and Information: a New Way of Conceptualizing Predicates and Inferences

The late 19th / early 20th century philosopher and mathematician Gottlob Frege famously came up with the Sense and Reference distinction in order to clarify issues in his logical system. Briefly put, the reference of a word (I’ll use my favorite example of “table”) is the actual object that the word signifies: the referent of the word “table” is the actual, physical table existing out there in the real world. The sense of a word is the way in which it exists as a psychological representation: the sense of “table” is how I conceive the table in my mind. This was important to Frege because examples where we have two (or more) words that signify a single referent can have a different sense, and therefore lead to different inferences, even if the referent is the same. How, though, might we relate these ideas?

“The morning star” and “the evening star” both refer to the planet Venus. They are two names that signify a single reference: if “morning star” = a and “evening star” = b, then both of the following statements are true: a = b; a = a

But, even though a = Venus and b = Venus, there is still something different between a = b and a = a, and that something is what Frege referred to as sense. One can make different inferences using a than they can with b. So, what is it in the sense that makes them different?

I would argue that it has to do with information. You gain some amount of information when you learn that a = Venus (i.e. that star you see in the morning is Venus), you learn some other information when you learn that b = Venus (i.e. that star you see in the evening is Venus), but you then integrate this information when you learn that a = b (that star you see in the morning is the same star you see in the evening). What gaining new information does is allow us to make more reliable predictions: if we know that a = Venus, then we can make predictions concerning a, such as predicting that if I look at it with a telescope, I will see the planet Venus rather than a star; same goes for b = Venus. Knowing that a = b allows me to predict that if I look at a this morning, then when I look at b tonight I will observe the same thing that I saw this morning.

Thus, we can say that the different sense of a single referent are different bits of information that pertain to that single referent. And so, names themselves are simply a way of presenting information to us: calling something a instead of b is a way of presenting the referent using the information value of a. The information value, here, being that information that maps onto reliable predictions: if I know the information presented by the name a about some object O, but I do not know the information presented by the name b about that same object O, then I can only make reliable predictions concerning the ways in which a is relevant to O. And so, names don’t necessarily signify an object, but they signify particular information about the object as the sense of the object.

When we are talking about multiple people, a and b could be syntactically identical, but still have a different sense for person A and person B. For instance, the word “home” has a different sense to person A than it does to person B such that inserting the word “home” into a sentence like “I am living back home” takes on a different meaning to person A than it does to person B. This results in the different inferences that A and B make if they both accept the sentence as being true: A might infer that it means living with one’s parents while B might infer that it means living in in the same city they were born in. Thus, A and B will make different predictions about how some speaker C who utters the phrase “I am living back home” actually lives: A may predict that upon going to C‘s house that A will find C‘s parents there while B will not make such a prediction.

Of note, given this view of sense as information, it is not that information has a truth-value, but that information, in the form of reliable predictions, is how truth-value is evaluated. A proposition is true if it grants reliable predictions about phenomena to which the proposition is relevant: the proposition “x is a table” allows me to predict how x will behave – if x behaves in all the ways my concept of table expects, then it is true that x is a table, otherwise it is false.

This goes with the theory I’ve been developing about information being the relevant ontological substance when considering objects in the world: a tablewise arrangement of atoms can be predicated with tableness insofar as this predication reduces uncertainty about how the tablewise arrangement of atoms will behave in relation to other arrangements of atoms. This means that predication is, instead of the Fregean notion of a function that takes names signifying objects as an argument, a function that maps information onto subjects (names signifying objects). The truth-value of the map is determined by whether the mapping increases information (reduces uncertainty i.e. allows reliable predictions to be made).

As a result, an inference is a sort of prediction using information. By saying:

∃xFx(c=x→Fc)

Then determining Fc to be true due to predicating F of c allowing for more reliable predictions to be made of c then allows me to infer that:

(Fc→Fd)⊢d=x

Meaning that (Fc→Fd) gives me some information about the relationship of d to the quantified variable x even without having empirical knowledge of d falling under the quantifier: I could make reliable predictions about d simply given this inference, making the inference an informational relationship between a given proposition and whatever propositions are inferred from it.

We can then think of discourse, with a basis in being signs that signify particular information about some referent as sense, as a way of attempting to not only convey certain information, but of aligning the sense people hold. All people have a (significant or trivial) different sense of some concept (i.e. person A has sense a and person B has sense b), and so discourse is an attempt to get the differences in sense represented by a and b as close to a = b as possible, which is how people come to understand one another: when our sense concerning some object O is the same such that a = b then we have perfect understanding. Whether perfect understanding is even possible or not is its own discussion altogether, but discourse is the attempt to get as close to a = b between two different people A and B as possible.

(As a quick aside, we might say that what culture consists of is the group of people to whom any particular expressions (either syntactically equal or not, so long as the referent is the same) of a and b about some object O are relatively close to being equal, or at least only slightly unequal. The more a and b differ between two people, the more ‘alien’ their cultures will feel to one another).

Given this, we can think of epistemic agreement between the thoughts of two (or more) people as a continuum. A necessary, but not sufficient, condition for epistemic agreement of thought a and thought b between person A and person B, is that a = O and b = O where O is the actual object (either physical or conceptual) that is the referent of the thoughts a and b. To move further up the continuum of A and B epistemically agreeing on their thoughts about O (i.e. have exactly equal information as pertains to O and therefore make exactly the same predictions about how O will interact with other such physical or conceptual objects) would then require that the actual thoughts they have about O (their sense of O) become more epistemically congruent (i.e. they will make a greater number of inferences and predictions about O that are the same). Once A and B epistemically agree to the point that a = b then it will be the case that both A and B come to normative agreement on a and b: if A and B are being intellectually honest, they will hold the same beliefs about a and b once a = b is epistemically agreed upon. And such is the point of discourse: two (or more) people attempting to move a and b as epistemically close together as possible as all persons involved in the discourse seek information about O.

I picture this sort of like everyone having a waveform representing their thoughts about the actual waveform. By adjusting the frequency and amplitude of our wave to match the actual wave, we then use discourse to match our phases with one another as we attempt to bring the waves a and b together along with O so that all of them constructively interfere: such a case would be full knowledge of O and full epistemic agreement between a and b (i.e. a = b). It may be impossible for all the waves to perfectly match, but discourse is a way of attempting to maximize that constructive interference.

Acquiring new information about O (like, in my wave illustration, getting more accurate data about the frequency and amplitude of the O wave) then produces an epistemic responsibility to disseminate that new information to others so as to allow for a greater epistemic congruence between a and b.

Interestingly, this can be relevant to the ideas of so-called epistemic oppression. A way of leveling the “knowing fields” is through conceptual engineering, which is a method of discourse wherein concepts can be developed to express the information inherent in the sense present in people’s minds due to differing life experiences and due to the differential application of the Context Principle (i.e. the different sense of the context itself even if the word in question is known to signify the same referent) on account of these differing life experiences.

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