What is it that makes an organization what it is? Is it the sum of the constituent people? An idea? The problem of sports organizations is that they don’t have anything that persists through time – the 1985 Chicago Bears is not the same thing as the 2019 Chicago Bears.
Mereology is the study of how things relate to other things within a whole. For something to be considered part of a whole, it must be reflexive, transitive, antisymmetric. Reflexive means that each part within a whole is also a part of itself – team member A on sports team X is a part of X but also a part of A. Transitive means that if team member A is part of team X and team X is part of league R, then team member A is also part of league R. Antisymmetric means that team member A and team member B, who are both on team X, are not the same person – two parts of a whole are distinct.
But what happens when those parts are switched out, such as the case in the Ship of Theseus. There are several ways of thinking about this, listed out on Wikipedia:
(a) Constitution view. If the objects in a whole are constituted of the same matter, then they are parts of a whole. This leads to absurd conclusions in the case of sports teams because then all human beings would be considered a part of every team by virtue of us all being composed of the same material.
(b) Mereological essentialism. A whole requires each of its parts or it ceases to be what it was. In the case of a sports team, we might alter this idea to say that if the constituent members of the team remain the same persons, then the team remains the same. If we hold this view, then a team definitely changes whenever even a single person on the team is traded away or quits.
(c) Dominant Sorts. A whole persists through time if it remains a certain sort of thing. This works if we’re talking about sport team X remaining a part of sport S even if the members of sport team X are interchangeable – the actual sport the team belongs to does not change. We could also say that the team remains a team, even as constituent players are switched out, but it still does not remain the same team.
(d) Nihilism—which makes the claim that no objects exist, except simples, so there is no persistence problem. The problem here is that humans have identity – each one is distinct from another, so they are not a simple object. A person can’t be changed out of a system without altering the system.
My point here is that it’s absurd to state that any team existing now has won some championship or another in the past because the two teams are not the same thing. Granted, most sports will credit the particular team makeup when talking about past achievements – the 1985 Chicago Bears, for instance, are known as the 1985 Chicago Bears, which gives the distinction to a particular cluster of people at a particular time. However, sports announcers will also say things like “team X haven’t won a championship in fifteen years” as if the team were the same as the one from fifteen years ago. Sports teams have no mereological persistence through time.