What is a Proposition?

One obvious answer could be something like the following:

A proposition is a statement of a state of affairs, which could be either true or false.

This seems to say exactly what we think a proposition is. It seems as though we could use these criteria (statement, possibility of being true/false) to determine if a given language form presented to us is a proposition. Not just that; it seems to us that the above definition tells us what a proposition is. That we can use our pre-existing ideas of ‘truth’ and ‘falsehood’, for example, to determine what entities out there are propositions, and what aren’t.

In the Philosophical Investigations, Wittgenstein points out that it is wrong-headed to speak of ‘truth’ and ‘falsehood’ as determining what a proposition is. For truth and falsehood themselves belong to the concept of a proposition. They are not, as it were, external criteria with which we use to judge possible propositions.

Wittgenstein compares the above ‘definition’ of a proposition with the following definition of what a king piece in chess is:

The piece that one can check.

In this case, would we say that we have in hand the concept ‘to check’, and the king is then whatever fits that concept — we go around ‘testing’ chess pieces for whether they indeed be ‘checked’, and when we find one that can, we conclude that it is the king? This seems ridiculous, for we all know that the the concept of ‘checking’ in chess is not independent of the concept of ‘king’; indeed, it is an intrinsic part of the concept ‘to check’ that one can check only the king and nothing else.

Wittgenstein means to suggest the same of the concept of a proposition. That is, we do not go around having independent notions of truth and falsehood that we then use to determine if certain linguistic entities are indeed propositions. Because we can understand truth and falsehood only if we also understand that these are concepts that apply to propositions.

This is often slightly disturbing to those with no prior exposure to Wittgenstein. If our apparently accurate definition of a proposition fails so fundamentally, then does there actually exist a definition of ‘proposition’ that is not, in some way, dependent on concepts that are internal to the concept of a proposition? No — it seems that ‘truth’ and ‘proposition’ must go together everywhere, as it were. Together, they form what Wittgenstein calls a language-game — a set of customs from which sprout many mutually defined objects. Chess is a game; a set of customary rules, and from these rules spring the concepts of ‘king’, ‘checking’, and so on, which are intertwined with one another and hence cannot be given a standalone definition in words alone (because to explain ‘king’ in words we have to explain ‘check’ in words, but to explain the latter in words we have to use the former as well, and so on). Similarly, Wittgenstein suggests that our ordinary linguistic and logical concepts, like that of a ‘proposition’, are really just part of language-games, meaning that we can’t hope to give all-determining definitions of them. Their meanings do not lie in abstract linguistic formulations, but in how they relate, very organically, to the other ‘pieces’ (concepts) in their respective language-games. But it would be a mistake to say that just because we cannot give them abstract linguistic definitions, that they are therefore ill-defined, or that we have a paradox. For it does not bother us that we cannot give an abstract definition of the ‘king’ in a chess game that is not implicitly dependent on a prior understanding of ‘king’. We accept that lack of definition as part of what it means to be a rule of a game. Similarly, Wittgenstein coaxes us to accept the lack of satisfactory definitions of many terms in ordinary language as simply part of the nature of those terms as pieces in language-games.