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I am confused about the relationship between sentences and propositions.

Admittedly what a proposition is has been controversial. I have heard people characterizing it as the meaning and truth-conditions of sentences on the one hand, and the bearer of truth-values on the other. According to the latter, it seems that only propositions (and not sentences) can be true or false (which might be tracking the data that it is true that snow is white, not it is true that "snow is white.")

However, I then lose track of what is a truth condition. Supposedly a truth condition for X is the condition for X to be true. If only propositions can be true or false, and they are themselves truth conditions, then they are the condition for themselves to be true...? Certainly in the tradition of understanding propositions as truth-conditions, people often say propositions are what makes a sentence true or false (e.g., in https://plato.stanford.edu/entries/truth/#TruTruCon, the author says `` for a simple sentence like ‘Snow is white’, [Tarski's theory of truth] tells us that the sentence is true if the referent of ‘Snow’ satisfies ‘white’'').

But how can we reconcile this claim with the idea that propositions, not sentences, are bearers of truth-values? [p.s.one conjecture is that there are two notions of truth at stake: syntactic truth predicate, and semantic truth value. The "truth" in "truth condition" stands for the syntactic truth predicate - the condition under which it is appropriate to assign truth predicate to a sentence; the "truth" in "truth value" is on the other hand a semantic property of the meaning (i.e. proposition) expressed by a sentence]

  • "Propositions are truth-conditions" is a sloppy shorthand. Propositions are abstract things that fix the sense of truth-apt sentences. Under extensional semantics, this sense can be expressed by truth conditions (but they are not it literally). I do not follow why senses rather than sentences being bearers of truth conditions needs any reconciling, it is the opposite idea, that scribbles (sentences) can be bearers of anything other than their own physical charateristics, that makes little sense. – Conifold Jul 7 at 5:10
  • I guess what requires reconciling is the two ideas i) propositions are bearers of truth values (not truth conditions) and ii) propositions are truth conditions (or as you pointed out, meanings that determine truth conditions). If both i) and ii) are right, then a proposition P is the condition of itself being true. There is no inconsistency here, but it seems weird (and perhaps it has more to do with our understanding of truth). Put it differently, it is more intuitive to think of truth conditions as conditions for sentences to be true, but that conflicts with i). – discretizer Jul 7 at 17:24
  • This is similar to identifying a set with its extension for technical purposes in math, you can then say that the extension is the extension of itself, which is weird. I do not think attaching truth conditions to sentences instead works intuitively. Symbols are empty husks that mean or bear nothing until they are interpreted. Unless we want to stuff in the entire interpretation apparatus, which may be controversial and vary from person to person, we might as well take already interpreted sentences as the bearers, which is basically what the propositions are. – Conifold Jul 8 at 18:19
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Can sentences be true or false?

Sentences are sequences of words, written, spoken, or otherwise made physically perceptible to human senses. As such they are physical objects and, therefore, can neither be true nor false, at least not in any usual sense of these words.

Sentences are used to convey meaning between human beings. We loosely characterise a sentence as true or false according to whether what we understand of the sentence seems true or false to us. Thus, it is something like the meaning of the sentence, as we personally conceive of it, which we think of as true or false.

However, different people may and often will understand the same sentence differently and thus have different views as to its meaning. So, even assuming they all know the same relevant facts, they may still disagree as to the truth of what the sentence means to them.

Broadly speaking, this should be seen as an inevitable consequence of a sentence being by nature a simplified and therefore imperfect means of expressions of what we mean.

Since we don't know how to convey what we mean more efficiently, we are stuck. However, we still have this notion that each of us is capable, to some extent, at least in principle, of actually knowing something like states of affair. I know the sun is shining merely by looking outside and seeing for myself that indeed the sun is shining. And we mostly agree on such things. Thus, we will agree that sentences like "The sun is shining" can be used to convey ideas with which we can agree. The fact that we agree shows we think such ideas are true.

However, we can't verify that our respective ideas of the sun shining are all identical. Thus, I suppose, we invented a new notion, that of propositions.

A proposition may be understood as a perfect, and as such fictional, idea of a state of affairs. An idea that, if we could have it in mind, we would be able to understand it and decide for ourselves whether it is true or false.

This doesn't quite justify our notion that ideas, let alone propositions, can be true or false. However, the more interesting question may be instead that of what it means to you that an idea be true, or false, to begin with. You are the one to decide on that.

That being said, it seems that most people understand this notion of proposition, and that we can usefully discuss propositions as being either true or false. This may be understood straightforwardly as a technical means to be able to discuss matters of logic without necessarily having to go into the messiness of language, or indeed into whatever it is that we mean when we express what we mean using language.

The more fundamental question, though, is that of what we do when we think of something as being true.

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