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One definition I encountered was something that is either true or false. (for example, I ate vegetables yesterday is a proposition).

Another definition I encountered is the meaning of a sentence (for example snow is white in English and snow is white in Spanish are the same proposition).

So which definition is correct?

Is the Liar Paradox a proposition? Are statements expressing opinions (Picasso is the best painter, and murder is wrong) propositions?

Please explain this concisely. Don't overcomplicate the explanation.

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3 Answers 3

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Philosophers use the term 'proposition' to mean several different things. The difference is so great, it is doubtful that it can mean all of them, so you would need to understand from the context which is meant.

Proposition can mean:

  • A statement, or declarative sentence that has a truth value.
  • A statement or declarative sentence with the indexicals and names unambiguously resolved.
  • The semantic content of a meaningful declarative or descriptive sentence.
  • The language-independent meaning of a declarative or descriptive sentence.
  • The object of propositional attitudes, i.e. the things that stand in place of P in expressions like "believes that P", "hopes that P", "fears that P", etc.
  • The object of that-clauses, i.e. the things that stand in place of P in expressions like "the fact that P", "the possibility that P", etc.

With the liar paradox, there are many different approaches. Some reject the sentence as meaningless or defective in some way, and so not a proposition. Others accept it as a kind of proposition. An opinion would fail to be a proposition if it is so vague as to be impossible to evaluate as true or false.

There is an article in the Stanford Encyclopedia on propositions that contains a lot more information.

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  • good and to the point +1
    – user67675
    Sep 26, 2023 at 5:09
  • Hi, good answer. Some follow up questions: I was checking the SEP article and just clarifying but some definitions of propositions can combine multiple other sub definitions right? Furthermore, why are concrete events or facts not propositions? @Bumble Sep 26, 2023 at 6:57
  • @Bumble "with the indexicals and names unambiguously resolved" What do you mean? In many cases, indexicals refer to things in the environment of the speaker. No statement can resolve that. Sep 26, 2023 at 15:27
  • @HelpMePlease Yes, I would say people often use proposition to mean several of these things. Minimally, a proposition is something with a truth value, but it can have additional senses depending on who is using the term. A statement about an event or a statement of fact would usually be considered a proposition. E.g. "Abraham Lincoln was assassinated in 1865" would usually qualify as a proposition.
    – Bumble
    Sep 26, 2023 at 17:17
  • @Speakpigeon I'm referring to the process of replacing indexicals, ambiguous names, anaphoric pronouns and other referring expressions with information from the context, in order to make a sentence unambiguous. For some theorists, a sentence such as, "It is raining where I am right now," does not qualify as a proposition because of the ambiguity. It would need to be resolved to something like, "It is raining in Edinburgh at 14:00 on 2023-09-26" before it counts as a proposition.
    – Bumble
    Sep 26, 2023 at 17:18
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At best an incomplete analysis of The Liar Sentence (should aid in the clearing up of confusions, all and sundry)

L = The Liar Sentence

  1. L v ~L [hidden/suppressed premise]

  2. L -> ~L [premise]

  3. ~L -> L [premise]

  4. L [assume for RAA]

  5. ~L [1, 3 MP]

  6. L & ~L [3, 4 Conj]

  7. ~L [3 - 5 RAA]

  8. L [2, 6 MP, assume for RAA]

  9. L & ~L [6, 7 Conj]

  10. ~~L [6 - 8 RAA]

  11. ~L & ~~L [6, 9 Conj] Neither L is true nor not L is true (L is false)

That is to say, if propositions are "stuff" that are either true/false, L is not a proposition. Equivalent to rejecting the law of the excluded middle: ~(p v ~p), false that either p(L) or not p (~L) ... where our story began (see hidden/suppressed premise 0)

That's all from me ...

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The way I’ve always understood propositions is the way in which the philosopher Quine argued was a problematic presumption. However, it’s a pretty sticky presumption, and useful despite its problems, so I’ve stuck with it!

So there are often multiple different ways to say the same thing when you use sentences to talk about the world. For example, we use the word “bachelor” to talk about men who aren’t married, so the sentences “Jim is a bachelor” and “Jim is an unmarried man” are said to mean the same thing.

A proposition might be understood as the “meaning” that all the sentences trying to say the same thing as each other are aiming at. Both “Jim is an unmarried man” and “Jim is a bachelor” express the same proposition. Similarly, sentences in other languages that are translations of those sentences are expressions of that proposition in other languages.

According to some influential philosophy of language positions, propositional content can also feature in non-linguistic contexts, like thoughts, representational depictions and metaphysical systems - what matters essentially is that all of these things are in some sense “about” the propositions they are expresssing.

So what kinds of things are propositions? Well, one view is that they are abstract objects like mathematical sets - all of the things that express the same proposition just form a set, and there might be no deeper sense of what this means than just that they are all the same. If you’re building an AI model of language use, something like this is probably at work.

Another view is that this sameness ties to one’s underlying metaphysics of the world - that what matters is that the sentences correspond to Reality in some key way. This is often why Truth-functional equivalence enters the picture, because the intention is that an underlying semantics determines whether two sentences mean the same thing - they are true in exactly the same situations as each other.

But importantly, one’s underlying theory of meaning doesn’t necessarily tie in with the practical question of learning to interpret what other people are trying to say, and this is why a lot of theorising about propositional content doesn’t always progress.

The practice of understanding whether two things mean the same is a constantly shifting sand, but getting by in a social world often means recognising a plurality of fictions about it across different contexts. Find a tool that works for you and see where it gets you, and you might find others useful at different stages of life!

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