In the propositional calculus it is a bearer of truth-values; the proposition indicated by, say the letter p, is deemed to have no further structure.

Is this all, or can more be said?

Consider the proposition:

p: Socrates is a man

The letter p bears truth or falsity in the calculus; but is silent about both the meaning of this proposition; and it's structure - which it decidedly has; is this structure, part of the philosophy of language rather than of logic now?

  • Is there some magical boundary between philosophy of language, and logic? Logikos just means 'of a word' not 'of a mechanisticl symbolic construct with propositions involved'.
    – user9166
    Apr 25, 2015 at 20:03
  • @jobermark: there isn't of course; which is why I'm asking... Apr 25, 2015 at 20:05
  • As an element of language say, must it involve the word is? Apr 25, 2015 at 20:06
  • Clearly not 'Socrates has a body' is a proposition commonly deduced from 'Socrates is a Man'. Maybe they tend to have copulae, but you can always insert one 'Mary does X' is a compact way of saying 'Mary is (one who does X)'.
    – user9166
    Apr 26, 2015 at 12:31
  • @jobermark: good point; I think this might be where Aristotles categories come in; in defining how the two parts of the proposition. Clearly having is different from is. Apr 26, 2015 at 12:36

2 Answers 2


I assume you mean the metaphysical status of propositions. The propositional calculus doesn't give much insight into determining what a proposition is--after all, it takes propositions for granted and attempts to develop a formal analysis of them. Similarly, mathematics won't tell you what a set is, but simply stipulate set axioms that are intended to model what we already understand a set to be.

However, the question has been approached pretty famously by Frege, Russell, and many others--you may be interested to see the debates on the topic. While there isn't unanimity on the answer to the question, I would claim that the "intended proposition" of a simple sentence is the set of all equivalent thoughts which the speaker attempts to communicate; the "public proposition" actually expressed by a simple sentence is the set of equivalent thoughts that a linguistic community tends to agree are expressed by the sentence.

To give just two important other notions of what propositions are: For Frege, they are abstract objects that refers to their truth-conditions. For modal realist David Lewis, propositions are sets of possible worlds.

  • I'll accept this; but it wasn't quite what I was looking for; I think my question was probably too loose. Apr 26, 2015 at 18:04

Remember that in propositional calculus, the idea is to work with 'abstractions' and that is why we work with 'p' instead of 'Socrates is a man' 'cause at this point we're not interested on the content of the proposition, its meaning, nor where its truth values come from (this last part is more concerned with philosophy of language and/or analytic philosophy). In propositional calculus the truth values are given, and we study what can be deduced from that.

  • Sure; that's why I tagged it with the Phil-lang tag too. Apr 25, 2015 at 20:01

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