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What is an exact definition of a proposition that we can use to apply to sentences in natural language? Are the following propositions?

1.) "I am calling you a liar."

2.) "4 is the square root of twelve." Is twelve really defined as it could be the number 12 with any radix or be a variable named "twelve" - how do we know?

1046136
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    Do you really insist upon "natural language" with propositional logic ? Then I'm afraid you will face some problems .. – Han de Bruijn Dec 14 '13 at 18:50
  • So then for 1. and 2. are they propositions or we cannot know? – 1046136 Dec 14 '13 at 19:04
  • I've only suggested that the joint venture (propositional logic - natural language) will turn out to be somewhat problematic in due time. Read this classic one from Alfred Tarski: http://www.alternatievewiskunde.nl/QED/if_then.htm . – Han de Bruijn Dec 14 '13 at 19:52
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    My personal opinion is that for logic & mathematics, we don't need to know what a proposition is. It's just something which is either true or false (or maybe lacks a truth-value, depending on our logic). The question of what a proposition is, is a philosophical one that's been argued about interminably. See [http://plato.stanford.edu/entries/propositions/] – MikeC Dec 15 '13 at 00:50

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According to Quine, is better to avoid speaking of propositions, because of their "ontological committment".

The link between logic and language is through sentences i.e. expressions of natural language.

Propositional logic is formalized using "sentential" variables ($p$ , $q$, ...): so you must call it sentential logic.

Of course, in philosophy you will meet again propositions (e.g. with the issue regarding truth-bearer).

Mauro ALLEGRANZA
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