Topic 9: Proposition

What is a proposition? There is much philosophical discussion (3) on this topic, but for our purposes,

A proposition is a thought that is capable of being true or false.

Examples

Thought	Proposition True or False?
The earth revolves around the sun.	Yes True
Winter is warmer than summer.	Yes False
revolves	No Neither
	A thought like this cannot be either true or false on its own. It can combine with other thoughts to form propositions (e.g., the first one above).
global warming	No Neither
	Similarly, this thought is not yet ‘fleshed out’ enough to count as a proposition. It is what we refer to as a thought bite.
Fermat’s last theorem	Depends
	The thought Fermat’s Last Theorem does not assert anything. It is about a theorem of Fermat; his last one, to be precise. That theorem (what is it? do you know? can you entertain that thought?) is a proposition and is true (4).
I am here.	Yes True
	In fact this is what is known as a necessary truth. It cannot be false, whenever entertained by anyone.
Would you like tea?	No Neither
	This thought anticipates an answer which may be true or false, but cannot be true or false itself.
Colorless green ideas sleep furiously	No Neither
	The thought is nonsensical (supposedly). (Chomsky, 1957. Syntactic Structures)

As illustrated in the examples above, there is a close connection between propositions and grammatical sentences of a language such as English. Every proposition corresponds to a grammatical sentence, though not every grammatical sentence expresses a proposition. Declarative sentences are those which express propositions.

-----

(3) See: http://plato.stanford.edu/entries/propositions

(4) See: http://mathworld.wolfram.com/FermatsLastTheorem.html