Re: My investigations into Godels Incompleteness Theorem

MoeBlee wrote:
And we may distinguish a sentence from the proposition that the
sentence expresses. The sentence is just a syntactical object - a
string. The proposition expressed by the sentence is something else,
which is harder to pin down. In Church's introductory chapter of his
textbook, he says that a proposition is that which only synonymous
sentences (even sentences not in the same language) have in common.

Here's how I have this in my notes from the Church text (his summary of
Fregean notions, I think). I hope I have done justice to "scripture":

The denotation of a sentence is the truth value (either truth or
falsehood) of the sentence.

The sense of a sentence is what is grasped when one understands the
sentence. Put another way, the sense of a sentence is that which two
sentences in different languages must have in common for the sentences
to be correct translations of each other. The sense of a sentence is
the proposition expressed by the sentence and is the intension of the
sentence (the concept of the sentence).

That a proposition is different from a sentence is seen by considering
replacing 'sentence' for 'proposition' in Lincoln's Gettysburg Address
in which he mentions, "[...] a new nation, conceived in liberty, and
dedicated to the proposition that all men are created equal."

MoeBlee

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