A Conversation Tripp and I Had the Other Day

[superabo]

So, deconstruct the dichotomy between connotation and denotation. (1) One cannot distinguish the things they denote... but (2) one can distinguish the things they connote!

What can (2) mean if (1) is true?

Comments

[nnn9245]

This is the most interesting non-math thought I've seen in months.

If you think of denotation as meaning that a computer can understand, or, more reflexively, as meaning that we can successfully model with elementary logic, then here's a thought (still not a resolution): If I view denotation as connoting "A definition of a word that, say, a computer is capable of understanding" and connotation as connoting "a definition of a word that, say, a computer is not capable of understanding."

So accepting the truth of sentence (1) as you claimed, we then have that sentence (2) is a sentence that an abstract being (say, a human) who understands connotation can see as clearly true, but that a computer that works within the system of logic itself cannot see as true. That is, (2) is a Godel sentence!