FOM: The Liar

Dean Buckner Dean.Buckner at
Tue Aug 20 15:58:47 EDT 2002

I prefer a simple version on Charles's lines.  Tennant's is
incomprehensible.  Can I not assert that today was rainy, without being able
to prove it in normal form.  Can I not deny that it was sunny without a
reductio in normal form?

A suggestion:

(1)  Caesar died

is grammatically a sentence (in English grammar I mean).  It states
something, and I can name what it states by tacking the word "that" onto the
sentence as follows

(2)  that Caesar died

This is a noun-like expression, and it names what I think, or say, or deny,
when I think, or say, or deny that Caesar died.

Since it is a noun-like expression, it follows that in taking on the word
"that" I somehow stripped out the main verb of the sentence (1).  But, lo, I
put it straight back by tacking on "it is true" to the noun-like sentence to

(3) it is true that Caesar died

which gets us straight back to (1).  From which it follows that "it is true"
contains the magical verb!  It also follows that, since noun-phrases do not
assert anything, but sentences do, that assertion, and the assertion of
truth, and the main verb of any indicative sentence are all the same thing.

This is not my idea, I hasten to say, but is one of the Great Lost Ideas of
History to be found in Antoine Arnauld's famous 17C textbook of logic.

You can apply this idea (that the assertion of truth is the main verb of
every sentence) to good effect with the Liar Paradox.  There is more to say,
but is anyone interested?.


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