Re: Liar's Paradox

On Apr 3, 3:58 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough) wrote:
Marshall says...

I take the view that the paradoxical aspect isn't the real issue
with the Liar's Paradox; rather it's the infinite regress, which
is every bit as present in the Truth Teller as in Liar. Neither
statement can be assigned a truth-value because both
statements require that they be assigned a truth value
before they can be assigned a truth value.

Then we have three types of sentences, true, false, and
sentences involving infinite regress. But then what about
the sentence

This sentence cannot be assigned a truth value, since it
involves infinite regress.

But then what about
the sentence

This sentence cannot be assigned a truth value, since it
involves infinite regress.

Call it 'S'. If S says anything at all, it expresses the conjunction
of:

1. S cannot be assigned a truth value.
2. Trying to assign S a truth value involves infinite regress.
3. The cause of the said in 1. is the said in 2.

Or perhaps simply 2. would suffice.

It could be (provably) false without contradiction and it could be
unprovably true.

But if we are engaged in a process of comparing what S says with
reality in order to determine its truth value, we must ask at some
step of the process whether the process involves infinite regress.
This takes us back to the first step of the process.

So, we are in fact involved in an infinite regress when try to
ascertain S's truth value.
Then, according to the clause that such sentences lack any truth
value, S lacks any truth value. Note that lacking any truth value can
be no truth value.

This does not necessarily render S true since S can be unable to make
the unique statement it would be making in English if it could make
any. I think this could only happen if S fails in referring the way it
is required in order to possess a truth value.

As usual, this leads to a sort meta-paradox (the way the Strengthened
Liar does):

S1) Trying to assign a truth value to S1 involves infinite regress.

We are compelled to pronounce S1 untrue and still assert:

'Trying to assign a truth value to S1 involves infinite regress'

Tokenism is called for now. Some tokens of S1 express a proposition
and some others don't.

And now:

S2) Trying to assign a truth value to any token of S2 involves
infinite regress.

If all tokens of S2 are able to effectively refer to all tokens of S2,
then no token of S2 can be true and if some were false, there would
also be a true one. Then we could plausibly be at the same time
compelled to assert some token of S2.

So, plausibly not all tokens of S2 succeed in referring to all tokens
of S2.

But if you rather meant something like:

S3) Trying to ascertain whether S3 is true, false or involves
infinite regress, involves infinite regress

This is again the same story all along.

Regards






.

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