Main Page | Report this Page
 
   
Science Forum Index  »  Logic Forum  »  Liar's Paradox
Page 4 of 4    Goto page Previous  1, 2, 3, 4
Author Message
Marshall
Posted: Fri Apr 11, 2008 10:37 am
Guest
On Apr 11, 10:44 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
wrote:
Quote:
On 2008-04-11, in sci.logic, Marshall wrote:

I honestly have no idea how to have a productive conversation
with you.

That's a pity, then -- though I seem to recall we have had some
moderately successful conversation on purely technical matters in the
past. I'm not being intentionally difficult and even when my questions
are a tad whimsically worded, they are usually intended in all
seriousness. On this occasion I genuinely am at a loss as to what to
make of your assertion that you think of ordinary statements involving
'truth' in terms of computational models, that is, it is literally
completely obscure to me what it would mean for anyone to think of
ordinary statements and questions such as

I hear you've been pestered in the news by an obnoxious Finnish
pedant. Is that true?

It's true I've been a bit churlish lately.

At first I thought he was mistaken, but on further reflection what
he said was perfectly true.

in any way that involves computational models.

I am certain that if you were sufficiently motivated, you
could imagine any number of different, plausible explanations
for what I intended by invoking computational models.

How about this:

1) People think.
2) Their individual thinking follows certain consistent patterns.
3) For a wide range of differing levels of accuracy, there
exist computational models that describes those patterns.

The original context was in discussing the sentence L, "this
statement is false" and sentence T, "this statement is true."

How might we examine such statements? We could look
at them in an informal, off-the-cuff way, I suppose. I note
that in the past, a number of posters have been happy just
to call one of them true and the other false, or whatever.
But objections to doing so arise. So we need something
stronger, something more certain, something approaching,
(dare I say it?) formality.

I can't speak for others, but for myself, in such situations
I naturally reach for a computational model, or something
like a programming language. When all you have is a hammer,
you are probably a carpenter of some kind, and I'm
a programmer.

So I whipped up a tiny computational model in my head
and translated L and T into that model. And as a result
of doing so I made the apparently *outrageous* claim
that both sentences involve infinite regress. Would you
agree or disagree with that?


Marshall
Aatu Koskensilta
Posted: Fri Apr 11, 2008 12:44 pm
Guest
On 2008-04-11, in sci.logic, Marshall wrote:
Quote:
I honestly have no idea how to have a productive conversation
with you.

That's a pity, then -- though I seem to recall we have had some
moderately successful conversation on purely technical matters in the
past. I'm not being intentionally difficult and even when my questions
are a tad whimsically worded, they are usually intended in all
seriousness. On this occasion I genuinely am at a loss as to what to
make of your assertion that you think of ordinary statements involving
'truth' in terms of computational models, that is, it is literally
completely obscure to me what it would mean for anyone to think of
ordinary statements and questions such as

I hear you've been pestered in the news by an obnoxious Finnish
pedant. Is that true?

It's true I've been a bit churlish lately.

At first I thought he was mistaken, but on further reflection what
he said was perfectly true.

in any way that involves computational models.

--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
herbzet
Posted: Fri Apr 11, 2008 12:49 pm
Guest
Marshall wrote:
Quote:

On Apr 11, 12:15 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi
wrote:
On 2008-04-05, in sci.logic, Marshall wrote:

Yes. Perhaps I have been around computers too long,
and it has narrowed my viewpoint unnecessarily. Knowing
this, and possibly being in possession of an enlightening
alternative, you are now in the position of being able to
widen my horizons.

I'm not sure what to make of your assertion that you think of ordinary
uses of 'truth' in terms of computational models and what not. Let's
consider an example. Suppose a friend of yours comes by and asks

I hear you've been pestered in the news by an obnoxious Finnish
pedant. Is that true?

Just how do computational models and such things enter into your
understanding of this question, or into your reaction or answer to it?

I honestly have no idea how to have a productive conversation
with you. I would like to. I've certainly been able to have many
productive usenet conversations with many other people before,
even when they have been very far above me in some particular
technical field, or very far below me. But I'm out of ideas.

In fact, none of my usual conversational techniques seem
to work worth a damn here. It's quite frustrating, and I feel
very glum about it.

Marshall

Oh, you'll get used to our resident obnoxious Finnish pedant.
Takes a while.

--
hz
Charlie-Boo
Posted: Wed Apr 23, 2008 8:29 pm
Guest
On Apr 2, 10:58 pm, raydpratt <raydpr...@gmail.com> wrote:
Quote:
When we call a statement true or false, we are saying that we have
compared that statement to a given fact or principle and either found
corraboration or contradiction.

No, we applied logic and it evaluated to true or false. For example,
"I am green or I am not green." is true without comparing it to
anything.

Quote:
 For example, if we say "All apples
are cubes that glow in the dark," we can only judge that statement as
being true or false by comparing the statement to what we know about
apples.

In the Liar's Paradox, we say "This very statement is false."

No we don't. We say "This is false." Very is an adverb so we don't
say very any noun e.g. statement. Rather we say very any adjective
e.g. "This is very false."
`

Quote:
The alleged paradox is that if the statement is true, then it is false as
it claims, but if it is false as it claims, then it has stated the
truth and cannot be false, ad infinitum.  Properly understood,
however, there is no paradox.

To judge the truth or falsity of "This very statement is false," we
must compare the statement not only to itself as explicitly required,
but also to what we know about finding the falsity of any general
statement.  This is implied by the use of the term "false," much like
the term "apple" would require us to compare a statement to what we
know about apples.  With the Liar's Paradox, the very fact of the
supposed paradox proves that the statement cannot be definitively
proven false.  And as such, the statement is ultimately true because
it admits that it falsely asserts that it is provably false.

Similarly, in the Truth Teller, we say "This very statement is true."
Although there is no alleged paradox, the statement's self-reference
to its own veracity is not sufficient evidence for its truth. The
informal fallacy called petitio principii, or begging the question,
occurs where a questioned fact is called in as proof of that fact, and
such proofs are always illegitimate.  However, we can go further here
and say that the statement is definately false because it falsely
claimed that it was provably true.

Very Respectfully,
Ray Donald Pratt
Marshall
Posted: Wed Apr 23, 2008 9:02 pm
Guest
On Apr 23, 11:29 pm, Charlie-Boo <shymath...@gmail.com> wrote:
Quote:
On Apr 2, 10:58 pm, raydpratt <raydpr...@gmail.com> wrote:

In the Liar's Paradox, we say "This very statement is false."

No we don't. We say "This is false." Very is an adverb so we don't
say very any noun e.g. statement. Rather we say very any adjective
e.g. "This is very false."

Being an adverb doesn't pay all that well, so "very" has a second
job as an adjective. It doesn't put in as many hours as an adjective
as it does as an adverb, so some people are not aware of the
fact. But it goes to the very heart of the matter.


Marshall
Jesse F. Hughes
Posted: Thu Apr 24, 2008 6:37 am
Guest
Charlie-Boo <shymathguy@gmail.com> writes:

Quote:
On Apr 2, 10:58 pm, raydpratt <raydpr...@gmail.com> wrote:

In the Liar's Paradox, we say "This very statement is false."

No we don't. We say "This is false." Very is an adverb so we don't
say very any noun e.g. statement. Rather we say very any adjective
e.g. "This is very false."


New to English?

"This very statement is false" is a perfectly good English statement.
I know that this may shock you, but some words have two meanings and
these two meanings can be different parts of speech.

Maybe you should have a little lie-down until the shock passes. This
could be earth-shattering news, I imagine.

--
Jesse F. Hughes

"I am the next legend--living, breathing and solving mega problems in
the here and now." -- James S. Harris
 
Page 4 of 4    Goto page Previous  1, 2, 3, 4   All times are GMT - 5 Hours
The time now is Sat Sep 06, 2008 1:36 am