Date: Mar 26, 2013 5:11 PM
Author: fom
Subject: Re: Mathematics and the Roots of Postmodern Thought

On 3/26/2013 1:18 PM, david petry wrote:
> On Tuesday, March 26, 2013 4:05:38 AM UTC-7, Dan wrote:
>

>> Gödel's theorem is here to stay .
>
> As I have argued previously, if we treat mathematics as a
> science and accept falsifiability as the cornerstone of mathematical
> reasoning, then Godel's theorem is utterly utterly trivial,
> while at the same time, his proof of the theorem is not a valid proof.
>
> https://groups.google.com/group/sci.math/msg/25be708362cb7e?
>



You write:

"When we talk, we want people to believe that we are telling the truth.
That simply cannot be denied. That is, when we communicate, we are
implicitly claiming that we are telling the truth. That's one of the
ground rules of communication. So, likewise, when we try to understand
what someone is saying, we take it as implicit that that person is
claiming to be telling the truth. So if we set about to analyze the
statement "I am lying", we must remember to take into consideration
the implicit claim to truth. So the statement must be interpreted as
equivalent to "<implicitly> I am telling the truth; <explicitly> I am
lying". And that is nothing more than a simple contradiction. There's
simply nothing paradoxical about it. It doesn't require any further
analysis"


I applaud you for believing that people use language
to communicate truths.

Just so we are clear, I criticize mathematical foundations
for ignoring the role of pragmatics. When everyone is playing
the orthodoxy card, the symbols in their theories are undefined.
Then, everyone is suddenly supposed to know what the symbols
mean through explanation and example. That is pragmatics.

What you confuse in this passage (relative to orthodoxy) is the
purport of semantics to be independent of the speaker's intent.

This is not an easy problem in general. You have taken one
particular example and formulated a proposed explanation for
it. How does your explanation generalize to arbitrary uses
of language? Or, why does a general theory of semantics that
leads to the (mischaracterized) problem not apply?

This is why I asked you how you might wish to view
meaning. Standard semantics associates meaning with
the truth conditions of a statement independent of the
speaker's intentions.

Under that view, your criticism is not applicable.