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Set Theory: Should you believe?
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Aatu Koskensilta
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Joined: 17 May 2005
Posts: 277

PostPosted: Fri Jul 21, 2006 11:53 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

David Bernier wrote:
Quote:
The listings for terms beginning with the letter C can be found here:
http://members.aol.com/jeff570/c.html

A quote from the entry for CATEGORICAL (axiom system) follows:

``Thus in his The Loss of Certainty (1980, p. 271) Morris Kline wrote:

Older texts did "prove" that the basic systems were categorical;
(...) But the "proofs" were loose (...) No set
of axioms is categorical, despite "proofs" by Hilbert and others.

This remark was corrected by C. Smorynski in an acrimonious review:

The fact is, there are two distinct notions of axiomatics and,
with respect to one, the older texts did prove categoricity and not
merely "prove".

[This entry was contributed by Carlos CÚsar de Ara˙jo.] "

One suspicion I have is that Smorynski's comment is related
to second order logic as distinguished from first order logic.

Yes. The categoricity proofs by Hilbert, Dedekind and others would today
be said to establish the categoricity of certain second order theories.
There are also categorical first order theories.

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

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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Rupert
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Joined: 18 May 2005
Posts: 372

PostPosted: Fri Jul 21, 2006 9:38 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Nam Nguyen wrote:
Quote:
Rupert wrote:

As I said, Nam Nguyen seems to be using "absolute truth" to mean
"something that is true independently of which semantics we use".

Imho, formally, it's near impossible to *directly* define "absolute
truth". On the other hand, if we *indirectly* define it as: anything
that is relative is not absolute, then we have a good chance to
indirectly understand "absolute truth". And relativity is something
we could easily define up-and-down the ladder of mathematical
introspection. For instance, the truth of 1 + 1 = 0 is relative
to what formal system we choose, hence it can't be an absolute truth.
Or the truth of (x=x) would depend on what logical system that's being
assumed, hence it's not an absolute truth. etc...

Imho, mathematical relativity could be grouped into 2 groups:

a) interpretation/semantic-based relativity: this is when a truth value
would depend on a reasoning being's (model) interpretation, or
(semantic) interpretation.

b) knowledge-based relativity: this is when knownability of the truth
value would depend on the knowledge on the reasoning being. For
instance, without loss of generality, let's k be a number so big
that Prime(k) is unknown to human being, then Prime(k) is knowledge-
relative. (If the theory is PA, then it's possible that PA can be
inconsistent and in which case Prime(k), for there would be no
model. But PA's shortest inconsistency-proof might be even
longer than proof of Prime(k). Hence "Prime(k) is true" is a
knowledge-based relative truth.)

And again, the truth that is relative is not an absolute truth.


All right, so this is one way of understanding what "absolute truth"
means. On this interpretation, in my view the question about whether
absolute truth exists is trivial. It is obvious and uninteresting that
no sentence can be true regardless of which semantics we use.

Quote:
Obviously no such thing exists.

I wouldn't go that far though.


Why not?

Quote:

--
-----------------------------------------------------

What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------
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Nam Nguyen
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Joined: 15 May 2005
Posts: 50

PostPosted: Fri Jul 21, 2006 6:05 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Rupert wrote:
Quote:

As I said, Nam Nguyen seems to be using "absolute truth" to mean
"something that is true independently of which semantics we use".

Imho, formally, it's near impossible to *directly* define "absolute
truth". On the other hand, if we *indirectly* define it as: anything
that is relative is not absolute, then we have a good chance to
indirectly understand "absolute truth". And relativity is something
we could easily define up-and-down the ladder of mathematical
introspection. For instance, the truth of 1 + 1 = 0 is relative
to what formal system we choose, hence it can't be an absolute truth.
Or the truth of (x=x) would depend on what logical system that's being
assumed, hence it's not an absolute truth. etc...

Imho, mathematical relativity could be grouped into 2 groups:

a) interpretation/semantic-based relativity: this is when a truth value
would depend on a reasoning being's (model) interpretation, or
(semantic) interpretation.

b) knowledge-based relativity: this is when knownability of the truth
value would depend on the knowledge on the reasoning being. For
instance, without loss of generality, let's k be a number so big
that Prime(k) is unknown to human being, then Prime(k) is knowledge-
relative. (If the theory is PA, then it's possible that PA can be
inconsistent and in which case Prime(k), for there would be no
model. But PA's shortest inconsistency-proof might be even
longer than proof of Prime(k). Hence "Prime(k) is true" is a
knowledge-based relative truth.)

And again, the truth that is relative is not an absolute truth.

Quote:
Obviously no such thing exists.

I wouldn't go that far though.


--
-----------------------------------------------------

What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------
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David Bernier
science forum Guru Wannabe


Joined: 01 May 2005
Posts: 101

PostPosted: Fri Jul 21, 2006 3:53 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Aatu Koskensilta wrote:
Quote:
Lee Rudolph wrote:
[...]


Quote:
I agree (based on observations of number theorists) that "one does
not say" that sort of thing, and I am open to being persuaded (indeed,
I am predisposed to be persuaded) that if a school of mathematicians
got into the habit of saying that sort of thing (while continuing to
do mathematics) then we (and possibly they) might want to say that
what they were doing (though still mathematics, and possibly very
fine mathematics) was no longer "number theory" (or, weaker, no longer
*just* "number theory"): but I don't see such a response
is self-evidently right.

That certainly would be the natural reaction. In fact, there already is
a discipline of mathematics where one can expect to hear such things. No
one calls it "number theory". It seems highly unlikely that there ever
could be a school of mathematics in which studying e.g. structures in
which the arithmetical consequences of ZFC hold was called "number
theory". That sort of a terminological shift would require a major
upheaval in the way people think about natural numbers.

In other words (I guess), is there anything more than historical
chance and prejudice behind the feeling (which I certainly share,
but don't feel particularly justified in sharing) that "natural
numbers should be *categorical*, dammit"?

It's a basic property of our conception of the natural numbers that they
don't bifurcate into a multitude of non-isomorphic structures. There are
some people of ultra-intuitionist and ultra-finitist peruasion -
Esenin-Volpin and Edward Nelson come to mind - who do think that there
are many different natural number lines and reject the ordinary
conception of the natural numbers as incoherent or unjustified. This
just goes to show, once again, that it is to a large extent a matter of
personal preference and inclination what one finds convincing and
coherent, and that even in mathematics there probably is no principle
someone competent hasn't doubted or rejected.

I consulted the web site ``Earliest Known Uses of Some of the
Words of Mathematics", for which I can't find the author.

The listings for terms beginning with the letter C can be found here:
http://members.aol.com/jeff570/c.html

A quote from the entry for CATEGORICAL (axiom system) follows:

``Thus in his The Loss of Certainty (1980, p. 271) Morris Kline wrote:

Older texts did "prove" that the basic systems were categorical;
(...) But the "proofs" were loose (...) No set
of axioms is categorical, despite "proofs" by Hilbert and others.

This remark was corrected by C. Smorynski in an acrimonious review:

The fact is, there are two distinct notions of axiomatics and,
with respect to one, the older texts did prove categoricity and not
merely "prove".

[This entry was contributed by Carlos CÚsar de Ara˙jo.] "

One suspicion I have is that Smorynski's comment is related
to second order logic as distinguished from first order logic.

If someone could elaborate on the meaning of what Smorynski wrote,
I'd appreciate it.

David Bernier
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Virgil
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Joined: 24 Mar 2005
Posts: 5536

PostPosted: Fri Jul 21, 2006 3:42 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <q810c29ku2cuf8h8u0p22semlvsgg19v5o@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

Quote:
On Thu, 20 Jul 2006 13:02:37 -0600, Virgil <virgil@comcast.net> wrote:

In article <utavb2tsrf1vme8aijr4a59bp5q450ks98@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

On Wed, 19 Jul 2006 21:32:14 -0600, Virgil <virgil@comcast.net> wrote:

In article <48ptb2h9tn62b5qq2hifgras3vakbotcnn@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

A good beginning discussion of the subject of mathematical definitions
is in Suppes's 'Introduction To Logic'. But in order not to inhibit
the
metastasis of your own convictions, I recommmend that you not read
such
books.

Well if there's one thing I detest more than assumptions of truth it's
metastasis of convictions when one is actually dealing instead with
demonstrations of truth.

As Zick has not demonstrated any truths

Neither have you, sport.

AS I am the one doubting the existence of any such things as absolute
truths or absolute falsehoods,

A veritable doubting Thomas.

my lack of demonstrating the
existence of
any such thing supports my position.

Well let's just say your lack of production in this regard doesn't
support much of anything including your position.

As Zich is the one affirming their existence, his lack of demonstration
tends to weaken his position.

But you've already admitted my general claim defies your critical
capacity.

Zick again exhibits his penchant for seeing things which do not exist.
I am critical of your general claim, as you have not been able to
bolster it with anything other than mere restatement of the claim itself.
Quote:

All we've dealt with so far is set theory as
a faith based institution of doddering ineptitude.

Don't be so hard on yourself, Zick.
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Virgil
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Joined: 24 Mar 2005
Posts: 5536

PostPosted: Fri Jul 21, 2006 3:37 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <jh00c2tp40c9o621j2u2cim6vrgs163cuh@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

Quote:
On Thu, 20 Jul 2006 13:12:21 -0600, Virgil <virgil@comcast.net> wrote:

In mathematics, all assumptions (axiom systems) are merely conditional,
to see what will follow from them. When what follows proves useful or
interesting, one tends to codify those assumptions. but that never
requires that one claims them true is any absolute sense. Such
assumptions are always "what if's".

It's clear in faith based math

"Faith based"? There is no "faith" required for axiomatic based
mathematics, only logic.
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Virgil
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Joined: 24 Mar 2005
Posts: 5536

PostPosted: Fri Jul 21, 2006 3:33 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <rimvb29t289hak5l58g1kadn0rkev5qnvi@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

Quote:
On Thu, 20 Jul 2006 12:56:26 -0600, Virgil <virgil@comcast.net> wrote:

In article <n68vb2p91g8m3nbbp0k4v7qbit7m6jfutn@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

On Wed, 19 Jul 2006 19:47:02 -0600, Virgil <virgil@comcast.net> wrote:

In article <tvbtb29qjsde0k18m272crf3092esavcsu@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

On Wed, 19 Jul 2006 14:47:00 -0600, Virgil <virgil@comcast.net> wrote:

You have not read my reference to " logical tautologies" correctly.

If, for example. "P and not P" would qualify as "false" does your
gobledegook require its negation, "P or not P", to be true?

"P and not P" is only universally false because it provides no
mechanical basis for alternatives since any "not (P and not P)"
converts into itself "not P and P".

Not in any respectable logic it doesn't. According to de Morgan's laws,
"not (P and not P)" is logically equivalent to "P or not P".

It may be equivalent to lots of things. The issue is whether it
converts into itself mechanically.

According to de Morgan, and others,
"not (P and not P)" and
"P or not P"
convert quite mechanically into each other but
"not (P and not P)" and
"not P and P"
do not convert into each other in any way at all.

I get dizzy just trying to read all this

Then you have no business trying to deal with formal logic, as this is
quite simple compared to most of it.
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Rupert
science forum Guru


Joined: 18 May 2005
Posts: 372

PostPosted: Fri Jul 21, 2006 1:33 am    Post subject: Re: Set Theory: Should you believe? Reply with quote

Lester Zick wrote:
Quote:
On 20 Jul 2006 02:18:57 -0700, "Rupert" <rupertmccallum@yahoo.com
wrote:


Lester Zick wrote:
On 18 Jul 2006 21:52:25 -0700, "Rupert" <rupertmccallum@yahoo.com
wrote:


Lester Zick wrote:
On 18 Jul 2006 18:19:16 -0700, "Rupert" <rupertmccallum@yahoo.com
wrote:


Nam Nguyen wrote:
Lester Zick wrote:
On Tue, 18 Jul 2006 07:03:50 GMT, Nam Nguyen <namducnguyen@shaw.ca
wrote:



Virgil wrote:

In article <q36ob213q98jmnaddpjfa95lk5ms282krq@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:



The question I have is whether you or others believe in the
possibility of universally exhaustively true mathematical axioms?


What is "truth"?

I can deal with the tautologous logical truth of implications like "if P
then (P or Q)", but other than those, which include the more complex
logical deductions from a set of axioms, I know of no absolute truth.

If we care to consider absolute truth, then there is no such
thing as an absolute truth.


Well thanks for the input. Can we take your word for this?

I don't see why not, unless an absolute truth could be demonstrated
to exist! Would

(1) (P => (P \/ Q))

constitute an absolute truth? Well, at this moment for some odd reason
"\/" to me means what "/\" means to a lot of people (and vice versa for
"/\")!. So (1) to me is not a truth; so it can not be an absolute
truth that *must be universally recognized without exception*!


If "absolute truth" means "something that is true regardless of which
semantics you use" then you're right, no absolute truths exist. This is
not a very interesting point.

I agree it's not a very interesting point since you assume this truth
absolute.


No, I don't. I certainly don't assume it absolute in Nam Nguyen's
sense. Clearly no truths are absolute in that sense.

Oho?

What I said was true relative to the semantics I was actually using. It
clearly would not be true relative to any conceivable semantics. This
is trivial.

Certainly it seems so to those prefer to deal in assumptions of truth
and assume so.


No "seems" about it. It's completely obvious. What contestable
assumption do you think I'm making?

I didn't say "contestable assumption". What I said was "assumption".
Assumptions refer to a lack of demonstration.

In some contexts, perhaps. In some contexts I would have thought it
also implied that there was some room for reasonable doubt.

Quote:
You certainly assume
what you don't demonstrate by calling it obvious.

It is obvious to any person of good sense.

Quote:
Obviously it is a
canonical assumption on your part that what you say is true. Whether
it is actually true or not however remains to be seen.


You have some doubt about it, do you? Would you like to elaborate on
this?

Quote:
I think people who talk about absolute truth usually mean something
different to what Nam Nguyen thinks it means

Not at all

What's your evidence?

If you would be so good as to clarify what Nam thinks "absolute truth"
means I'll try to supply it.

As I said, Nam Nguyen seems to be using "absolute truth" to mean
"something that is true independently of which semantics we use".
Obviously no such thing exists.

Quote:
It may or may not be "different to" what
others think but I have no doubt it will be "different from" what you,
Nam, and others think.

if I intuit your point correctly. The claim I make is
intended literally and exactly.


What claim?

What claim were you referring to?

When? I can't see where I mentioned any claim. Quote me referring to a
claim and I'll tell you what claim I was referring to.

Quote:
We seem to be in a "he said/she
said" mode at this point where it's difficult to discern what each of
us is referring to. My claim in general terms is that the alternative
to absolute falseness is universally true.


What do "absolute falseness" and "universally true" mean?

Quote:
, and I make no comment
about whether absolute truth exists in on of these senses or whether
what I said was absolutely true in one of these senses. I merely claim
that it was true.

That is: not even "tautologous logical
truth" would be absolute.


Yes but tautological alternatives to necessary and universal falseness
would perforce have to be necessarily and universally true.

Again, as has been questioned by another poster, what does "universal
falseness", or "universally true" mean?

~v~~

--
-----------------------------------------------------

What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------

~v~~

~v~~

~v~~
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Virgil
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Joined: 24 Mar 2005
Posts: 5536

PostPosted: Thu Jul 20, 2006 11:21 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <qamvb2tgsdg8ehtjk5b50t548ugih45ciq@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

Quote:
On Thu, 20 Jul 2006 12:40:52 -0600, Virgil <virgil@comcast.net> wrote:

In article <bo7vb2pc405sis5hkqn05phm7jiut84v6j@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

On Wed, 19 Jul 2006 20:11:06 -0600, Virgil <virgil@comcast.net> wrote:

In article <8intb2dm8drmqqbih0p19tmgbcjunep3vk@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:


"Not" is the tautological alternative to "not not". The excluded
middle is the reason we must reduce possible predicates to an
absolute
mechanical minimum.

Then where do "not not not" and "not not not not", and so on, fit in?

Do "not" and "not not" exhaustive possibilities for truth?

Not to me.

Then what does?

Zick is the one making claims about them, I merely express doubt.

A universal skeptic no less.

Zick has yet to exhibit any "exhaustive alternatives" that do not
require presuming anything.

Whereas you presume the contrary.

That is your presumption, not mine. In the matter of "exhaustive
alternatives" I am agnostic.
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Virgil
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Posts: 5536

PostPosted: Thu Jul 20, 2006 11:19 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

In article <u7mvb216tu9aa62tl6854d9fqemi92e72c@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

Quote:
Zick has presented no "exhaustive alternatives", he merely keeps talking
as if there were some.

And Verge keeps talking as if there were none.

I am talking as if it has not been established whether there are any, at
least until one has assumed something on which to base distinguishing
alternatives.

Assumed the truth of something used to establish the truth of what is
assumed.

I am familiar with assuming something true in order to show that it is
actually false, but have never seen any assumption successfully used to
prove itself true.

As usual, I request an example of Zick's alleged assumption used to
prove itself true.

And as usual, Zick will not provide one.
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Nam Nguyen
science forum addict


Joined: 15 May 2005
Posts: 50

PostPosted: Thu Jul 20, 2006 11:05 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

Lester Zick wrote:

Quote:
On Thu, 20 Jul 2006 20:38:34 GMT, Nam Nguyen <namducnguyen@shaw.ca
wrote:



Rupert wrote:


Nam Nguyen wrote:


Rupert wrote:

If "absolute truth" means "something that is true regardless of which
semantics you use" then you're right, no absolute truths exist. This is
not a very interesting point.

Right. That's why it seems interesting (to me) that occasionally there
are "faithful debates" about what shouldn't be interesting: "absolute"
truth!

I think when these debates take place people are usually getting
interested in absolute truth in a different sense to the sense you're
talking about.

Would you be able to give a specific example of another different
sense, in which an *absolute* truth could be defined and be interested
by *more than one person*?


Universal truth, truth mechanically contrary to universal falseness?

In the context of math and logic discussion, when we say *specific
example* we mean a specific mathematical statement of certain
specific logical framework (meta statement would be OK too). Just
_simply uttering_ "Universal truth", "universal falsenes", "truth
mechanically contrary to universal falsenes" doesn't make these
specific examples or anything meaningful, other than nonsensical
babbling.

Quote:
~v~~

--
-----------------------------------------------------

What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------
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DontBother@nowhere.net
science forum Guru Wannabe


Joined: 13 Jul 2006
Posts: 114

PostPosted: Thu Jul 20, 2006 10:43 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

On Thu, 20 Jul 2006 20:38:34 GMT, Nam Nguyen <namducnguyen@shaw.ca>
wrote:

Quote:


Rupert wrote:

Nam Nguyen wrote:

Rupert wrote:

If "absolute truth" means "something that is true regardless of which
semantics you use" then you're right, no absolute truths exist. This is
not a very interesting point.

Right. That's why it seems interesting (to me) that occasionally there
are "faithful debates" about what shouldn't be interesting: "absolute"
truth!

I think when these debates take place people are usually getting
interested in absolute truth in a different sense to the sense you're
talking about.

Would you be able to give a specific example of another different
sense, in which an *absolute* truth could be defined and be interested
by *more than one person*?

Universal truth, truth mechanically contrary to universal falseness?

~v~~
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DontBother@nowhere.net
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Joined: 13 Jul 2006
Posts: 114

PostPosted: Thu Jul 20, 2006 10:41 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

On Thu, 20 Jul 2006 13:02:37 -0600, Virgil <virgil@comcast.net> wrote:

Quote:
In article <utavb2tsrf1vme8aijr4a59bp5q450ks98@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

On Wed, 19 Jul 2006 21:32:14 -0600, Virgil <virgil@comcast.net> wrote:

In article <48ptb2h9tn62b5qq2hifgras3vakbotcnn@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

A good beginning discussion of the subject of mathematical definitions
is in Suppes's 'Introduction To Logic'. But in order not to inhibit the
metastasis of your own convictions, I recommmend that you not read such
books.

Well if there's one thing I detest more than assumptions of truth it's
metastasis of convictions when one is actually dealing instead with
demonstrations of truth.

As Zick has not demonstrated any truths

Neither have you, sport.

AS I am the one doubting the existence of any such things as absolute
truths or absolute falsehoods,

A veritable doubting Thomas.

Quote:
my lack of demonstrating the existence of
any such thing supports my position.

Well let's just say your lack of production in this regard doesn't
support much of anything including your position.

Quote:
As Zich is the one affirming their existence, his lack of demonstration
tends to weaken his position.

But you've already admitted my general claim defies your critical
capacity.

Quote:
All we've dealt with so far is set theory as
a faith based institution of doddering ineptitude.

Zick has illustrated doddering ineptitude by his own performance, but
that ineptitude has not been up much of anything else.

Yes but it's a considerable improvement over the faith based math
mathematikers are so smug about.

~v~~
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DontBother@nowhere.net
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Posts: 114

PostPosted: Thu Jul 20, 2006 10:34 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

On Thu, 20 Jul 2006 13:20:28 -0600, Virgil <virgil@comcast.net> wrote:

Quote:
In article <9mbvb256ohuvh013g668td8mspu9rfgmhg@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

It is one of the quirks of moderm mathematics that the meaning of
"definition" has been converted to "arbitrary assertion" or "fiat"
solely in order to validate assumptions of truth without coming right
out and saying so.

Not in standard mathematics. If it is so in the sort of mathematics
Zilch does, then his sort is definitely substandard.

In standard mathematics, definitions are no more than abbreviations, so
that anything said using a definition could, in theory, be said without
it, though at greater length, and often less comprehensibility

So whyn't you take it up with Dave who believes axioms are true by
definition?

~v~~
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DontBother@nowhere.net
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PostPosted: Thu Jul 20, 2006 10:31 pm    Post subject: Re: Set Theory: Should you believe? Reply with quote

On Thu, 20 Jul 2006 13:12:21 -0600, Virgil <virgil@comcast.net> wrote:

Quote:
In article <d1bvb29uf4ujvoib634ps0hqppje11iufa@4ax.com>,
Lester Zick <DontBother@nowhere.net> wrote:

I didn't say "contestable assumption". What I said was "assumption".
Assumptions refer to a lack of demonstration. You certainly assume
what you don't demonstrate by calling it obvious.

In mathematics, all assumptions (axiom systems) are merely conditional,
to see what will follow from them. When what follows proves useful or
interesting, one tends to codify those assumptions. but that never
requires that one claims them true is any absolute sense. Such
assumptions are always "what if's".

It's clear in faith based math that assumptions are always conditional
and never true. That's why the title of the thread is "Set Theory:
Should you believe?" and not "Set Theory: Who can say what's true?"
All we can expect in set theory are confessions of faith and not any
demonstrations of truth in universal terms.

Quote:
Obviously it is a
canonical assumption on your part that what you say is true. Whether
it is actually true or not however remains to be seen.

But it is something that Zilch is unable to see.


My claim in general terms is that the alternative
to absolute falseness is universally true.

A claim which means nothing, unless Zilch can establish that there is an
absolute falseness. Is that anything like establishing that "Satan"
exists?

In your case yes. If you can't even analyze the general claim you're
much better off in faith based set theory.

~v~~
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