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On 30 Aug 2006 17:24:44 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:
>Lester Zick wrote:
>> On 30 Aug 2006 15:19:23 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:
>>
>> >Lester Zick wrote:
>> >> On 29 Aug 2006 16:28:45 -0700, "MoeBlee" <jazzmobe@xxxxxxxxxxx> wrote:
>> >>
>> >> >Lester Zick wrote:
>> >> >> >I'm not talking about "the universe" but about a universe (also
>> >> >> >understood as a domain of discourse) for a given model.
>> >> >>
>> >> >> I believe Ross's comment was that there is a universe. Not that there
>> >> >> was a model of a universe replete with all kinds of assumptions that
>> >> >> mathematikers find more amenable to their talents than the universe
>> >> >> itself.
>> >> >
>> >> >> And I for one find his assumption that there is a universe far
>> >> >> more convincing than your assumptions regarding imaginary models of
>> >> >> the universe.
>> >> >
>> >> >See, that is exactly the kind of thing I'm talking about. You THINK
>> >> >that I'm talking about imaginary models of "THE universe" [all caps
>> >> >added] even though I said I am NOT talking about that.
>> >>
>> >> Then you're not being responsive to Ross's comment.
>> >
>> >No, I was precisely responsive, as I stated that set theory is not
>> >inconsistent for its lack of a universal set.
>>
>> Which means exactly what in relation to Ross's comment that there is a
>> universe?
>
>He claims that ZFC is inconsistent for the fact that there is no
>universal set in ZFC. But the lack of a universal set in ZFC does not
>make ZFC inconsistent.
Who cares? We have it from Virgil that axioms and definitions in
modern math aren't true.
>> Aha! But that wasn't his comment. His comment was that there is a
>> universe.
>
>Yes, but if you read any of about a thousand posts by him, you'll find
>his argument that a lack of a universal set in ZFC makes ZFC
>inconsistent. The particular appearence of the slogan is an ellipses
>for that argument.
To which you replied tangentially and not directly. Frankly I could
care less about the full context of a nonsensical argument.
>> >> >As to the other poster, his gravamen is that ZF has no universal set,
>> >> >which reduces just to the fact that it is a theorem of ZF that there is
>> >> >not an x such that for all y, the pair y,x is not in the relation e,
>> >> >which is not a contradiction and does not contradict the axioms of ZF,
>> >> >and does not contradict that there is a universe for any structure
>> >> >whose domain is {the universal quantifier symbol, the equality symbol,
>> >> >the membership symbol}.
>> >>
>> >> I have no idea what this comment is directed at.
>> >
>> >It is further explanation of why his argument that set theory is
>> >inconsistent is incorrect.
>>
>> Oh well. I thought we were discussing infinity.
>
>I addressed the idea that ZFC is insonsistent for not having a
>universal set.
But not for not having a true definition for the subject of this
thread?
>> >> >I wouldn't so much say it 'true' as I would say it provides a
>> >> >systematization.
>> >>
>> >> So if my concern is truth why would I bother with a systemization you
>> >> can't even claim is true?
>> >
>> >So that your comments about it would be informed, rather than ignorant,
>>
>> And you know my characterization of it is ignorant how exactly?
>
>Most recently, your characterization of the question of truth of
>assumptions. And, my interest willing, I'll point out your next
>ignorant charcterization too.
But we already know from Virgil that definitions and assumptions in
modern math aren't true.
>> >in view of its role as an axiomatization, since there is no consistent
>> >recursively axiomatized theory that expresses a certain amount of
>> >arithmetic while every sentence of the theory is true in all models. If
>> >you're not interested in standard mathematics, then fine. But IF you
>> >are going to skewer it, then you should at least know what is IS. (Yes,
>> >I know, you say you know enough about it to know that it is bunk, etc.
>> >etc. But you only THINK you know that much about it. You really know
>> >virtually NOTHING about it.)
>>
>> Whereas you only THINK you really know virtually all there is to know
>> of my ignorance?
>
>No I don't opine as to the overall extent of your ignorance. Only as to
>your ignorance of the mathematics you presume to skewer.
Which is exactly what you do opine.
>> >> The problem isn't systemization. I'm all for systemization. I'm just
>> >> not for any old systemization whatever just because it's a system.
>> >
>> >Fine. And so you would benefit from the study of mathematical logic in
>> >which rigorous and objective bases are given for comparing systems.
>>
>> Thanks for the information. Is this another example of what you only
>> THINK you really know virtually all there is to know of my ignorance?
>
>Again, I don't know of what else you may be ignorant beyond the basic
>mathematics you presume to skewer.
Thanks for sharing what you can't demonstrate.
>> >> >> The difficulty is that things you assume
>> >> >> to be true are only assumptions.
>> >> >
>> >> >We know that. Some people think certain assumptions are true in some
>> >> >platonic way. But that platonisim is NOT required to work with the
>> >> >assumptions withOUT assuming that they are platonically true but rather
>> >> >studying the RELATIONS among certain assumptions and certain
>> >> >conclusions.
>> >>
>> >> You can study whatever you want in whatever way you want. What I want
>> >> to study mathematically is what is or isn't demonstrably true. And
>> >> there's no way to do that in any system which fails to recognize any
>> >> general criterion of truth and falsity.
>> >
>> >Your remarks would be pertinent if you had some familiarity with
>> >mathematical criteria of truth and falsity as given rigorously by
>> >formal semantics for formal languages.
>>
>> Thanks again for the insight. May I count on you to do all my thinking
>> for me or just the parts you object to?
>
>My correctly pointing out that you remarks are not pertinent since they
>are mis-, ill-, and un- informed about their subject doesn't entail
>that I have any interest in thinking for you. On the contrary, I
>recommend you learn something about the subject so that you CAN think
>about it for youself.
You mean so I can share your own faith?
>> >But you don't just leave it up to those interested, since you also
>> >comment ignorantly about such systems without knowing anything about
>> >them, especially about their formal semantics in which truth and
>> >falsehood are mathematically defined.
>>
>> And what precisely would be the point of talking if you knew what you
>> were talking abot? I find ignorance an ever so much more constructive
>> basis for good conversation.
>
>It's a good starting point, but not a good basis for the kind of
>critiques you like to make.
Once more you enlighten the heathen, Moe, on the missionary position
in modern math.
>> >Believe me, you raise no expectations.
>>
>> Then why even discuss it? You think I should gaze at the navels of
>> others instead of my own. Your point is taken. It's not a very good
>> point but there it is.
>
>No, you went right past the point I've already made: Remain ignorant,
>fine. But then your crtiques are not the least bit meaningful.
Then they fall to the level of your own.
>> >I've mentioned VERY specific ways in which your comments and
>> >characterizations are incorrect regarding mathematics.
>>
>> Oh I agree that's what you've said. You just haven't demonstrated any
>> of what you've said to be true. You've only tried to justify it by
>> further problematic appeals to tendentious opinions of what
>> constitutes math and logic.
>
>You missed it again. I may well leave open what constitutes logic and
>mathematics, but still point out that YOUR criticisms of CERTAIN (a
>particular kind of) logic and mathematics are criticisms based on your
>ignorance of that CERTAIN logic and mathematics.
Which shorn of overt opinion is reduced to naught.
>> >The reason many
>> >of my comments are of the form "mathematics doesn't do it that way" is
>> >because you say that mathematics DOES do it that way. I then point out
>> >that you only THINK mathematics does it that way, as you operate in the
>> >void of your ignorance on the subject.
>>
>> Thanks once more for another insight of inestimable if somewhat
>> problematic value.
>
>The value is to answer your challenge.
We're still waiting. Perhaps in the meanwhile you could answer the
question posed in the title of the thread?
>> >I am informing you of certain mathematics that I know and have a good
>> >understanding of. I don't coment on mathematics that I do not yet have
>> >a good understanding.
>>
>> Who cares?
>
>My remark applies to your claim that I had set myself up as some kind
>of spokesperson for standard mathematics.
And my remark applies to your undemonstrated opinions.
>> You're certainly welcome to comment on whatever you wish in
>> whatever terms you wish as long as you don't try to characterize your
>> comments as true without independently demonstrating their truth.
>
>If I claim a mathematical theorem (including a metahtheorem), then I
>can post a proof, or refer you to book or article that has a proof that
>I have read and understood, or tell you that I only know that the claim
>is purported to be proven and is published but that I have not yet gone
>over the proof. Then you can take it from there to think for yourself
>about the proof if you like.
Like I said "who cares?" if you can't demonstrate the truth of your
opinions.
>> >No, I'm not critiquing your philosophy and mathematics, since I don't
>> >even know what they are.
>>
>> Well then I expect a little research might be in order.
>
>I asked you what your system of logic is. You told me that is summed up
>by:
>
>~v~~
Which it is. I'm surprized you don't understand.
>You are more than welcome to expound upon that anytime you like. In the
>meantime, all I get from it is that it looks like some kind of chevron
>or military insignia on a patch or uniform of some sort.
Appearances are indeed deceiving to those who deal not in truth but
arbitrary assumptions and definitions. Of course you could look it up
in "Epistemology 201: The Science of Science" but I won't hold my
breath.
>> >Given your virtually TOTAL unfamiliarity with even the most basic
>> >matters of mathematical logic and set theory, unless you are truly a
>> >moron, you could not have read anything but posts (which, given their
>> >brief and isolated context, can not be an adequate exposition of a
>> >systematic treatment) or disonconnected snips from a book or two.
>>
>> And I thank you once more for your opinions on the subject. Of course
>> you might in time consider turning to others of my shortcomings as
>> your opinion on this particular point has become a trifle tedious.
>
>Tedious, as is this discussion with you in general. Any repetition you
>can count to my answering your commentary that is repetitious.
Tedious as in discussions of ones undemonstrated opinions.
>> >You went right past my point. (Talk about unresponsive.) Please re-read
>> >my paragraph to which you replied and quoted.
>>
>> And how 'bout if you please go yourself.
>
>You forgot to say, 'sport'.
"sport".
~v~~
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