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Topic: Matheology § 223: AC and AMS
Replies: 102   Last Post: Apr 18, 2013 12:26 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 223: AC and AMS
Posted: Mar 18, 2013 7:10 PM

In article <m4ydnY_JbpdHENrMnZ2dnUVZ_vGdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 3/18/2013 2:05 PM, WM wrote:
> > On 18 Mrz., 17:36, fom <fomJ...@nyms.net> wrote:
> >

> >> Science is based on principles.
> >
> > One may believe in principle that it is possible in principle to find
> > in principle a second prime triple. But in mathematics we prove that
> > these principles are violated.

> >>
> >> One may choose *in principle*
> >>
> >> One may name *in principle*
> >>
> >> Although related, they are not the
> >> same.

> >
> > They are exactly the same for immaterial objects.
> > Or what do you understand by "choosing a number" - in principle?

>
> Now, just so we are clear. You have asked a question.
> on materials in the literature that support my own ideas.
>
> In the future, I would appreciate reciprocation in kind.
>
> The syntax of definability in mathematics, except in
> so far as it has been obfuscated with careless uses
> of other syntactic forms in model theory, corresponds
> with the syntax of definite description. One may find
> a specific discussion of the definitional syntactic form
> I have in mind here in "Some Methodological Investigations
> on the Definability of Concepts" by Tarski.
>
> There is a qualified version of naming in description
> theory called a "descriptively-defined name" whose
> debate often revolves around the planet Neptune. As a
> name, 'Neptune' had entered the vocabulary of astronomers
> before it had been materially witnessed as a material
> object. This example is interesting to description
> theorists precisely because it conflicts with various
> semantic theories based on Russellian acquaintance.
>
> One of the problems with descriptions -- and definitions
> in general -- is that there can be a multiplicity of them.
>
> In "Language Acts" Searle attempts to address this problem
> with a cluster theory of descriptions.
>
> In "Naming and Necessity" Kripke attempts to describe
> a scenario skeptical of Searle's theory. Although
> never formally introduced, Kripke's scenario is now
> called the causal theory of naming.
>
> In "Pragmatism and Reference" David Boersema begins his
> book with an analysis of these positions. At the end of
> his analysis, he says the following in (dialectical)
> support of Searle's position:
>
>
> "There is another reason to suggest that although thesis (5)
> [from Kripke interpreting Searle's arguments],
>
> (5)
> The statement 'If X exists, then X has most of the Phi's"
> is known a priori by the speaker
>
> may indeed be a thesis of Searle's view, he would be
> glad to accept it as such (and in fact this could be
> seen by Kripke as not a point against Searle's view).
> It is this: if one believes that names have essences
> (or, rather that objects named have essences), and if
> one believes that at least one of the descriptions
> associated with this name 'picks out' this essence, then one
> might be more inclined to accept the claim that the
> disjunctive set is analytically true of the object, and, as
> a corollary, that the sufficiently reflective speaker knows
> this analytic truth a priori.
>
> "Thesis (6): [from Kripke interpreting Searle's arguments],
>
> (6)
> The statement 'If X exists, then X has most
> of the Phi's" expresses a necessary truth
> (in the idiolect of the speaker)
>
> As noted earlier, Kripke holds that this necessity thesis,
> like the aprioriticity thesis (5) is false. Again,
> if we make the amendment from 'most of the Phi's' to
> 'some of the Phi's,' such a statement is true of
> Searle's view, but it is not so obvious that this is
> so objectionable or unintuitive. If Kripke is saying
> that for the cluster account it must be the case that
> X exists, then some description must be believed to
> be true of X (and is true of X), then indeed Searle
> is committed to the thesis (assuming Searle is
> committed to names having meanings). But, again, as
> with thesis (5), this seems to be a commitment to a fact
> about language and the use of names, not a commitment
> to facts about any objects. Furthermore, if one believes
> that at least one description of the disjunctive set of
> descriptions associated with a name picks out this
> essence, then this thesis may not only be acceptable,
> but desirable."
>
>
> Now, Aristotle talks about "essence" in his writing
> and the remarks above are referring to his use. But, just
> as Frege tried to ground his systems with the "truth of actuality"
> Aristotle tried to ground "essence" with "substance".
>
> These things are unnecessary in mathematics if one places
> the coherence of mathematical facts prior to the actuality
> of mathematical facts.
>
> All that matters is that for any name used by mathematicians,
> it is related to a name that can be understood as 'essential'
> in the sense of these requirements on "naming in principle"
>
> If one treats mathematics "in principle" as being organized
> according to "what is prior and what is posterior" relative
> to the use of formal sentences in a deduction, then every
> object to which a mathematician would refer has a "first"
> description. Thus, there is a principled way to understand
> how names in mathematics could have essences.
>
> A foundational theory such as set theory provides the
> context. As a foundation, it is presupposed when mathematics
> is done informally.
>
> The argument here culminates in an admissibility criterion.
> In order to be a faithful model, a model of set theory must
> be shown to have a *canonical well ordering*.
>
> Then, all of the names used by mathematicians fall under the
> theory of "descriptively-defined names" with the issue of
> multiplicity addressed by the faithfulness criterion.
>
>
> In the post,
>
> news://news.giganews.com:119/5bidnemPpsnq13zNnZ2dnUVZ_sOdnZ2d@giganews.com
>
> you will find a discussion of these matters
> with regard to set theory addressed in through
> examination of finite situations.
>
>
>
> you will find that I tried to start a more
> general discussion of how this assumption
> relates to the axiom of choice through the
> implicit dependence of the satisfaction maps
> on extra-logical names.
>
>
> why would a mathematician care about such
> things?
>
> In every book on set theory, one finds
>
> "ZF has no universal class"
>
> "the set universe V"
>
> This is simply nonsense. My formal theory
> is designed to address that by extending
> any and every model by exactly one point.
> It does so by focusing on descriptions and
> names.
>
> It is a theory that will probably go to the
> grave with me.

One must be cautious when asking for a definition from fom.

He may give it to you.

=========================================================================

WM has several times claimed that the standard bijection from the set of
all binary sequences to the set of all paths of a Complete Infinite
Binary Tree is a linear mapping from the set of all binary sequences
regarded as a linear space over |R to the set of all paths of a CIBT.

While the mapping is easily shown to be bijective, it fails to be a
linear mapping as WM describes it:

> The isomorphism is from |R,+,* to |R,+,*. Only in one case the
> elements of |R are written as binary sequences and the other time as
> paths of the Binary Tree. Virgil is simply too stupid to understand
> that.everal flaws in WM's claim that the identity map on induces a linear map on 2^|N.

WM's flaws in making that claim work include, but are not necessarily
limited to:

(1) not all members of |R will have any such binary expansions, only
those between 0 and 1, so that not all sums of vectors will "add up" to
be vectors within his alleged linear space, and

(2) some reals (the positive binary rationals strictly between 0 and 1)
will have two distinct and unequal-as-vectors representations, requiring
that some real numbers not be equal to themselves as a vectors, and

(3) WM's method does not provide for the negatives of any of the vectors
that he can form, so his "space" does not qualify as a linear space in
that way, either.

On the basis of the above problems, and possibly others as well that I
have not yet even thought of, I challenge WM's claim to have represented
the set |R as the set of all binary sequences, much less to have imbued
that set of all binary sequences with the structure of a real vector
space or the showed the identity mapping to be a linear mapping from one
vector space to another.

Note that while WM's model doe not achieve what he claims for it, there
is another model, which a reasonably competent mathematician should be
able to find, which does make the mapping into an isomorphism of linear
spaces.

It is a shame that someone so obviously of limited ability at
mathematics as WM should feel himself so driven to try and correct his
betters.
--

Date Subject Author
3/14/13 Alan Smaill
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 Virgil
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/14/13 mueckenh@rz.fh-augsburg.de
3/14/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 fom
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/17/13 mueckenh@rz.fh-augsburg.de
3/17/13 Virgil
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 fom
3/19/13 Virgil
3/19/13 fom
3/19/13 Virgil
3/19/13 Virgil
4/17/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 Virgil
3/19/13 fom
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 fom
3/18/13 fom
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/18/13 fom
3/19/13 mueckenh@rz.fh-augsburg.de
3/19/13 Virgil
3/19/13 fom
4/17/13 Virgil
4/18/13 fom
3/18/13 Virgil
3/18/13 mueckenh@rz.fh-augsburg.de
3/18/13 Virgil
3/18/13 Virgil
3/18/13 Virgil
3/16/13 Virgil
3/16/13 Virgil
3/17/13 fom
3/15/13 fom
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/15/13 Virgil
3/15/13 mueckenh@rz.fh-augsburg.de
3/15/13 Virgil
3/15/13 fom
3/15/13 fom
3/15/13 Virgil
3/15/13 fom
3/16/13 Virgil
3/14/13 Virgil
3/14/13 Virgil
3/16/13 mueckenh@rz.fh-augsburg.de
3/16/13 Virgil
3/17/13 fom