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Topic: Matheology § 161
Replies: 3   Last Post: Nov 25, 2012 3:43 PM

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Posts: 25
Registered: 8/19/12
Re: Matheology § 161
Posted: Nov 25, 2012 2:37 PM
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On Nov 25, 12:55 am, Graham Cooper <> wrote:
> On Nov 25, 6:37 pm, WM <> wrote:

> > Matheology § 161
> > {{Yet another application of set theory?}} I propose here, then, first
> > to illustrate, and then to discuss theoretically, the nature and ideal
> > outcome of any recurrent operation of thought, and to develope, in
> > this connection, what one may call the positive nature of the concept
> > of Infinite Multitude.

> > Prominent among the later authors who have dealt with our problem from
> > the mathematical side, is George Cantor. [...] With this theory of the
> > Mächtigkeiten I shall have no space to deal in this paper, but it is
> > of great importance for forming the conception of the determinate
> > Infinite.

> > A map of England, contained within England, is to represent, down to
> > the minutest detail, every contour and marking, natural or artificial,
> > that occurs upon the surface of England.

> > Our map of England, contained in a portion of the surface of England,
> > involves, however, a peculiar and infinite development of a special
> > type of diversity within our map. For the map, in order to be
> > complete, according to the rule given, will have to contain, as a part
> > of itself, a representation of its own contour and contents. In order
> > that this representation should be constructed, the representation
> > itself will have to contain once more, as a part of itself, a
> > representation of its own contour and contents; and this
> > representation, in order to be exact, will have once more to contain
> > an image of itself; and so on without limit. We should now, indeed,
> > have to suppose the space occupied by our perfect map to be infinitely
> > divisible, even if not a continuum.

> > That such an endless variety of maps within maps could not physically
> > be constructed by men, and that ideally such a map, if viewed as a
> > finished construction, would involve us in all the problems about the
> > infinite divisibility of matter and of space, I freely recognize.

> > Suppose that, for an instance, we had accepted this assertion as true.
> > Suppose that we then attempted to discover the meaning implied in this
> > one assertion. We should at once observe that in this one assertion,
> > "A part of England perfectly maps all England, on a smaller scale,"
> > there would be implied the assertion, not now of a process of trying
> > to draw maps, but of the contemporaneous presence, in England, of an
> > infinite number of maps, of the type just described. The whole
> > infinite series, possessing no last member, would be asserted as a
> > fact of existence.

> > We should, moreover, see how and why the one and the infinitely many
> > are here, at least within thought's realm, conceptually linked. Our
> > map and England, taken as mere physical existences, would indeed
> > belong to that realm of "bare external conjunctions." Yet the one
> > thing not externally given, but internally self-evident, would be that
> > the one plan or purpose in question, namely, the plan fulfilled by the
> > perfect map of England, drawn within the limits of England, and upon a
> > part of its surface, would, if really expressed, involve, in its
> > necessary structure, the series of maps within maps such that no one
> > of the maps was the last in the series.

> > This way of viewing the case suggests that, as a mere matter of
> > definition, we are not obliged to deal solely with processes of
> > construction as successive, in order to define endless series. A
> > recurrent operation of thought can be characterized as one that, if
> > once finally expressed, would involve, in the region where it had
> > received expression, an infinite variety of serially arranged facts,
> > corresponding to the purpose in question.

> > [Josiah Royce: "The world and the individual", MacMillan, London
> > (1900) p. 500ff]

> > The repeated application of the fotocopier has been proposed as a
> > cheap replacement for expensive electron microscopes. Unfortunately I
> > have forgotten the name of the inventor of this idea.

> > Regrads, WM
> there are no mathematicians reading.
> logic is a study of literature only, no different to knowing vast
> journals of legal precedents, the entire art history of the Incubus
> period, the works of Shakespear or illustrated Medical Journals.
> You are talking to Clayton's Arts Graduates who wish to further the
> 'study' of logic, which opposes the _application_ of logic.
> --
> if( if(t(S),f(R)) , if(t(R),f(S)) ).
>     if it's sunny then it's not raining
> ergo
>        if it's raining then it's not sunny
> S: if stops(S) gosub S
> G. GREENE:  this proves stops() must be un-computable!

The most famous English map maker who first made an attempt to
complete n entire atlas is to be found here,

this is interesting,the awesome prevailing mathematics about that time
was dominated by three French mathematicians:
René Descartes (1596 ? 1650), Pierre de Fermat (1601 ? 1662) and
Blaise Pascal
(1623 ? 1662).

time to reflect on any mathematical developments that had a direct
effect on the description of surface space and problems of longditute

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