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Re: Matheology § 161
Posted:
Nov 25, 2012 2:37 PM


On Nov 25, 12:55 am, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Nov 25, 6:37 pm, WM <mueck...@rz.fhaugsburg.de> 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 selfevident, 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]http://www.archive.org/stream/worldindividual00royciala#page/n0/mode/...... > > > 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 uncomputable! > SCI.LOGIC
The most famous English map maker who first made an attempt to complete n entire atlas is to be found here, http://www.shakespearesengland.co.uk/2010/08/04/themapsofjohnspeed/
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).
http://www.math.yorku.ca/Who/Faculty/Kochman/M4400/Probability.pdf
time to reflect on any mathematical developments that had a direct effect on the description of surface space and problems of longditute



