fom
Posts:
1,969
Registered:
12/4/12


Re: Matheology § 223: AC and AMS
Posted:
Mar 19, 2013 8:05 PM


On 3/19/2013 2:01 PM, Virgil wrote: > In article <GNidnVy8wrn7PNXMnZ2dnUVZ_qidnZ2d@giganews.com>, > fom <fomJUNK@nyms.net> wrote: > >> On 3/19/2013 12:04 PM, WM wrote: >>> On 19 Mrz., 17:34, fom <fomJ...@nyms.net> wrote: >>>> On 3/19/2013 11:28 AM, WM wrote: >>>> >>>> >>>> >>>> >>>> >>>>> On 18 Mrz., 23:50, fom <fomJ...@nyms.net> wrote: >>>> >>>>>>> If you are unable to prove by yourself that the set of finite words is >>>>>>> countable, then further discussion with you is meaningless. >>>> >>>>>> What I can or cannot prove to myself is not >>>>>> an issue. >>>> >>>>> Exactly that is the issue  and nothing else! >>>> >>>>>> What is needed here is an agreed upon standard >>>>>> of proof. >>>> >>>>> You think if there are enough fools to agree on a foolish standard, >>>>> that would be enough? You think if there are enough fools to assert >>>>> that countably many words are sufficient to label uncountably many >>>>> words, that must be true? >>>> >>>>> Deplorable slave! >>>> >>>> It seems that I have graduated from >>>> being a parrot. >>>> >>>> I am now acknowledged as a human >>>> being. >>> >>> No, you are in an Aschexperiment: >> >> >> "As soon as the idea of acquiring >> symbols and laws of combination, >> without given meaning, has become >> familiar, the student has the notion >> of what I will call a symbolic >> calculus; which, with certain symbols >> and certain laws of combination, is >> symbolic algebra: an art, not a >> science; and an apparently useless >> art, except as it may afterwards >> furnish the grammar of a science. >> The proficient in a symbolic calculus >> would naturally demand a supply >> of meaning. Suppose him left without >> the power of obtaining it from >> without: his teacher is dead, and he >> must invent meanings for himself. >> His problem is: Given symbols and >> laws of combination, required meanings >> for the symbols of which the right >> to make those combinations shall be >> a logical consequence. He tries, >> and succeeds; he invents a set of >> meanings which satisfy the conditions. >> Has he then supplied what his teacher >> would have given, if he had lived? >> In one particular, certainly: he has >> turned his symbolic calculus into a >> significant one. But it does not >> follow that he has done it in a way >> which his teacher would have taught >> if he had lived. It is possible >> that many different sets of meanings >> may, when attached to the symbols, >> make the rules necessary consequences." >> >> Augustus De Morgan >> > Have you run cross a book by de Morgan called "A Budget of Paradoxes"? > If I recall correctly, it contains an acidly accurate description of > people like WM, as well as many amusing anecdotes.
No. I know the things I know from these writers only in passing, from seeking some sense in all of the arguing that has little to do with mathematics.
I am certain it must be a joy to read. These days I often think of what has become the child's nursery rhyme "Humpty Dumpty". Lewis Carroll had been a logician. I own one of his books (from Dover).
"... all the king's horses and all the king's men couldn't put Humpty together again"
Some of these logicians and mathematicians have wonderful wit in addition to their other talents.
Apparently, de Morgan has too.

