fom
Posts:
1,968
Registered:
12/4/12


Re: Ordinals describable by a finite string of symbols
Posted:
Jul 7, 2013 3:13 PM


On 7/7/2013 1:10 PM, Julio Di Egidio wrote: > "fom" <fomJUNK@nyms.net> wrote in message > news:6LSdnVj9KObNO0TMnZ2dnUVZ_sadnZ2d@giganews.com... >> On 7/7/2013 8:06 AM, Julio Di Egidio wrote: >>> "Julio Di Egidio" <julio@diegidio.name> wrote in message >>> news:krbohl$av6$1@dontemail.me... >>> >>>> We know it when you know it, it selfrepresents >>> >>> Oops, I just meant: We know it when we know it... >> >> It is common among the men with whom I >> work to hear, "It is what it is". >> >> I take it to be an article of faith > > Is that all you could gather? Then I'll give you another pearl to think > about: dogmatism and scepticism are the two sides of the same coin. But > take your time... >
Well, I had been thinking in terms of the fact that experience has an unavoidable subjective sense. It invariably admits the reduction of linguistic expressions to mere syntax. But, it is also the subjective experience that affords meaningful interpretation.
It is in the transition from subjective to objective where all of the difficulties seem to arise.
The sense in which mathematicians had to face this is nicely summarized in DeMorgan,
"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
My coworkers, however, would tend to make the remark along the lines of their respective faiths. And, to be honest, when suspended in a rowboat on two wires 300 feet above grade, I do too.

