🚀 go-pugleaf

In article <9172@medusa.cs.purdue.edu> muttiah@cs.purdue.edu (Ranjan Samuel Muttiah) writes:
>
>A. These views are not mine, but belong to quite an ingenious writer.
>
>B. Can anyone depart so far from good sense as to convince himself
>   that truth is arbitrary and depends on names, when it is agreed
>   that the Greeks, the Latins, and the Germans all have the same
>   geometry ?
>
>------------
>
>To be continued ...
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A. What you say is right. Nevertheless, there is difficulty that 
   must be resolved/

B. one thing troubles me, the fact that notice that I never know,
   discover, or prove any truth without using words or other signs 
   in my mind.

A. Indeed, if characters were lacking, we would never distinctly
   know or reason about anything.

B. But when we examine figures in geometry, we often bring truths
   to light through careful contemplation of them.

A. Indeed so. But we must also realize that these figures must be
   regarded as characters, for a circle drawn on a paper is not a
   circle, nor is it necessary that it be, but it is sufficient that
   it be taken by us for a circle.

B. But it does have a certain similarity with a circle, and that
   certainly isn't arbitrary.

A. I admit that, and as a consequence, figures are the most of
   characters. But what similarity do you think there is between
   ten and the character '10' ?

B. There is some relation or order among the characters which is
   also found among things, especially if the characters are well
   designed.

A. Indeed, but what similarity do the primary elemetns themselves 
   have with things, for example, '0' with nothing, or 'a' with a
   line ? You are forced to admit, at very least, that no
   similarity is necessary in these elements.  This for example,
   is the case with respect to the words 'light' and 'bearing'
   even though the composite word 'lightbearer' is related to the
   words 'light' and 'bearing', in a way that corresponds to the 
   relation between the thing signified by 'lightbearer' and the
   things signified by 'light' and 'bearing'.

B. But the Greek word phosphoros has the same relation to phos
   and phero.

A. The Greeks could have used another word instead.

B. True. But yet I notice that if characters can be applied to
   reasoning, there must be some copmlex arrangement, some order
   which agrees with things, an order, if not in individual words
   (though that would be better), then at least in their conjecture 
   and inflection.  And a corresponding variegated order is found
   in all languages in one way or another. [My comment: very true
   of chinese].  This gives me the hope that we can avoid the
   difficulty.  For though the characters are arbitrary, their use
   and connection have something that is not arbitrary, namely, a 
   certain correspondence between characters and things, and 
   certain relations among different characters expressing the same
   things.  And this correspondence or this relation is the ground
   of truth.  For it brings it about that whether we use these
   characters or others, the same thing always results, or at least
   something equivalent, that is, something corresponding in
   proportion always results.  This is true even if, as it happens,
   it is always necessary to use some characters. for thinking.

A. Well done! You have completely untangled yourself in an
   execllent way. And the analytic or arithmatic calculus confirms
   this.  For, with numbers, things will always come out the same
   way, whether one uses the decimal system or, as some have done, 
   the duodecimal system. And if, after that, you use seeds or other
   countable things to show what you explained in a different way
   using the calculi, it will always come out the same.  This is
   also true in analysis, even though using different characters,
   different properties of things appear more easily.  But the basis
   of TRUTH IS ALWAYS IN THE VERY ARRANGEMENT OF CHARACTERS.  For
   example, if you call 'a ** 2' the square of 'a', then by taking
   'b + c' for 'a', you will have as the square '+ b ** 2 + c ** 2
   +2bc.'  Or, by taking 'd - e' for 'a', you will have the 
   square '+ d ** 2 + e ** 2 - 2de.'  In the prior case we express
   the relation of the whole 'a' to it's parts 'b' and 'c', and in
   the latter case we express the relation of the part 'a' to the
   whole 'd' and to 'e', that which is in 'd' over and above 'a'.
   However, by substituting, it is obvious that it always comes
   to the same thing.  You see that, by whatever decision the
   characters are chosen, as long as a certain order and measure
   is observed in their use, everything will always agree.
   Therefore, although truths necessarily presuppose some characters,
   indeed, sometimes they deal with characters themselves, truths
   don't consist in what is arbitrary in the characters, but in
   what is invariant in them, namely, in the realtion they have
   to things.  And it is always true, independent of any decision
   of ours, that if, given such and such characters, such and such
   reasoning will succeed, then it will likewise succeed given
   others whose relation to former ones is known; however, the
   reasoning preserves a relation to the former ones that results
   from the relation among the characters.  This is something
   obvious from substituting and comparing.
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End.
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