SUO: Re: Sign Relations
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| "Two points determine a line."
| ~~ A Popular Plain Notion
|
| "Two lines determine a point."
| ~~ A Projective Plane Notion
Jean-Marc Orliaguet wrote:
>
>
> Well, put simply, to say that O determines S, or that O "causes" S
> to not be what it could have been otherwise, means that the relation
> between O and S , no matter how you define it, is not symmetrical.
>
> Would you agree with this?
>
> JM
Jean-Marc,
I have "yet another dental appointment" (YADA) today --
if only I could have the luck that some mathematicians
have had with their dentists, I would have more theorems
than fillings today! -- anyway, I will answer briefly
now and try to get back and down to the details later.
I see nothing in my definition of choice for sign relations
that prescribes or proscribes almost any variety of symmetry
ruling among the elements of the relational domains O, S, I.
The entanglements of "causality" and "determination" are
incidentally amusing, of course, but we would have to go
back through the whole "Reply to the Necessitarians" one
more time just to get a start on the issue. Maybe later.
Whatever names on which we ultimately settle, the formal
or structural question of primary import here is whether
we are bandying about a 3-adic relation that articulates
into some logical combination of 2-adic relations or not.
Most people regard causal chains as having that billiard
ball character where cue ball 'o' strikes solid ball 's',
which hits, in its turn, striped ball 'i' -- but that is
a degenerate example of a genuine semiosis, and not even
the physicists dare to fancy that the cosmos is all that
simple any more. Since Heisenberg, if not since Peirce,
we have come to recognize that that the "causal picture"
and the "spacetime picture" are mutually suspended in a
relation of "complementarity" with regard to each other.
And the rise of the complexity-sensitive sciences shows
us the surprises that await us if we deign to admit the
pervasiveness of nonlinear dynamics through the narrow
slits of our conceptual frameworks. It is easy to see
that there is a relationship between nonlinearity and
triadicity, and maybe we can discuss this later today.
Cheers,
Jon
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤