SUO: Re: Relations And Their Divisitudes
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
RATD. Note 14
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Tom,
I think that the kind of determination that I am
calling on here ought to be clear by now. Still,
the immortal phrase "two points determine a line"
is only immortal so long as it is content to live
within the time immemorial bounds of that special,
but eminently imitable style of geometry to which
we commonly set the name of Euclid. More generic,
we must say "two points determine a set of lines",
observing parametrically that the set in question
may have a cardinality other than one, even zero.
Thus not all determination is "unique determination", but is more generously
to be regarded as "determination in measure" or "moderate determination" or,
as one says, "constraint". It is as much to say that the existence, actual
or formal, of one description of thing constrains the existence, actual or
formal, of some other description of thing to fall within some portion of
the universe of possibility that is otherwise open to that sort of thing.
The "otherwise open to it" is not just a meta-rhetorical fluoresce, but
the explication of that conditionality will have to wait for its time.
Constraint, in its turn, is key, passe partout, to the very idea and
the full developing state of information.
This is one of the reasons why the concept of "determination" figures
so prominently in Peirce's theory of sign relations, most especially
in this definition of "sign" in relation to the definition of logic:
| A sign is something, 'A',
| which brings something, 'B',
| its 'interpretant' sign
| determined or created by it,
| into the same sort of correspondence
| with something, 'C', its 'object',
| as that in which itself stands to 'C'.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54, also available here:
| http://members.door.net/arisbe/menu/library/bycsp/L75/L75.htm
More details on how the definition of a sign relation bears on
the definition of logic are given in the contexts of this text:
| On the Definition of Logic [Version 1]
|
| Logic will here be defined as 'formal semiotic'.
| A definition of a sign will be given which no more
| refers to human thought than does the definition
| of a line as the place which a particle occupies,
| part by part, during a lapse of time. Namely,
| a sign is something, 'A', which brings something,
| 'B', its 'interpretant' sign determined or created
| by it, into the same sort of correspondence with
| something, 'C', its 'object', as that in which it
| itself stands to 'C'. It is from this definition,
| together with a definition of "formal", that I
| deduce mathematically the principles of logic.
| I also make a historical review of all the
| definitions and conceptions of logic, and show,
| not merely that my definition is no novelty, but
| that my non-psychological conception of logic has
| 'virtually' been quite generally held, though not
| generally recognized. (CSP, NEM 4, 20-21).
|
| On the Definition of Logic [Version 2]
|
| Logic is 'formal semiotic'. A sign is something,
| 'A', which brings something, 'B', its 'interpretant'
| sign, determined or created by it, into the same
| sort of correspondence (or a lower implied sort)
| with something, 'C', its 'object', as that in
| which itself stands to 'C'. This definition no
| more involves any reference to human thought than
| does the definition of a line as the place within
| which a particle lies during a lapse of time.
| It is from this definition that I deduce the
| principles of logic by mathematical reasoning,
| and by mathematical reasoning that, I aver, will
| support criticism of Weierstrassian severity, and
| that is perfectly evident. The word "formal" in
| the definition is also defined. (CSP, NEM 4, 54).
|
| Charles Sanders Peirce,
|'The New Elements of Mathematics', Volume 4,
| Edited by Carolyn Eisele, Mouton, The Hague, 1976.
More information on Peirce's notion of determination can be found here:
Determination -- Ontology List
01. http://suo.ieee.org/ontology/msg02377.html
02. http://suo.ieee.org/ontology/msg02378.html
03. http://suo.ieee.org/ontology/msg02379.html
04. http://suo.ieee.org/ontology/msg02380.html
05. http://suo.ieee.org/ontology/msg02384.html
06. http://suo.ieee.org/ontology/msg02387.html
07. http://suo.ieee.org/ontology/msg02388.html
08. http://suo.ieee.org/ontology/msg02389.html
09. http://suo.ieee.org/ontology/msg02390.html
10. http://suo.ieee.org/ontology/msg02391.html
11. http://suo.ieee.org/ontology/msg02395.html
12. http://suo.ieee.org/ontology/msg02407.html
13. http://suo.ieee.org/ontology/msg02550.html
14. http://suo.ieee.org/ontology/msg02552.html
15. http://suo.ieee.org/ontology/msg02556.html
16. http://suo.ieee.org/ontology/msg02594.html
17. http://suo.ieee.org/ontology/msg02651.html
18. http://suo.ieee.org/ontology/msg02673.html
19. http://suo.ieee.org/ontology/msg02706.html
20. http://suo.ieee.org/ontology/msg03177.html
21. http://suo.ieee.org/ontology/msg03185.html
22. http://suo.ieee.org/ontology/msg03188.html
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o