[Inquiry] Re: Kaina Stoicheia

[Jon Awbrey]

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KS.  Note 23

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| The individuating internal cause is called the 'material cause'.
| Thus the integrant parts of a subject or fact form its 'matter',
| or material cause.
|
| The individuating external cause is called the 'efficient',
| or 'efficient cause';  and the causatum is called the 'effect'.
|
| The defining internal cause is called the 'formal' cause,
| or 'form'.  All those facts which constitute the definition
| of a subject or fact make up its form.
|
| The defining external cause is called the 'final cause',
| or 'end'.
|
| It is hoped that these statements will be found to hit
| a little more squarely than did those of Aristotle and
| the scholastics the same bull's eye at which they aimed.
| From scholasticism and the medieval universities, these
| conceptions passed in vaguer form into the common mind
| and vernacular of Western Europe, and especially so in
| England.
|
| Consequently by the aid of these definitions I think
| I can make out what it is that the writer mentioned
| has in mind in saying that it is not the law which
| influences, or is the final cause of, the facts,
| but the facts that make up the cause of the law.
|
| He means that the general fact which the law of gravitation
| expresses is composed of the special facts that this stone at
| such a time fell to the ground as soon as it was free to do so
| and its upward velocity was exhausted, that each other stone did
| the same, that each planet at each moment was describing an ellipse
| having the centre of mass of the solar system at a focus, etc. etc.;
| so that the individual facts are the material cause of the general fact
| expressed by the law;  while the propositions expressing those facts are
| the efficient cause of the law itself.
|
| This is a possible meaning in harmony with the writer's sect of thought;
| and I believe it is his intended meaning.  But this is easily seen not
| to be true.  For the formula relates to all possible events of a given
| description;  which is the same as to say that it relates to all possible
| events.  Now no collection of actual individual events or other objects of
| any general description can amount to all possible events or objects of that
| description;  for it is possible that an addition should be made to that
| collection.  The individuals do not constitute the matter of a general;
| those who with Kant, or long before him, said that they do were wanting in
| the keen edge of thought requisite for such discussions.  On the contrary,
| the truth of the formula, its really being a sign of the indicated object,
| is the defining cause of the agreement of the individual facts with it.
|
| Namely, this truth fulfills the first condition, which is that it might
| logically be although there were no such agreement.  For it might be true,
| that is, contains no falsity, that whatever stone there might be on earth
| would have a real downward component [of] acceleration even although no stone
| actually existed on earth.  It fulfills the second condition, that as soon as the
| other factor (in this case the actual existence of each stone on earth) was present,
| the result of the formula, the real downward component of acceleration would exist.
| Finally, it fulfills the third condition, that while all existing stones might
| be accelerated downwards by other causes or by an accidental concurrence of
| circumstances, yet the downward acceleration of every possible stone would
| involve the truth of the formula.
|
| C.S. Peirce, ["Kaina Stoicheia"], NEM 4, 253-254
|
| C.S. Peirce, ["Kaina Stoicheia"], MS 517 (1904), pp. 235-263 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by
| Charles S. Peirce, Volume 4, Mathematical Philosophy',
| Mouton, The Hague, 1976.
|
| Cf. "New Elements", pp. 300-324 in 'The Essential Peirce, Volume 2 (1893-1913)',
| Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1998.

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