[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Note 35

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| Our next business is to find which is which.
| For this purpose we must consider that each
| principle is to be proved by the kind of
| inference which it supports.
|
| The ground of deductive inference then must be established deductively;
| that is by reasoning from determinant to determinate, or in other words
| by reasoning from definition.  But this kind of reasoning can only be
| applied to an object whose character depends upon its definition.
| Now of most objects it is the definition which depends upon the
| character;  and so the definition must therefore itself rest on
| induction or hypothesis.  But the principle of deduction must
| rest on nothing but deduction, and therefore it must relate
| to something whose character depends upon its definition.
| Now the only objects of which this is true are symbols;
| they indeed are created by their definition;  while
| neither forms nor things are.  Hence, the principle
| of deduction must relate to the symbolizability of
| of symbols.
|
| The principle of hypothetic inference must be established hypothetically,
| that is by reasoning from determinate to determinant.  Now it is clear that
| this kind of reasoning is applicable only to that which is determined by what
| it determines;  or that which is only subject to truth and falsehood so far as
| its determinate is, and is thus of itself pure 'zero'.  Now this is the case
| with nothing whatever except the pure forms;  they indeed are what they
| are only in so far as they determine some symbol or object.  Hence the
| principle of hypothetic inference must relate to the symbolizability
| of forms.
|
| The principle of inductive inference must be established inductively,
| that is by reasoning from parts to whole.  This kind of reasoning can
| apply only to those objects whose parts collectively are their whole.
| Now of symbols this is not true.  If I write 'man' here and 'dog' here
| that does not constitute the symbol of 'man and dog', for symbols have
| to be reduced to the unity of symbolization which Kant calls the unity
| of apperception and unless this be indicated by some special mark they
| do not constitute a whole.  In the same way forms have to determine the
| same matter before they are added;  if the curtains are green and the
| wainscot yellow that does not make a 'yellow-green'.  But with things
| it is altogether different;  wrench the blade and handle of a knife
| apart and the form of the knife has disappeared but they are the
| same thing -- the same matter -- that they were before.  Hence,
| the principle of induction must relate to the symbolizability
| of things.
|
| All these principles must as principles be universal.
| Hence they are as follows:--
|
| All things, forms, symbols are symbolizable.
|
| CSP, CE 1, pages 281-282.
|
| Charles Sanders Peirce, "On the Logic of Science",
| Harvard University Lectures of 1865, pages 161-302 in:
|
|'Writings of Charles S. Peirce:  A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.

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