[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Note 36

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| All these principles must as principles be universal.
| Hence they are as follows:--
|
| All things, forms, symbols are symbolizable.
|
| The next step is to prove each of these principles.
| First then, to prove deductively that all symbols are
| symbolizable.  In every syllogism there is a term which
| is predicate and subject.  But a predicate is a symbol
| of its subject.  Hence, in every deduction a symbol is
| symbolized.  Now deduction is valid independently of
| the matter of the judgment.  Hence all symbols are
| symbolizable.
|
| Next;  to prove inductively that all things are symbolizable.
| For this purpose we must take all the collocations of things we
| can and judge by them.  Now all these collocations of things have
| been selected upon some principle;  this principle of selection is
| a predicate of them and a 'concept'.  Being a concept it is a symbol.
| And it partakes of that peculiarity of symbols that it must have
| information.  We have no concepts which do not denote some things
| as well as connoting;  because all our thought begins with experience.
| But a symbol which has connotation and denotation contains information.
| Whatever symbol contains information contains more connotation than is
| necessary to limit its possible denotation to those things which it
| may denote.  That is every symbol contains more than is sufficient
| for a principle of selection.  Hence every selected collocation of
| things must have something more than a mere principle of selection,
| it must have another common quality.  Now by induction this common
| quality may be predicated of the whole possible denotation of the
| concept which serves as principle of selection.  And thus every
| collocation of things we can select is symbolized by its principle
| of selection.  Now by induction we pass from this statement that all
| things we can take are symbolizable to the principle that all things
| are symbolzable.  Q.E.D.  This argument though inductive in form is
| of the highest possible validity, for no case can possibly arise to
| contradict it.
|
| Thirdly, we have to prove hypothetically that all forms are symbolizable.
| For this purpose we must consider that 'forms' are nothing unless they
| are embodied, and then they constitute the synthesis of the matter.
| Hence the knowledge of them cannot be directly given but must be
| obtained by hypothesis.  Now we have to explain this fact, that
| all forms are to be regarded as subjects for hypothesis, by a
| hypothesis.  For this purpose, we should reflect that whatever
| is symbolizable is symbolized by terms and their combinations.
| Now we saw at the last lecture that the process of obtaining
| a new term is a hypothetic inference.  So that everything
| which is symbolizable is to be regarded as a subject for
| hypothesis.  This accounts for the same thing being true
| of forms, if we make the hypothesis that all forms are
| symbolizable.  Q.E.D.  This argument though only an
| hypothesis could not have been stronger for the
| conclusion involves no matter of fact at all.
|
| CSP, CE 1, pages 282-283.
|
| 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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