[Inquiry] Re: Extension x Comprehension = Information

[Jon Awbrey]

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ECI.  Note 39

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| In the case of hypothesis we have
| given some remarkable state of things:
|
| X is P,
|
| where X is an object of denotation;
| we explain this by supposing that:
|
| X is Q,
|
| and Q always contains more information than P.
| If Q, therefore, has no more comprehension than P,
| it is better to say "X is Q" than "X is P".
|
| It is 'clearer' to say that Every man is mortal
| than to say that Every man is either a good mortal
| or a bad mortal.
|
| But in the case of hypothesis, Q always comprehends
| more than P.  To decide then between the two;  we have
| to consider whether Q has more denotation than P for if
| it has, the information of P is increased more in Q than
| its comprehension is and 'vice versa';  and we must be
| decided which to take by our motives.
|
| This is the case of a preference between hypotheses.
| But in the first proceedure from facts, P is a mere
| conjunctive term, destitute of any denotation before
| this proposition.  Hence in this case the information
| is increased absolutely, the connotation only relatively,
| and the hypothesis is absolutely needed and must be taken
| as a 'pis aller' unless opposed by some other argument and
| until a better one presents itself.
|
| Polarization for instance is a series of phenomena which it is
| impossible to name or define without the use of a hypothesis.
|
| CSP, CE 1, pages 285-286.
|
| 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.

Nota Bene.  For the sake of readability in this transcription,
I supply quotation marks around formulas and change a couple of
Greek letters to Roman characters, using T for Sigma and Q for Pi.

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