[Arisbe] Re: Inquiry Into Information

[Jon Awbrey]

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| Let us now take the two statements, S is P, T is P;
| let us suppose that T is much more distinct than S and
| that it is also more extensive.  But we 'know' that S is P.
| Now if T were not more extensive than S, T is P would contain
| more truth than S is P;  being more extensive it 'may' contain
| more truth and it may also introduce a falsehood.  Which of these
| probabilities is the greatest?  T by being more extensive becomes
| less intensive;  it is the intension which introduces truth and the
| extension which introduces falsehood.  If therefore T increases the
| intension of S more than its extension, T is to be preferred to S;
| otherwise not.  Now this is the case of induction.  Which contains
| most truth, 'neat' and 'deer' are herbivora, or cloven-footed
| animals are herbivora?
|
| In the two statements, S is P, S is Q, let Q be at once more 'formal' and
| more 'intensive' than P;  and suppose we only 'know' that S is P.  In this
| case the increase of formality gives a chance of additional truth and the
| increase of intension a chance of error.  If the extension of Q is more
| increased than than its intension, then S is Q is likely to contain more
| truth than S is P and 'vice versa'.  This is the case of 'à posteriori'
| reasoning.  We have for instance to choose between
|
| Light gives fringes of such and such a description
|
| and
|
| Light is ether-waves.
|
| CSP, CE 1, pages 188-189.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'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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