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Jon Awbrey


Registered: Feb 2004
Posts: 557

Information = Comprehension x Extension

ICE. Note 46

| Every induction, then, and every hypothesis yields a certain amount of truth.
|
| I might also show that no induction or hypothesis is completely true except
| such as we call cognitions 'a priori'. For the chance against it is infinite.
| Hence, the question what is the 'probability' of an induction or hypothesis is
| senseless and the true question is how much truth does an induction contain.
| For the same reasons by how much truth should not be meant what proportion
| of inferences therefrom are true but simply of how much value are certain
| premisses in giving us truth by induction or hypothesis.
|
| We must distinguish therefore the truth which an inductive or
| hypothetic conclusion may have by accident from that which it
| must have from the nature of the facts explained. The former
| cannot properly be estimated. The latter can. For to consider
| first induction; if the same conclusion result inductively as the
| least truthful explanation possible of two different sets of facts,
| it is plain that a certain amount of truth it is obliged to have
| on account of each instance, that is on account of the extension
| of the subject of the fact. And each instance determines a certain
| amount of truth independently of the others. So that the number of
| different kinds of instances measures the least amount of truth the
| induction can have. In the same way with hypothesis the number of
| different properties explained measures the least possible truth
| of the hypothesis.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 293-294.
|
| 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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Jon Awbrey


Registered: Feb 2004
Posts: 557

Information = Comprehension x Extension

ICE. Note 47

| In this way truth is measured upon a scale of numbers from 'one' to 'infinity'.
| And thus we cannot measure the ratio of the truth to the falsehood but only
| the ratio between the pregnancy of two sets of facts. Of any particular
| conclusion therefore we can only judge by ascertaining by further
| experience whether it can be improved. But the comparative
| usefulness of the facts upon which it proceeds may be
| estimated with an approach to precision.
|
| We may sum up then by the rule that the value of facts is in proportion
| to their number; and that from given facts the best inference when
| all possible retrenchment has been made, is the one which being
| inductive has the most comprehensive subject and which being
| hypothetic has the most extensive predicate.
|
| This seems to complete the logical theory of inference ...
|
| C.S. Peirce, 'Chronological Edition', CE 1, 294.
|
| 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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Jon Awbrey


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Posts: 557

Information = Comprehension x Extension

ICE. Note 48

| I fear I have wearied you in these lectures by dwelling so much upon
| merely logical forms. But to the pupil of Kant as to the pupil of
| Aristotle the Analytic of Logic is the foundation of Metaphysics.
| We find ourselves in all our discourse taking certain points for
| granted which we cannot have observed. The question therefore
| is what may we take for granted independent of all experience.
| The answer to this is metaphysics. But it is plain that we
| can thus take for granted only what is involved in logical
| forms. Hence, the necessity of studying these forms. In
| these lectures, one set of Logical forms has been pretty
| thoroughly studied; that of Hypothesis, Deduction,
| Induction. Another set has been partly studied,
| that of Denotation, Information, Connotation.
|
| Corresponding to these there are evidently certain conceptions of
| objects in general. To denotation corresponds the conception of
| an 'object', to information the conception of a real kind, and
| to connotation the conception of a logos or quality. So to
| Induction corresponds the conception of a Law, to Hypothesis
| the conception of a Case under a Law, and to Deduction the
| conception of a Result.
|
| There are also principles of the Judgment corresponding to
| these conceptions of which we have instances in the laws
| that all things, forms, symbols are symbolizable.
|
| All the principles that can be so derived from the forms of logic
| must be valid for all experience. For experience has used logic.
| Everything else admits of speculative doubt.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 302.
|
| 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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