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Confirmation

This text explores key concepts in logic and confirmation theory, including Nicod's Criterion and the Raven Paradox. It discusses how generalizations can be confirmed, disproved, or remain inconclusive based on the observations of elements categorized as F and G. The text emphasizes the equivalence of statements and how non-black objects can misleadingly affirm hypotheses about ravens. It also touches on the concept of infinitesimals, elaborating on their role in logical reasoning. This analysis aims to clarify the intricate relationships between observations and hypotheses in philosophical and logical discourse.

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Confirmation

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  1. Confirmation Infinitesimal Confirmation

  2. Review • Nicod’s Criterion: • A generalization is confirmed (to some degree) by an F that is G. • A generalization is disproved by an F that is not G. • A generalization is neither confirmed nor disproved by non-Fs that are not G or by non-Fs that are G. • The contrapositive of All Fs are G is All non-Gs are non-Fs. • The Equivalence Confirmation Thesis: Logically equivalent statements are confirmed by the same things.

  3. The Raven Paradox • A red herring confirms the hypothesis that all non-black things are non-ravens. • The hypothesis that all non-black things are non-ravens is logically equivalent to the hypothesis that all ravens are black. • If (1) and (2), then a red herring confirms the hypothesis that all ravens are black. • [So] A red herring confirms the hypothesis that all ravens are black.

  4. The Conclusion • A red herring confirms the hypothesis that all ravens are black. • Nicod’s Criterion (c): A generalization is neither confirmed nor disproved by non-Fs that are not G or by non-Fs that are G.

  5. The Conclusion • An infinitesimal (i) is an infinitely small value.

  6. The Conclusion • A red herring confirms the hypothesis that all ravens are black. • Nicod’s Criterion (c): A generalization is neither confirmed nor disproved by non-Fs that are not G or by non-Fs that are G.

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