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Vanzo, Alberto (2005) Kant's Treatment of the Mathematical Antinomies in the First Critique and in the Prolegomena: A Comparison. [Articolo di periodico (a stampa)]

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Abstract (inglese)

This paper deals with an apparent contradiction between Kant’s account and solution of the mathematical antinomies of pure speculative reason in the Critique of Pure Reason and in the Prolegomena. In the first Critique, Kant claims that the theses are affirmative judgements, of the form “A is B”, and the antitheses are infinite judgements, of the form “A is not-B”. The theses and the antitheses are contradictorily opposed (i.e., the one true and the other false). Their proofs are valid only if a certain condition takes places, that is, if the world has a determinate magnitude. Otherwise, they are both false, and their proofs are wrong. Given transcendental realism, this condition takes place and the mathematical antinomies arise. Given transcendental idealism, this condition does not take place, the theses and the antitheses are false, and the mathematical antinomies disappear. At a first glance, according to the Prolegomena, the theses are affirmative judgements and the antitheses are not infinite judgements, but negative judgements, of the form “A is not B”. Admitted transcendental idealism, the subject common to theses and antitheses, namely, the concept of “world”, is inconsistent. Both judgements are false by the rule “non entis nulla sunt praedicata” and the antinomies do not take place. These accounts seem to be incompatible with each other. Are the antitheses infinite or negative judgements? Are the antinomies solved because the world does not have a determinate magnitude, or because its notion is inconsistent?

The paper proves that the contrast between the first Critique and the Prolegomena is only apparent. It depends on an error in the most natural interpretation of the paragraphs on the mathematical antinomies in the Prolegomena. The paper offers a different interpretation, which removes the contrast with the Critique. The theses and the antitheses are false because their subject is inconsistent, as the Prolegomena maintain. Their proofs are wrong because the world has not a determinate magnitude, as the Critique claims.


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Tipo di EPrint:Articolo di periodico (a stampa)
Anno di Pubblicazione:2005
Parole chiave (italiano / inglese):Kant, antinomies, Critique of Pure Reason, Prolegomena
Settori scientifico-disciplinari MIUR:Area 11 - Scienze storiche, filosofiche, pedagogiche e psicologiche > M-FIL/06 Storia della filosofia
Area 11 - Scienze storiche, filosofiche, pedagogiche e psicologiche > M-FIL/01 Filosofia teoretica
Struttura di riferimento:Dipartimenti > Dipartimento di Filosofia
Codice ID:107
Depositato il:10 Lug 2007
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