In his table of judgements, Kant added infinity as a third quality. An infinite judgement ‘All S are non-P’ is said to differ from the affirmative ‘All S are P’ because it ascribes a negative predicate; and it differs from the negative ‘No S is P’ because it has a richer content. The present paper puts three interpretations of this surplus content to six tests. Among other things, it is examined whether these interpretations marry up with Kant’s solution to the (...) first antinomy, his conception of analyticity and the principle of complete determination. The unpleasant conclusion is that none of the interpretations can make its mark as the most adequate one. It thus remains unclear what Kant had in mind when positioning infinite judgements besides affirmative and negative ones. (shrink)

Kant distinguishes concept negation from copula negation. While the latter results in a negative judgement, i.e. a judgement denying a property of certain objects, the former gives rise to a negative concept, such as ‘immortal’. Since Kant’s remarks on concept negation are scattered and inconclusive, five interpretations are worked out and put to the test: logical negation, pseudo-negation, attribution of a zero degree, possibility-restricted negation and genus-restricted negation. Whereas the first four interpretations fail for a number of reasons, genus-restricted negation (...) turns out to be tenable. (shrink)

In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known as analytical (...) philosophy. This paper identifies three Bolzanian theoretical innovations that warrant his inclusion in the analytical tradition: the commitment to ‘logical realism’, the adoption of a substitutional procedure for the purpose of defining logical properties and a new theory of a priori cognition that presents itself as an alternative to Kant's. All three innovations concur to deliver what counts as the most important development of logic and its philosophy between Aristotle and Frege. In the final part of the paper, I defend Bolzano against a common objection and explain that these theoretical innovations are also supported by views on syntax, which though marginal are both workable and philosophically interesting. (shrink)

In his booklet "Contributions to a better founded presentation of mathematics" of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...) account of the fragmentary logic of Beyträge, and it shows that there is a tension between that logic and Bolzano's methodological ban on ?kind crossing? (shrink)