This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

In this paper, I provide a thorough discussion and reconstruction of Bernard Bolzano’s theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano’s proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out between Bolzano’s (...) ideas on grounding and cut-free proofs in Gentzen’s sequent calculus. My thesis is, however, that they bear an even stronger resemblance to the normal natural deduction proofs employed in proof-theoretic semantics in the tradition of Dummett and Prawitz. (shrink)

Lecture notes from Husserl's logic lectures published during the last 20 years offer a much better insight into his doctrine of the forms of meaning than does the fourth Logical Investigation or any other work published during Husserl's lifetime. This paper provides a detailed reconstruction, based on all the sources now available, of Husserl's system of logical grammar. After having explained the notion of meaning that Husserl assumes in his later logic lectures as well as the notion of form of (...) meaning as it features in ‘doctrine of the forms of meaning’, I present a system of rules that describes all the various forms of meaning that Husserl singles out in his lectures. (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)

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)

In his earlyContributions to a Better-Grounded Presentation of Mathematics Bernard Bolzano tries to characterizerigorous proofs.Rigorousis,prima facie, any proof that indicates the grounds for its conclusion. Bolzano lists a number of methodological constraints all rigorous proofs should comply with, and tests them systematically against a specific collection of elementary inference schemata that, according to him, are evidently of ground-consequence-kind. This paper intends to give a detailed and critical account of the fragmentary logic of theContributions, and to point out as well some (...) difficulties Bolzano’s attempt runs into, notably as to his methodological ban on ‘kind crossing’. (shrink)

This paper analyzes and evaluates Bolzano's remarks on the apagogic method of proof with reference to his juvenile booklet "Contributions to a better founded presentation of mathematics" of 1810 and to his ?Theory of science? (1837). I shall try to defend the following contentions: (1) Bolzanos vain attempt to transform all indirect proofs into direct proofs becomes comprehensible as soon as one recognizes the following facts: (1.1) his attitude towards indirect proofs with an affirmative conclusion differs from his stance to (...) indirect proofs with a negative conclusion; (1.2) by Bolzano's lights arguments via consequentia mirabilis only seem to be indirect. (2) Bolzano does not deny that indirect proofs can be perfect certifications (Gewissmachungen) of their conclusion; what he denies is rather that they can provide grounds for their conclusions. (2.1) They cannot do the latter, since they start from false premises and (2.2) since they make an unnecessary detour. (3) The far-reaching agreement between his early and late assessment of apagogical proofs (in the Beyträge of 1810 and the Wissenschaftslehre of 1837) is partly due to the fact that he develops his own position always against the background of Wolff's and Lambert's views. (shrink)

In Section 1, the author argues that Bolzano does not have a Meinongian view of merely possible objects, not even in the context of his theory of intentionality. In section 2, it is argued that Williamson’s necessitist conception, according to which there is a merely possible golden mountain, was not anticipated by Bolzano. An eternalist reconstruction is rejected as well. The argument takes recourse to Bolzano’s semantics of temporal statements, which also underlies his argument for the eternity of substances and (...) makes it plausible to assume that Bolzano had a perdurantist view, according to which there are merely possible objects just in case there are actual objects whose generation is to be metaphysically explained, in terms of grounding, by recourse to a merely possible object’s being replaced by an actual object. Furthermore, it is argued that merely possible objects à la Bolzano are not substances, in his narrow sense of the term, and that his case for such objects in connection with his view of generation is less than convincing. However, section 3 argues that Bolzano’s conception combines with his view of substance to yield an interesting perdurantist conception of personal identity. (shrink)