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- Binder, David, et al.
(författare)
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The Logical Writings of Karl Popper
- 2022
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Bok (refereegranskat)abstract
- This open access book is the first ever collection of Karl Popper's writings on deductive logic.Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.
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| 2. |
- Eckert, Jörn, et al.
(författare)
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Einleitung
- 2004
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Ingår i: Juristische Fakultäten und Juristenausbildung im Ostseeraum: zweiter Rechtshistorikertag im Ostseeraum = Law faculties and legal education in the Baltic sea area: second Conference in Legal History in the Baltic Sea Area. - Uppsala : Kungl. Gustav Adolfs akademien för svensk folkkultur. - 9185190756 ; , s. 13-15, s. 9-12, s. 1-13, s. -357
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 6. |
- Olsson, Erik J, et al.
(författare)
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Meinen und Entscheiden
- 2004
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Ingår i: Logik in der Philosophie. - 3935025661 ; , s. 161-178
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 7. |
- Schroeder-Heister, Peter
(författare)
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Axiomatic Thinking, Identity of Proofs and the Quest for an Intensional Proof-Theoretic Semantics
- 2022
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Ingår i: Axiomatic Thinking I. - Cham : Springer International Publishing. ; , s. 145-163
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Starting from Hilbert’s Axiomatic Thinking, the problem of identity of proofs and its significance is discussed in an elementary proof-theoretic setting. Identifying two proofs, one of which is obtained from the other one by removing redundancies, leads, when used as a universal method, to a collapse of all proofs of a provable proposition into one single proof and thus trivialises proof identity. Principles of proof-theoretic harmony with restricted means of redundancy reduction might be used instead, though this limits one to a certain format of formal systems. The discussion of proof identity suggests the claim that annotations of proofs telling the reader which rule is applied at a particular step, must be considered part of the proof itself. As a general perspective, it is advocated that the investigation of intensional aspects of proofs should be given more space in proof theory and proof-theoretic semantics.
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| 9. |
- Widebäck, Filip, 1963-
(författare)
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Identity of proofs
- 2001
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the early seventies it was conjectured that a certain mathematically well-defined equivalence relation (bh-equivalence) on proofs in natural deduction captures the informal notion of identity of proofs. The conjecture can be divided into two parts, a soundness part and a completeness part. The soundness part is that bh-equivalent proofs are identical. The completeness part is that identical proofs are bh-equivalent. It is argued that soundness can not be mathematically proved. It must be taken for granted or rejected. Completeness, on the other hand, can not be taken for granted. It must be proved or disproved, although the question is not a mathematically precise question.The main result of this thesis is that the completeness part of the conjecture is true for the system of minimal implicational logic, provided that soundness can be taken for granted. The result is obtained by first proving that the notion of bh-equivalence is Post-complete. Roughly, if bh-equivalence is extended by a new schematic rule for identifying proofs, then all proofs of the same theorem are identical. In other words, there is only one schematic extension of bh-equivalence, the trivial equivalence relation that identifies all proofs of a theorem. It is then argued that the identity relation on proofs is non-trivial, i.e. that there are non-identical proofs. This proves the completeness part of the conjecture.The thesis also contains a new proof (for the above system) of so-called confluence and a conjecture characterizing bh-equivalence in a new way.
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