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1

Science – Logic – Philosophy. An old problem resuscitated

100%
Materna P.
Logic and Logical Philosophy
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2012
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vol. 21
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issue 2
107-126
EN
I argue that Hume’s and Carnap’s criticism of philosophy (metaphysic) contains a rational core and that this core can be much more sharply formulated as soon as a procedural theory of concepts is applied. Also, a possible solution to the problem can be suggested in a much more definite manner.
2

On the interaction of semantics and deduction in Transparent Intensional Logic (Is Tichý's logic a logic?)

100%
Raclavský J.
Logic and Logical Philosophy
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2014
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vol. 23
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issue 1
57–68
EN
It is sometimes objected that Tichý’s logic is not a logic because it underestimates deduction, providing only logical analyses of expressions. I argue that this opinion is wrong. First of all, to detect valid arguments, which are formulated in a language, there needs to be logical analysis to ascertain which semantical entities (Tichý’s so-called constructions) are involved. Entailment is defined as an extralinguistic affair relating those constructions. The validity of an argument, composed of propositional constructions, stems from the properties of the constructions. Such properties are displayed by the derivation rules of Tichý’s system of deduction.
3

Can concepts be defined in terms of sets?

100%
Marie D., Materna P.
Logic and Logical Philosophy
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2010
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vol. 19
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issue 3
195–242
EN
The goal of this paper is a philosophical explication and logical rectification of the notion of concept. We take into account only those contexts that are relevant from the logical point of view. It means that we are not interested in contexts characteristic of cognitive sciences, particularly of psychology, where concepts are conceived of as some kind of mental objects or representations. After a brief recapitulation of various theories of concept, in particular Frege’s and Church’s ones, we propose our own theory based on procedural semantics of Transparent Intensional Logic (TIL) and explicate concept in terms of the key notion of TIL, namely construction viewed as an abstract, algorithmically structured procedure.
4
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Algorithmic Theories of Problems. A Constructive and a Non-Constructive Approach

88%
Pezlar I.
Logic and Logical Philosophy
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2017
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vol. 26
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issue 4
473–508
EN
In this paper we examine two approaches to the formal treatment of the notion of problem in the paradigm of algorithmic semantics. Namely, we will explore an approach based on Martin-Löf’s Constructive Type Theory (CTT), which can be seen as a direct continuation of Kolmogorov’s original calculus of problems, and an approach utilizing Tichý’s Transparent Intensional Logic (TIL), which can be viewed as a non-constructive attempt of interpreting Kolmogorov’s logic of problems. In the last section we propose Kolmogorov and CTT-inspired modifications to TIL-based approach. The focus will be on non-empirical (i.e., mathematical and logical) problems only.
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