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1

Is Transparent Intensional Logic a non-classical logic?

100%
Materna P.
Logic and Logical Philosophy
|
2014
|
vol. 23
|
issue 1
47–55
EN
It is shown that: (a) classicality is connected with various criteria some of which are fulfilled by TIL while some other are not; (b) some more general characteristic of classicality connects it with philosophical realism whereas (radical) anti-realism is connected with non-classical logics; (c) TIL is highly expressive due to its hyperintensionality, which makes it possible to handle procedures as objects sui generis. Thus TIL is classical in obeying principles of realism and non-classical in transcending some principles taught by textbooks of classical logic.
2

DENOTATION AND REFERENCE

100%
Materna P.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2010
|
vol. 17
|
issue 1
3-20
EN
The terms denotation and reference are commonly used as synonyms. A more fine-grained analysis of natural language as offered by 'Transparent Intensional Logic' (TIL) shows that we can distinguish these terms in the case of empirical expressions. The latter are shown to denote non-trivial intensions while their reference (if any) is the value of these intensions in the actual world.
3

Concepts as hyperintensional objects

100%
Materna P.
Logic and Logical Philosophy
|
2014
|
vol. 23
|
issue 2
133–170
EN
The author defends the view that the notion of concept, if used in the logical (not cognitivist) tradition, should be explicated procedurally (i.e., not set-theoretically). He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.
4

ON TICHÝ’S ATTEMPT TO EXPLICATE SENSE IN TERMS OF TURING MACHINES

100%
Materna P.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2018
|
vol. 25
|
issue 1
41 – 52
EN
In Tichý (1969), it is shown that semantics of natural language can be pursued procedurally. Tichý supported his argument by defining elementary functions of logic (truth functions, quantifiers) using Turing machines and attempting to define the sense of empirical expressions using a simple semantic version of oracle. From the way how Turing machines and later constructions are defined it follows that even the sense of empirical expressions can be successfully handled but that the sense and denotation can be in principle effectively obtained while the actual value at the actual world can be, of course, never computed. The present paper comments on this attempt and it compares the Turing machines argument with the possibilities given by TIL constructions. Turing machines guarantee the effective character of computing while the constructions do not, but expressive power of constructions is incomparably stronger, not only because Tichý’s possible worlds from 1969 are a temporal: they define essentially 1st order operations and can be reinterpreted as one possible world enjoying (discrete) temporal changes. Both the TM conception and the “constructivist” one know that the question “which possible world is the actual one” cannot be ever answered by effective (computational) methods and their analyses of empirical expressions are therefore compatible.
5

Can concepts be defined in terms of sets?

63%
Marie D., Materna P.
Logic and Logical Philosophy
|
2010
|
vol. 19
|
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.
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