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1

TICHÝ’S TWO-DIMENSIONAL CONCEPTION OF INFERENCE

100%
Pezlar I.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2013
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vol. 20
|
issue suppl. 2
54 – 65
EN
In this paper we revisit Pavel Tichý’s novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege’s Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivation behind the introduction of this non-classical concept of inference, but also on further inspection of selected Tichý’s arguments, which we see as the most compelling or simply most effective in providing support for his two-dimensional account of inference. Main attention will be given to exposing the failure of one-dimensional theory of inference in its explanation of indirect (reductio ad absurdum) proofs. Lastly, we discuss shortly the link between two-dimensional inference and deduction apparatus of Tichý’s Transparent Intensional Logic.
2

PAVEL TICHÝ A TEORIE DEDUKCE

88%
Šebela K.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2013
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vol. 20
|
issue suppl. 2
66 – 74
EN
This paper focuses on the theory of deduction, developed by the Czech logician Pavel Tichý. Research on deduction in Tichý’s logic is still not very advanced. Tichý’s own deduction system is a generalization of Gentzen’s natural deduction and although it is an interesting topic in itself, I’d rather focus on the theory or philosophy of deduction that motivates Tichý’s choice of deduction system. Some of Tichý’s expressions suggest that in the question of the status of the theory of deduction in logic he held the prevailing modern approach, but this contradicts the fact that most of his writings concern selected problems of logical semantics. Having introduced Tichý’s original conception of deduction, I pay attention to the so called object-conception of logic, which explains the special position of the theory of deduction in his conception.
3

PREČO LEN (NUTNÉ) PRAVDY AKO PREDPOKLADY DEDUKTÍVNYCH ÚSUDKOV?

88%
Gahér F., Bielik L.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2013
|
vol. 20
|
issue suppl. 2
75 – 97
EN
The aim of the paper is to examine Tichý’s understanding of the term “assumption”. We show that Tichý distinguishes two approaches to inference: the one-dimensional view that treats inferences as a sequences of logical rules or axioms as well as hypotheses and their logical consequences; and the two-dimensional view specifying inference as a derivation of one entailment from (the set of) another entailment(s). It is claimed that Tichý is right in his critique of Meinong’s concept of assumption as ‘assertion without conviction’. Nevertheless, Tichý – in addition to his logical concept of assumption – uses, though unreflectively, also the epistemic concept of assumption. Henceforth, we claim that accepting Tichý’s rejection of the epistemic hypothetical assumptions we couldn’t use logic as an instrument for empirical knowledge enhancement. We believe, to the contrary, that the epistemic assumptions may become a basis for derivations and knowledge enhancement, even though they do not represent necessary truths.
4

EXPLIKACE A DEDUKCE: OD JENODUCHÉ K ROZVĚTVENÉ TEORII TYPŮ

88%
Raclavský J.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2013
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vol. 20
|
issue suppl. 2
37 – 53
EN
In the first part of the paper, the author argues that explicating systems which fall under the simple theory of types are limited in explicating our conceptual scheme. Such limitation is avoided if one utilizes, instead, a ramified type theory, especially the one developed by Pavel Tichý. In the third part of the paper, the author explains the role of so-called constructions and derivation systems within such a framework, elucidating how deduction demonstrates properties of objects.
5

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

88%
Materna P.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2018
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vol. 25
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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.
6

DEDUCTION IN TIL: FROM SIMPLE TO RAMIFIED HIERARCHY OF TYPES

75%
Duží M.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2013
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vol. 20
|
issue suppl. 2
5 – 36
EN
Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First the author briefly recapitulates the rules of simple-typed calculus as presented by Tichý. Then she proposes the adjustments of the calculus so that it will be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. She shows that operating in a hyperintensional context is far from being technically trivial. Yet it is feasible. To this end we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions.
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