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1

DEDUCTION IN TIL: FROM SIMPLE TO RAMIFIED HIERARCHY OF TYPES

100%
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.
2

COMMUNICATION IN A MULTI-CULTURAL WORLD

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Duží M.
Organon F. medzinárodný časopis pre analytickú filozofiu
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2014
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vol. 21
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issue 2
198 – 218
EN
The goal of this paper is to demonstrate that procedurally structured concepts are central to human communication in all cultures and throughout history. This thesis is supported by an analytical survey of three very different means of communication, namely Egyptian hieroglyphs, pictures, and Inca knot writing known as khipu. The author ś thesis is that we learn, communicate and think by means of concepts; and regardless of the way in which the meaning of an expression is encoded, the meaning is a concept. Yet we do not define concepts within the classical set-theoretical framework. Instead, within the logical framework of Transparent Intensional Logic, we explicate concepts as logical procedures that can be assigned to expressions as their context-invariant meaning. In particular, complex meanings, which structurally match complex expressions, are complex procedures whose parts are sub-procedures. The moral suggested by the paper is this. Concepts are not flat sets; rather, they are algorithmically structured abstract procedures. Unlike sets, concepts have constituent sub-procedures that can be executed in order to arrive at the product of the procedure (if any). Not only particular parts matter, but also the way of combining these parts into one whole ‘instruction’ that can be followed, understood, executed, learnt, etc., matters.
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Procedurální sémantika TIL

100%
Duží M.
Filosofický časopis (Philosophical Journal)
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2016
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vol. 64
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issue 6
901-929
EN
In this contribution I focus on perhaps the most significant and, at the same time, the most revolutionary characteristic of Tichy’s transparent intensional logic (TIL), which is procedural semantics. Despite the fact that in the second half of the last century there was already a clear need for an explication of hyperintensionality – a structual explication, if possible – hyperintensionality was defined only in a negative way. Hyperintensionality is the kind of context in which the substitution of logically equivalent expressions fails and it is necessary to have a more refined distinction of meanings than one of mere equivalence. Tichý, however, not only defined hyperintensions positively as algorithmically-structured procedures, that is TIL constructions which are assigned to expressions as their context-invariant meanings, but at the same time he showed that in the framework of this system it can hopefully adequately solve all the problems which traditional PWS semantics of possible worlds could not deal with. In this article I demonstrate that structured procedures are the central element of our communication across various cultures, specialisations and time. At the same time, however, I outline the problems which this evidently plausible conception of meaning brings with it, and I propose a solution to them.
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