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. (shrink)
On the one hand, Pavel Tichý has shown in his Transparent Intensional Logic (TIL) that the best way of explicating meaning of the expressions of a natural language consists in identification of meanings with abstract procedures. TIL explicates objective abstract procedures as so-called constructions. Constructions that do not contain free variables and are in a well-defined sense ´normalized´ are called concepts in TIL. On the second hand, Kolmogorov in (Mathematische Zeitschrift 35: 58–65, 1932) formulated a theory of problems, using NL (...) expressions. He explicitly avoids presenting a definition of problems. In the present paper an attempt at such a definition (explication)—independent of but in harmony with Medvedev´s explication—is given together with the claim that every concept defines a problem. The paper treats just mathematical concepts, and so mathematical problems, and tries to show that this view makes it possible to take into account some links between conceptual systems and the ways how to replace a noneffective formulation of a problem by an effective one. To show this in concreto a wellknown Kleene’s idea from his (Introduction to metamathematics. D. van Nostrand, New York, 1952) is exemplified and explained in terms of conceptual systems so that a threatening inconsistence is avoided. (shrink)
To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable (...) as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. (shrink)
Buzaglo (as well as Manders (J Philos LXXXVI(10):553–562, 1989)) shows the way in which it is rational even for a realist to consider ‘development of concepts’, and documents the theory by numerous examples from the area of mathematics. A natural question arises: in which way can the phenomenon of expanding mathematical concepts influence empirical concepts? But at the same time a more general question can be formulated: in which way do the mathematical concepts influence empirical concepts? What I want to (...) show in the present paper can be described as follows. The problem articulated by Buzaglo deserves some semantic refinements. Following explications are needed: What is meaning? (In particular: What are concepts?) What are questions? (Or, equivalently: Semantics of interrogative sentences.) -/- Further, a useful notion will be the notion of problem. Taking over the notion of conceptual system from Materna (Conceptual Systems. Logos, Berlin, 2004) and using Tichý’s Transparent intensional logic (TIL) I can try to solve the problem of the relation between mathematical and empirical concepts (not only for the case of expanding some mathematical concepts). (shrink)
I argue that Hume’s and Carnap’s criticism of philosophy (meta-physic) 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.
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. (shrink)
If concepts are explicated as abstract procedures, then we can easily show that each empirical concept is a not an effective procedure. Some, but not all empirical concepts are shown to be of a special kind: they cannot in principle guarantee that the object they identify satisfies the intended conditions.
Problems are defined as abstract procedures. An explication of procedures as used in Transparent Intensional Logic (TIL) and called constructions is presented and the subclass of constructions called concepts is defined. Concepts as closed constructions modulo α- and η-conversion can be associated with meaningful expressions of a natural or professional language in harmony with Church’s conception. Thus every meaningful expression expresses a concept. Since every problem can be unambiguously determined by a concept we can state that every problem is a (...) concept and every concept can be viewed as a problem.Kolmogorov’s idea of a connection between problems and Heyting’s calculus is examined and the non-classical features of the latter are shown to be compatible with realistic logic using partial functions. (shrink)
The modern (Russellian) theory of definition conceives definitions as abbreviations, so that the question of adequateness (let alone of truth-value) of definitions becomes meaningless. In this paper we show that beside Russellian conception of definitions understood as abbreviations, there is an Aristotelian conception, which exploits the notion of essence and that this conception can be rehabilitated from the standpoint of the modern logic (in particular by means of Pavel Tichý’s Transparent Intensional Logic). Also Carnap’s ‘explication’ indicates that what we feel (...) to be a definition is frequently distinct from a Russellian definition. (shrink)
The boundary between analytic and synthetic sentences is well definable. Quine’s attempt to make it vague is based on a misunderstanding: instead of freeing semantics from shortcomings found, e.g. in Carnap’s work, Quine actually rejects semantics of natural language and replaces it by behavioristically articulated pragmatics. Semantics of natural language as a logical analysis is however possible and it can justify hard and fast lines between analyticity and syntheticity.
In [Laurence, Margolis 2003] the authors try - within their polemics against F.Jackson’s views in [Jackson 1998] - to decide the question whether concepts are a priori (in their formulation “to be defined a priori”). Their discussion suffers - as a number of similar articles - from a typical drawback: some problem whose solution requires an exact notion of concept is handled as if the latter were quite clear. The consequence of this ‘conceptual laxity’ is that a) the topic of (...) the discussion is not very clear (what does the phrase ‘concepts must be defined a priori’ mean?); b) the relevance of the Quinean criticism of the “second dogma of empiricism”, i.e., of Quine’s claim that “science sometimes overturns our most cherished beliefs” and therefore there is no sharp boundary between analytic and synthetic is uncritically accepted; c) no distinction is made between the question whether the relation between an expression and its meaning is a priori and the question whether the relation between a concept and the object identified by the concept is a priori. The present article intends to elucidate and then to answer the questions that can be asked when we say something like “concepts are a priori ”. (shrink)
This paper defendsintensional essentialism: a property (intensional entity) is not essential relative to an individual (extensional entity), but relative to other properties (or intensional entities). Consequently, an individual can have a property only accidentally, but in virtue of having that property the individual has of necessity other properties. Intensional essentialism is opposed to various aspects of the Kripkean notion of metaphysical modality, eg, varying domains, existence as a property of individuals, and its category of properties which are both empirical and (...) essential with respect to particular individuals and natural kinds. The key notion of intensional essentialism isrequisite. A requisite is explicated as a relation-in-extension between two intensions (functions from possible worlds and moments of time)X, Y such that wherever and wheneverX is instantiatedY is also instantiated. We predict three readings of the sentence. Every wooden table is necessarily wooden , one involving modalityde re and the other two modalityde dicto. The first reading claims that no individual which is a wooden table is necessarily wooden. The claim is backed up by bare particular anti-essentialism. The two other interpretations claim that it is necessary that whatever is a wooden table is wooden. However, as we try to show, one is logically far more perspicuous thanks to the concept of requisite and thus preferable to more standardde dicto formalizations. (shrink)
Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).
There is a distinctive kind of command, namely commands to answer specific questions. An imperative sentence denoting such a command has an interrogative sentence corresponding to it-a sentence denoting the respective question. LetImp, Int, andQ be such an imperative sentence, the interrogative sentence corresponding to it, and the question denoted by the interrogative sentence, respectively.LetQ be an empirical question, i.e., and ((ητ)ω)-object. LetP be an ((ητ)ω)-construction constructingQ. Then the analysis ofImp has the form (QL).LetQ be an analytical question, i.e., a (...) molecular extensional η-construction. LetQ=C, whereC is a ℊ-object (over the extended base). Then the analysis ofImp has the form (QL′).The imperative sentences whose analyses have the form (QL) or (QL′) can be called ‘question-like imperative sentences’ or simply ‘QL-imperative sentences’.No imperative sentence whose analysis differs from (QL) and (QL\t') can be associated with a question. Therefore, no transformation of such an imperative sentence should result in a correct interrogative sentence.Fulfilling an order which is determined by a QL-imperative sentenceImp, one simultaneously gives the right answer to the questionQ (which is associated withImp). One who does not fulfil this order either wrongly answersQ or does not answerQ at all. (shrink)
The author tries to formulate what a determinist believes to be true. The formulation is based on some concepts defined in a systems-theoretical manner, mainly on the concept of an experiment over the sets A m (a set of m-tuples of ‘input values’) and B n (a set of n-tuples of ‘output values’) in the time interval (t 1, ..., t k ) (symbolically E[t 1,..., t k , A m , B n ]), on the concept of a behavior (...) of the system S m,n (=(A m , B n )) on the basis of the experiment E[t 1, ..., t k , A m , B n ] and, indeed, on the concept of deterministic behavior .... The resulting formulation of the deterministic hypothesis shows that this hypothesis expresses a belief that we always “could find” some “hidden parameters”. (shrink)