Pavel Materna

Procedural Semantics for Hyperintensional Logic

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds of linguistic context in a fully compositional and anti-contextual way.

Are wooden tables necessarily wooden? : Intensional essentialism versus metaphysical modality ()

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.

Rules of Existential Quantification into "Intensional Contexts"

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’).

The Notion of Problem, Intuitionism and Partiality

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.

Once More on Analytic vs. Synthetic

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.

‘Parmenides principle’ (The analysis of aboutness)

A explication of aboutness (principle of subject matter) within transparent intensional logic.

Can concepts be defined in terms of sets

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.

Applying simple theory of types to data bases

Abstract Whereas the logical apparatus used for formulation and solution of problems connected with the data base systems is mostly a 1st order logic, here a modified version (“T-system”) of Churchs simple theory of types is used. It is shown that the T-system 1. (a) is a more adequate tool for analyzing natural language , which may be important when one builds up an abstract model of a fragment of reality and when one creates a suitable philosophy of data base systems; 2. (b) has greater expressive power than the 1st order systems, which enables, e.g. to distinguish between queries according to what is the structure of the required answer, and moreover, not to be restricted by the well-known limitations of the 1st order logics; 3. (c) is based on the notion of function as on the most fundamental notion, which makes it possible to deal more directly with functional dependencies and to exploit more universally the key importance of the attribute concept; 4. (d) by using the concept of construction offers a good tool for E-C mapping and for forming query languages that are more universal than the current ones. The analysis of these properties of the T-system is accompanied by examples from the area of the data base systems theories; especially, a comparison with Codds domain relational calculus and with Chens and Pirottes approaches is made. No problem of implementation is touched in this paper.

Properties of mathematical objects (Gödel on classes, properties and concepts)

In terms of a sufficiently fine-grained theory we should distinguish between classes, properties and concepts. Since properties are best modeled as a kind of non-trivial intensions while mathematical objects are never non-trivial intensions we should not speak about properties of mathematical objects. When we do use the term property in mathematics (as Godel did) we either mean classes, or the more fine-grained entities to be called concepts. In the latter case concepts have to be defined so that various distinct concepts could identify one and the same object. The notion of construction in transparent intensional logic makes it possible to construe concepts as abstract procedures. At the same time we have to distinguish between this notion and the notion of construction in constructivist systems: the former – unlike the latter – are objective and, therefore, acceptable for a realist. 03A05, 00A30

Quine’s criticism of the “First dogma of empiricism”

Quine’s argumentation is shown to be invalid since its conclusion would need one premise more; such a premise is shown to be false.