Marie Duží

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the premises, it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information.

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical, provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional.

In 1905 Bertrand Russell took on the problem of definite descriptions, and his analysis became the standard up until 1950 when Peter Strawson criticised Russell’s solution as inadequate. Since then many opponents as well as proponents of the Russellian solution have been involved in a long-term debate on definite descriptions. In this paper I show that both sides of the contention are partly right and partly wrong, because sentences of the form “The F is a G” are ambiguous. However, the ambiguity does not concern reference shift of the description ‘the F’. Rather, the ambiguity consists in different topic-focus articulations of a given sentence involving occurrences of ‘the F’. I demonstrate that when ‘the F’ is used as part of the topic of such a sentence the existence of the object denoted by ‘the F’ is not only entailed by but also presupposed by the sentence. On the other hand, ‘the F’ used in the focus of a sentence triggers merely existential entailment. Thus sentences differing only in their topic-focus articulation should have assigned different logical forms. In order to make such hidden features explicit, I apply the procedural semantics of Transparent Intensional Logic, furnishing sentences with hyperpropositions that are precisely defined in terms of TIL constructions. These are procedures assigned to sentences as their context-invariant structured meanings. Moreover, I generalise the phenomenon of the topic-focus distinction to sentences of any form, proposing an adequate analytic schema of sentences that come with a presupposition.

V příspěvku podávám přehled vývoje logické sémantiky se zřetelem zejména na vý­voj Tichého Transparentní intenzionální logiky (TIL) od pozdních šedesátých let až do­dnes, a na ní vystavěné Maternovy logické teorie pojmu. Článek si neklade za cíl podat vyčerpávající historický přehled, nýbrž soustřeďuje se na podíl česko-slovenské logické školy a ukazuje, že tento podíl je nezanedbatelný. Navíc je však tento přehled zároveň i kritický. Ukazuje silné stránky logického rámce TIL, ale zároveň upozorňuje na někte­ré diskutabilní stránky či otevřené problémy, které zůstávají zejména právě v procedu­rální teorii pojmu. Z nich nejpalčivějším je problém procedurální identity pojmu, a tím také kritéria synonymie.

In the paper we offer a logical explication of the frequently used, but rather vague, notion of point of view. We show that the concept of point of view prevents certain paradoxes from arising. A point of view is a means of partial characterisation of something. Thus nothing is a P and at the same time a non-P, because it is a P only relative to some point of view and a non-P from another point of view. But there is a major, complicating factor involved in applying a logical method that is supposed to provide a formal and rigorous counterpart of the intuitively understood notion: ‘point of view’ is a homonymous expression, and so there is not just one meaning that would explain points of view. Yet we propose a common scheme of the logical type of the entities denoted by the term ‘point of view’. It is an empirical function: when applied to the viewed object in question, it results in a evaluating proposition about the object. If there is an agent applying the criterion, the result is the agent’s attitude to the respective object. The paper is organised into two parts. In Part I we first adduce and analyse various examples of typical cases of applying a point of view to prevent paradox. These cases are examined according to the type of the viewed object: a) the viewed object is an individual and b) the viewed object is a property or an office. In Part II we then show that the method described in Part I can be applied also to the analyses of agents’ attitudes. We explain how an agent can believe of something that it is a P and at the same time a non-P: the agent applies different viewpoint criteria to the viewed object. The inversion of perspective consisting in the perspective shifting from the believer on to the reporter in the case of attitudes de re, and from the reporter to the believer in the case of attitudes de dicto, is also analyzed. We show that there is no smooth logical traffic back and forth between such attitudes unless some additional assumptions are added, and prove that they are not equivalent. By way of conclusion, we explicate the notion of conceptual point of view and analyze cases of viewpoints given by conceptual distinction. We show, finally, that the proposed scheme of the type of point of view can be preserved, this time, however, in its extensional version.

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, I briefly recapitulate the rules of simple-typed calculus as presented by Tichý. Then, I propose the adjustments of the calculus so that it 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. I show 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.

The problem of the meaning of a reasonable natural language expression is solved. First, traditional ”denotational” approach is criticized. The meaning of a sentence is not its truth value, similarly the meaning of, eg, ”The president of U.S.A.” is not Bill Clinton, etc. Frege met this problem when analyzing the so called propositional attitudes in which ”denotational” approach has lead to the paradox of analysis. His well-known solution consists in splitting the meaning into sense and reference. But this is rejected in the paper as well, for its radical contextualism. In the first attempt, meaning is defined as an intension — mapping from possible worlds and time points — or extension, respectively. The problem of the propositional attitudes is seemingly solved. The proposition that Morning Star = Evening Star is diffe_rent than that of Morning Star = Morning Star. But, alas, in the case of analytical expressions we get the paradox of omniscience. A fine-grained solution is, therefore, proposed: the meaning is a closed construction denoted by the respective expression. Yet this solution is still not precise enough. Eventually the meaning is a concept which is the equivalence class of quasi-identical constructions indiscernible from the conceptual point of view. Finally, homonymous, synonymous and equi_valent expressions are precisely defined. Concluding we state that only synonymous expressions, having exactly the same meaning, ie. representing one and the same concept, can be mutually substituted in propositional attitudes without lea_ding to paradoxes.

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.