Jaroslav Peregrin

The paper presents an argument against a "metaphysical" conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: "the realm of the natural", constituted by the things of our empirical world, and "the realm of the formal", constituted by the structures that we use as "prisms" to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic

Frege has proposed to consider names as denoting objects, predicates as standing for concepts and sentences as denoting truth values. He was, however, aware that such denotation does not exhaust all what is to be said about meaning. Therefore he has urged that in addition to such denotation (Bedeutung) an expression has sense (Sinn). The sense is the "way of presentation" of denotation; hence the expressions Morning Star and Evening Star have identical denotations, but different senses. Carnap has proposed to replace Frege's distinction between Sinn and Bedeutung by the distinction between intension and extension. Extension is, according to Carnap, what is shared by every two expressions which can be truthfully declared equivalent; where equivalence means a bit different things for different grammatical categories. In the formalism of the classical logic, the equivalence of two terms T1 and T2 is expressed by the formula T1=T2, that of two sentences ↔ ↔ S1 and S2 is by the formula S1↔ ↔S2, and that of two unary predicates P1 and P2 by the formula..

The relationships between logic and natural language are multiverse. On the one hand, logic is a theory of argumentation, proving and giving reasons, and such activities are primarily carried out in natural language. This means that logic is, in a certain loose sense, about natural language. On the other hand, logic has found it useful to develop its own linguistic means which sometimes in a sense compete with those of natural language. This has led to the situation where the systems of logic can be taken as interesting "models" of various aspects of natural language. Â Â Â Â Â Â Â The alliance of logic and linguistics has flowered especially from the beginning of the seventies, when scholars like Montague, Lewis, Cresswell, Partee and others showed how semantics of natural language can be explicated with the help certain suitable logical calculi and the corresponding model theory. (Montague went so far as to claim that in view of this, there is no principal difference between natural and formal languages - but this is, as far as I can see, rather misguiding.) Since that time, the interdisciplinary movement of formal semantics (associating not only linguists and logicians, but also philosophers, computer scientists, cognitive psychologists and others) has yielded a rich repertoire of formal theories of natural language, some of them (like Hintikka's game-theoretical semantics or the dynamic logic of Groenendijk and Stokhof) being based directly on logic, others (like the situation semantics of Barwise and Perry or DRT of Kamp) exploiting different formal strategies. Â Â Â Â Â Â Â Moreover, although the enterprise of formal semantics (i.e. of modeling natural language semantics by means of certain formal structures) seems to be the principal point of contact between linguistics and logic, there are also other cooperative enterprises. One of the most fruitful ones seems to be the logical analysis of syntax, which has resulted from elaboration of what was originally called categorial grammar. (However, even this enterprise can be seen as importantly stimulated by Montague.) Â Â Â Â Â Â Â All in all, the region in which logic and theoretical linguistics overlap has grown both in size and fertility..

The article addresses two closely related questions: What are the criteria of adequacy of logical formalization of natural language arguments, and what gives logic the authority to decide which arguments are good and which are bad? Our point of departure is the criticism of the conception of logical formalization put forth, in a recent paper, by M. Baumgartner and T. Lampert. We argue that their account of formalization as a kind of semantic analysis brings about more problems than it solves. We also argue that the criteria of adequate formalization need not be based on truth conditions associated with logical formulas; in our view, they are better based on structural (inferential) grounds. We then put forward our own version of the criteria. The upshot of the discussion that follows is that the quest for an adequate formalization in a suitable logical language is best conceived of as the search for a Goodmanian reflective equilibrium

A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. These are 'natural' concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descendants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called formally sound and complete iff it proves all and only formulas valid in this sense. Though the step from material to formal validity and completeness may seem to be merely an unproblematic case of explication, I argue that it is not; and that mistaking the latter concepts for the former ones may lead to serious conceptual confusions.

Existuje obrovské množství definic logiky; avšak je tu jistá jednotící myšlenka, která se proplétá většinou z nich, a to je ta, že logika nám má pomoci klasifikovat úsudky, způsoby argumentace či důkazy na „správné“ a „nesprávné“, a tímto způsobem nám má pomoci lépe „usuzovat“. A protože úsudek či argumentační schéma je věcí kroku od nějakých premis k nějakému závěru a jeho správnost můžeme vyjadřovat také tak, je jeho závěr odvoditelný z jeho premis či z nich vyplývá . Toto úzké pojetí logiky nás vede přímo k jejímu modernímu chápání jakožto zkoumání vyplývání či odvoditelnosti. Nazvěme takové kritické zkoumání argumentací, úsudků či odvození základní agendou logiky

Saul Kripke ’s book Naming and Necessity (which first appeared in 1972 as a paper within a volume on natural language semantics1) is felt, by many linguists and philosophers, as a milestone of the semantic analysis of natural language. Prior to it, many semanticists took for granted that the meaning of any expression must be a two-level matter, consisting of something of the kind of what Frege called Sinn and Bedeutung or what Carnap christened as intension and extension. The first of the components is what the speaker knows when she understands the expression (and the knowledge of which is independent of any knowledge of facts external to the language in question), while the second amounts to some kind of chunk of the real world which gets denoted or referred to by the expression. Thus, the intension of the king of France is what you get to know as soon as you come to understand the phrase, and the extension is what (if anything) happens to be picked out by the intension in the actual world in the actual moment. This is to say that an expression gets to into the contact with its extension only via the intension (which we can imagine also as a kind of a criterion for picking up the thing). Intension, then, is what amounts to the meaning of the expression in the intuitive sense of the word2. Now Kripke’s considerations challenged this very two-level structure of meaning: he argued that especially proper names get their semantics via a direct, inmediated contact with the world – that their meaning does not mediate their contact with a thing, but directly is the thing. This may be not so surprising in case of proper names (after all, it is even disputable whether they can be counted to the language – for you cannot find them in dictionaries), but Kripke went on to argue that the same holds also for some other expressions, especially natural kind terms such as “cow” or “water”. Kripke’s argumentation is concise and flattening; and it has been provoking a lot of discussions..

V knize konfrontuji běžné pojetí jazyka, podle kterého je význam záležitostí vztahu slovo-věc, se strukturalistickým pohledem, podle kterého význam nemůže existovat bez toho, aby byly výrazy určitým způsobem provázány mezi sebou. Ukazuji, že takový strukturalismus není jen věcí Ferdinanda de Saussura, ale že se vyskytuje (pod jménem holismus) i v základech (post)analytické filosofie Quina, Davidsona, Sellarse a Brandoma. Ukazuji také, že není neslučitelný s formálně-logickým přístupem k významu, jaký byl rozpracován Carnapem, Montaguem a dalšími.

The beginning of this century hailed a new paradigm in linguistics, the paradigm brought about by de Saussure's Cours de Linguistique Genérále and subsequently elaborated by Jakobson, Hjelmslev and other linguists. It seemed that the linguistics of this century was destined to be structuralistic. However, half of the century later a brand new paradigm was introduced by Chomsky's Syntactic Structures followed by Montague's formalization of semantics. This new turn has brought linguistics surprisingly close to mathematics and logic, and has facilitated a direct practical exploitation of linguistic theory by computer science

Analytic philosophy is based on the assumption that our world is a world grasped in terms of (this or another) language and that the question of the character of any entity is closely connected with the question of the linguistic grasp of that entity. The father of this philosophical trend was Gottlob Frege: he showed the way to capture the semantic aspect of language in a systematic way without resorting into psychologism; he also showed that logical analysis can be an extremely powerful tool for capturing meaning. Frege's teaching was further developed by Bertrand Russell, Rudolf Carnap, Ludwig Wittgenstein, Willard Van Quine and other philosophers. This philosophy, in connection with which the term linguistic turn is also often mentioned, is characterized by viewing language as a means of picturing the world and truth as the correspondence between statement and reality. Whereas some of the analytic philosophers (Carnap, Alfred Tarski) understood the relation between language and the world as a matter of a better or worse adaptation of the structure of language to the autonomous structure of the world, others (Wittgenstein, Quine, Nelson Goodman) realized that the structure of the world is always a matter of the language we use approaching the world