Jaroslav Peregrin

Ve svém článku ‘Je elementární logika totéž co predikátová logika prvního řádu?’ (Pokroky matematiky, fyziky a astronomie 42, 1997, 127-133) klade Jiří Fiala nesmírně zajímavou otázku, zda je opodstatněné ztotožňovat elementární logiku s predikátovou logikou prvního řádu; s pomocí argumentů propagovaných již delší dobu finským logikem a filosofem Jaako Hintikkou (viz již jeho Logic, Language-Games and Information, Clarendon Press, Oxford, 1973; nejnověji jeho The Principles of Mathematics Revisited, Cambridge University Press, Cambridge, 1996) naznačuje, že by tomu tak být nemuselo. Myslím, že uváděná argumentace stojí za bližší rozbor. Hintikka v podstatě říká: Kvantifikované formule predikátové logiky jsou svou podstatou o vybírání prvků z univerza; například ∀x∃yR(x,y) neříká nic jiného než to, že ke každému x můžeme vybrat y, které je k němu ve vztahu R. Obecněji říká Hintikka to, že každá formule je vlastně zápisem určité hry (ve smyslu matematické teorie her), jejíž některé tahy spočívají ve vybírání individuí. Na základě tohoto se pak ptá: je nějaký rozumný důvod, proč se omezovat jenom na hry toho typu, které jsou vyjádřitelné formulemi standardního predikátového počtu? Proč připouštět jen hry s úplnou informací (tj. ty, při kterých jsou při každém tahu k dispozici všechny tahy předchozí), proč vylučovat hry jiné; tudíž proč připouštět jen lineárně uspořádané kvantifikátory, a nepřipustit i kvantifikátory uspořádané třeba jen částečně? Hintikkova argumentace je příkladem argumentace typu formule logiky prvního řádu jsou ve skutečnosti o tom a o tom, tudíž ... . Uveďme pro ilustraci jiný nedávný příklad stejného argumentačního schématu, který pochází od Johana van Benthema (Exploring Logical Dynamics, CSLI, Stanford, 1997). Ten říká: Kvantifikátory jsou v podstatě modality, kvantifikované formule jsou tedy formule modální a jsou tudíž o existenci nějakých alternativ: formule ∀xP(x) říká, že P(x) je nutné, neboli že P(x) platí v každém „dosažitelném možném stavu věcí“, zatímco formule ∃xP(x) říká, že P(x) je možné, neboli že platí alespoň v jednom takovém stavu věcí..

In this paper we first propose an exact definition of the concept of inferential role, and then go on to examine the question whether subscribing to inferentialism necessitates throwing away existing theories of formal semantics, as we know them from logic, or whether these could be somehow accomodated within the inferentialist framework. The conclusion we reach is that it is possible to make an inferentialist sense of even those common semantic theories which are usually considered as incompatible with inferentialism, such as the standard semantics of second-order logic.

When Bob Brandom, six years after publishing his opus magnum Making it explicit (hereafter MIE)1, produced his slender Articulating reasons2, many people expected that finally they would have a concise introduction to his philosophical views. Their expectations, however, were to be dashed: Articulating reasons is a heterogeneous collection of texts elaborating on some of the topics of MIE and hardly digestible without the background of MIE3. As yet, Brandom has produced nothing that could be taken as introductory. His subsequent books are either collections of essays addressing topics contained in or connected with MIE (Tales of the mighty dead4, Reason in Philosophy5 or the not yet published Perspectives on Pragmatism6), or engaged with Brandom's new philosophical doctrine, viz. analytic pragmatism, which is the case of Between Saying and Doing7. The last one, of course, is not unrelated to MIE, but it emphasizes different aspects of the enterprise; hence it is unlikely to pave the way to MIE for a perplexed reader. Until recently I was convinced that no readable introduction to Brandom's views therefore existed. Now I see I was mistaken. Though I knew that there was a book devoted to Brandom, by Jeremy Wanderer, I suspected it was more of a scientific biography than an introduction to the inferentialism of MIE; but in fact it is precisely the book I was missing: a congenial and comprehensible introduction to the ideas of Brandom's MIE. Hurrah!, a book my students, desperately wrestling with MIE, can be referred to!

The paper addresses foundational questions concerning the dynamic semantics of natural language based on dynamic logic of the Groenendijko-Stokhofian kind. Discussing a series of model calculi of increasing complexity, it shows in detail how the usual semantics of dynamic logic can be seen as emerging from the account for certain inferential patterns of natural language, namely those governing anaphora. In this way, the current ‘dynamic turn’ of logic is argued to be reasonably seen not as the product of changing the focus of logic from the relation of entailment to „a structure of human cognitive action“ (van Benthem), but rather as merely another step in our long-term effort to master more and more inferential patterns.

Th is review article discusses Rebecca Kukla and Mark Lance’s (2009) book on normative speech act theory and Joseph Heath’s (2008) book on rule following, putting them into the context of the general problem of normativity of human discursive practices (and human practices in general). Th e upshot of the discussion is that while Heath’s book advances our understanding of the normative dimension of human life, prominently including human language, Kukla and Lance’s one presents a deeply interesting attempt at a framework for the study of discourse taking normativity of language at face value

This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language.

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

Though, at first sight, logical formalization of natural language sentences and arguments might look like an unproblematic enterprise, the criteria of its success are far from clear and, surprisingly, there have only been a few attempts at making them explicit. This paper provides a picture of the enterprise of logical formalization that does not conceive of it as a kind of translation from one language (a natural one) into another language (a logical one), but rather as a construction of a 'map' of (a piece of) the 'inferential landscape' of the natural language. The criteria that appear to govern the enterprise are labeled as those of reliability, ambitiousness, transparency and parsimony. These criteria, it is argued, do not provide for an excavation of a ready-made logical structure, but rather help us achieve a "reflective equilibrium" between the normative authority of logic and the answerability of logic to a natural language

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..

The “dynamic turn” in semantic theory of natural language, which has been taking place roughly during the last decade, has resulted into seeing the meaning of a sentence as a “context-change-potential”, as a function which maps the set of possible contexts on itself. The development of theories of this kind has been stimulated especially by the effort to semantically cope with the anaphoric items of natural language . The most significant species of dynamic semantic theories are represented by Kamp´s “discourse representations theory” and Groenendijk and Stokhof´s “dynamic logic”. The former sees sentences as means of building and rebuilding “discourse representations structures”; the latter, which tries to be an expressly logical objects to “discourse markers” into the same set. The paper presents basic principles of theories of both of these kinds and indicates how they can help us analyse natural language locutions involving anaphora

The proof of correctness and completeness of a logical calculus w.r.t. a given semantics can be read as telling us that the tautologies (or, more gen erally, the relation of consequence) specified in a model theoretic way can be equally well specified in a proof theoretic way, by means of the calculus (as the theorems, resp. the relation of inferability of the calculus). Thus we know that both for the classical propositional calculus and for the clas sical predicate calculus theorems and tautologies represent two sides of the same coin. We also know that the relation of inference as instituted by any of the common axiom systems of the classical propositional calculus coin cides with the relation of consequence defined in terms of the truth tables; whereas the situation is a little bit more complicated w.r.t. the classical predicate calculus (the coincidence occurs if we restrict ourselves to closed ∀xFx is inferable from Fx without being its conse formulas; otherwise..

Knihu Kritika depolitizovaného rozumu (podtitul Úvahy (nejen) o nové normalizaci, Václav Bělohradský a kol., Grimmus, Všeň 2010) jsem si kupoval s vědomím, že s její- mi autory se asi nebudu ve všem shodovat, nicméně také s přesvědčením, že problém, na který poukazuje její název, je skutečně závažný, a s nadějí, že se o něm třeba dozvím něco z úhlu pohledu, který mi není vlastní, a tak se mi podaří ho nahlédnout plastičtěji. Bohužel jsem zjistil, že název knihy je pouze krycí; že nejde o boj s depolitizací rozumu, ale naopak o zčásti otevřený a zčásti partyzánský boj proti skutečné politizaci, tj. proti demokratické- mu prostředí, ve kterém se otázky zá- kladního směřování společnosti mohly stát předmětem politických diskuzí a politických střetů, ve jménu absolutizace určitých velice konkrétních, pokud ne pří- mo politických, pak ideologických názorů. Jak říkám, jsem přesvědčený, že problém depolitizace rozumu tu skutečně je. Lidé, zdá se mi, skutečně mají čím dál více pocit, že všechna rozhodnutí jsou na nějakých těch odbornících, jimž do toho nejenom není potřeba mluvit, ale ani by se jim do toho mluvit nemělo. Máme stát zadlužovat? To přece musejí říci ekonomové. Mají se zakazovat politické strany? To my nevíme, ale vědět to musejí politologové či sociologové. Je potrat vražda, nebo medicínský zákrok? To by nám měli říci biologové, filozofové nebo bůhvíkdo, ale hlavně někdo, kdo to dokáže vyčíst z příslušných faktů.