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..

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

Summary. I do not think there is one true answer to the question What is logic?. There are, clearly, good and less good answers, and there are answers which are plainly wrong; but the term 'logic' has been employed, throughout the history of the subject matter, in such diverse ways that no single one of the uses can be said to be the correct one. However, even among the answers which are acceptable on historico-semantical grounds there are still, without doubt, good and less good ones, in the sense of more and less useful. In this paper, I will argue for a certain, rather narrow conception of logic; and I am going to argue that it is not only an acceptable answer, but also one which is more useful and fruitful than its alternatives

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

While the traditional view was that in order to understand language and our linguistic practices we must explain meaning, the 'pragmatic turn' emerging within the writings of various philosohpers of the second half of the twentieth century caused a basic change of the perspective: the tendency is to concentrate directly on explaining the linguistic practices and leave the need for explaining meaning to emerge (or, as the case may be, not to emerge) subsequently. I argue that after this turn we should explain the peculiar kinds of 'meaningfulness' that characterizes our expressions in terms of what Sellars called "pattern governed behavior". Furthermore, I argue that the turn should not make us discard meanings, but only to reappraise them: to see them as the roles of expressions vis-à-vis the rules that govern our language games.

While most theoreticians of meaning in the first half of the twentieth century subscribed to a representational theory (viewing meanings as entities stood for by the expressions), the second half of the century was marked by the rise of various versions of use-theories of meaning. The roots of this ‘pragmatist turn’ are detectable in the writings of the later Wittgenstein, the Oxford speech act theorists (Austin, Grice) and the American neopragmatists (Quine, Sellars). Though it is now rather popular (and sometimes even fashionable) to invoke the use-theory of meaning, it is by far not so popular to inquire what such a theory really is. In this paper we try to give at least a part of the answer, whereby we find out that the usual conception of such a theory is unsatisfactory. We propose that for an improvement we must, together with Wittgenstein and Sellars, conceive language as a (tool of a) rule-based activity, which enables us to replace the concept of disposition, usually constituting the backbone of the use-theory, by the concept of propriety. The resulting normative version of the use-theory then becomes the investigation of the rules which expressions acquire vis-`a-vis the rules of the relevant language games – especially of the rules of inference.

Normativity is one of the keywords of contemporary philosophical discussions. It is clear that philosophy has to do not only with theories, but also with norms (especially in ethics); but more and more current philosophers are busy arguing that, in addition, those parts of philosophy where norms are prima facie not in high focus, such as philosophy of language or philosophy of mind, have kinds of "normative dimensions". However, not everybody subscribes to this enthusiasm for normativity. Within philosophy, there is, for example, an ongoing fierce discussion between 'normativists' and 'anti-normativists' about the normativity of meaning1 . A similar, thought I think both much broader and much deeper discussion concerning normativity has been launched within the context of philosophical and scientific accounts for human societies. Should we, explaining how a society works, merely state the facts concerning the behavior of the members of the society in the way natural scientists describe the behavior of ants in an anthill, or how they describe the 'behavior' of particles in an atom, or do we, over and above this, need to take a recourse to some 'normative facts'? This dispute, of course, partly reincarnates of traditional debate about the differences between Geisteswissenschaften and Naturwissenschaften as we know it from Dilthey, Schleimermacher or Max Weber; in this very specific form it, however, acquires a rather 2 transparent shape, in which it seems it might be resolvable by critical scrutiny . The current dispute is fuelled by the anti-normativists' rejection of normativism as the general claim that to account for human societies (and their products, such as meanings), we need to account for something over and above ordinary, causal, scientific facts; whereas the 'normativists' argue that to have a truly explanatory account of human societies, human languages or human practices we cannot make do stating what there is – that in some sense we need to say something about what ought to be..

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 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

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..

In Meaning and Structure, Peregrin argues that recent and contemporary (post)analytic philosophy, as developed by Quine, Davidson, Sellars and their followers, is largely structuralistic in the very sense in which structuralism was originally tabled by Ferdinand de Saussure. The author reconstructs de Saussure's view of language, linking it to modern formal logic and mathematics, and reveals close analogies between its constitutive principles and the principles informing the holistic and neopragmatistic view of language put forward by Quine and his followers. Peregrin also indicates how this view of language can be made compatible with what is usually called 'formal semantics'. Drawing on both the Saussurean tradition and recent developments in analytic philosophy of language, this book offers a unique study of the ways in which the concept of meaning can be seen as consisting in the concept of structure.

In this paper I put forward a thesis regarding the anatomy of “cultural evolution”, in particular the way the “cultural” transmission of behavioral patterns came to piggyback, through us humans, on the transmission effected by genetic evolution. I claim that what grounds and supports this new kind of transmission is a complex behavioral “meta-pattern” that makes it possible to grasp a pattern as something that “ought to be”, i.e. that transforms the pattern into what we can call a rule. (Here I draw especially on the philosophical insights of Wilfrid Sellars.) In this way I interlink empirical research done in evolution theory with some more speculative philosophical theories, thus shedding new light on the former and adding an empirical footing to the latter

After putting forward his celebrated deflationary theory of truth (Horwich, 1998a), Paul Horwich added a compatible theory of meaning (Horwich, 1998b). I am calling also this latter theory deflationism (although it may be a slightly misleading name in that, as Paul himself notes, his theory of meaning is deflationary more in the sense of being forced by the deflationary theory of truth than of being particularly deflationary in itself). In contrast, what I call inferentialism is the theory of meaning which I am going to advocate here – the view, in a nutshell, that meaning is a matter of inferential role. Various versions of this theory have been defended by Wilfried Sellars, Robert Brandom and a couple of other philosophers including myself. And the thesis I wish to present in this paper – to put it as a provocation right off – is that Paul is an inferentialist led astray. Both deflationism and inferentialism can be seen as elaborations of what can be called the use theory of meaning; for both seem to agree that.

Suppose for a moment, that J.R.R. Tolkien, the famous author of the cult fantasy saga Lord of the Rings, did not publish anything of his writings during his lifetime; suppose that after his death the manuscripts of all his writings are lying on his table. Where, then, is the Middlearth, the glorious land of hobbits, dwarfs, elfs and human heroes, situated? We might be tempted to say that it is within our world, namely inside the pile of the papers on the writer’s table - for it exists solely through the letters written on these papers. However, to say this would be wrong - surely we do not expect that should the heroes of the book walk in a straight line long enough, they would cross the boundaries of the book and appear in Mr. Tolkien’s room. Middlearth is, of course, not within our world - despite existing solely due to certain things which are within it. Now the situation is not substantially different actually, when Middlearth does not exist solely through a single pile of papers, but rather through millions of printed copies of Tolkien’s books and through the minds of millions of their readers. Again, the land exists exclusively through the existence of entities which are parts of our world, but this does not mean that the land itself is a part of our world. The point of this anecdotal excursion is now that this relationship between our world and Middlearth is, in a sense, similar to the relationship between our physical space of things and „the space of reasons“ ; or between „the causal story“ and „the justificatory story“. Like Middlearth, the space of reasons exists exclusively due to us, humans, and our minds, and in this sense we might be tempted to situate it in our world, to see it as a certain, perhaps scattered, compartment of the world of things within which we live; but just as in the case of Middlearth, this might be dangerously misguiding.