Jaroslav Peregrin

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

A few decades ago, only isolated groups of philosophers counted the phenomenon of normativity as one of their principal interests. Rules and norms have always, of course, been in the purview of moral philosophers, who often took them as exceedingly abstract entities, if not directly metaphysical. Philosophers from the border territories of philosophy and social sciences, on the other hand, were interested in more concrete norms, namely those that emerge and survive within human societies. Philosophers of law stood between these two extremes, studying law as a matter of socially instituted norms which, however, might be seen as a projection of something more esoteric. The research programs of these groups of philosophers had little overlap. And for philosophers of mind, of language, or of science (with the exception of a few philosophers of social sciences, such as Peter Winch), norms were at most only of marginal interest. This situation has changed hugely over recent decades. I think the catalyst was the interest in rules and norms within the philosophy of language, which was kindled by the ongoing reception of the later Wittgenstein. Other philosophers, like Michael Dummett and Wilfrid Sellars, also deserve part of the credit. Via philosophy of language, interest in norms invaded sections of philosophy of mind, too, and the previously isolated studies of various types of norms slowly became interconnected, if not directly integrated. No wonder that more and more general studies of the nature of rules and norms are now reaching the light of day. Andrei Marmor's Social Conventions is one of the most recent contributions. Marmor sees a social convention as a specific kind of norm characterized especially by its arbitrariness. More precisely, a rule is conventional, according to the author, iff (i) some people follow it; (ii) they have a reason to follow it; and (iii) there is an alternative rule that they could have followed for the same reason. The point of departure for Marmor's analysis is David Lewis's theory of convention F1F, which, however, he considers too narrow and hence extends it considerably. Lewis's idea is that norms result from certain spontaneous processes by which society reacts to coordination problems..

It is a trivial fact that if we have a square table filled with numbers, we can always form a column which is not yet contained in the table. Despite its apparent triviality, this fact underlies the foundations of most of the path-breaking results of logic in the second half of the nineteenth and the first half of the twentieth century. We explain how this fact can be used to show that there are more sequences of natural numbers than there are natural numbers, that there are more real numbers than natural numbers and that every set has more subsets than elements (all results due to Cantor); we indicate how this fact can be seen as underlying the celebrated Russell paradox; and we show how it can be employed to expose the most fundamental result of mathematical logic of the twentieth century, Gödel's incompleteness theorem. Finally, we show how this fact yields the unsolvability of the halting problem for Turing machines

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..

What is a minimal proof-theoretical foundation of logic? Two different ways to answer this question may appear to offer themselves: reduce the whole of logic either to the relation of inference, or else to the property of incompatibility. The first way would involve defining logical operators in terms of the algebraic properties of the relation of inference—with conjunction $$\hbox {A}\wedge \hbox {B}$$ A ∧ B as the infimum of A and B, negation $$\lnot \hbox {A}$$ ¬ A as the minimal incompatible of A, etc. The second way involves introducing logical operators in terms of the relation of incompatibility, such that X is incompatible with $$\{\lnot \hbox {A}\}$$ { ¬ A } iff every Y incompatible with X is incompatible with {A}; and X is incompatible with $$\{\hbox {A}\!\wedge \!\hbox {B}\}$$ { A ∧ B } iff X is incompatible with {A,B}; etc. Whereas the first route leads us naturally to intuitionistic logic, the second leads us to classical logic. The aim of this paper is threefold: to investigate the relationship of the two approaches within a very general framework, to discuss the viability of erecting logic on such austere foundations, and to find out whether choosing one of the ways we are inevitably led to a specific logical system

Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory and similar tools of the analysis of language should be understood as capturing the semantically relevant, especially inferential, structure of language. From this vantage point, the reader gains a new light on many of the traditional concepts and problems of logic and philosophy of language, such as meaning, reference, truth and the nature of formal logic.

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

Atomists explain properties of wholes as compositions of properties of their parts; in particular properties of complex expressions as composed of properties of their parts. Especially, semantic atomists explain meanings of complex expressions as composed of meanings of their parts. Holists deny themselves this way: they insist that at least in some cases properties of wholes are more basic than, or not reducible to, properties of their parts; in particular, semantic holists claim that meanings of (at least some) wholes are more basic than meanings of parts. Now as atomists have composition as the way of getting themselves from the meanings of parts to the meanings of wholes, holists need something to get them from the meanings of wholes to those of their parts. What is usually invoked in this context is the concept of intersubstitutivity, which is, however, not always wholly clear.

Recent results of Partee, Rooth, Krifka and other formal semanticians confirm that topic-focus articulation (TFA) of sentence is relevant for its semantics. The essential import of TFA, which is more apparent in case of a language with relatively free word order such as Czech than in case of English, has been traditionally intensively studied by Czech linguists. In this paper we would like to indicate the possibility of the account for TFA in terms of the theory of generalized quantifiers, drawing on the results of both these groups of theoreticians. The basic intuition which we accept as our point of departure is the intuition of topic as the “semantic subject” and focus as the “semantic predicate”; we point out that the role of topic is to specify the entity the sentence is “about” (thereby triggering a presupposition), while that of the focus is to reveal a characterization of this entity, and usually a characterization that is in some sense exhaustive. Then we show that it may be plausible to consider topic and focus as arguments to an implicit generalized quantifier, which may get overridden by an explicit focalizer

In part one, I give an (unsystematic) overview of the development of logical tools which have been employed in the course of the analysis of referring expressions, i.e. definite and (specific) indefinite singular terms, of natural language. I present Russell's celebrated theory of definite descriptions which I see as an attempt to explain definite reference in terms of unique existence (and reference in general in terms of existence simpliciter); and I present Hilbert's E-calculus as an attempt to explain existence in terms of choice. Then I turn to contemporary, dynamic approaches to the analysis of singular terms and point out that only within a dynamic framework can the Russellian and Hilbertian ideas yield a truly satisfactory analysis of singular terms, and consequently of reference and coreference. I call attention to the fact that current results of formal semantics demonstrate the advantages of viewing singular terms as denoting updates, i.e. as a means of changing the context (information state), and especially that part of the context which I call the individually

Imagine a Paleolithic hunter, who has failed to hunt down anything for a couple of days and is hungry. He has an urgent desire, the desire to eat, which he is not able to fulfill – his desire is frustrated by the world. Now imagine our contemporary bank clerk, who went to work forgetting his wallet at home and is hungry too. He too is not able to fulfill his urgent desire to eat because it is frustrated by the world. From the viewpoint of the two individuals the situation is very similar. However, it differs in at least one crucial respect. While the hunter cannot eat because there is no food available to him anywhere near (at least as far as he can find out), the clerk can easily find tons of food - it is enough to visit a nearest supermarket. The reason why he cannot get the food is not that it would be physically impossible, but because taking food from store's shelves without paying is forbidden. This story reminds us that many of the barriers that constrain our lives and make us find our way merely within the space delimited by them are no longer barriers in the literal sense of the word - they are no longer produced by the conspiracy of the causal laws that form our physical niche. Rather they are produced by the conspiracy of attitudes of our fellow humans - they are deliberate rules, rather than inexorable natural laws. In this way evolution is canalized not by the environment relatively independent of it, but rather by the ploy of the organisms it itself has brought into being. I think that realizing the full import of this autocatalyctic situation may lead us, on the one hand, to the appreciation of certain philosophical doctrines, pervasive especially after Kant, regarding normativity as the hallmark of the human, while, on the other hand seeing how they get enlightened by scientific doctrines regarding the development of the human race its continuities/discontinuities with its animal cousins.

It is now often taken for granted that facts are entia non grata, for there exists a powerful argument (dubbed the slingshot), which is backed by such great names as Frege or Gödel or Davidson (and so could hardly be wrong), that discredits their existence. There indeed is such an argument, and it indeed is not wrong on the straightforward sense of wrong. However, in how far it knocks down any conception of facts is another story, a story which is anything but simple and perspicuous. In his book, Stephen Neale takes pains to excavate the origins of the argument and the presuppositions which it needs to be usable for the purpose of exorcising facts. In the introduction of the book, Neale expresses his conviction that his analysis of the slingshot will not only compromise its usability for the purpose of discrediting facts, but also save representationalist conceptions of language and mind from the attacks of the antirepresentationalist philosophers like Davidson and Rorty. „Representational philosophy,“ he claims, „survives the Davidson-Rorty onslaught because non-truth-functional logics and ontologies of facts, states of affairs, situations and propositions survive not only the actual arguments deployed against them, but also the most precise and powerful slingshot arguments that can be constructed.“ However, what he does take his analyses to show is that „the most precise and powerful slingshot arguments demonstrate conclusively that the logical and ontological theories originally targeted must satisfy non-trivial conditions if they are to avoid logical or ontological collapse.“ (P. 12) The book starts with the discussion of the philosophy of Donald Davidson, who appears to have brought the slingshot argument to the current prominence within philosophical discussions. Here we encounter the first variant of the slingshot: Consider two sentences φ and ψ and a proper name d. Consider the definite descriptions ‘the object x such that (x = d and φ)’ and ‘the object x such that (x = d and ψ)’..

For many centuries, a predominant view of meaning was that the meaning of a word is some kind of chunk of mind-stuff (“idea”) glued to the word and animating it. However, while the traditional view was that we must first understand meaning, which enables us to understand language and hence our linguistic practices, a new approach to semantics that has emerged in the second half of the twentieth century, and which I see as marking the future of meaning, suggests that it is our linguistic practices on which we must concentrate from the beginning. In this paper I suggest a specific understanding of these practices, yielding the conclusion that meanings are reasonably seen as creatures of our activity of setting up certain systems of rules, thus opening up new kinds of virtual spaces which we can “enter”. Meaning is what emerges within the intricately orchestrated space that we have somehow managed to bring into being by means of accepting the rules which are in charge of our language games, especially the game of giving and asking for reasons

There have been, I am afraid, almost as many answers to the question what is logic? as there have been logicians. However, if logic is not to be an obscure "science of everything", we must assume that the majority of the various answers share a common core which does offer a reasonable delimitation of the subject matter of logic. To probe this core, let us start from the answer given by Gottlob Frege (1918/9), the person probably most responsible for modern logic: the subject matter of logic is "truth", and especially its "laws"1. How should we understand the concept of "laws of truth"? The underlying point clearly is that the truth/falsity of our statements is partly a contingent and partly a necessary, lawful matter: that "Paris is in France" is true is a contingent matter, whereas that "Paris is in France or it is not in France" is true is a necessary matter (let us, for the time being, leave aside the Quinean scruples regarding the delimitation of necessarily true statements). Logic,then, should focus on the statements that are true as a matter of law (i.e. necessarily), or, more generally, the truth of which "lawfully depends" on some other statements (i.e. which are true as a matter of law provided these other statements are true). This renders Fregean laws of truth as, in general, a matter of "lawful truth-dependence" - i.e. of entailment or inference (again, let us now disregard any possible difference between these two concepts). This yields a conception of logic as a theory of entailment or inference, a conception which looms behind many other specifications of the subject matter of logic and which, I think, is ultimately correct. However, we can also see the logician – and this is the view we will stick to here – as trying to separate true sentences from false ones; or, equivalently, to map sentences onto truth and falsity. Let us first consider the case of a non-empirical language with a single, definite truth valuation – like the language of Peano arithmetic..

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

Abstrakt. Běžně se má za to, že pravidla hrají v rámci myšlení jenom marginální úlohu. Myšlení je přece proces, který je svou podstatou svobodný, ne-mechanický a kreativní – a tudíž nikoli řízený nějakými pravidly. Často se má dokonce za to, že je to právě absence pravidel, která dělá z lidského myšlení to, čím je, a co člověka principiálně odlišuje od stroje. V ostrém kontrastu k tomuto pohledu stojí Wittgensteinův výrok, že vlastně nemůžeme překročit hranice logiky – že nemůžeme myslet tak, aby to bylo s pravidly logiky v rozporu. Jak mohl Wittgenstein tvrdit něco, co zní tak očividně nesmyslně? V přednášce se chci podívat na roli, kterou v rámci myšlení hrají pravidla, z poněkud jiného pohledu, než jak to bývá běžné. Nemyslím, že by existovala nějaká pravidla, která by obecně vedla naše myšlenkové pochody; jsem však přesvědčen, že jistý druh pravidel hraje z hlediska myšlení skutečně klíčovou roli – jsou to ta, která konstituují 'prostor významů', o něž se naše myšlení standardně opírá.

Když jsem v roce 1992 začínal na filosofické fakultě UK přednášet teorii sémantiky, cítil jsem intenzivní potřebu poskytnout studentům nějaký učební text. O překotném vývoji tohoto interdisciplinárního oboru, který odstartovalo v sedmdesátých letech úspěšné “zkřížení logiky s lingvistikou” Richardem Montaguem a dalšími a který se nezpomalil dodnes, totiž v češtině neexistovaly prakticky žádné zprávy (s čestnou výjimkou přístupu tzv. transparentní intenzionální logiky, který byl dílem českého emigranta Pavla Tichého a o kterém u nás psal Pavel Materna). Přehledové publikace, jaké jsou potřeba pro někoho, kdo se chce v dané problematice zorientovat, se ovšem v té době i po světě teprve začínaly objevovat: v roce 1990 vyšla kniha An Introduction to Semantics Gennara Chierchii a Sally McConell-Ginnetové a v roce 1991 vydala skupina holandských logiků pod kolektivním pseudonymem L.T.F. Gamut dvousvazkovou knihu Language and Meaning. Za této situace jsem se pokusil co nejrychleji sepsat učební text, který by moji studenti i jiní zájemci o sémantiku mohli použít; a protože o jeho vydání paradoxně projevila větší zájem filosofická fakulta Masarykovy univerzity v Brně (kde jsem já osobně nikdy neučil; ale zájem o sémantiku tam neúnavně podněcoval a vydání mého textu tam zprostředkoval kolega Materna) než filosofická fakulta mojí domovské Karlovy univerzity, vyšel tento text v Brně, a to pod názvem Úvod do teoretické sémantiky.

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..

In considering the very possibility of deviant logic, we face the following question: what makes us see an operator of one logical system as a deviant version of an operator of another system? Why not see it simply as a different operator? Why do we see, say, intuitionist implication as an operator 'competing' with classical implication? Is it only because both happen to be called implications?1 It is clear that if we want to make cross-systemic comparisons, we need an 'Archimedean point' external to the systems compared. Some logicians and philosophers, including Quine (1986), come close to saying that no such Archimedean point is available, and hence that there can be no deviant logics, for if two operators are governed by different axioms, then they are simply two different operators (or, if you prefer, operators with different meanings). From this viewpoint, intuitionist implication is no less different from classical implication than, say, intuitionist or classical conjunction. This conclusion is indeed plausible if we consider logical calculi simply as algebraic structures2; however, things are different if we see them as a means of accounting for something that is already 'there' before we establish the structures and is to be explicated by them. From such a perspective, two operators of different systems may be variants of the same operator in virtue of the fact that they are both means of capturing the same pretheoretical item. What might these items be? Sometimes it seems that logicians tacitly assume that there are some mythical archetypes of implication, conjunction etc., located somewhere in some Platonic heaven or somehow underlying the a priori structures of our mind, which logic tries to capture (for better or worse). However, when it comes to the comparison of the concrete outcomes of our logical efforts, say the classical and the intuitionist implications with the archetypal Implication, the latter can never be materialized so distinctly as to be of any help. A more constructive proposal is that the operators are related to elements or constructions of our language..

The concept ofsemantic interpretation is a source of chronic confusion: the introduction of a notion ofinterpretation can be the result of several quite different kinds of considerations.Interpretation can be understood in at least three ways: as a process of dis-abstraction of formulas, as technical tool for the sake of characterizing truth, or as a reconstruction of meaning-assignment. However essentially different these motifs are and however properly they must be kept apart, these can all be brought to one and the same notion of interpretation: to the notion of a compositional evaluation of expressions inducing a possible distribution of truth values among statements.

It is a common wisdom that whereas consequence or entailment is a semantic concept, provability is a syntactic concept. However, what exactly does this mean? What is provability? In the traditional, intuitive sense, to prove something is to demonstrate its truth, and indeed the Latin word for proof is demonstratio. Hence in this sense, we cannot prove something unless it is true. Now in the course of his well known proof of the incompleteness of arithmetic, Gödel showed that provability within the axiomatic system of Peano arithmetic (PA) can be reconstructed as a number-theoretic predicate Pr and he showed that within the system there exists a statement G so that..