Jaroslav Peregrin

Vuvodnim rocniku ORGANONu Pavel Cmorej ve svych @@piton lch z logicjce syntaxe predvadel, jak je prirozeny jazyk mozne nahlizet prismatem 'standardni' logiky. Historicky ovsem neexistuje jedna logika,ale ruzne logicke systemy, ktere spolu castecne soupeii (tak jako treba klasicka a intuicionisticka logika), castecne jeden druhy rozsiruji (Iako treba klasicky vyrokovy a klasicky predikatovy pocet) ci se navzajem doplnuji (Iako napriklad modalni a temporalni logika). To co je v logice obecne prijimano za standard, je fakticky vysledkem interakce a soutezeni ruznych neustale vznikajicich systemu

Logic is usually considered to be the study of logical consequence – of the most basic laws governing how a statement’s truth depends on the truth of other statements. Some of the pioneers of modern formal logic, notably Hilbert and Carnap, assumed that the only way to get hold of the relation of consequence was to reconstruct it as a relation of inference within a formal system built upon explicit inferential rules. Even Alfred Tarski in 1930 seemed to foresee no kind of consequence other than one induced by a set of inference rules: "Let A be an arbitrary set of sentences of a particular discipline. With the help of certain operations, the so-called rules of inference , new sentences are derived from the set A , called the consequences of the set A . To establish these rules of inference, and with their help to define exactly the concept of consequence, is again a task of special metadisciplines; in the usual terminology of set theory the schema of such definition can be formulated as follows: The set of all consequences of the set A is the intersection of all sets which contain the set A and are closed under the given rules of inference." (p. 63) Thereby also the concept of truth came to be reconstructed as inferability from the empty set of premises. (More precisely, this holds only for non-empirical, necessary truth; but of course logic never set itself the task of studying empirical truth.) From this viewpoint, logic came to look as the enterprise of explication of consequence in terms of inference

The contemporary popularity of the prefix post has found its expression also in the realm of analytic philosophy - there arises something which has come to be called postanalytic philosophy. We put forward that this branch of the analytic movement, germinating in the writings of the late Ludwig Wittgenstein, of Willard Van Orman Quine and Willfrid Sellars, and coming to full blossom with Nelson Goodman, Donald Davidson, Hilary Putnam and Richard Rorty, springs first and foremost from the repudiation of the doctrine of logical atomism as entertained by Bertrand Russell and the early Wittgenstein. The dismantling of this doctrine means especially the denial of the following four points: (1) the atomistic character of language; (2) the sharp boundary between analytic and contingent statements; (3) the sharp boundary between 'given' and 'inferred' knowledge; and also (4) the essential cummulativity of knowledge. Postanalytic philosophy is thus essentially holistic; and we put forward that in fact postanalytic philosophy equals analytic philosophy minus logical atomism

The contemporary popularity of the prefix post has found its expression also in the realm of analytic philosophy - there arises something which has come to be called postanalytic philosophy. We put forward that this branch of the analytic movement, germinating in the writings of the late Ludwig Wittgenstein, of Wllard Van Orman Quine and Willfrid Sellars, and coming to fill blossom with Nelson Goodman, Donald Davidson, Hilary Putnam and Richard Rorty, springs first and foremost from the repudiation of the doctrine of logical atomism as entertained by Bertrand Russell and the early Wittgenstein. The dismantling of this doctrine means especially the denial of the following four points: the atomistic character of language; the sharp boundary between analytic and contingent statements; the sharp boundary between ġiven\' and ínferred\' knowledge; and also the essential cummulativity of knowledge. Postanalytic philosophy is thus essentially holistic; and we put forward that in fact postanalytic philosophy equals analytic philosophy minus logical atomism

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of prooftheoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones

In his “Making it Explicit”,1 Robert Brandom set up a new philosophical paradigm, concentrating especially on the link between language and the world, but extendable (in the way familiar from the dawn of the linguistic turn) to the rest of philosophy. He views modern philosophy in terms of the tension between “representationalist” and “inferentialist” approaches to language (which, according to him, also underlies the much more commonly cited struggle between empiricism and rationalism); and elaborating on the ideas of his teacher Wilfrid Sellars he develops a distinctive kind of inferentialist framework.

Normativity is one of the keywords of contemporary philosophical discussions (which partly reincarnate traditional debates about the differences between Geisteswissenschaften and Naturwissenschaften ). But are the philosophers who argue for the irreducible role of normativity within accounts for human societies obliged to assume, as Stephen Turner has recently put it, the existence of a "non‐natural, non‐empirical stuff that is claimed to be necessarily, intrinsically there and to in some sense account for the actual"?

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

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..

Within human communities, the phenomenon of rules is ubiquitous. We have the allimportant rules that are codified by our law; we have rules that are not authoritatively written down, but are usually followed (like the rule that if somebody helps me, I should be prepared to help him in turn); we have traffic rules; and the rules of various games and sports. Yet, from the scientific viewpoint, rules are not easy to account for. How is their emergence to be explained (in a way compatible with evolution), and how is their existence to be construed, especially in cases when they are not written down? Are we to consider a rule as primarily a linguistic object; or are we to reduce it to some regularity of behavior? Neither of these two forms of existence holds much allure. Firstly, insofar as some rules clearly exist without being recorded, there is no linguistic object with which they can be identified. (After all, we talk about the encoding of the law, which seems to suggest that the law articulates something existing independently of the code.) And secondly, reducing the existence of a rule to a plain regularity of behavior would extinguish any distinction between billiard balls 'following the rules' of mechanics and human subjects following the rules of their society. Hence it would seem that, though there must be more to rules than regularities, at least some rules must be capable of existing exclusively 'within' human conduct – being, as Willfrid Sellars (1949, 299) put it, written "in flesh and blood, or nerve and sinew, rather than in pen and ink".

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..

Logic is usually considered to be the study of logical consequence – of the most basic laws governing how a statement’s truth depends on the truth of other statements. Some of the pioneers of modern formal logic, notably Hilbert and Carnap, assumed that the only way to get hold of the relation of consequence was to reconstruct it as a relation of inference within a formal system built upon explicit inferential rules. Even Alfred Tarski in 1930 seemed to foresee no kind of consequence other than one induced by a set of inference rules: "Let A be an arbitrary set of sentences of a particular discipline. With the help of certain operations, the so-called rules of inference, new sentences are derived from the set A, called the..

In a memorable paper, Donald Davidson (1986, p. 446) insists that "there is no such thing as a language, not if a language is anything like what many philosophers and linguists have supposed". I have always taken this as an exaggeration, albeit an apt exaggeration that might be philosophically helpful. Now when it comes to predication, what I would have expected to hear from the same author would be along the lines of "there is no such thing as predication ... ". But instead of this I hear something very different (Davidson, 2005, p. 77): [I]f we do not understand predication, we do not understand how any sentence works, nor can we account for the structure of the simplest thought that is expressible in language. At one time there was much discussion of what was called the "unity of proposition"; it is just this unity that a theory of predication must explain. The philosophy of language lacks its most important chapter without such a theory, the philosophy of mind is missing its crucial first step if it cannot describe the nature of judgment; and it is woeful if metaphysics cannot say how a substance is related to its attributes. I find myself at odds with just about everything written in this paragraph; and what is worse, my disagreement stems from a notion of language which I believe I have acquired also by reading Davidson. Reading this passage, I desperately sought for an indication that it was leading up to some catch, and not meant to be taken at face value. But, alas, I am afraid there is none. To avoid misunderstanding: I see nothing wrong in understanding predication as a clearly delimited linguistic phenomenon. We put together one kind of expression, which we have come to call the subject, with a different kind of expression, called the predicate, possibly..

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.

Today, a steadily growing number of philosophers regard Wilfrid Sellars as a principal pillar not just of American analytic philosophy, but of twentieth century philosophy in general. But not so long ago, things were different: though Sellars has held the acclaim of a first-rate philosopher for a couple of decades, it is only recently that he has achieved the nimbus of a philosopher whom you must read. It is largely due to his outstanding disciples and followers, from Paul Churchland and Ruth Millikan to Richard Rorty, Jay Rosenberg and Robert Brandom. In many respects, Wilfrid Sellars is a philosopher who somehow eludes the context of his contemporaries. In comparison with brilliant essayists such as Quine or Rorty, he writes in an old fashioned, slightly convoluted style, which is liable to confuse an unprepaired reader. Surrounded by philosophers who see philosophy as shrinking to a residual enterprise, such as merely the logical analysis of language, he does not shy away from claiming that "the aim of philosophy is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term". In contrast to the extreme specialists for whom even logical analysis is a theme too broad to entertain, his strategy is, in deVries' words, "to approach philosophical problems not as independent, individual cases, in principle amenable to piecemeal treatment, but as always constituted within a larger context and requiring not resolution by the establishment of some particular thesis, but the development of a more insightful or more adequate model that permits us to see how the particular phenomenon or puzzle fits within a larger, coherent whole". For all these reasons, it is highly challenging to grasp the bulk of Sellars’ teaching. It cannot be mastered piecemeal because its faraway components often mutually underpin each other in a way that is bound to escape his novice readers.

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!