The basic idea of logical expressivism in the Brandomian tradition is that logic makes inferential relations explicit and thereby accessible to critical discussion. But expressivists have not given a convincing explanation of what the point of logical theories is. Peregrin provides a starting point by observing a distinction between making explicit and explication in Carnap’s sense of replacing something unclear and vague by something clear and exact. Whereas logical locutions make inferential relations explicit within a language, logical theories use formal (...) languages to explicate inferential roles and meanings of ordinary-language expressions. But Peregrin also holds that the whole point of logical theories is to provide perspicuous models of inferential structures in ordinary language practice. This turns explication into a mere continuation of making explicit by other means, and it leads to a one-sided conception of logic which has no room for evaluating inferential practice in light of logical theories. As a more convincing alternative, I suggest that expressivists rely on the method of reflective equilibrium. This approach is closely related to Carnapian explication, but it has the potential of correcting informal inferential practice without dubious ambitions to replace ordinary languages by logical formalisms. (shrink)

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. (shrink)

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. (shrink)

Wenn es aber Wirklichkeitssinn gibt, und niemand wird bezweifeln, daß er seine Daseinsberechtigung hat, dann muß es auch etwas geben, das man Möglichkeitssinn nennen kann. Wer ihn besitzt, sagt beispielsweise nicht: Hier ist dies oder das geschehen, wird geschehen, muß geschehen; sondern er erfindet: Hier könnte, sollte oder müßte geschehn; und wenn man ihm von irgend etwas erklärt, daß es so sei, wie es sei, dann denkt er: Nun, es könnte wahrscheinlich auch anders sein. So ließe sich der Möglichkeitssinn geradezu (...) als die Fähigkeit definieren, alles, was ebensogut sein könnte, zu denken und das, was ist, nicht wichtiger zu nehmen als das, was nicht ist. (shrink)

Theories of language in the twentieth century tend towards one of two radically different models. One paradigm holds that expressions ‘stand for’ entities and their meanings are the entities stood for by them. According to the other, expressions are rather tools of interaction and their meanings are their functions within the interaction, their aptitudes to serve it in their distinctive ways.

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. (shrink)

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. (shrink)

Metaphysics is usually understood as the investigation of being qua being and of its ultimate categories. Given this characterization, it may be hard to grasp why anyone might wish to oppose metaphysics, why anyone might claim that metaphysics ”leads the philosopher into complete darkness” (Wittgenstein, 1958, p.18)? What could be so misleading about the investigation of the most abstract vestiges of being? One source of disparagement towards metaphysics, of course, stems from the relativist conviction that there is no absolute being, (...) and hence nor are there any ultimate categories of being. Another ‘reason’ for some philosophers of this century (notably Carnap) to reject metaphysics appeared to consist in their reinterpretation of the word ”metaphysics”, in effect, simply as ”nonsensical philosophy”. However neither of these reasons seems to be the Wittgensteinian one. The way I propose to envisage this reason takes us back to Plato with his distinction between Being and Becoming (echoed, in one or another form, within the conceptions of so many subsequent philosophers). It is the distinction between the ‘higher’ realm of ideas with its crisp, eternal truths, and the ‘lower’ realm of appearances in which anything appears only as a fuzzy and transient reflection of something from the higher realm. The original message harbored in this Platonistic picture is clearly that the vast and hardly graspable flux of appearances shelters something firm and invariable, something potentially fully capturable by human reason which can then use it as a prism to comprehend and understand the everchanging phenomena. However, as I will claim, the picture of a ‘higher’ reality behind phenomena is dangerous in that it can delude a philosopher into feeling that he can solve empirical questions by a quasiempirical investigation of a non-empirical realm: a ‘metaphysical reality’. (shrink)

Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.

Filosofové odedávna snili o jazyce, který by byl z hlediska řešení těch problémů, se kterými se potýkají (případně všech lidských problémů vůbec), vhodnější než jazyk, jímž nás obdařila příroda. Mnozí z nich si představovali, že filosofické problémy vznikají zčásti nebo zcela v důsledku toho, že přirozený jazyk není dostatečně přesným prostředkem vyjádření našich idejí a myšlenek - a že by se tedy vše spravilo, kdyby byl k dispozici jazyk, jehož výrazivo by bylo s našim myšlením - případně s naším světem (...) - v dokonalém souladu. Podle tohoto názoru je tím, co filosof (ale i vědec) potřebuje, jakási „abeceda lidských myšlenek“, která by nám umožnila „pomocí spojení jejích písmen a analýzy slov, která se z nich skládají, objevit a posoudit všechno ostatní“ (Leibniz) K tomu, aby se taková „abeceda“ dala vytvořit, ovšem zbývala jedna ‘maličkost’: bylo třeba posbírat a zinventarizovat všechny naše myšlenky a ideje, zjistit, pro které vyjádření nemáme, případně které vyjadřujeme nějak ‘nevhodně’, a tyto nedostatky a nesrovnalosti odstranit. Problém byl ovšem v tom, že nikdo neměl nejmenší ponětí, jak tohle udělat: a Leibnizův projekt calculu philosophicu, stejně tak jako jiné podobné nápady, zůstal navždy pouhou utopií. (shrink)

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. (shrink)

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.. (shrink)

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. (shrink)