Jaroslav Peregrin

Wilfrid Sellars's analysis of the concept of meaning led, in effect, to the conclusion that the meaning of an expression is its inferential role. This view is often challenged by the claim that inference is a matter of syntax and syntax can never yield us semantics. I argue that this challenge is based on the confusion of two senses of "syntax"; and I try to throw some new light on the concept of inferential role. My conclusion is that the Sellarsian view that something can have meaning only if it is subject to inferences is viable, and that inferential role is a plausible explication of meaning. However I also argue, pace Sellars, that the inferential nature of meaning does not prevent us from engaging in the enterprise of Carnapian formal semantics

Kniha, jako je tato, nemůže být tak docela dílem jediného člověka. Dovést ji do podoby koherentního celku bych nedokázal bez pomoci svých kolegů, kteří po mně text četli a upozornili mě na spoustu chyb a nedůsledností, které se v něm vyskytovaly. Můj dík v tomto směru patří zejména Vojtěchu Kolmanovi, Liboru Běhounkovi a Martě Bílkové. Za připomínky k různým částem rukopisu jsem vděčen i Pavlu Maternovi, Milanu Matouškovi, Prokopu Sousedíkovi, Vladimíru Svobodovi, Petru Hájkovi a Grahamu Priestovi. Kniha vznikla v rámci projektu podpořeného grantem AV ČR číslo A0009001/00.

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..

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.

The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of 'inferentially native' logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered

Ve standardních výkladech moderních dějin studia mysli ve dvacátém století se dočteme, že zatímco kolem poloviny tohoto století ovládl studium mysli zpozdilý behaviorismus, v šedesátých letech nastoupila „kognitivní revoluce“, která nadvládu behaviorismu smetla a otevřela cestu ke skutečně nepředpojatému a adekvátnímu studiu mysli. V tomto textu se chci nad tímto standardním výkladem zamyslet a zpochybnit ho: konkrétně chci poukázat na to, že behaviorismus nebyl ve všech ohledech tak zpozdilý, jak by se z tohoto pohledu mohl jevit; a že „kognitivní revoluce“ neznamenala jenom vymanění se z nepřiměřenýchmetodologických okovů, ale i otevření prostoru pro to, čemu budu říkat „magická teorie mysli“ a co podle mého názoru nepatří ani do vědy, ani do rozumné filosofie.Standard accounts of the modern history of the study of mind in the twentieth century tell us that while around the half of the century the study came to be dominated by inept behaviorism, the sixties witnessed the onslaught of the "cognitive revolution", which wiped out the dominance of behaviorism and opened the way for the truly unprejudiced and adequate study of mind. In this text I want to reconsider this account and challenge it: in particular, I want to point out that behaviorism was not in all respects so inept as it may suggest; and that the "cognitive revolution" did not mean merely breaking out of inadequate methodological fetters, but rather also an opening of space for what I will call the "magical theory of mind" and what I think belongs neither to science, nor to reasonable philosophy.

Frege has proposed to consider names as denoting objects, predicates as standing for concepts and sentences as denoting truth values. He was, however, aware that such denotation does not exhaust all what is to be said about meaning. Therefore he has urged that in addition to such denotation (Bedeutung) an expression has sense (Sinn). The sense is the "way of presentation" of denotation; hence the expressions Morning Star and Evening Star have identical denotations, but different senses. Carnap has proposed to replace Frege's distinction between Sinn and Bedeutung by the distinction between intension and extension. Extension is, according to Carnap, what is shared by every two expressions which can be truthfully declared equivalent; where equivalence means a bit different things for different grammatical categories. In the formalism of the classical logic, the equivalence of two terms T1 and T2 is expressed by the formula T1=T2, that of two sentences ↔ ↔ S1 and S2 is by the formula S1↔ ↔S2, and that of two unary predicates P1 and P2 by the formula..

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’.

The followers of Wilfrid Sellars are often divided into “right” and “left” Sellarsians, according to whether they believe, in Mark Lance's words, that “linguistic roles constitutive of meaning and captured by dot quoted words are ‘normative all the way down.’” The present article anatomizes this division and argues that it is not easy to give it a nontrivial sense. In particular, the article argues that it is not really possible to construe it as a controversy related to ontology, and goes on to argue that it is also not easy to construe it as one concerning the translatability of the normative idiom into the non-normative one. The conclusion is that the only coherent interpretation of this disagreement is as a disagreement about the possibility and desirability of assuming a standpoint “inside” our linguistic practices.

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.

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..

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.