Jan Wolenski

This is a collection of essays about logic and its applications to various philosophical problems. In general, it is argued that logic constitutes an important device of philosophical analysis. Concerning the nature of logic the author defends the thesis that first-order logic is the logic. Among the philosophical problems to which logic is applied in the essays are: truth, consistency, realism, foundations of semantics, psychologism, undetermination of theories by empirical data, modalities, value concepts, identity, vagueness, God's existence, transcendentals, legal reasoning, category mistakes, bivalence, the cognitive relation, and meaningfulness.

Until Tarski’s semantic truth definition, the concept of truth was used informally in metalogic (metamathematics) or even proposed to be eliminated in favour of syntactic concepts, as in Rudolf Carnap’s early programme of philosophy via logical syntax. Tarski demonstrated that the concept of truth can be defined using precise mathematical devices. If L is a language for which the truth definition is given, it must be done in the metalanguage ML. According to this construction, semantics for L must be performed in ML. The most important example concerns the arithmetic of natural numbers. According to Tarski’s theorem of undefinability, the set of truths of this theory cannot be defined in it – such a definition can be formulated in the metatheory. This fact illuminates the relation between syntax and semantics. If Th is a rich theory and presented as a syntactic theory (a calculus), its semantics is not reducible to its syntax. According to Tarski’s view, related to his work in the simple theory of types, semantics for L can be always constructed in the morphology of ML, provided that L is of the finite order. Two problems arise: what does the word “morphology” mean and how to formulate these ideas, when the framework is based on the distinction between first‑order logic and higher‑order logic. As far as the issue concerns morphology, it is possible to consider it as an extended syntax, i.e. vocabulary which does not refer to semantic concepts or defines such notions by not‑semantic, e.g. set‑theoretical, categories. If the hierarchy of logical types is replaced by the distinction of logics of various orders, in particular between first‑order and higher‑order (it is sufficient to use second‑order), it is possible to show that semantics of first‑order rich theories cannot be defined inside them.

This volume is a result of the international symposium “The Tradition of the Lvov-Warsaw School in European Culture,” which took place in Warsaw, Poland, September 2015. It collects almost all the papers presented at the symposium as well as some additional ones. The contributors include scholars from Austria, the Netherlands, Ireland, and Poland. The papers are devoted to the history and reception of the Lvov-Warsaw School, a Polish branch of analytic philosophy. They present the School’s achievements as well as its connections to other analytic groups. The contributors also show how the tradition of the School is developed contemporarily. The title will appeal to historians of analytic philosophy as well as historians of philosophy in Central Europe.

The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a phenomenological view the relevant evidence is provided by intuition , and this should be the case in either ordinary perceptual knowledge or in mathematical knowledge. Intuition is to be understood in terms of fulfillments of intentions. Knowledge is a product of intuition and intention. In the case of mathematical knowledge it is said that there is a construction for a mathematical statement S if and only if the intention expressed by S is fulfilled . Constructions are thus viewed as intuition processes that could actually or possibly be carried out. In elementary parts of mathematics they might be characterized in terms of certain classes of recursive functions. This view is discussed in the case where S is taken to be a singular statement about natural numbers or finite sets, and also where S is taken to be a general statement about such objects. The distinction between intuition of and intuition that is also investigated in this context. ;It is pointed out how on a phenomenological view a number of central problems about mathematical intuition can be avoided: problems about the analogousness of perceptual and mathematical intuition, about causal accounts of knowledge in mathematics, and about structuralism in mathematics. The bearing of the account on issues concerning constructivism and platonism is also discussed

The paper deals with dispute between naturalism and antinaturalism in meta-ethics. Different standpoints are discussed, especially those of cognitivism, non-cognitivism and emotivism, which leads to certain typology. The author introduces the category of bonitive statements, statements concerning the good, which logic is analogous to the one which determinates relations between deontic statemens. Generalized Hume’s argument on the axiological statements as impossible to be derived from non-axiological is concerned. In particular, it is argued that it does not support antinaturalistic thesis. The standpoint of axiological presentationism is proposed, which makes a link between non-cognitivism and the thesis according to which bonitive statements can be true or false and axiological presentationism can taken as a form of naturalism.

MEDIEVAL AND RENAISSANCE LOGICSMARK D. JOHNSTON, The spiritual logic of Ramon Llull. Oxford: Clarendon Press,1987. xi + 336 pp. £35.00E. J. ASHWORTH, Thomas Bricot: Tractatus Znsolubilium. Nijmegen: Ingenium, 1986. xxiii+ 155 pp. 44 Dfl.CYPRIANI REGNERI, Demonstratio logicae verae iuridica. Edited by G. Kalinowski. Bologna: Cooperativa Libraria Universitaria Editrice Bologna, 1986. xxviii + 167 pp. No price stated.GIROLAMO SACCHERI, Euclides vindicatus. Edited and translated by George Bruce Halsted: second, expanded, edition. New York: Chelsea Publishing Company 1986. xxx + 255 pp. $16.95.THE NINETEENTH CENTURYT. HAILPERIN, Boole's logic andprobability. Second edition. Amsterdam, New York,Oxford and Tokyo: North-Holland, 1986. xii + 428 pp. $76.00.WALTER PURKERT and HANS JOACHIM ILGAUDS, Georg Cantor 1845-1918. Basel/Boston/Stuttgart: Birkhauser Verlag, 1987. 262 pp., 26 plts. SFr. 48.MAX H. FISCH, Peirce, semeiotic, andpragmatism: essays by Max H. Fisch. Edited by Kenneth Laine Ketner and Christian J. W. Kloesel. Bloomington: Indiana University Press, 1986. xiv + 464 pp. $45.00.LOGIC AND LANGUAGEJOËLLE PROUST, Qusesting de forme. logique et proposition analtique de kant á Carnap. Paris Fayard, 1986. xxviii + 504 pp. FF 160H. PALMER, Presupposition and transcendental inference. London and Sydney: Croom Helm, 1985. 208 pp. £15.95EDITIONSALFRED TARSKI, Collected papers. Edited by Steven R. Givant and Ralph N. McKenzie. Vol. I, 1921-1934, 659 pp. Vol. 11, 1935-1944, 699 pp. Vol. 111, 1945-1957, 682 pp. Vol. IV, 1958-1979, 757 pp. Basel, Boston, Stuttgart: Birkhäuser,1986. SF 1280KURT GöDEL, Collected works, Volume 1. Edited by Solomon Feferman, John W. Dawson Jr., Stephen Kleene, Gregory H. Moore, Robert M. Solovay and Jean van Heijenoort. New York: Oxford University Press; Oxford: Clarendon Press; 1986. xviii + 474 pp. £25.00.MISCELLANEOUSJ. MACNAMARA, A border dispute. The place of logic in psychology. Cambridge, Mass. and London: M. I. T. Press. 1986. xviii + 212 pp. £22.50.G. LOLLI, La macchina e le dimostrazioni. Bologna: il Mulino, 1987. 157 pp. L. 15.000.

This paper investigates the basis arguments of so-called legal logic and their relation to logic in its standard meaning. There is no doubt that legal arguments belong to logic in the wide sense (sensu largo), but their reduction to schemes of formal logic (logica sensu stricto) is a controversial issue. It can be demonstrated that only some legal arguments fall under explicit rules of formal logic, that is, having a deductive character. Most such reasoning is fallible, and its correctness depends on appealing to extra-logical principles taken from legal norms. For instance, if we say, “If it is permitted more, then it is permitted less” (argumentum a maiori ad minus), we assume that the concepts expressed by the words “more” and “less” are already defined.

This paper briefly discusses the relations between logic and metalogic in history. Metalogic is understood as a reflection on logic in its various senses, particularly sensu stricto (formal, mathematical) and sensu largo (formal logic plus semantic plus methodology of science). It is shown that metalogic in its contemporary understanding arose after mathematical logic had become a mature discipline. Special passage is devoted to metalogic in Poland. The last part of the paper discussed so-called logocentric predicament.

Przedmiotem artykułu jest pojęcie pamięci zbiorowej, rozpatrywanej przez pryzmat ‘historii przeżytej’ – występującej w dwu postaciach: ‘przeżytej w sensie przedmiotowym’ i ‘przeżytej w sensie treściowym’ – oraz ‘historii zobiektywizowanej’. Uwzględniając polskie kontrowersje wokół książek Jana Tomasza Grossa: Sąsiedzi. Historia zagłady żydowskiego miasteczka i Strach. Antysemityzm w Polsce tuż po wojnie, autor kwestionuje pojęcie jednolitej pamięci zbiorowej i jej normatywne roszczenia. Pamięć kolektywna i dominująca narracja historyczna są często przedmiotem manipulacji politycznych jako sposobu na potwierdzenie jedności społecznej poprzez wykluczenie cudzych wspomnień. Pamięć o przeszłości jest w rzeczywistości podzielona między różne grupy społeczne i etniczne, które nigdy nie tworzyły spójnej jedności. Nie ma możliwości pogodzenia tych przeciwnych wspomnień; jedynym możliwym sposobem nadania pamięci zbiorowej kształtu pożądanego w porządku demokratycznym jest konfrontacja i negocjowanie tych rozbieżnych poglądów, czyli dokonywanie ‘transakcji dialogicznych’.

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities.

Cet article présente et analyse les conceptions d’Henri Poincaré sur l’impossibilité logique de dériver des propositions impératives à partir de propositions indicatives. Dans un premier temps, le point de vue de Poincaré est comparé à celui de David Hume. Dans un second temps, il est démontré que la thèse de Poincaré a été, implicitement ou explicitement, essentielle dans les tentatives de construction d’une logique des normes en tant que catégorie linguistique spéciale ainsi que d’une logique déontique. La logique déontique permet en effet de formuler des principes généraux concernant la séparabilité logique des énoncés déontiques (énoncés contenant des opérateurs déontiques) et non-déontiques. L’article se conclut avec quelques remarques sur la réception des idées poincaréiennes dans la littérature logique et philosophique – la deuxième question est illustrée par la philosophie du droit.

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