| Max Urchs. Klassiche Logik. Eine Einführung, Logica Nova. Akademie-Verlag, Berlin 1993, 170+xii. The author gives a concise elementary introduction to classical propositional and predicate logic. The aim of the book is to help students in studying the basics of these logic. In accordance to his aim, the included ten lectures are accompanied by exercises and solutions for all the exercises. The whole book is written in the polish tradition of logic and so it focuses on the explication and treatment of consequence operations, which are divided into semantic ones and syntactic ones. Urchs explains that the language is the subject of logic, because premises and conclusions of logical entailments are linguistic entities. According to this, one of the main businesses of logic is seen in the translation of the logical form of sentences of some given language into the formal language of logic. In order to reach better adequacy of this translation, the logic enriches and improves its own formal means for analyzing. In this context is settled down the shift from propositional logic to predicate logic. In all parts of the book Urchs introduces the most important metatheoretical results significant for the given logical theory. So, concerning propositional logic, he not only reports results about consistency and completeness, but gives proofs for these results and for deduction theorem and functional completeness too. In all parts of his book the author stresses question of decidability and computability. In this connection, however, one could wish to have introduced the distinction between constructive and nonconstructive metaproofs. |
The author stresses the ontological dimension of logic,
points at direct philosophical consequences of fundamental results of modern logic and
metamathematics. A little puzzling for a newcomer in logic could render some places where
the author doesn't clearly enough discern between truth, true in a model and logical
truth, so when he writes (p.49) the truth of a formula is preserved by substitution. Some
places of the book remind of logical atomism, e.g., when the author writes (p.53) that the
inner structures of elementary propositions mirror the structures of reality. Exceeding in an introduction to logic usually treated topics, in the second part of his book Urchs has included lectures about set theory, relations and structures and number theory. Based on the so developed framework, the author is able to deliver a nice introduction to the theorems of Gödel and Church and connected metamathematical results. In all his parts the Klassische Logik is written self-explaining, understandable and introducing into the philosophy behind the formal stuff developed in it. So, the book will be very helpfully for everyone interested in exact analytical philosophical methods. Werner Stelzner (Jena) V. S. Mes'kov, O.Yu. Karpinskaya, O. V. Russia is a country of long distances. Therefore, you may prefer to travel by plane. However, there may be several reasons not to take plane. The authors of "Logic: Science and Art" invented a new one -- travelling by train you may get in touch with logic. Reading the book, you will become introduced not only to logic, but also to |
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| some inventions of Russian's students, to the rights and
duties of a Russian conductor, to the customs in Russian trains, and, by the way, to a
considerable part of the intellectual and practical life in Soviet Union and Russia. I
suppose, you have the feeling that this is not a textbook on logic, and not a novel.
Probably, you are right. Nevertheless, it is possible to read it as a textbook, or as a
novel. The setting of the story is easy told: some people travel by train in the same compartment, two of them being the curious conductor and a professional logician. During their long journey they have some trouble and adventures, and a lot of time to reflect on the "logical background" of their conversation on what happened. With a nice trick the authors succeeded to present even correct formal formulations without interrupting the plot. Besides an introduction into propositional and first order logic the book contains discussions on what is logic about, on names, on definitions, and (appendix I) on inductive reasoning. Obviously the book does not aim to substitute a traditional textbook of logic. On the contrary, the authors recommend some usual textbooks available in Russia to the reader. The book seems to be written mainly for two types of readers: for the students of logic, who permanently ask "What is logic for?" (all for us who teach know these students); and for anybody, who wants to have a first entertaining overview. Doubtlessly, the book should be interesting also for all people curious about life in Russia, and for logicians engaged in didactic questions. Uwe Scheffler (Berlin) |
Elke Brendel. Die Wahrheit über der Lügner. Eine philosophish-logische Analyse der Antinomie des Lügner. Walter de Gruyter, Berlin-New York 1992, 230 pp. This book consists of three parts. Part I. serves as a general introduction to the whole and it is devoted to intuitive explanations of the Liar antinomy as well as the adequacy-conditions for its solution. In particular, the authors presents various versions of the Liar, including the strengthened Liar, discusses concepts of an antinomy and a paradox, and states four adequacy conditions for any acceptable solution of the Liar. The conditions are these: 1. the solution must be consistent; 2. a formal machinery used in the solution must preserve to a great extent arguments expressible in natural language; 3. the solution must be sufficiently strong in order to avoid other antinomies 4. if the Liar-sentence is regarded as meaningful, then a formal representation of the intuitive formulation of the antinomy must be expressible in the system which serves as a framework of the solution. Part II. is historical. One can find in it a short history of the Liar from Epimenides to modern mathematical logic. A special attention is laid on Aristotle, Wilhelm of Ockham, Paulus Venetus, Thomas Bricot, and Bernard Bolzano. The distinction of semantic and set-theoretic antinomies is also introduced here. The author also argues that the strengthened Liar is a good criterion for distinguishing of both kinds of antinomies. Part III. is obviously principal in the whole book. It contains a critical review of selected modern solution of the Liar. This part begins with a brief outline of syntax and semantics of a language in which formal reconstructions of the antinomy are performed in the next chapters. Generally speaking, it is the language at least of the second order which contains the predicate "is true" and means |
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| needed for employing godelization. For this language,
Tarski's theory of truth is given and the related hierarchy of languages is introduced.
This last device is used for showing Tarski's solution of the Liar. Next, Brendel outlines
various other solutions, including those proposed by Robert L. Martin, Saul Kripke, Anil
Gupta, Jon Barwise and John Etchemendy, John L. Austin, Bradley H. Dowen, and Graham
Priest. Thus, the book reviews most major solutions to the Liar: truth-value gaps
theories, situation semantic, set theory with non-well-founded sets, systems within stable
truth-values and paraconsistent logic. Brendel herself decisively favors the Tarskian
solution via the hierarchy of languages. Her position may well expressed by the
title of the last chapter of the book: Zurück zu Tarski (Back to Tarski). Why? Because,
Brendel argues, Tarski's solution is universal, natural, and modestly expensive. In
particular, she tries to demonstrate that also other solution cannot avoid the distinction
of various levels of language. Of course, she clearly sees that the Tarskian solution has
some disadvantages. For example, it produces a problem of the highest metalanguage, that
is the metalanguage for all other languages. Brendel's book has several virtues. First of all, it is the most extensive and rigorous (from the point of view of modern logic) treatment of the Liar and its history. It is strange but since 1910 when Rustow's, Der Lügner. Theorie/Geschichte und Auflösung (today obsolete) was published, no historic-systematic monography on the Liar has appeared. Thus, the reviewed book fills an essential |
gap in the current philosophical literature. Although Brendel
does not pretend to give a complete history of the Liar, perhaps some omissions should be
noted; I restrict myself to few additions from the recent history. First, it was
Lukasiewicz who formulated in 1915 this version of the Liar which was later used by
Tarski. Also Lukasiewicz proposed a solution consisting in regarding the Liar-sentence as
ill-informed; however, his proposal was not based on the language/metalanguage
distinction. Second, although Tarski produced the full theory of the Liar in framework of
the Hierarchy of Languages, he followed ideas elaborated in Poland by Lesniewski. In
particular, Lesniewski was responsible for the diagnosis of the Liar which became the
starting point for Tarski. Third, one should also remember about solution-proposals of
Dorothy Grover (Inheritors), and Patrick Grim and Gary Mar (The Chaotic Liar). One can expect that Brendel's own position will awake various reactions. Everything depends on evaluation of the costs which must be paid for solution of the Liar. One is clear: nothing is free of charge here. Thus, one must decide which cost is lesser, for instance the stratification of our language into levels or admitting truth-value gaps. On my part, I agree with Brendel that the Tarskian solution is the best. Thus, I welcome this book as a very valuable contribution to philosophy of logic. Jan Wolenski, Jagellonian University, Krakow, Poland |
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| Peter Geach. Philosophical Encounters. ed.
by Harry A. Lewis. Synthese Library, Studies in
Epistemology, Logic, Methodology and Philosophy of Science, vol. 213, Kluver
Academic Publishers, Dordrecht-Boston-London, 1991, XI+320 p. Peter Geach is one of the foremost contemporary British philosophers who has made a valuable contribution to logic and philosophy. His work and ideas invariably roused a keen interest of colleagues, and caused vigorous scientific discussions. Therefore it was a good proposal of Dr Esa Saarinen to celebrate P. Geach's work and to present it by this collective monograph. The aim of the editor (as he maintain in the preface) was to reflect the spirit of P. Geach's philosophical career, and that is why the book under review has the shape of open debate. The book is organized into three parts. The first part acquaints a reader with (some facts of) P. Geach's intellectual development. It contains A Philosophical Autobiography written by P. Geach specially to this volume, and extracts from the correspondence between Professor W.V.O. Quine and P. Geach. These extracts "throw new light on many familiar themes from the writings of both philosophers: among them the objects of belief and other attitudes, issues in set theory, the nature of causality, and evolution in epistemology." (p. IX) The second part of the book contains original articles presented by some leading contemporary philosophers and logicians. Articles are grouped into four sections linked with some of topics in professor Geach's areas of interest: the history of philosophy, logic, theory of identity, and the philosophy of religion. |
P. Geach contributed short introductory article to each
section (excluding the section about identity -- but it can be considered as a sub-section
of the extended section of logic and identity). Let mi give here the list of all the
contributors of this part: D.P. Henry, A. Kenny, B. Wolniewicz, G.H. von Wright, J.E.J.
Altham, G.E.M. Anscombe, J. Hintikka, J.D. McClawle, M. Dummett, A.W. Mller, C.F.J.
Williams, N. Malcom, H. Meynell, and of course, P. Geach himself. I thing that this
impressive list speaks for itself. A very interesting peculiarity of the book is that P.
Geach gives his critical responses to each paper. These replies form the final part of the
book: this part is also a fascinating and rather instructive reading, especially, if to
read P. Geach's replies with the articles to which they refer. A complete bibliography of
P. Geach's works (running to 173 items) is a valuable addition to the volume. So much for the structure of the book. I will now consider some of the articles in more detailed manner. Taking into account a specificity of this journal, and the fact that it is hardly possible in a short review to deal with all the papers of the book. I shall take a closer look only at those of articles which are of interest directly from the logical point of view. Boguslaw Wolniewicz presents some considerations On the Discontinuity of Wittgenstein's Philosophy. In this paper he deals with the following problem: "How is Wittgenstein's later philosophy related to his earlier one?" He gives a comparative analysis of Tractatus and Philosophical Investigations. And his answer to the above question is the following: there is a chasm between "early Wittgenstein" and "late Wittgenstein". According to Wolniewicz, Tractatus contains a profound and highly coherent philosophy of language based upon a radically new kind of metaphysics (metaphysics of facts and situations), while Investigations does |
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| not have any clear doctrine about language, and
does not deal with language at all. Wolniewicz considers the "language-games"
discussed in Investigations as prelinguistic sign-systems ("one-class
systems"), and distinguishes such systems from real languages which are
"two-class systems". He concludes that Philosophical Investigations are
the expression of a dramatic departure from Frege's tradition towards psychologism and is
(unlike Tractatus) "a formless accumulation of ambiguous hints and loose
remarks…." (p. 79). P. Geach flatly disagrees with such an opinion, and considers
it as a result of "extraordinary failure of understanding". Georg von Wight deals with Possibility, Plentitude and Determinism. His paper concerns both tense and modal logics, and also contains some comments on ancient authors. Von Wright starts from the well-known Diodorus's "definition" of possibility -- D-possibility ("everything which is possible either is or will be true"). He also considers other D-modalities, and then he consequently introduces concepts of F-modalities (e.g. F-necessity is "necessity of truth as fact"). E(epistemic)-modalities, R(real)-modalities etc., and analyses thes concepts. P. Geach evaluates this article as "a worthy pies of work", and emphasized that all von Wright's work in area of tense (and modal) logic deserves careful study. This estimation can be rightfully applied to P. Geach's own article which prefaces the section Logic. In this article P. Geach continues to develop the views which he has expressed in some previous papers -- about the necessity of more widespread logical training, and the methodology of logic |
teaching. He stressed that many educated people
are logically analphabetic, and points out that people's ordinary intuition often does not
work ("men's logical vision is likely to be myoptic if unaided by logical
spectacles" (p. 100)). He corroborates these claims by some striking examples. P.
Geach vigorously objects of teaching of so-called "traditional logic",
especially against "the doctrine of distribution". He maintains that there is
nothing logically sound in this doctrine. And he is right, on the whole. However
it seems to me that such too severe criticism of traditional logic can be
accepted only with a serious reserve. Of course, it would be inadmissible to limit oneself
exclusively to teaching of traditional logic. Especially if the question is about
uncritical reproduction of all those mistakes, prejudices, and confusions which have been
accumulated in "traditional" textbooks. Nevertheless, studying of some elements
of traditional approach to analysis of reasoning can have a certain propaedeutic
importance, surely subject to the modifications and amendments according to demands of
modern logic. J.E.J. Altham (in Plural and Pleonetetic Quantification) investigates relational quantifiers, such as "there are more js than cs", "nearly every j is c", and "many js are c". He also deals with pleonetetic logic, that is the logic of the quantifier "most" ("most js are c"), considers some interesting examples with this quantifier, and gives some principles for monadic pleonotetic logic. G.E.M. Anscombe's paper has the title On a Queer Pattern of Argument. The question is about the formally valid pattern of reasoning: 1o If p, then q. p and q. |
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| Then she considers some concrete arguments constructed in
accordance to this pattern. Let me adduce here one of these arguments (Anscombe's Argument
A): 1. If that tree falls down, it will block the road for a long time. 2. That's not true if there's a tree-clearing machine working. 3. If the tree doesn't fall, there will be a tree-clearing machine working. The tree will fall and the road will he blocked for a long time. Anscombe asks: "How is it… that there is obviously something screwy about this argument?" (p. 121). She does not give any answer to this question. (In conclusion of the paper she notices that she raised a problem rather then clarified anything). P. Geach points out that the problem consists in interpretation of conditionals. He suggests to consider a conditional (if…then…) met in the above pattern of arguments as a ceteris paribus conditional. He also claims that the second premise of Anscombe's examples must be not the one she gives but rather: "Not: if r and p, then q". Then be concludes that from this there is no way to get the conclusion 'p and q', if we read the 'if' as a ceteris paribus 'if' throughout. But I think that here a quite different solution is possible: the solution on the basis of interpretation of "if…then…" as a necessary conditional connection. Let us take a closer look at premises of the above pattern. We can easily get (p ® q) ® p from 2o and 3o. But it means |
that p must be a necessary proposition (because in directly
follows from a true (1o!) proposition which expresses a necessary conditional
connection)! And it is not strange at all that a necessary proposition (p) proved to be
true. Thus, an effect of "queerness" of the above pattern arises only on account
of inappropriate selection of examples. Premises of this pattern can be true only when p
represents a propositions of necessary character, and examples of the concrete arguments
should be selected accordingly. Jaakko Hintikka in Geach and Methodology of the Logical Study of Language considers the methodological situation in contemporary Sprachlogik and logical semantic at large. He analyses a powerful tradition on philosophy of language which was initiated by Gottlob Frege and developed by such philosophers and logicians as early Wittgenstein, Quine, and Davidson. A characteristic feature of this tradition consists in using the strategy of illuminating ordinary language by translating it into quantificational forms. Hintikka asks: "Why is it supposed to be useful to translate ordinary language into logical notation for the purpose of logical, philosophical, or linguistic clarification?" (p. 137). He points out two main weakness of the Fregean (and neo-Fregean) approach: (1) the problem of "miraculous translation"; (2) the overestimation of the unproblematic character of the semantics of logical languages. James McCawle deals with Natural Deduction and Ordinary Language Discourse Structure. He aims at "rapprochement" between formal logic and the psychology of reasoning, and tries to alter the Fitch system of natural deduction so that to keep to minimum "the discrepancies" between natural language argumentative texts and the corresponding formal proofs. I find this aim as a rather questionable one: firstly -- it is doubtful whether this aim can be ever attained; secondly -- one may doubt as well, whether it is necessary and useful to reproduce psychological processes in logical formalism. It seems to me that alone such a formulation of the aim indicates |
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| at a serious deviation towards psychologism in logic.
The papers of the section Identity are of especial interest. The editor of the book is right when he points out that no discussion of P. Geach's work would be complete without mention of his views on identity. Readers will not be disappointed in the paper of this section: Michael Dummett deals with the question Does Quantification Involve Identity? |
Anselm Muller investigates Conceptual
Surroundings of Absolute Identity. Christopher (in On Sameness
and Selfhood considers the topic of personal identity. P. Geach's replies to
these articles form in effect and original paper on Identity Theory which
elucidates and develops his approach to the problems. To summing up, I do evaluate this book as excellent and rewording reading which can be recommended both for pure logicians and for "general" readers who are interested in contemporary British philosophy. Yaroslav Shramko |