| Jan Šebestík, Bernard Bolzano, L'histoire des
science, Textes et études. J. Vrin, Paris 1992, pp.522. In order to present a general outlook about the content of this extensive monograph a survey of its structure may serve as a guideline. The work of J. Šebestík contains besides various technical components a chronology, primary and secondary bibliographies, a German-French terminological dictionary, a notation list and indexes) a foreword, an introduction and a conclusion four principal parts subdivided into fourteen chapters in all. Part I (pp. 33 - 112), primarily devoted to Bolzano's mathematical papers published from 1804 till 1817, analyses his geometrical ideas, among others his views on the theory of parallels and topology, and topics connected with the arithmetization of analysis. Part II (pp. 115 - 293) deals in four chapters with Bolzano's logic and philosophy of logic as elaborated in the first two volumes of his Wissenschaftslehre; the fifth chapter of this part discusses very briefly Bolzano's philosophy of science proper expounded extensively in the fourth volume of the Wissenschaftlehre. Part III (pp. 297 - 431) concerned with Bolzano's mathematical system, presents his doctrines of sets, magnitudes and numbers, the construction of real numbers and the theory of real functions, together with some related topics of his Grössenlehre. Part IV (pp. 435 - 474) handles the subject-matter of infinity systematically developed in Bolzano's posthumously published Paradoxien des Unendlichen (1851). Šebestík's monograph combines very aptly the approach of a historian of science who wants to explain, in the given case, Bolzano's position in respect to his forerunners and successors, with that of a philosopher of science, who attempts to study substantive problems of Bolzano's logic and his contribution to mathematics from a systematic point of view. In both case, the author avoids the trap of an uncritical attitude towards a man whose merits in the field of science or |
philosophy are without any doubts. Šebestík emphasizes with
right various brilliant ideas of B. Bolzano which, however, had no immediate impact on the
growth of scientific knowledge, but does not conceal the weak points of his doctrines
which are due, as I suppose, to some of his philosophical prejudices. Šebestík
synthesizes results achieved by contemporary bolzanists and historians of logic and
mathematicians, and enlarges them by new insights, especially when dealing with Bolzano's
mathematical ideas. By utilizing the publications of French and Czech authors which are
not usually - especially for linguistic barriers - taken much into account, he overtly
confesses the double medium of his home. Because of professional reasons I shall now discuss in some detaily only part II. The first chapter of this section attempts to elucidate with much skil what Bolzano meant by his entities-in- -itself, a controversial topic of bolzanian studies. The second one analyses the logic of ideas and concepts, and the third one what is today called Bolzano's logic of variation. What has to be, according my view, highly appreciated is, in the next chapter, connected with an explication of his doctrine of entailment (Abfolge). There have to be raised some critical remarks too. They have to do rather with what is not investigated in detail, than with the way how Bolzano's logical conceptions are reconstructed. It is quite obvious that Šebestík had to adopt a selection of topics which were to be studied profoundly and which were mentioned only in general. He is well aware of this dilemma: in some cases he simply refers to other authors, e.g. when dealing with Bolzanos's views on probability or his Schlusslehre (pp. 254, note 90; 257, note 93). Nevertheless, at least two aspects of Bolzano's logical ideas would have deserved, for historical and systematic reasons, an appropriate attention. First, I mean his "logico-ontological" atomism connected with his vain attempt to find the most simplest concepts which cannot be further analyzed into more elementary ones and his distinction between logical concepts in the strict |
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| sense and all other ones. Second, the discrepancy between
Bolzano's theoretical attitude toward the indirect proof and his practical approach as a
working mathematician may shad light on the inner tension of his thought, of his
activities in logic, methodology of deductive sciences, rationalistic philosophy and
mathematics itself. To sum up: Šebestík's monograph which is an excellent achievement in scholarship, has to be acknowledged as a valuable contribution to bolzanian studies and history of logic and mathematic as well. Karel Berka Clifford Brown. Leibniz and Strawson. A New Essay in Descriptive Metaphysics. Philosophia Verlag Munich, Hamden,
Wien, 120p. hardbound Clifford Brown's book is both a critical reply on Peter Strawson's views concerning Leibniz' conception of individuals and individuation, as explained in his "Individuals" and a skilled and sophisticated outline of what Brown claims to find in Leibniz' work on the mentioned topic. The book is divided into an Introduction and seven chapters. It contains an index (pp. 118-121) and a bibliography (pp. 113-117). The caption of chapter 7 is the concluding and stringent result of Brown's examination of Strawson's views on Leibniz and individuals: "Alternatives that are as Unhistorical and as Unnecessary as they are Unappealing". The "Envoi" of chapter 7 present a short summary of the previous 6 chapters. The main background of the book is: - Leibniz' concept of individuals and individuation, which appears to be somewhat strange for 20th century common sense people with all its windowless monades, preestablished harmony and all that stuff and - Strawson's interest in at least a "possible Leibniz", because he "offers a marked and |
significant contrast to Strawson's own theses" (Brown,
p. 12). Strawson himself grounded his views on individuals and the identification of them
on the concepts of space and time and our location in it. That's why he came to the
conclusion, that "identifying thought about particulars necessarily incorporates a demonstrative element." (cited after Brown, p. 12). Although Brown claims, "that Strawson's account of Leibniz'
position is substantially and not trivially different from the position which Leibniz
actually held" (p. 13), he uses the following seven main critical points of Strawson
on Leibniz, in order to reject Strawson's critique and to outline those positions, which
he thinks to be held by the historical Leibniz: 1. The basic individuals are monades, the models for which are minds. 2. Each monad has a unique complete individual concept in purely universal terms, therefore the identity of indiscernibles holds as a necessary truth. 3. Monades can be individuated without reference to bodies or persons. 4. Each monad represents the entire universe from its own point of view. 5. There is no concept "public space" for Leibniz and therefore a plurality of monades with quali- tatively identical states of consciousness is logically possible. Leibniz fails to provide for the identification of individuals. 6. Even if we assume contrary to Leibniz a public space there can be individuals with different spatial positions but with the same description in universal terms. 7. Leibniz therefore has the following unappealing alternatives: (a) Reduce the (empirical) identity of indiscerni- |
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| bles from a necessary truth to a postulated contingent one,
satisfied only in our actual world. (b) Make complete individual concepts rather than minds the basic individuals. The result is logical purity without empirical reality. (c) Make complete individual concepts rather than minds the basic individuals and to allow instantiations of them. For instantiations of concepts the identity of indiscernibles must be made contingent. This mixed interpreta- tion is truest to the historical Leibniz. (on the 7 points cf. p.12/13) The reader shall decide by himself, whether these points meet his own view on Leibniz or not. Anyhow, these seven points are the foil of Brown's reply to Strawson's concept of Leibniz. Chapter 1 (Monades as Basic Individuals, pp. 15-31) is an answer to the first point. It makes clear, that Leibniz has a quite sophisticated model of reality, distinguishing three levels: the monades, the aggregates of monades and the appearances of aggregates, each with its own relating active/passive characteristics and further subdivision especially on the level of aggregates (cf. p. 21ff.). And while Strawson thinks Leibniz' monades to be non-spatial and unembodied, Brown proves how monades are meaningful embodied in spatio-temporal relations, since Leibniz held a relational concept of space and time. Space and time are for Leibniz only derived structures. On each level of Leibniz' reality we find genuine individuals, so not only monades are individuals. Chapter 2 (Complete Individual Notions, pp. 32-43) is an attack on Strawson's second thesis. Brown shows that "Leibniz clearly rejected the thesis that complete concepts include only universal, or general, terms" (p. 38). Descriptions in purely universal terms (named `full concepts' as opposed to `complete concepts', characterizing individual substances) express only species or abstracted kinds. Leibniz' thesis of |
individuals as infima species expresses a special
(and nowadays uncommon) understanding of species. The main point is that the
uniqueness of an individual is internally represented in the complete concept, not through
external characteristics like space-time-coordinates. It is a metaphysical thesis of
Leibniz' whole system that the concept of two individual substances, which differ only
numerically, is an erroneous idea. (cf. p.41). In Strawson's thesis 3 the three levels of
reality are not distinguished. Chapter 3 (Body, pp. 44-52) explains both the role of
`body' on each of Leibniz' reality levels and Leibniz' treatment of those things, which
are called `bodies' in every-day life. Brown shows that Leibniz claimed that in our actual
world all finite monades are bodied. The function of `body' for Leibniz is to enable the
finite monades to stand in relation to its world. And if Leibniz admits the metaphysical
possibility of a world of unbodied monades, "then God supplies them with the function
of matter through a miracle" (cf. p. 50). So Strawson's thesis 3 is at least
misleading. How then are the individuals interrelated, if they are characterized only by intrinsic proper-ties? Chapter 4 (Relations, pp. 53-71) tries to solve this problem. It contains an interesting discussion and rejection of Leibniz' critics Russell, Parkinson and, of course, Strawson. Brown shows that Leibniz did not deny the reality of relational events. The main point linking the irreducibility of relations and the substance--metaphysics (according to Brown, and against Russell founding the predicate-inclusion-thesis of Leibniz and not derivative from it) is the distinc-tion between possibility and compossibility. Two separate relational events in two monades must be compossible, because "the Universe [is not] a collection of all possible ... since all possible are not compossible" (Leibniz, cited after Brown, p. 60). What is commonly viewed as a relation with "one leg" in each participant of the relation can be described as a set of compossible relational events in each monad. |
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| Chapter 5 (Public Space and Private Worlds,
pp. 72-80) shows in which sense Leibniz accepts a public space and not only private spaces
of each monad. The correlatives of each finite monad's perception are objective, moreover
on the level of aggregates and phenomenas. Leibniz wrote in a letter to de Volder:
"Every change, spiritual as well as material, has its own place [sedes], so
to speak, in the order of time, as well as its own location in the order of co-existents,
or space." (cited after Brown, p. 79). In that sense Strawson was wrong in claiming,
that according to Leibniz there is no public space. A public space is for Leibniz
derivative but objecti-ve and it doesn't play the same ultimative role in individuation as
for Strawson. There remains the problem of only numerically distinct individuals, having the same conscious-ness or having the same description in universal terms. An what about symmetric universes acc-ording to Leibniz' ontological views? The chapter 6 (Individuation, pp. 81-99) contains an extensi-ve discussion of Leibniz' views on the principle of identity of indiscernibles, on real and personal id-entity, on basic particulars for which the principle holds, on its epistemical fallibility but metaphysi-cal truth. Once more Brown makes clear that "the identity of indiscernibles is thus grounded on and established for individual substances only." (p. 90) "All and only monades and the real and personal identities dependent on monades must of necessity be individually unique." (p.92). Brown distinguishes several versions of the principle and shows that Leibniz held only one version of it, which is grounded on complete individual concepts and that he did not pay attention to difference in name. So, once more, Strawson is refuted and the mentioned title of chapter 7 seems to be justified. The book treats a quite special theme and it needs educational background. So, it is not quite clear - at least for the reviewer - why the |
book was published in the Series `Introductions'.
Nevertheless, Brown wrote an interesting and thorough book. The book does not explain why
so many people have a concept of Leibniz which is similar to Strawson's (as Brown realizes
at p.2 13) and what Leibniz-style ontology can contri-bute to, say, modern science. What
use can ma-ke a physicist of the concept of monades? The monograph does, however,
historical justice and it leads our attention to an interesting theoretical concept in
descriptive metaphysics and in philosophical logic as well. Ralf
Dombrowski Walter P. van Stight. Brouwer's Intuitionism. (Studies in the History and Philosophy of Mathematics; Vol. 2). Elsevier Science Publishers B.V., North Holland, Amsterdam-New York-Oxford-Tokyo, 1990, xxvi + 530 pp. "Brouwer's Intuitionism" is a very nice book, excellently written with remarkable sympathy for Luitzen Egbertus Jan Brouwer (1881-1966), whose work constitutes one of the most exciting chapters of the philosophy and foundation of mathematics. The author succeeds in characterizing the development of Intuitionism by showing the correlations of Brouwer's "Life, Art and Mysticism". Intuitionism he shows in a very complex phenomenon and not an isolable question of the pure foundation of mathematics. Van Stight expresses his main intention in the preface: "This book tries to present an ordered account of Brouwer's views an can be establi-shed from all the evidence available and show that together they form a coherent and consis-tent philosophy and foundation of mathematics" (p. xi-xii). Van Stight's 1971 dissertation with the same title creates the basis of his investigations. But in |
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| 1971 Brouwer's published papers were the only source
available. Now the unpublished writings are also taken into consideration. Chapter I "The Brouwer Bibliography" (pp.1-19) provides a complete list of Brouwer's known writings, both published and unpublished. The Appendices (pp. 387-505) contain a selection of Brouwer's writings that are not accessible to a general reader "either because they have not been published of have only been published in Dutch" (p. xiii). The latter are published both in Dutch and in van Stight's English translations. What is the method of description and interpre-tation of such a difficult and complex subject? "For an understanding of Brouwer's ideas the 'genetic' approach seemed most appropriate and natural and it prompted the overall design of this book: a genealogy" [should be "genealogy" - I.M.] of Brouwer's Intuitionism starting from the man Brouwer" [Chapter II "Brouwer, Life and Work"], "followed by his philosophy of life" [Chapter III "Brouwer's Philosophy"], "his conception of mathematics" [Chapter IV "Brouwer's Philosophy of Mathematics], "and its methodology" [Chapter V "Language and Logic"], "and finally his Intuitionist Mathematics" (p. xii) [= Chapter VI]. This method yields a description and interpretation of Brouwer's Intuitionism in several ways; the author throws light on a interesting, complex, but also problematic personality. Van Stight focuses his analysis on Brouwer's own writings and only some selected circumstan-ces and persons with significant influence on him. This makes the book very valuable, regard-less of the fact that the reader cannot expect special discussions either concerning the influence of Brouwer on other thinkers such as e.g. Ludwig Wittgenstein or with respect to the modern development of Intuitionism. There is only one exception: There are parts which deal with the formalization of Intuitionist Logic including a list of selected contributions, separately presented as an extraction of the final list of literature. One of van Stight's basic assumptions in that Brouwer's early nonmathematical writings - Profession of Faith of L.E.J. Brouwer (1898), Life, Art and Mysticism (1905) - |
express the nearly unmodified source of his "fundamental
ideology": Life, Art and Mysticism "is the clearest expression of his
philosophy of life, which inspired his intuitionism..." (p. 35). Analogously he
assumes that Brouwer's dissertation On the foundation of mathematics represents
the fruitful root of his philosophy of mathematics: "Practically all his
intuitionist innovations can be traced back to the Foundations: his rejection of
the principle of the excluded middle, the concept 'meta-mathematics' and even the later
development of choice sequences" (p. 44). The author divides up the most interesting years 1905-1928 into periods as follows: - Until 1908 the "'First Act of Intuitionism' had been the exposure of existing language as the villain, totally inadequate as a carrier of mathema-tical thought and guilty of distorting the mathematical reality" (p. 70). - 1909-1913: The topological years. - 1912: Brouwer's return to the battlefield of the Foundations of Mathematics with his inaugural address Intuitionism and Formalism. Now he ana-lyses the Intuition of Time as the fundamental phenomenon and shifts his emphasis to Set Theory. - 1918-19: Begründung der Mengenlehre unab-hänging vom logischen Satz vom ausgenschlosse-nen Dritten is regarded as the "Second Act of Intuitionism" which Weyl called the "Brouwer Revolution". - 1923: Brouwer's attitude of 1908 that the Prin-ciple of Excluded Middle (PEM) is unreliable when applied in as infinite system had been changed to a new conviction "that contradictions can be shown to arise from the unjustified use of the PEM in mathematics" (p. 85). For the first time Brouwer criticizes the Principle of Reciprocity of Complementary Species (Elimination of Double Negation). - 1923-1928: Several unsuccessful attempts to find an absolutely rigorous proof of the Fundamental Hypothesis of Brouwer's function |
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| theory, first stated in 1918, result in the abrupt
ending of Brouwer's re-construction program.This hypothesis assert "that for all
functions defined on the continuum the function value of each point is wholly determined
by a definite segment of the sequences generating the point" (p.91). In view of recent developments of logical theories like Relevant Logic, Paraconsistent Logic, Linear Logic (including its intuitionist variant), and seve-ral other substructural logics. I think that van Stight is right in saying that his book "serves as a reminder of the roots of Intuitionism in the vi-sion of its founder. His vision of the true nature of mathematics inspired his Intuitionist innovati-ons, it should be the guide in our interpretation of his notions and principles and remain a continuing source of further intuitionist developments" (p.xiv). Notwithstanding some orthographic mistakes concerning titles of Brouwer's writings (e.g. on pp. 10, 71, 93, 104, 106, 133) the book meets very high technical standards. Ingolf Max Nikolay Milkov. Kaleidoscopic Mind: An Essay in Post-Wittgensteinian Philosophy. Rodopi, Amsterdam-Atlanta, 1992, x + 412p. The book is an ambitious one, aiming "to suggest a new method of philosophy" (49), "to give a 'new system of categories'" (13), and "to help answer all questions which are subject of ... critical inquiry" (12), but also "to give an understanding of Wittgenstein philosophy" (6) and even "to retranslate all Wittgenstein's discoveries concerning the philosophy of language into the 'language' of conventional philosophy" (49). The reviewer's opinion is that the book fails to fulfil these ambitions (though |
this may not be true according to the standards the book
itself proposes). Nevertheless, the manner of its failure is of some interest. The author
is a Bulgarian, who wrote his dissertation on logical atomism and translated three
Wittgenstein's books into Bulgarian (Tractatus, Philosophical Investigations, Remarks on
the Foundations of Mathematics), in 1989-90 was a visiting scholar in Bielefeld (with Eike
von Savigny) and in 1990-91 in Oxford. For the last 8 years he has been working on a
book-length history of the older analytic philosophy, which is to appear in 1993 under the
title The Varieties of Understanding: English Philosophy since 1899. The ambitions of the
book seem to reflect the experience many of the former Communist countries philosophers
made after contacts with the West became possible: that contemporary philosophy - despite
all its sophisticatedness in certain local, small scale problems - is rather naive or
perhaps silent in certain global, large scale questions, which belong to the
philosophi-cal tradition and which remained popular and considered important in the former
Communist countries. Such are the questions of the right method in philosophy, of the
central problem of philosophy, of its systematicity etc. The reviewer shares this experience and feels a sort of sympathy to the author's undertaking. However, he is rather unhappy with what the book actually provides. The method recommen-ded is called "analectical" - which means it is a combination of the analytic and the dialectic approach (76) - and its basic feature is (besides being unexplainable - p. 68) feature is that we should separate what was thought to be one or bring together what was considered separate (73) ... but the method does not tell what in which case. The method has its counterpart in the field of ontology: everything is at the same time one and many; in the philosophy of mind and epistemology: the mind as well as its objects is of kaleidoscopic nature, is a flashing of aspects (89 et passim). The manner of presentation is rather kaleidoscopic as well: the reader finds him- |
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| or herself in the middle of a flow of analogies, examples, excerpts from other philosophers (the author refers to Wittgenstein to justify that - writing in fragments and expecting the reader to build the connections between them him - or herself). Numerous misprints and sometimes quite uncommon English do not help either. | The author has read a lot, and possibly
wider than it is usual in the West, he knows his Wittgenstein well, but his text is
probably too vague for anyone who does not share his preconceptions. Josef
Moural |