Wittgenstein’s ‘ethnological approach’ to the philosophy of mathematics, in particular his discussion of calculation as an experiment and the limits of empiricism in mathematics, is presented against three interrelated backdrops: (1) James’ critique of Spencer’s evolutionary empiricism, specifically regarding necessary truths; (2) the Cambridge Anthropological Expedition to Torres Straits, led by Haddon and Rivers, whose Reports implicitly confuted Spencer; and (3) the subsequent work of Malinowski, especially his supplement to Ogden and Richards’ The Meaning of Meaning, a (...) book sent to Wittgenstein upon its publication in 1923. String figures as mathematics is a main illustrative example. (shrink)

This paper presents the main lines of reasoning in the Wittgenstein notes entitled ‘Cause and Effect: Intuitive Awareness,’ in the form of a series of dialogues between Wittgenstein, Russell, and a few other philosophical voices. Two of the dialogues relate to what, in Remarks on the Foundations of Mathematics, Wittgenstein called ‘the similarity of my treatment with relativity theory.’.

Sand drawings are introduced in relation to the fieldwork of British anthropologists John Layard and Bernard Deacon early in the twentieth century, and the status of sand drawings as mathematics is discussed in the light of Wittgenstein’s idea that “in mathematics process and result are equivalent”. Included are photographs of the illustrations in Layard’s own copy of Deacon’s “Geometrical Drawings from Malekula and other Islands of the New Hebrides” (1934). This is a brief companion to my article “Wittgenstein on (...) class='Hi'>string figures as mathematics” (2022), published in the journal Philosophical Investigations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:_Russell_ journal (home office): E:CPBRRUSSJOURTYPE2502\REVIEWS.252 : 2006-02-27 11:52 Reviews  HISTORY OF PHILOSOPHICAL ANALYSIS C P Philosophy / Purdue U. West Lafayette,  ,  @. Scott Soames. Philosophical Analysis in the Twentieth Century, Vol. : The Dawn of Analysis; Vol. : The Age of Meaning. Princeton: Princeton U. P., . Pp. xix, ; xxii, . . (hb), . (pb) for each volume. he last twenty years have seen (...) an explosion in books and papers on RusTsell ’s philosophy and its contemporary significance. There is good reason to think that this will continue as the contents of the Collected Papers are digested by Russell scholars and as more specialists contribute to the history of analytic philosophy more generally. Given all this good news, it is disconcerting to find a -page discussion of Russell, in a well-reviewed book by a first-rate philosopher, repeating many of the errors and misconceptions about Russell that scholars have worked so hard against. Soames’ discussion of Russell in the volumes under review is in fact so distressing that it alone compromises the book as a suitable introduction to the history of analytic philosophy. After briefly reviewing the outline of the two volumes, I discuss the errors concerning Russell, and conclude by drawing some lessons for Russell scholarship. Soames’ focus is on what he takes to be the most important and influential work of analytic philosophers, beginning with Moore’s Principia Ethica and ending in  with Kripke’s Naming and Necessity lectures. Kripke, in fact, marks the culmination of one of the two great achievements of analytic philos- _Russell_ journal (home office): E:CPBRRUSSJOURTYPE2502\REVIEWS.252 : 2006-02-27 11:52  Reviews ophy that Soames sees in this period: … the two most important achievements that have emerged from the analytic tradition in this period are (i) the recognition that philosophical speculation must be grounded in pre-philosophical thought, and (ii) the success achieved in understanding, and separating one from another, the fundamental methodological notions of logical consequence, logical truth, necessary truth, and apriori truth. (: xi) Moore is credited with the methodological innovation required by (i), as once we accept that what we think we know prior to philosophical reflection is a constraint on our epistemology, Moore’s response to scepticism, which Soames endorses, inevitably follows. But even Moore, and nearly every other figure that Soames discusses, is guilty of confusing necessity, analyticity and apriority. Soames endorses Kripke’s basic point that necessity is a metaphysical concept that can come apart from the epistemic notion of apriority and the semantic category of analytic propositions. Volume  repeats this charge several times, using it to undermine Moore’s views on ethics in Part One, Russell’s conception of analysis in Part Two, and logical positivism in Part Three. It is noteworthy that Soames takes Ayer’s Language, Truth and Logic as representative of logical positivism, ignoring contemporary scholarship on the Vienna Circle just as much as he ignores Russell scholarship. Part Four reconstructs Wittgenstein’s views in the Tractatus and Volume  ends with a discussion of Quine’s “Two Dogmas of Empiricism”. The second volume begins with a part on Wittgenstein’s Philosophical Investigations. This paves the way for Soames’ discussion of ordinary language philosophy in Parts Two and Three, which Soames sees as closely tied to the later Wittgenstein. Ryle’s Concept of Mind, Strawson’s early views on truth, Hare’s theory of goodness as well as Malcolm’s paradigm-case argument and Austin’s Sense and Sensibilia are investigated in these chapters. Part Four presents Grice’s theory of conversational implicature as the final nail in the coffin of ordinary language philosophy. In Part Five, Soames returns to Quine, this time discussing the ambitious arguments of Word and Object and the more general project of naturalized epistemology. Part Six articulates Davidson’s program for constructing a theory of meaning for natural languages along the lines of a Tarskistyle theory of truth, and Volume  ends with an extended discussion of the promise and limitations of Kripke’s Naming and Necessity. The material on Russell is entirely confined to four chapters in Volume : Chapter : “Logical Form, Grammatical Form, and the Theory of Descriptions ”, Chapter : “Logic and Mathematics: The Logicist Reduction”, Chapter : “Logical Constructions and... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:702 JOURNAL OF THE HISTORY OF PHILOSOPHY 33:4 OCTOBER t99 5 appears more as an anomalous figure in the spirit of Kierkegaard than a thinker of the mainstream. For Jaspers, philosophy is a vehicle to provoke a spiritual sense of the wonder of existence rather than an autonomous vocation which strives to recast its questions in increasingly radical ways. Most typically, Jaspers's emphasis on darker aspects of the human (...) predicament--guilt, anxiety, and death as the seminal existential motifs--does not exclude a more positive vision of Existenz as revealed through transcendence. The limits do not provoke a discourse of radical finitude which skirts the edges of presence, but instead indirectly point toward a transcendent mystery, or the "encompassing" (19-2o). If there is an aspect of Jaspers's philosophy that remains inadequately addressed in either volume, it is his preoccupation with the role of tragedy in the post-war era? In light of the premier importance that Hegel, Nietzsche, and Heidegger all grant to tragedy, Jaspers's passionate treatment of this topic in the context of the catastrophe of Western Europe merits far closer attention. Does not the issue of tragedy provide indispensable dues to chart the landscape of twentieth-century thought, and to amplify the differences which prevail in the portrait of politics as displayed by such diverse philosophers as Jaspers and Heidegger, Derrida and Levinas? FRANK SCHALOW DiUard University Norman Malcolm. Wittgenstein: A Religious Point of View? Edited with a response by Peter Winch. Ithaca, New York: Cornell University Press, a994. Pp. xi + 14o. Norman Malcolm at the outset of this, his posthumously published last book, focuses on the question: What did Wittgenstein mean when he said to his friend M. O'C. Drury, "I am not a religious man, but I cannot help seeing every problem from a religious point of view"? It was the right question. But Malcolm then--again on the first page of his book-proceeded to place restrictions on it, which were quite foreign to the spirit of Wittgenstein 's remark and which virtually crippled it. (1) He took Wittgenstein to be speaking of not social, psychological, or presumably even personal problems, but only of philosophical ones. (2) He chose to say that in Wittgenstein's later philosophy "there is not strictly a religious point of view, but something analogous to a religious point of view" (1, Malcolm's emphases). There is no reason to think that Wittgenstein would have accepted either of these restrictions on his remark. Nor does Peter Winch accept them in his forty-page discussion, which follows Malcolm's text in this book. In the upshot Malcolm finds "four analogies between Wittgenstein's conception of the grammar of language and his view of what is paramount in a religious life" (92). In both, he says, Wittgenstein emphasizes "an end to explanation," a sense of an "illness" pervading the human situation, "an inclination to be amazed at the existence of some ' Karl Jaspers, TragedyIs Not Enough, trans. Harald A. T. Reiche, Harry T. Moore, and Karl W. Deutsch (Boston: Beacon Press, 1952), 31-4O,93- io5_ BOOK REVIEWS 703 thing," and "doing, acting [having.] priority over intellectual understanding and reasoning " (92). But are such "analogies" really the crux of the "religious point of view" in terms of which Wittgenstein said that he could "not help seeing every problem"? When we recall that Wittgenstein's later philosophy was a proibund attack upon what he regarded as the idolatry of science, logic, and mathematics (an idolatry of which he himself, in the Tractatt~,, was partly guilty), and that he was also bent on undermining the accompanying subjectivized and privatized view of the human mind, as well as the scientistic reading of religious beliefs and primitive religions, we may be inclined to see his philosophy as clearing the way for the simple noninstitutionalized Tolstoian faith which he himself accepted. Philosophy and religion were on the same track in his mind (and not merely related by "analogies") when he wrote: "All that philosophy can do is to destroy idols. And that means not creating a new one--for instance, as in the 'absence of an idol' " (MS 213, 89). Peter Winch... (shrink)

The essays in this volume investigate the question of where, and in what sense, the bounds of intelligible thought, knowledge, and speech are to be drawn. Is there a way in which we are limited in what we think, know, and say? And if so, does this mean that we are constrained – that there is something beyond the ken of human intelligibility of which we fall short? Or is there another way to think about these limits of intelligibility (...) – namely, as conditions of our meaning and knowing anything, beyond which there is no specifiable thing we cannot do? -/- These issues feature prominently in the writings of Kant and Wittgenstein who each engaged with them in unique and striking ways. Their thoughts on the matter remain provocative and stimulating, and accordingly the contributions to this volume address the issues surrounding the limits of intelligibility both exegetically and systematically: they examine how they figure in Kant’s and Wittgenstein’s most significant works and put them in touch with contemporary debates that are shaped by their legacy. These debates concern, inter alia, logically and morally alien thought, the semantics and philosophy of negation, disjunctivism in philosophy of perception and ethics, paraconsistent approaches to contradiction, and the relation between art, literature, and philosophy. The book is divided into four parts: Part I gives a first assessment of the issues, Part II examines limits as they feature in Kant, Part III as they feature in Wittgenstein, and Part IV suggests some ways in which the questions at issue might be reconsidered, drawing upon ideas in phenomenology, dialetheism, metamathematics, and the works of other influential authors. -/- Limits of Intelligibility provides insight into a theme that is central to the thought of two of the most important figures in modern philosophy, as well as to recent metaphysics, philosophy of language, philosophy of logic, epistemology, and ethics. (shrink)

At once a distinguished mathematician and an important figure in the Vienna Circle, Hans Hahn conducted a seminar in 1924-25 on the Principia Mathematica to "a very large audience" of mathematicians and philosophers. Translated from the German and edited by Brian McGuinness, with a biographical introduction by Karl Menger, the present volume consists largely of papers in the philosophy of mathematics covering the years 1929-34. "Our adoption of Russell’s position," writes Hahn, "may cause some surprise in Germany where all ears (...) are tuned, to the controversy between... Hilbert and Brouwer." It turns out, however, that Wittgenstein has made the decisive move: mathematics consists of tautologies, Russell having "shown" how to get by without sets. (shrink)

Arthur Pap’s work played an important role in the development of the analytic tradition. This role goes beyond the merely historical fact that Pap’s views of dispositional and modal concepts were influential. As a sympathetic critic of logical empiricism, Pap, like Quine, saw a deep tension in logical empiricism at its very best in the work of Carnap. But Pap’s critique of Carnap is quite different from Quine’s, and represents the discovery of limits beyond which empiricism (...) cannot go, where there lies nothing other than intuitive knowledge of logic itself. Pap’s arguments for this intuitive knowledge anticipate Etchemendy’s recent critique of the model-theoretic account of logical consequence. Pap’s work also anticipates prominent developments in the contemporary neo-Fregean philosophy of mathematics championed by Wright and Hale. Finally, Pap’s major philosophical preoccupation, the concepts of necessity and possibility, provides distinctive solutions and perspectives on issues of contemporary concern in the metaphysics of modality. In particular, Pap’s account of modality allows us to see the significance of Kripke’s well-known arguments on necessity and apriority in a new light. (shrink)

We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, (...) emphasises its refined composition and rigorous internal structure. (shrink)

This paper is about the differences between probabilities and beliefs and why reasoning should not always conform to probability laws. Probability is defined in terms of urn models from which probability laws can be derived. This means that probabilities are expressed in rational numbers, they suppose the existence of veridical representations and, when viewed as parts of a probability model, they are determined by a restricted set of variables. Moreover, probabilities are subjective, in that they apply to classes of events (...) that have been deemed (by someone) to be equivalent, rather than to unique events. Beliefs on the other hand are multifaceted, interconnected with all other beliefs, and inexpressible in their entirety. It will be argued that there are not sufficient rational numbers to characterise beliefs by probabilities and that the idea of a veridical set of beliefs is questionable. The concept of a complete probability model based on Fisher's notion of identifiable subsets is outlined. It is argued that to be complete a model must be known to be true. This can never be the case because whatever a person supposes to be true must be potentially modifiable in the light of new information. Thus to infer that an individual's probability estimate is biased it is necessary not only to show that the estimate differs from that given by a probability model, but also to assume that this model is complete, and completeness is not empirically verifiable. It follows that probability models and Bayes theorem are not necessarily appropriate standards for people's probability judgements. The quality of a probability model depends on how reasonable it is to treat some existing uncertainty as if it were equivalent to that in a particular urn model and this cannot be determined empirically. Bias can be demonstrated in estimates of proportions of finite populations such as in the false consensus effect. However the modification of beliefs by ad hoc methods like Tversky and Kahneman's heuristics can be justified, even though this results in biased judgements. This is because of pragmatic factors such as the cost of obtaining and taking account of additional information which are not included even in a complete probability model. Finally, an analogy is drawn between probability models and geometric figures. Both idealisations are useful but qualitatively inadequate characterisations of nature. A difference between the two is that the size of any error can be limited in the case of the geometric figure in a way that is not possible in a probability model. (shrink)

BonJour’s intricately argued and provocative book raises a fundamental challenge for the empiricist: if we lack the capacity for direct apprehension of necessary truths, how do we know so much? How do we know about logic and mathematics and other apparently a priori subjects? How do we know about generalities, about the past and the future, about objects that are not present? How do we know about the relations that hold between premises and conclusions? If the first half of BonJour’s (...) book is right, the empiricist is unable to answer these questions, for she is unable to explain how our beliefs in such things are justified. Lacking such an explanation, the empiricist would be committed to an extreme and unacceptable form of skepticism—call this the indispensability argument. The rationalist, by contrast, has an answer to these questions, and if the second half of BonJour’s book is right, the answer is both epistemologically and metaphysically unobjectionable— call this the possibility argument. (shrink)

This paper has two purposes. (1) To justify the claim that there is an important distinction underlying the saying/showing distinction of the Tractatus; the distinction which Kant characterises as that between historical and rational knowledge. (2) To argue that it is because the Tractatus accepts Frege/Russell logic as a complete representation of all thought according to laws, that what is shown cannot be recognised as knowledge. This is done by interpolating Frege's logical innovations between the views of Kant and Wittgenstein (...) on logic and mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.2 (2001) 193-210 [Access article in PDF] Zeno Against Mathematical Physics Trish Glazebrook Galileo wrote in The Assayer that the universe "is written in the language of mathematics," and therein both established and articulated a foundational belief for the modern physicist. 1 That physical reality can be interpreted mathematically is an assumption so fundamental to modern physics that chaos and super-strings are examples (...) of physical theories developed on the basis of success in mathematics. The mathematics came first, then the physical theory. Quantum theory is an awkward and similar case in point. Despite the fact that there is much agreement among physicists about the mathematical theory, its physical interpretation remains a matter of controversy. There are several interpretations, all of which challenge our everyday assumptions about reality. This led Bohr in 1935 to call for "a radical revision of our attitude towards the problem of physical reality." 2 Arthur Fine, originally a staunch defender of realist interpretations of quantum theory, saw the success of Bohr's Copenhagen interpretation as the end of Einsteinian realism, and subsequently Fine declared that "realism is well and truly dead." 3 Mathematical operators simply do not correspond with real entities in any conceivable way.Ilkka Niiniluoto has argued convincingly, however, that realism is alive and well in quantum theory. 4 The problem is that Bohr is right: quantum theory can be considered to concern the real only upon radical revision of ordinary conceptions of reality. Quantum theory does not describe the real in any meaningful sense of "the real." Rather, it is mathematical projection: ideal rather than real. [End Page 193]Aristotle did not hold that the physicist deciphers nature mathematically. He distinguished the physicist from the mathematician at Physics 2.2 by analogy to the definitions of "snub nose" and "curved." 5 The definition of "snub nose" requires the mention of a nose, that is, of matter which is inseparable from motion, whereas "curved" and other mathematical concepts like " 'odd' and 'even', 'straight'... 'number,' 'line,' and 'figure,' " which are separable from matter and from motion, are investigated by the mathematician. 6 Aristotle claims that physics is different from mathematics because the mathematician investigates physical lines, but not qua physical, and the physicist investigates mathematical lines "but qua physical, not qua mathematical." 7A peculiar consequence of my argument is that it establishes a common principle between two thinkers whose beliefs are otherwise so fundamentally in opposition. Zeno's paradoxes are commonly read as a denial of motion. For Aristotle, that move is axiomatic to the physicist. At 185a15 he considers arguments against this assumption outside the realm of objections to which the physicist must reply. If I am right that Zeno's paradoxes of motion challenge the very notion of mathematical physics, then he and Aristotle agree, contra Galileo, that the universe is not written in the language of mathematics. They simply come to this point from opposite directions, Zeno from an Eleatic thesis that physical reality is illusion, Aristotle from the natural scientist's pragmatic commitment to a truth about nature.I intend to use Zeno's paradoxes of motion to argue that the application of mathematical concepts to the physical world results in paradox. Zeno's arguments are limited within mathematics to geometry. This paper is accordingly a beginning from which I hope more work can be done later. Furthermore, Zeno's paradoxes are standardly read as directed against anyone who disagrees with Parmenides' thesis that there is but one thing which is motionless and indivisible. The paradoxes achieve this end by means of a reductio against the possibility of dividing space and time. That there are four paradoxes is accordingly explicable by the fact that there are four possibilities for the divisibility of space and time. The Achilles argues against the possibility that space and time are both infinitely divisible; the Dichotomy, against the infinite divisibility of space and finite divisibility of time; the Arrow, against the infinite divisibility of time and the finite divisibility of space; and finally, the Stadium shows that time and space cannot both... (shrink)

From Descartes and Cartesian mind-body dualism in the 17th century though to 21st-century concerns about artificial intelligence programming, The Bloomsbury Companion to the Philosophy of Consciousness presents a compelling history and up-to-date overview of this burgeoning subject area. Acknowledging that many of the original concepts of consciousness studies are found in writings of past thinkers, it begins with introductory overviews to the thought of Descartes through to Kant, covering Brentano's restoration of empiricism to philosophical psychology and the major figures (...) of the late 19th and early 20th centuries: Russell, Wittgenstein, Ryle and James. These opening chapters on the forces in the history of consciousness lay the groundwork needed to understand how influential contemporary thinkers in the philosophy of mind interpret the concept of consciousness. Featuring leading figures in the field, Part II discusses current issues in a range of topics progressing from the so-called hard problem of understanding the nature of consciousness, to the methodology of invoking the possibility of philosophical zombies and the prospects of reductivism in philosophy of mind. Part III is dedicated to new research directions in the philosophy of consciousness, including chapters on experiment objections to functionalism and the scope and limits of artificial intelligence. Equipped with practical research resources including an annotated bibliography, a research guide and a glossary, The Bloomsbury Companion to the Philosophy of Consciousness is an authoritative guide for studying the past, present and future of consciousness. (shrink)

For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics grew from his Early and Middle philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

BonJour’s intricately argued and provocative book raises a fundamental challenge for the empiricist: if we lack the capacity for direct apprehension of necessary truths, how do we know so much? How do we know about logic and mathematics and other apparently a priori subjects? How do we know about generalities, about the past and the future, about objects that are not present? How do we know about the relations that hold between premises and conclusions? If the first half of BonJour’s (...) book is right, the empiricist is unable to answer these questions, for she is unable to explain how our beliefs in such things are justified. Lacking such an explanation, the empiricist would be committed to an extreme and unacceptable form of skepticism—call this the indispensability argument. The rationalist, by contrast, has an answer to these questions, and if the second half of BonJour’s book is right, the answer is both epistemologically and metaphysically unobjectionable— call this the possibility argument. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

A central theme in Wittgenstein’s post-Tractatus remarks on the limits of language is that we ‘cannot use language to get outside language’. One illustration of that idea is his comment that, once we have described the procedure of teaching and learning a rule, we have ‘said everything that can be said about acting correctly according to the rule’; ‘we can go no further’. That, it is argued, is an expression of anti-reductionism about meaning and rules. A framework is presented (...) for assessing the debate between reductionist and anti-reductionist readings of Wittgenstein’s views about meaning and use. It is argued that that debate cannot be settled merely by reference to Wittgenstein’s general opposition to reductionism. An important argument for anti-reductionism about rules and meaning, from Remarks on the Foundations of Mathematics, is discussed. Putative evidence of reductionism about meaning in the Brown Book is considered; an alternative reading is proposed. The nature of Wittgenstein’s anti-reductionism is examined. It is argued, first, that Wittgenstein accepts that semantic and normative facts supervene on non-semantic, non-normative facts and, second, that at many points his treatment of meaning and rules goes beyond the kind of pleonastic claim that is often taken to define non-reductionist, quietist, positions in philosophy. (shrink)

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – (...) a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others. (shrink)

Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of mathematics. Readers are (...) introduced to all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. The book also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The exposition is always closely informed by ongoing research in the field and sometimes draws on the author’s own contributions to this research. This means that Gottlob Frege—a German mathematician and philosopher widely recognized as one of the founders of analytic philosophy—figures prominently in the book, both through his own views and his criticism of other thinkers. (shrink)

An in-depth history of the linguistic turn in analytic philosophy, from a leading philosopher of language This is the second of five volumes of a definitive history of analytic philosophy from the invention of modern logic in 1879 to the end of the twentieth century. Scott Soames, a leading philosopher of language and historian of analytic philosophy, provides the fullest and most detailed account of the analytic tradition yet published, one that is unmatched in its chronological range, topics covered, and (...) depth of treatment. Focusing on the major milestones and distinguishing them from detours, Soames gives a seminal account of where the analytic tradition has been and where it appears to be heading. Volume 2 provides an intensive account of the new vision in analytical philosophy initiated by Ludwig Wittgenstein’s Tractatus Logico-Philosophicus, its assimilation by the Vienna Circle of Moritz Schlick and Rudolf Carnap, and the subsequent flowering of logical empiricism. With this “linguistic turn,” philosophical analysis became philosophy itself, and the discipline’s stated aim was transformed from advancing philosophical theories to formalizing, systematizing, and unifying science. In addition to exploring the successes and failures of philosophers who pursued this vision, the book describes how the philosophically minded logicians Kurt Gödel, Alfred Tarski, Alonzo Church, and Alan Turing discovered the scope and limits of logic and developed the mathematical theory of computation that ushered in the digital era. The book’s account of this pivotal period closes with a searching examination of the struggle to preserve ethical normativity in a scientific age. (shrink)

continent. 2.2 (2012): 66–75 ~*~ We’re Doomed. Pessimism is the night-side of thought, a melodrama of the futility of the brain, a poetry written in the graveyard of philosophy. Pessimism is a lyrical failure of philosophical thinking, each attempt at clear and coherent thought, sullen and submerged in the hidden joy of its own futility. The closest pessimism comes to philosophical argument is the droll and laconic “We’ll never make it,” or simply: “We’re doomed.” Every effort doomed to failure, every (...) project doomed to incompletion, every life doomed to be unlived, every thought doomed to be unthought. Pessimism is the lowest form of philosophy, frequently disparaged and dismissed, merely the symptom of a bad attitude. No one ever needs pessimism, in the way that one needs optimism to inspire one to great heights and to pick oneself up, in the way one needs constructive criticism, advice and feedback, inspirational books or a pat on the back. No one needs pessimism, though I like to imagine the idea of a pessimist activism. No one needs pessimism, and yet everyone—without exception—has, at some point in their lives, had to confront pessimism, if not as a philosophy then as a grievance—against one’s self or others, against one’s surroundings or one’s life, against the state of things or the world in general. There is little redemption for pessimism, and no consolation prize. Ultimately, pessimism is weary of everything and of itself. Pessimism is the philosophical form of disenchantment—disenchantment as chanting, a chant, a mantra, a solitary, monophonic voice rendered insignificant by the intimate immensity surrounding it. In pessimism, the first axiom is a long, low, funereal sigh. ~*~ We’re Still Doomed. No one has time for pessimism. After all, there are only so many hours in a day. Whatever our temperament, happy or sad, engaged or disengaged, we know pessimism when we hear it. The pessimist is usually understood as the complainer, forever pointing out what is wrong with the world without ever once offering a solution. But more often than not pessimists are the quietest of philosophers, submerging their own sighs within the lethargy of discontent. What little sound it makes is of interest to no one—“I’ve heard it all before,” “tell me something I don’t know,” sound and fury, signifying nothing. In raising problems without solutions, in posing questions without answers, in retreating to the hermetic, cavernous abode of complaint, pessimism is guilty of that most inexcusable of Occidental crimes—the crime of not pretending it’s for real. Pessimism fails to live up to the most basic tenet of philosophy—the “as if.” Think as if it will be helpful, act as if it will make a difference, speak as if there is something to say, live as if you are not, in fact, being lived by some murmuring non-entity both shadowy and muddied. Had it more self-assurance and better social skills, pessimism would turn its disenchantment into a religion, possibly calling itself The Great Refusal. But there is a negation in pessimism that refuses even such a Refusal, an awareness that, from the start, it has already failed, and that the culmination of all that is, is that all is for naught. Pessimism tries very hard to present itself in the low, sustained tones of a Requiem Mass, or the tectonic rumbling of Tibetan chant. But it frequently lets loose dissonant notes at once plaintive and pathetic. Often, its voice cracks, its weighty words abruptly reduced to mere shards of guttural sound. ~*~ Maybe It’s Not So Bad, After All. If we know pessimism when we hear it, this is because we’ve heard it all before—and we didn’t need to hear it in the first place. Life is hard enough. What you need is a change of attitude, a new outlook, a shift in perspective... a cup of coffee. If we have no ears for pessimism, this is because it is always reducible to something as reliably mutable as a voice. If pessimism is so frequently disparaged, it is because it brings everyone down, determined as it is to view each day as a bad day, if only by virtue of the fact that it is not yet a bad day. For pessimism the world is brimming with negative possibility, the collision of a bad mood with an impassive world. In fact, pessimism is the result of a confusion between the world and a statement about the world, a confusion that also prevents it from fully entering the hallowed halls of philosophy. If pessimism is so often dismissed, this is because it is often impossible to separate a “bad mood” from a philosophical proposition (and do not all philosophies stem from a bad mood?) The very term “pessimism” suggests a school of thought, a movement, even a community. But pessimism always has a membership of one—maybe two. Ideally, of course, it would have a membership of none, with only a scribbled, illegible note left behind by someone long forgotten. But this seems unrealistic, though one can always hope. ~*~ Anatomy of Pessimism. Though it may locate itself at the margins of philosophy, pessimism is as much subject to philosophical analysis as any other form of thought. Pessimism’s lyricism of failure gives it the structure of music. What time is to the music of sorrow, reason is to a philosophy of the worst. Pessimism’s two major keys are moral and metaphysical pessimism, its subjective and objective poles, an attitude towards the world and a claim about the world. For moral pessimism, it is better not to have been born at all; for metaphysical pessimism, this is the worst of all possible worlds. For moral pessimism the problem is the solipsism of human beings, the world made in our own image, a world-for-us. For metaphysical pessimism, the problem is the solipsism of the world, objected and projected as a world-in-itself. Both moral and metaphysical pessimism are compromised philosophically; moral pessimism by its failure to locate the human within a larger context, and metaphysical pessimism by its failure to recognize the complicity in the very claim of realism. This is how pessimism makes its music of the worst, a generalized misanthropy without the anthropos . Pessimism crystallizes around this futility—it is its amor fati , rendered as musical form. ~*~ Melancholy of Anatomy. There is a logic of pessimism that is fundamental to its suspicion of philosophical system. Pessimism involves a statement about a condition . In pessimism each statement boils down to an affirmation or a negation, just as any condition boils down to the best or the worst. With Schopenhauer, that arch-pessimist, the thinker for whom the philosopher and the curmudgeon perfectly overlap, we see a no-saying to the worst, a no-saying that secretly covets a yes-saying (through asceticism, mysticism, quietism), even if this hidden yes-saying is a horizon at the limits of comprehension. With Nietzsche comes the pronouncement of a Dionysian pessimism, a pessimism of strength or joy, a yes-saying to the worst, a yes-saying to this world as it is. And with Cioran yet another variation, futile yet lyrical, a no-saying to the worst, and a further no-saying to the possibility of any other world, in here or out there. With Cioran one approaches, but never reaches, an absolute no-saying, a studied abandonment of pessimism itself. The logic of pessimism moves through three refusals: a no-saying to the worst (refusal of the world-for-us, or Schopenhauer’s tears); a yes-saying to the worst (refusal of the world-in-itself, or Nietzsche’s laughter); and a no-saying to the for-us and the in-itself (a double refusal, or Cioran’s sleep). Crying, laughing, sleeping—what other responses are adequate to a life that is so indifferent? ~*~ Cosmic Pessimism. Both moral and metaphysical pessimism point to another kind, a pessimism that is neither subjective nor objective, neither for-us nor in-itself, and instead a pessimism of the world-without-us. We could call this a cosmic pessimism ... but this sounds too majestic, too full of wonder, too much the bitter aftertaste of the Great Beyond. Words falter. And so do ideas. And so we have a cosmic pessimism, a pessimism that is first and last a pessimism about cosmos , about the necessity and possibility of order. The contours of cosmic pessimism are a drastic scaling-up or scaling-down of the human point of view, the unhuman orientation of deep space and deep time, and all of this shadowed by an impasse, a primordial insignificance, the impossibility of ever adequately accounting for one’s relationship to thought—all that remains of pessimism is the desiderata of affects—agonistic, impassive, defiant, reclusive, filled with sorrow and flailing at that architectonic chess match called philosophy, a flailing that pessimism tries to raise to the level of an art form (though what usually results is slapstick). ~*~ Song of Futility. An ethics of futility pervades pessimism. Futility, however, is different from fatality, and different again from simple failure (though failure is never simple). Failure is a breakage within the heart of relations, a fissure between cause and effect, a fissure hastily covered over by trying and trying again. With failure, there is always plenty of blame to go around; it’s not my fault, it’s a technical difficulty, it’s a miscommunication. For the pessimist, failure is a question of “when,” not “if”—failure as a metaphysical principle. Everything withers and passes into an obscurity blacker than night, everything from the melodramatic decline of a person’s life to the banal flickering moments that constitute each day. Everything that is done undone, everything said or known destined for a kind of stellar oblivion. When scaled up in this way, failure becomes fatality. Fatality is the hermeticism of cause and effect. In fatality, everything you do, whatever you do, always leads to a certain end, and ultimately to the end—though that end, or the means to that end, remain shrouded in obscurity. Nothing you do makes a difference because everything you do makes a difference. Hence the effects of your actions are hidden from you, even as you deceive yourself into thinking that, at last, this time you will outwit the order of things. By having a goal, planning ahead, and thinking things through carefully, we attempt, in a daily Prometheanism, to turn fatality to our advantage, to gain a glimpse of an order that seems buried deeper and deeper in the fabric of the universe. But even fatality has its comforts. The chain of cause and effect may be hidden from us, but that’s just because disorder is the order we don’t yet see; it’s just complex, distributed, and requires advanced mathematics. Fatality still clings to the sufficiency of everything that exists... When fatality relinquishes even this idea, it becomes futility. Futility arises out of the grim suspicion that, behind the shroud of causality we drape over the world, there is only the indifference of what exists or doesn’t exist; whatever you do ultimately leads to no end, an irrevocable chasm between thought and world. Futility transforms the act of thinking into a zero-sum game. ~*~ Song of the Worst. At the center of pessimism lies the term pessimus , “the worst,” a term as relative as it is absolute. The worst is about as bad as it gets, “the worst” as “the best” in disguise, shrouded by the passage of time or the twists and turns of fortune. For the pessimist, “the worst” is the propensity for suffering that gradually occludes each living moment, until it eclipses it entirely, overlapping perfectly in death... which, for the pessimist, is no longer “the worst.” Pessimism is marked by an unwillingness to move beyond “the worst,” something only partially attributable to a lack in motivation. In pessimism “the worst” is the ground that gives way beneath every existent—things could be worse, and , things could be better. “The worst” invariably implies a value judgment, one made based on scant evidence and little experience; in this way, pessimism’s greatest nemesis is its moral orientation. Pessimism’s propositions have all the gravitas of a bad joke. Perhaps this is why the true optimists are the most severe pessimists—they are optimists that have run out of options. They are almost ecstatically inundated by the worst. Such an optimism is the only possible outcome of a prolonged period of suffering, physical or metaphysical, intellectual or spiritual. But does this not also describe all the trials and tribulations of each day—in short, of “life?” It seems that sooner or later we are all doomed to become optimists of this sort (the most depressing of thoughts...) ~*~ Song of Doom. Rather than serving as a cause for despair, gloom and doom are the forms of consolation for any pessimist philosophy. Neither quite affects nor quite concepts, gloom and doom transform pessimism into a mortification of philosophy. Doom is not just the sense that all things will turn out badly, but that all things inevitably come to an end, irrespective of whether or not they really do come to an end. What emerges from doom is a sense of the unhuman as an attractor, a horizon towards which the human is fatally drawn. Doom is humanity given over to unhumanity in an act of crystalline self-abnegation. Gloom is not simply the anxiety that precedes doom. Gloom is literally atmospheric, climate as much as impression, and if people are also gloomy, this is simply the by-product of an anodyne atmosphere that only incidentally involves human beings. Gloom is more climatological than psychological, the stuff of dim, hazy, overcast skies, of ruins and overgrown tombs, of a misty, lethargic fog that moves with the same languorousness as our own crouched and sullen listening to a disinterested world. In a sense, gloom is the counterpoint to doom—what futility is to the former, fatality is to the latter. Doom is marked by temporality—all things precariously drawn to their end—whereas gloom is the austerity of stillness, all things sad, static, and suspended, a meandering smoke hovering over cold lichen stones and damp fir trees. If doom is the terror of temporality and death, then gloom is the horror of a hovering stasis that is life. At times I like to imagine that this realization alone is the thread that connects the charnel ground Aghori and the graveyard poets. ~*~ Song of Spite. There is an intolerance in pessimism that knows no bounds. In pessimism spite begins by fixing on a particular object of spite—someone one hardly knows, or someone one knows too well; a spite for this person or a spite for all of humanity; a spectacular or a banal spite; a spite for a noisy neighbor, a yapping dog, a battalion of strollers, the meandering idiot walking in front of you on their smart phone, large loud celebrations, traumatic injustices anywhere in the world regurgitated as media blitz, spite for the self-absorbed and overly performative people talking way too loud at the table next to you, technical difficulties and troubleshooting, the reduction of everything to branding, spite of the refusal to admit one’s own errors, of self-help books, of people who know absolutely everything and make sure to tell you, of all people, all living beings, all things, the world, the spiteful planet, the inanity of existence... Spite is the motor of pessimism because it is so egalitarian, so expansive, it runs amok, stumbling across intuitions that can only half-heartedly be called philosophical. Spite lacks the confidence and the clarity of hatred, but it also lacks the almost cordial judgment of dislike. For the pessimist, the smallest detail can be an indication of a metaphysical futility so vast and funereal that it eclipses pessimism itself—a spite that pessimism carefully places beyond the horizon of intelligibility, like the experience of dusk, or like the phrase, “it is raining jewels and daggers.” ~*~ Song of Sleep. A paraphrase of Schopenhauer: what death is for the organism, sleep is for the individual. Pessimists sleep not because they are depressed, but because for them sleep is a form of ascetic practice. Sleep is the askesis of pessimism. If, while sleeping, we have a bad dream, we abruptly wake up, and suddenly the horrors of the night vanish. There is no reason to think that the same does not happen with the bad dream we call “life.” ~*~ Song of Sorrow. Nietzsche, commenting on pessimism, once castigated Schopenhauer for taking things too lightly. He writes: ...Schopenhauer, though a pessimist, really —played the flute. Every day, after dinner: one should read his biography on that. And incidentally: a pessimist, one who denies God and the world but comes to a stop before morality—who affirms morality and plays the flute... what? Is that really—a pessimist? We know that Schopenhauer did possess a collection of instruments, and we also know that Nietzsche himself composed music. There is no reason to think that either of them would ever banish music from the Republic of philosophy. But Nietzsche’s jibes at Schopenhauer are as much about music as they are about pessimism. For the pessimist who says no to everything and yet finds comfort in music, the no-saying of pessimism can only be a weak way of saying yes—the weightiest statement undercut by the flightiest of replies. The least that Schopenhauer could’ve done is to play the bass. I’m not a big fan of the flute, or, for that matter, wind instruments generally. But what Nietzsche forgets is the role that the flute has historically played in Greek tragedy. In tragedy, the flute ( aulos ) is not an instrument of levity and joy, but of solitude and sorrow. The Greek aulos not only expresses the grief of tragic loss, but it does so in a way that renders weeping and singing inseparable from each other. The classicist Nicole Loraux calls this the mourning voice . Set apart from the more official civic rituals of funerary mourning, the mourning voice of Greek tragedy constantly threatens to dissolve song into wailing, music into moaning, and the voice into a primordial, disarticulate anti-music. The mourning voice delineates all the forms of suffering—tears, weeping, sobbing, wailing, moaning, and the convulsions of thought reduced to an elemental unintelligibility. In the collapsed space between the voice that speaks and the voice that sings, pessimism discovers its mourning voice. Pessimism: the failure of sound and sense, the disarticulation of phone and logos . Have we rescued Schopenhauer from Nietzsche? Probably not. Perhaps Schopenhauer played the flute to remind himself of the real function of the mourning voice—sorrow, sighs, and moaning rendered indistinguishable from music, the crumbling of the human into the unhuman. Failure par excellence of pessimism. ~*~ Song of Nothing. In Buddhist thought, the First Noble Truth of existence is encapsulated in the Pali term dukkha , conventionally translated as “suffering,” “sorrow,” or “misery.” The Buddhist teachings are clear, however, that this is an objective claim, and not simply one point of view among others. Existence is suffering and sorrow—and yet this is not, the teachings tell us, a pessimistic attitude. It is likely that Schopenhauer, reading the Buddhist texts available to him, recognized some filiation with the concept of dukkha . But dukkha is a multi-faceted term. There is, certainly, dukkha in the usual sense of the suffering, strife, and loss associated with living a life. But this is, in turn, dependent on the finitude and temporality of dukkha , existence as determined by impermanence and imperfection. And this ultimately points to the way in which both suffering and finitude are grounded by the paradoxical groundlessness of dukkha as a metaphysical principle—the insubstantiality and the emptiness of all that is. Beyond what is worse to me, beyond a world ordered for the worst, there is the emptiness of dukkha as an impersonal suffering... the tears of the cosmos. In this context, it is easy to see how Schopenhauer’s pessimism attempts to compress all the aspects of dukkha into a nothingness at the core of existence, a Willlessness coursing through the Will. Though one thing for certain is that with Schopenhauer we do not find the “ever-smiling” countenance of Buddhism—or do we? The texts of the Pali Canon also contain lists of the different types of happiness—including the happiness of renunciation and the strange happiness of detachment. But Buddhism considers even the different types of happiness as part of dukkha , in this final sense of nothingness or emptiness. Perhaps Schopenhauer understood Buddhism better than he is usually given credit for. Thus the experiment of Schopenhauer’s philosophy—the point at which a Western pessimus and an Eastern dukkha overlap or exchange glances. Empty sorrow, a lyricism of indifference. The result is a strange, and ultimately untenable, nocturnal form of Buddhism. ~*~ Cioran once called music a “physics of tears.” If this is true, then perhaps metaphysics is its commentary. Or its apology. ~*~ Pessimism would be more mystical were it not for its defeatism. Mysticism is much too proactive for the pessimist, and pessimism too impassive even for the mystic. At the same time, there is something enviable about mysticism—despite its sufferings. There is a sense in which pessimists are really failed mystics. ~*~ You, the Night, and the Music. In a suggestive passage, Schopenhauer once noted that, “music is the melody to which the world is the text." Given Schopenhauer’s view on life—that life is suffering, that human life is absurd, that the nothingness before my birth is equal to the nothingness after my death—given all this, one wonders what kind of music Schopenhauer had in mind when he described music as the melody to which the world is text—was it opera, a Requiem Mass, a madrigal, or perhaps a drinking song? Or something like Eine kleine Nachtmusik , a little night music for the twilight of thought, a sullen nocturne for the night-side of logic, an era of sad wings sung by a solitary banshee. Perhaps the music Schopenhauer had in mind is music eliminated to non-music. A whisper would suffice. Perhaps a sigh of fatigue or resignation, perhaps a moan of despair or sorrow. Perhaps a sound just articulate enough that it could be heard to dissipate. ~*~ Teach me to laugh through tears. ~*~ Pessimism always falls short of being philosophical. My back aches, my knees hurt, I couldn’t sleep last night, I’m stressed-out, and I think I’m finally coming down with something. Pessimism abjures all pretenses towards system—towards the purity of analysis and the dignity of critique. We didn’t really think we could figure it out, did we? It was just passing time, taking a piss, something to do, a bold gesture put forth in all its fragility, according to rules that we have agreed to forget that we made up in the first place. Every thought marked by a shadowy incomprehension that precedes it, and a futility that undermines it. That pessimism speaks, in whatever voice, is the singing testimony to this futility and this incomprehension—take a chance and step outside, lose some sleep and say you tried... ~*~ Is there a music of pessimism? And would such a music be audible? ~*~ The impact of music on a person compels them to put their experience into words. When this fails, the result is a faltering of thought and language that is itself a kind of music. Cioran writes: “Music is everything. God himself is nothing more than an acoustic hallucination.” ~*~ If a thinker like Schopenhauer has any redeeming qualities, it is that he identified the great lie of Western culture—the preference for existence over non-existence. As he notes: “If we knocked on the graves and asked the dead whether they would like to rise again, they would shake their heads.” In Western cultures it is commonly accepted that one celebrates birth and mourns death. But there must be a mistake here. Wouldn’t it make more sense to mourn birth and celebrate death? Strange though, because the mourning of birth would, presumably, last the entirety of that person’s life, so that mourning and living would the be same thing. ~*~ To the musical idea of the harmony of the universe corresponds the philosophical principle of sufficient reason. Like the music of mourning, pessimism gives voice to the inevitable breakdown of word and song. In this way, music is the overtone of thought. ~*~ The Patron Saints of Pessimism. The patron saints of pessimism watch over suffering. Laconic and sullen, the patron saints of pessimism never seem to do a good job at protecting, interceding, or advocating for those who suffer. Perhaps they need us more than we need them. Lest we forget, there do exist patron saints of philosophy, but their stories are not happy ones. There is, for instance, the fourth century Saint Catherine of Alexandria, or Catherine of the Wheel, named after the torture device used on her. A precocious fourteen year old scholar, Catherine was subject to continual persecution. After all forms of torture failed—including the “breaking wheel”—the emperor finally settled for her decapitation, a violent yet appropriate reminder of the protector of philosophers. There are also patron saints of music and musicians, but theirs too are sad stories. In the second century, Saint Cecilia was also subject to persecution and torture. As she knelt to receive the blade that would separate her head from her body, she ardently sang a song to God. It took three attempts before she was fully decapitated, all the while she continued, perhaps miraculously, to sing. Does pessimism not deserve its own patron saints, even if they are unworthy of martyrdom? But in our search, even the most ardent nay-sayers frequently lapse into brief moments of enthusiasm—Pascal’s love of solitude, Leopardi’s love of poetry, Schopenhauer’s love of music, Nietzsche’s love of Schopenhauer, and so on. Should one then focus on individual works of pessimism? We could include Kierkegaard’s trilogy of horror— Sickness Unto Death , The Concept of Dread , and Fear and Trembling —but all these are undermined by their fabricated and unreliable authors. Besides, how can one separate the pessimist from the optimist in works like Unamuno’s The Tragic Sense of Life , Shestov’s Postetas Clavium , or Edgar Saltus’ under-read The Philosophy of Disenchantment ? Even in cases where the entire corpus of an author is pessimistic, the project always seems incomplete—witness Cioran’s trajectory, from his first book, On the Heights of Despair , to the last unpublished notebooks of acrid and taut aphorisms. And this is to say nothing of literary pessimism, from Goethe’s sorrowful Werther, to Dostoevsky’s underground man, to Pessoa’s disquiet scribbler; Baudelaire’s spleen and ennui, the mystical Satanism of Huysmans and Strindberg, the hauntologies of Mário de Sá-Carniero, Izumi Kyoka, H.P. Lovecraft, grumpy old Beckett... even the great pessimist comedians. All that remains are singular, perhaps anomalous statements of pessimism, a litany of quotes and citations crammed into fortune cookies. Patron saints are traditionally named after a locale, either a place of birth or of a mystical experience. Perhaps the better approach is to focus on the places where pessimists were forced to live out their pessimism—Schopenhauer facing an empty Berlin lecture hall, Nietzsche mute and convalescent at the home of his sister, Wittgenstein the relinquished professor and solitary gardener, Cioran grappling with Alzheimer’s in his tiny writing alcove in the Latin Quarter. ~*~ There’s a ghost that grows inside of me, damaged in the making, and there’s a hunt sprung from necessity, elliptical and drowned. Where the moving quiet of our insomnia offers up each thought, there’s a luminous field of grey inertia, and obsidian dreams burnt all the way down. ~*~ If pessimism has any pedagogical value, it is that the failure of pessimism as a philosophy is inextricably tied to the failure of pessimism as voice. I read the following, from Shestov’s The Apotheosis of Groundlessness : When a person is young he writes because it seems to him he has discovered a new almighty truth which he must make haste to impart to forlorn humankind. Later, becoming more modest, he begins to doubt his truths: and then he tries to convince himself. A few more years go by, and he knows he was mistaken all round, so there is no need to convince himself. Nevertheless he continues to write, because he is not fit for any other work, and to be accounted a superfluous person is so horrible. (shrink)

Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered and rejected. (...) Constructive empiricism cannot be realist about abstract objects; it must reject even the realism advocated by otherwise ontologically restrained and epistemologically empiricist indispensability theorists. Indispensability arguments rely on the kind of inference to the best explanation the rejection of which is definitive of constructive empiricism. On the other hand, formalist and logicist anti-realist positions are also shown to be untenable. It is argued that a constructive empiricist philosophy of mathematics must be fictionalist. Borrowing and developing elements from both Philip Kitcher's constructive naturalism and Kendall Walton's theory of fiction, the account of mathematics advanced treats mathematics as a collection of stories told about an ideal agent and mathematical objects as fictions. The account explains what true portions of mathematics are about and why mathematics is useful, even while it is a story about an ideal agent operating in an ideal world; it connects theory and practice in mathematics with human experience of the phenomenal world. At the same time, the make-believe and game-playing aspects of the theory show how we can make sense of mathematics as fiction, as stories, without either undermining that explanation or being forced to accept abstract mathematical objects into our ontology. All of this occurs within the framework that constructive empiricism itself provides the epistemological limitations it mandates, the semantic view of theories, and an emphasis on the pragmatic dimension of our theories, our explanations, and of our relation to the language we use. (shrink)

It is reported that in reply to John Wisdom’s request in 1944 to provide a dictionary entry describing his philosophy, Wittgenstein wrote only one sentence: “He has concerned himself principally with questions about the foundations of mathematics”. However, an understanding of his philosophy of mathematics has long been a desideratum. This was the case, in particular, for the period stretching from the Tractatus Logico-Philosophicus to the so-called transitional phase. Marion’s book represents a giant leap forward in this direction. In the (...) preface, Marion provides a diagnosis for why it has taken such a long time to obtain an accurate picture of Wittgenstein’s ideas in the foundations of mathematics. When the Remarks on the Foundations of Mathematics came out in 1956 the reception by specialists, such as Kreisel, was negative. This led many Wittgenstein scholars to set aside the issues in the foundations of mathematics and go on with the business of the day, focusing on Wittgenstein’s philosophy of language and psychology. However, these early negative appraisals were severely limited by two facts. First of all, the nature of the Remarks was a hindrance to an understanding of what Wittgenstein was up to. The book was edited by Wittgenstein’s literary executors by collating together passages from several manuscripts dating from 1937 to 1944, cutting, however, many passages in between remarks. Second, many of the original manuscripts and typescripts of the transitional phase were not available and thus it was virtually impossible to obtain a balanced picture of Wittgenstein’s development. Finally, a stark contraposition between the early and late Wittgenstein did not encourage people to work seriously on the development of Wittgenstein’s position from the Tractatus through the transitional period to the later writings. (shrink)

Western science claims to provide unique, objective information about the world. This is supported by the observation that peoples across cultures will agree upon a common description of the physical world. Further, the use of scientific instruments and mathematics is claimed to enable the objectification of science. In this work, carried out by reviewing the scientific literature, the above claims are disputed systematically by evaluating the definition of physical reality and the scientific method, showing that empiricism relies ultimately upon (...) the human senses for the evaluation of scientific theories and that measuring instruments cannot replace the human sensory system. Nativist and constructivist theories of human sensory development are reviewed, and it is shown that nativist claims of core conceptual knowledge cannot be supported by the findings in the literature, which shows that perception does not simply arise from a process of maturation. Instead, sensory function requires a long process of learning through interactions with the environment. To more rigorously define physical reality and systematically evaluate the stability of perception, and thus the basis of empiricism, the development of the method of dimension analysis is reviewed. It is shown that this methodology, relied upon for the mathematical analysis of physical quantities, is itself based upon empiricism, and that all of physical reality can be described in terms of the three fundamental dimensions of mass, length and time. Hereafter the sensory modalities that inform us about these three dimensions are systematically evaluated. The following careful analysis of neuronal plasticity in these modalities shows that all the relevant senses acquire from the environment the capacity to apprehend physical reality. It is concluded that physical reality is acquired rather than given innately, and leads to the position that science cannot provide unique results. Rather, those it can provide are sufficient for a particular environmental setting. (shrink)

In the Preface of the Tractatus Wittgenstein presents his proposal of “drawing limits” separating sense from nonsense as a way to get rid of philosophical problems caused by “misunderstandings of the logic of our language.” Such limits, we will later discover, will be drawn by means of a method which allows one to determine whether a given projection of a strings of signs was made in accordance with the rules of logical syntax, or else violated them, thus generating (...) metaphysical propositions. Notwithstanding its centrality for the Tractatus, the idea of drawing such limits seems to be in tension with Wittgenstein’s actual procedure in most of the book, which from its very first numbered proposition introduces “metaphysical” theses again and again in order to achieve the results programmatically indicated in the Preface—hence the need for the self-undoing message of 6.54, urging the reader to recognize those propositions “as nonsensical, when he has used them—as steps—to climb up beyond them.” That tension creates some of the most challenging questions in the debate about how to read the Tractatus—questions such as: how are we supposed to use Wittgenstein’s propositions as “steps in a ladder”? What exactly does “throwing the ladder away” amount to? And what does it mean to “see the world aright” after “overcoming” those propositions? This paper attempts to answer those questions by means of a close reading of an exemplary set of propositions dealing with solipsism and the limits of language. Although limited in scope, the hope is that such reading might stand as a test case for parallel readings of other parts of the book. (shrink)

Carnap’s work was instrumental to the liberalization of empiricism in the 1930s that transformed the logical positivism of the Vienna Circle to what came to be known as logical empiricism. A central feature of this liberalization was the deployment of the Principle of Tolerance, originally introduced in logic, but now invoked in an epistemological context in “Testability and Meaning”. Immediately afterwards, starting with Foundations of Logic and Mathematics, Carnap embraced semantics and turned to interpretation to guide the choice (...) of a theoretical language for science. The first thesis of this paper is that recourse to an intended interpretation led to a partial retrenchment of the conventionalism implied by the Principle of Tolerance. It required that the choice of a language be based on abstraction from a context; this procedure later became a component of the process of explication that was distinctive to Carnap’s mature views. The interpretive origin of formal systems also ensured their likely syntactic consistency, an issue on which Carnap was strongly criticized by figures such as Beth and Gödel. The second thesis of this paper is that this reliance on an intended interpretation enabled constructed formal systems to be relevant to the development of empirical science. (shrink)

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic (...) and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:God, Evil and the Limits of Theology by Karen KilbyVincent BirchGod, Evil and the Limits of Theology by Karen Kilby (London: T&T Clark, 2020), 176 pp.Karen Kilby's God, Evil and the Limits of Theology is a collection of essays reminiscent in multiple respects of Herbert McCabe's God Matters. Kilby cites McCabe on only a handful of occasions, but, more so than the references, the form (...) and the content of Kilby's volume bring McCabe to mind. Like McCabe's book, God, Evil and the Limits of Theology consists of mostly short and readable but highly provocative essays, notwithstanding that Kilby's essays are more academic in form and hang together thematically better than McCabe's text. Regarding content, it is clear that Kilby is aligning herself in certain respects with the tradition of grammatical Thomism that McCabe helped initiate, though it might be better to consider Kilby's work an exercise in "grammatical apophaticism," since Thomas figures prominently in only three of the eleven essays. Even the "grammatical" attribution should be applied with caution, though Kilby does use the term herself, because Ludwig Wittgenstein, whose influence puts the "grammatical" in grammatical Thomism, is not at all explicitly drawn upon for theological purposes. Nevertheless, as will become clear through our discussion of the essays in particular, the arguments and themes of the collection build upon and assist in providing a valuable expansion of the line of thinking carried on by grammatical Thomists.The first four essays treat various concerns in Trinitarian theology, and the first, entitled "Perichoresis and Projection: Problems with Social Doctrines of the Trinity," does some important preliminary critical work before Kilby makes her own constructive contribution to Trinitarian theology. For Kilby, social Trinitarianism (Jurgen Moltmann, Colin Gunton, and Patricia Wilson-Kastner are some proponents with whom she engages) is characterized by the idea that the Trinity, conceived as the interpenetration or perichoresis of three persons ("person" applied with fairly minimal negation), should be understood more as a rich source of [End Page 733] insight for apprehending the proper nature of human sociality than as a fundamentally mysterious doctrine. As the title of the chapter suggests, Kilby's primary critique of social theories of the Trinity is that they entail projection of human experience and reality into the Godhead, and she takes this critique a step further in arguing that it is of the very nature of social theories of the Trinity that they do just that. Her defense consists of a key claim that recurs throughout the rest of the Trinitarian essays—that human beings cannot know what it means for God to be three persons but one God. Consequently, social Trinitarians' bold descriptions of insights pertaining to how the three persons are united in perichoresis could be only a product of projection. Kilby concludes this essay by gesturing toward her constructive alternative to social theories of the Trinity: the doctrine of the Trinity does not give insight into God; rather, it determines the grammar for the structure of Christianity.Kilby follows up her first chapter with a study of Thomas Aquinas's Trinitarian theology, and as might be suggested by the conclusion of her first essay, she offers a thoroughly apophatic interpretation of Thomas, very much in the vein of David Burrell's Aquinas: God and Action. That is, Kilby claims that Thomas is not giving us insight into God but only manifesting the limits of our God-talk. Kilby is critical of various contemporary retrievals of Thomas that attempt to show some sort of "making sense" in Thomas's Trinitarian theology, and she focuses her argument regarding what might be called its "nonsense" on Thomas's uses of the terms "procession" and "relation." Kilby claims these terms appear to lose all intelligible connection to human experience when applied to the Trinity, especially noting the tension between, on the one hand, the subsisting relations being identical to the divine essence and, on the other, their being really distinct from each other. It is precisely the apparent incoherencies that arise within Thomas's Trinitarian theology that corroborate for Kilby that Thomas's theology offers... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:112 HISTORY OF PHILOSOPHY Gallie's Peirce and Pragmatism (1952). She believes that the translation of Peirce's theory of the categories into the conceptual framework of British empiricism and naturalism misrepresents Peirce's cosmology which had very peculiar traits--traits which the author associates with the Platonic tradition. She shows in detail how Peirce tried at first (1868) to relate his three categories to the Scotist, Scholastic, concepts of "essence" and (...) "substance," and how, in his various phaneroscopic experiments, he gradually repudiated the Scholastic languages and by 1902 was ready to interpret his three categories as an adequate ontology. What led Peirce in this direction was his critique of perceptual judgment. He realized that subject and object are in dynamical, social, and historical relation to each other. A logical object is, therefore, also a "dynamic object" or objective. This insight led him at first to regard his doctrine of signs and their interpretation as a humanist or idealist doctrine, for the idealists had also recognized objects as objectives. Nynfa Bosco is quick to appreciate that this interpretation of acts of knowing is closely related to Gentile's idealism. But gradually a more ontological and Platonic interpretation emerges in Peirce, until in the end "thirdness" is a modernist version of the reality of universals. She believes Peirce's greatest achievement was his exposition of "thirdness" as an ontological mediation between modern idealism and Scholastic realism and his theory of evolution as a continuity of physical and mental events. The volume closes with chapters on Peirce's mathematics, ethics, esthetics, philosophy of religion, theology, and psychology. Those chapters are not mere expositions but critical evaluations. To review Nynfa Bosco's criticisms would take us far beyond the limits of an historical review. Suffice it to say that her criticisms are acute as well as sympathetic, and that they reflect well some of the differences between Italian and American tendencies in philosophical analysis. For several reasons, in short, this work deserves to be known internationally. It probably deserves also to be translated, though a translator would find it difficult to maintain the liveliness of her Italian style, which makes reading the book a pleasure as well as an instruction. HERBERT W. SCHNEIDER Claremont, Calilornia L'Iddalism de Lachelier. By Gaston Mauchaussat. (Paris: Presses Universitaires, Biblioth6que de Philosophie Contemporaine [N.F. 18], 1961. Pp. 224.) This is really an intellectual biography of Jules Lachelier (1832-1918); it traces the development of his idealism from 1866 to 1913 and of his moral BOOK REVIEWS I13 philosophy from 1868 to 1918. According to Lachelier himself, there was a significant change in his thinking when, in 1875, he ceased being a teacher, but M. Mauchaussat finds significant elements of the later development even in his earliest works. In general, according to this account, there was a continuous development from subjective to Platonic idealism and from empirical ethics to his axiological theodicy. The documentation and exposition are detailed and precise. The figure of Lachelier emerges as an important historical link between the romantic idealism of the early nineteenth century and the objective value theory or "philosophie de l'esprit" of the twentieth. Though Lachelier himself seems to have forgotten or discounted the early influence on him of Maine de Biran, the author of this biography finds good evidence that his early "Berkeleyan" idealism was derived largely from Maine de Biran and led him to make a careful study of the empirical psychology of thinking and of the importance of habit. D~s 1858, lisant l'introduction du M6moire de Maine de Biran sur l'influence de I'habitude, il en tire cette cons6quence que les esprits ne peuvent d6velopper leurs diverses puissances que par leur union avec le corps et qu'en somme l'homme pense parce qu'il parle (p. 13). It is evident that Lachelier's primary concern was to find in an empirical idealism a mediator between dogmatic naturalism and the equally dogmatic "spiritualism" which the school of Victor Cousin had established in academic circles. It was Ravaisson who guided him in this search. His course at the Ecole Normale Superieur, to which he was called in 1864, gave him an opportunity to work... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:112 HISTORY OF PHILOSOPHY Gallie's Peirce and Pragmatism (1952). She believes that the translation of Peirce's theory of the categories into the conceptual framework of British empiricism and naturalism misrepresents Peirce's cosmology which had very peculiar traits--traits which the author associates with the Platonic tradition. She shows in detail how Peirce tried at first (1868) to relate his three categories to the Scotist, Scholastic, concepts of "essence" and (...) "substance," and how, in his various phaneroscopic experiments, he gradually repudiated the Scholastic languages and by 1902 was ready to interpret his three categories as an adequate ontology. What led Peirce in this direction was his critique of perceptual judgment. He realized that subject and object are in dynamical, social, and historical relation to each other. A logical object is, therefore, also a "dynamic object" or objective. This insight led him at first to regard his doctrine of signs and their interpretation as a humanist or idealist doctrine, for the idealists had also recognized objects as objectives. Nynfa Bosco is quick to appreciate that this interpretation of acts of knowing is closely related to Gentile's idealism. But gradually a more ontological and Platonic interpretation emerges in Peirce, until in the end "thirdness" is a modernist version of the reality of universals. She believes Peirce's greatest achievement was his exposition of "thirdness" as an ontological mediation between modern idealism and Scholastic realism and his theory of evolution as a continuity of physical and mental events. The volume closes with chapters on Peirce's mathematics, ethics, esthetics, philosophy of religion, theology, and psychology. Those chapters are not mere expositions but critical evaluations. To review Nynfa Bosco's criticisms would take us far beyond the limits of an historical review. Suffice it to say that her criticisms are acute as well as sympathetic, and that they reflect well some of the differences between Italian and American tendencies in philosophical analysis. For several reasons, in short, this work deserves to be known internationally. It probably deserves also to be translated, though a translator would find it difficult to maintain the liveliness of her Italian style, which makes reading the book a pleasure as well as an instruction. HERBERT W. SCHNEIDER Claremont, Calilornia L'Iddalism de Lachelier. By Gaston Mauchaussat. (Paris: Presses Universitaires, Biblioth6que de Philosophie Contemporaine [N.F. 18], 1961. Pp. 224.) This is really an intellectual biography of Jules Lachelier (1832-1918); it traces the development of his idealism from 1866 to 1913 and of his moral BOOK REVIEWS I13 philosophy from 1868 to 1918. According to Lachelier himself, there was a significant change in his thinking when, in 1875, he ceased being a teacher, but M. Mauchaussat finds significant elements of the later development even in his earliest works. In general, according to this account, there was a continuous development from subjective to Platonic idealism and from empirical ethics to his axiological theodicy. The documentation and exposition are detailed and precise. The figure of Lachelier emerges as an important historical link between the romantic idealism of the early nineteenth century and the objective value theory or "philosophie de l'esprit" of the twentieth. Though Lachelier himself seems to have forgotten or discounted the early influence on him of Maine de Biran, the author of this biography finds good evidence that his early "Berkeleyan" idealism was derived largely from Maine de Biran and led him to make a careful study of the empirical psychology of thinking and of the importance of habit. D~s 1858, lisant l'introduction du M6moire de Maine de Biran sur l'influence de I'habitude, il en tire cette cons6quence que les esprits ne peuvent d6velopper leurs diverses puissances que par leur union avec le corps et qu'en somme l'homme pense parce qu'il parle (p. 13). It is evident that Lachelier's primary concern was to find in an empirical idealism a mediator between dogmatic naturalism and the equally dogmatic "spiritualism" which the school of Victor Cousin had established in academic circles. It was Ravaisson who guided him in this search. His course at the Ecole Normale Superieur, to which he was called in 1864, gave him an opportunity to work... (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively (...) pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

This book offers a thought-provoking critique of analytic philosophy focusing on four central figures--Russell, Wittgenstein, Carnap, and Quine. In Wang's view, what lies "beyond" analytic philosophy is the abandonment of Empiricist accounts of how we know and epistemological limitations on what can be known. In making the foundations of science the center of "legitimate" philosophy, Analytic Empiricism has blocked important global perspectives found, for example, in continental and oriental philosophies. Wang advocates a Kantian transcendental dialectic: What explanation is required (...) if we are to do justice to the many facets of knowledge, including artistic, poetic, emotional, and ethical as well as scientific? His thesis is that "intuition" must reclaim a central place in the answer. (shrink)

For well over a century the dominant narrative covering the major thinkers and themes of early modern British philosophy has been that of “British Empiricism”, within which the great triumvirate of Locke-Berkeley-Hume are taken to be the dominant figures. Although it is now common to question this schema as a way of analyzing and understanding the period in question, it continues to command considerable authority and acceptance. (One likely reason for this is that no credible or plausible alternatives structures (...) or schemas of analysis have suggested themselves.) Be this as it may, the analysis of the rival systems of Clarke, Berkeley and Hume makes clear that this narrative, however deeply entrenched it may be, is wholly misleading and both distorts and obscures key themes and figures in the period in question. (shrink)

Climate change economists have called it “the most important number you’ve never heard of” and the “holy grail of climate economic analysis.” It is the social cost of carbon (SCC), and its purpose is to reflect—in one dollar figure—the harm caused by emitting a single ton of carbon dioxide into the atmosphere. The SCC is an essential concept for environmental cost-benefit analysis, and for the idea of an “optimal tax” on carbon emissions. It is also the subject of fierce debate (...) in the academic literature and in American politics. This book offers the most systematic analysis yet of the social cost of carbon, its theoretical basis, and its proper role in climate economics and climate policy design. It explains that the SCC is not one concept but four, each of which is addressed to a distinct task in climate economics. Moreover, these four concepts can be sorted into two families that correspond to the two main branches of welfare economics, social choice theory and general equilibrium theory. The book explains these radically different theoretical frameworks and how a mathematically identical pair of SCC concepts can emerge from each. It then argues that the analytical power of each SCC concept is limited by its inability to capture the full array of ethical considerations that bear on responsible climate policy. Despite these limitations, the book explains how at least some SCC concepts can and should be put to work in real-world climate change policy analysis. (shrink)

Fin de siecle Vienna was once memorably described by Karl Kraus as a "proving ground for the destruction of the world." In the decades leading to the World War that brought down the Austro-Hungarian empire, the city was at once an operetta dream world masking social and political problems and tension, as well as a center for the far-reaching explorations and innovations in music, art, science, and philosophy that would help to define modernity. One of the most powerful critiques of (...) the retreat into fantasy was that of the philosopher Ludwig Wittgenstein, whose early career in Vienna has helped frame debates about ethical and aesthetic values in culture. In Wittgenstein's Vienna Revisited Allan Janik expands upon his work Wittgenstein's Vienna (co-authored with Stephen Toulmin) to amplify a number of significant points concerning the genesis of Wittgenstein's thought, the nature of Viennese culture, and criticism of contemporary culture. Although Wittgenstein is the central figure in this volume, Janik places considerable emphasis on other influential figures, both Viennese and non-Viennese, in order to break down some of the persistent stereotypes about the philosopher and his surrounding culture, especially the myths of "carefree" Vienna and Wittgenstein the positivist. The persistence of these myths, in Janik's view, stems in part from the inability of many historians to differentiate past from present in the evaluation of intellectual currents. Janik reviews a number of figures overlooked in assessing Wittgenstein: Otto Weininger, Kraus, Schoenberg, Nietzsche, Wagner, Ibsen, Offenbach, and Georg Trakl. All of these, Janik demonstrates, are absolutely necessary to understand what was at stake in the debates on aestheticism and the critique of a modern culture. Wittgenstein's efforts to recognize the limits of thought and language and thus to be fair to science, religion, and art account for his place of honor among critical modernists. These essays elucidate Wittgenstein's perspective on our culture. (shrink)

Working through Balaska’s deeply perceptive, elegantly written, and profoundly honest book, Wittgenstein and Lacan at the Limit, a reader steeped in the recent academic literature about either or both of its main figures may come to feel herself placed at what is, itself, a certain kind of limit. The limit I mean is the limit of a familiar type of theoretical discourse about the constitution and structure of language and subjectivity as Wittgenstein and Lacan treat them: it includes the discourses (...) that seek, for instance, to articulate how language and sense are constituted in the Tractatus, and thus what is really meant by “logical form” and “nonsense” there; or those that aim to comprehend the true relationship of our biological nature to language, culture, and the advent of freedom in Lacan; or, again, those that try to find, in either thinker’s works, the precise location of the delicate logical buttonhole that would alone permit us entry, from within everyday language and life, to the absoluteness of an ineffable beyond. These discourses all treat of language and life, but handle these phenomena at arm’s length, theorizing the structure of each and the form of their relationship in such a way as to establish, ultimately, their mutual convertibility to one another, their mutual absorption into a third, more inclusive term, or adduce translations from the dense theoretical matrices of one thinker’s treatment of them to the other’s. Balaska’s book, doing none of these things, rather succeeds in bringing out how an interconnected reading of the Wittgenstein of the Tractatus and Lacan may speak to and inform our response to a certain kind of experience that is characteristic for both thinkers, and typical as well of those moments and occasions of our lives in which we may find ourselves drawn to reflect on what meaning is and how we relate to it. (shrink)

It is reported that in reply to John Wisdom’s request in 1944 to provide a dictionary entry describing his philosophy, Wittgenstein wrote only one sentence: “He has concerned himself principally with questions about the foundations of mathematics”. However, an understanding of his philosophy of mathematics has long been a desideratum. This was the case, in particular, for the period stretching from the Tractatus Logico-Philosophicus to the so-called transitional phase. Marion’s book represents a giant leap forward in this direction. In the (...) preface, Marion provides a diagnosis for why it has taken such a long time to obtain an accurate picture of Wittgenstein’s ideas in the foundations of mathematics. When the Remarks on the Foundations of Mathematics came out in 1956 the reception by specialists, such as Kreisel, was negative. This led many Wittgenstein scholars to set aside the issues in the foundations of mathematics and go on with the business of the day, focusing on Wittgenstein’s philosophy of language and psychology. However, these early negative appraisals were severely limited by two facts. First of all, the nature of the Remarks was a hindrance to an understanding of what Wittgenstein was up to. The book was edited by Wittgenstein’s literary executors by collating together passages from several manuscripts dating from 1937 to 1944, cutting, however, many passages in between remarks. Second, many of the original manuscripts and typescripts of the transitional phase were not available and thus it was virtually impossible to obtain a balanced picture of Wittgenstein’s development. Finally, a stark contraposition between the early and late Wittgenstein did not encourage people to work seriously on the development of Wittgenstein’s position from the Tractatus through the transitional period to the later writings. (shrink)

Book Symposium on Cheryl Misak's Cambridge Pragmatism: From Peirce and James to Ramsey and WittgensteinCheryl Misak's Cambridge Pragmatism is posited on the thought that the link between belief and action is a pragmatist hallmark. It is this central commitment that Misak sees running through the work of the towering figures of the two Cambridges—C.S. Peirce, William James, Bertrand Russell, Frank Ramsey, and Ludwig Wittgenstein. It is on this basis that Misak holds that these figures can be termed 'pragmatists.' My objective (...) in this comment is to make two arguments in light of Misak's hallmark thesis. The first argument is that if Misak is right, then the term 'Cambridge... (shrink)

This paper discusses an important phase in Ludwig Wittgenstein’s analytic philosophy through a comparative examination of the profound correspondences that exist between his concept of silence and the poetics of another crucial authorial figure of the 20th century: James Joyce. Based on the hypothesis that there are striking resemblances between their early works, that is, between Joyce’s realistic short-story collection Dubliners and Wittgenstein’s Tractatus Logico-Philosophicus, the article employs mostly close-reading, analytical-interpretative and comparative methods. It argues that silence was an intentional (...) intellectual, aesthetic and ethical choice of both these authors, their way to preserve the autonomy of metaphysics and to honour the beauty of the unspoken. Starting from their common critical treatment of the habitual and largely alienated speech, the discussion connects Wittgenstein’s philosophical attitudes regarding the imprecision and inadequacy of every-day language and Joyce’s notion of ‘spiritual paralysis’ of the city-life, which he saw as the main motive for writing his collection about fin-desiècle Dublin. On the grounds of their shared views about the limits of words, behind which there are worlds that cannot be properly uttered, the idea of silence – or the highly significant narrative absence – grows to permeate the work of both. In the case of Wittgenstein, it is a call for a new philosophy, or anti-philosophy, which in negating metaphysics in effect preserves its independence from a discursive speech which cannot express it, whereas in the case of Joyce, correspondingly (and almost simultaneously), it is a quest for a new literary mode that will foreground a particular Modernist allusiveness, rhetoric of omission and deliberately incomplete, gnomonical narrative structures. (shrink)

We identify new, rather serious, physical and mathematical inconsistencies of the current formulation of noncanonical or nonunitary string theories due to the lack of invariant units necessary for consistent measurements, lack of preservation in time of Hermiticity-observability, and other shortcomings. We propose three novel reformulations of string theories for matter of progressively increasing complexity via the novel iso-, geno-, and hyper-mathematics of hadronic mechanics, which resolve the current inconsistencies, while offering new intriguing possibilities, such as: an axiomatically consistent (...) and invariant inclusion of gravity, the reduction of macroscopic irreversibility to the most primitive level of vibrations of the universal substratum (ether), or the treatment of multi-valued, irreducible, biological structures. We then identify three corresponding classical formulations of string theories for antimatter via the novel anti-isomorphic isodual mathematics. We finally outline the intriguing features of the emerging new cosmologies (including biological structures, as it should be for all cosmologies), such as: universal invariance (rather than covariance) under a symmetry isomorphic to the Poincaré group and its isodual; equal distributions of matter and antimatter in the universe (as a limit case); continuous creation; no need for the missing mass; significantly reduced dimensions; possibility of experimental identification of antimatter in the universe; identically null total characteristics of time, energy, linear and angular momentum, charge, etc.; and other intriguing features. (shrink)

This paper argues that there is an important continuity between Wittgenstein's early remarks on religion and his later treatment of the theme as it appears in his lectures in the 1930s and in his personal diary notes at that time. This continuity pertains to 3 features. First, the early and later Wittgenstein share a critical stance on methodological naturalism, that is, the view that the method of philosophy is relevantly similar to that of the natural sciences. Importantly, religion figures as (...) one of Wittgenstein's examples of the limits of the factual language of natural sciences. Second, both the early and the later Wittgenstein connect religion to the problem of seeing one's life as meaningful while denying the possibility of establishing any objectively understood meaning of life. Third, both evoke the idea of different types of judgments, the conditions of which are independent of each other. Although religious faith is not grounded in factual knowledge and cannot be justified by appeal to empirical evidence or conceptual argumentation, it is not groundless either. Rather, in accordance with Kant who claims that faith may have a nontheoretical justification, Wittgenstein shows that religious faith may result from a personal experience of one's life as a meaningful whole. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Carnap’s Construction of the World. The Aufbau and the Emergence of Logical Empiricism by Alan W. RichardsonRolf GeorgeAlan W. Richardson. Carnap’s Construction of the World. The Aufbau and the Emergence of Logical Empiricism. Cambridge: Cambridge University Press, 1998. Pp. x + 242. Cloth, $49.95.According to the author, the “received view” of Carnap’s Kantian treatise of 1928, Der Logische Aufbau der Welt, promulgated mostly by Quine (10), (...) takes it to be a continuation of Russell’s “external world program,” an attempt at “providing a systematic reduction of empirical discourse generally to discourse involving only sense data” (21). One of Richardson’s aims is to show that this is wrong: while Carnap holds that our knowledge begins in sensation, our “elementary experiences” are not conscious and thus do not obey Russell’s “principle of acquaintance.” While we have no conscious access to the first elements of cognition, logical constructions based on them lead to sense qualities, phenomenal items, and eventually to physical and even cultural objects.These constructions are also meant to solve the problem of objectivity. According to Carnap, individual streams of experience are not comparable at all, but “certain structural properties agree for all streams of experience” (Aufbau §66, 32), a point that Kant had also made: “In the relation between sensations lies something that is generally valid, even though each sensation has only private validity” (Reflection 653).Richardson describes Carnap’s constructions in a couple of well written and accessible chapters (31–91), one of them an overview, the other a discussion of the problem of objectivity. Then comes the “Kantian Problematic,” (92–116), centered on the synthetic a priori. He repeats Michael Friedman’s now familiar but mistaken point that, due to the limitations of Aristotelian logic, Kant could not have formulated simple statements about order structures: “between any two points there lies another” could not be formulated in any logic he knew, and he therefore had to call in pure intuition to handle mathematical constructions. But he could, and in fact did, make just such claims in the vernacular, which was the sole vehicle for the pellucid formulations of the classical theory of the continuum, from Bolzano to Weyerstrass.The next chapter brings us the heart of Richardson’s concerns, which is to establish neo-Kantian antecedents of the Aufbau. There are some biographical details of doubtful merit. The neo-Kantian Bauch is identified as Carnap’s “dissertation director,” and, in a perhaps unconscious slight to Carnap’s intelligence, as “the philosopher from whom Carnap learned what he knew about Kant” (116). Ten years before Carnap had indeed taken a seminar in the Critique of Pure Reason from Bauch, but perusal of the latter’s work does not encourage the thought that he had much to do with the thesis “Der Raum” (1922). In the event, a German ordinarius did not usually have a hand in the construction of a thesis, and often did not even read it. His job was to accept it on behalf of the university. We now know, for example, that Bauch’s teacher Rickert had an assistant evaluate Heidegger’s Habilitationsschrift never reading it himself. (It passed.)Richardson’s reflection on the neo-Kantian project relies mostly on Cassirer. This points to another problem with the Bauch connection. Bauch was a zealous anti-Semite, and did not think much of Cassirer and the Marburg school in general. He gave up the editorship of Kantstudien in 1916 because of the Jewish presence in the Kant Society, and [End Page 179] founded his own group and journal. Carnap nonetheless chose Kantstudien to publish his dissertation, perhaps to put more distance between himself and Bauch. Space does not permit me to cite Bauch’s vicious remarks about Einstein; he could not have guided Carnap through the discussion of physical space in “Der Raum.”I return to Richardson’s reconstruction. According to the neo-Kantian, objective knowledge is found in mathematical physics, not in uninformed experience. He acknowledges that theoretical physics relies on conventions, and that these conventions go beyond mere experience to provide the mathematical structure necessary for objectivity (131). The responses to the problem this poses... (shrink)

"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced (...) topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index. (shrink)

In this paper I address Jacques Derrida's consistent phenomenological critique of his colleague Louis Althusser. Over the course of many decades, Derrida explicitly draws attention to what he takes to be Althusser's problematic pre-critical scientism, which is the direct result of the latter's failure to engage with Husserl and Heidegger. However, as I attempt to show, Althusser sought to reveal deeper problems associated with transcendental-critical questions in post-Kantian philosophy. For Althusser, questions concerning the ‘conditions of possibility’ of knowledge and experience (...) reproduce the idealist problematic that he calls ‘empiricism’. Charting a different trajectory within contemporary French philosophy, Althusser combines insights from Spinoza, Marx, and other figures often unmentioned by Derrida to produce a novel, non-transcendental philosophical approach to key problems that arise in epistemology and the philosophy of science. (shrink)

Starting in 1946, Polanyi begins to criticize a comprehensive system of ideas that he names positivism. His criticism is twofold. On the one hand, it has the narrow aim of pointing out the inconsistencies of a positivist account of science, according to which the essence of scientific objec­tivity lies in establishing rigorous mathematical relations between measured variables employing fixed rules. On the other hand, it examines the broad assumptions underlying this view, namely radical empiricism and skeptical doubt. The present (...) paper analyzes both aspects of this criticism, stressing its crucial role in the development of Polanyi’s philosophy. (shrink)

This paper explores a specific problem within an important philosophical genre of the fourteenth century: the debates over the perfection of species. It investigates how the problem of defining limits for continuous magnitudes – a problem typical of Aristotelian physics – was integrated into these debates at the levels of genera, species, and individuals as these entities began to be conceptualized in quantitative terms. After explaining the emergence of this problem within fourteenth-century metaphysics, the paper examines the contributions of (...) three philosophers – Hugolinus of Orvieto, John of Ripa, and Paul of Venice – who offered varying solutions to the challenge of defining limits between species. It demonstrates that two primary solutions arose, inspired by continuous and discrete mathematical objects. It is shown that whereas Hugolinus of Orvieto advocates for a continuist model, John of Ripa proposes a discrete one. The last part of the paper examines Paul of Venice's hybrid approach, which combines elements from both models, facilitating a more comprehensive treatment of species particularly difficult to analyse, namely geometric figures. The conclusions of this comparative study underscore how profoundly the metaphysical reflections of the Middle Ages contributed to the analysis of the structure of the continuum and the extension of the notion of quantity to various objects. (shrink)

This book is a collection of Rush Rhees' recent articles on Wittgenstein along with a record of Wittgenstein's comments on continuity made in private conversations in 1938. The first part of the book is on the Tractatus. It begins with a review of Anscombe's Introduction of which Rhees generally approves and then goes on to discuss the "picture theory" and language's capacity to get hold of reality. Rhees argues against Maslow that elementary statements are more than psychological phenomena but must (...) be spoken of in a purely formal sense. Commenting on Black's Companion he argues that Wittgenstein did not have in mind any ontological implications of logic when he was working on the Tractatus. Rhees uses his critique of Pitcher's Philosophy of Wittgenstein and an article on that philosophy to form the transition to the discussion of the later Wittgenstein. He insists that Wittgenstein taught more a method of seeing the depth of certain problems than a set of solutions to those problems. He introduces the theme of "publicness" by arguing that language involves the ability to "say something" and must thus involve publicity. In his article on "Wittgenstein's Builders" he argues that this ability to say something rests on the interrelation of language games and the unity of a form of life. Using this as a basis, he speaks of the Wittgensteinean approach to ethics as one of studying the way of saying something ethically in a certain language game rather than one of studying ethics in general. The essay on continuity begins with a discussion of the dependence of mathematical language on everyday language for meaning. Here Wittgenstein argues that mathematical language derives its sense from experiential language and not from eternal and immutable objects. He discusses the mathematical notion of continuity with an eye to the limits of its sense and shows that its sense is limited by ordinary notions of space and continuity and tests relating to them. This book is worth reading for both the presentation of basic approaches to understanding Wittgenstein and for the record of Wittgenstein's remarks on continuity which are unavailable elsewhere.--J. V. W. (shrink)

This book fills the need for a first rate anthology of readings in the philosophy of mathematics. The subject is interpreted broadly and several familiar and easily accessible papers, such as Nagel's "Logic Without Ontology," Carnap's "Empiricism, Semantics and Ontology," and Quine's "Two Dogmas of Empiricism" take up valuable space. An entire section consists of papers dealing with Wittgenstein's views on mathematics. The introduction is succinct and helpful. But a more careful selection of inaccessible papers, the addition of (...) introductions to the individual parts, and a more extensive bibliography would have made this a much more useful anthology.—R. J. B. (shrink)