In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skolem's primitive recursive arithmetic and Goodstein's equational calculus, Wittgenstein represented generality by the use of free (...) variables. This has the effect that negation of unbounded universal and existential propositions cannot be expressed. This is claimed in the second section to be the basis for Wittgenstein's criticism of the universal validity of the law of excluded middle. In the last section, there is a brief discussion of Wittgenstein's remarks on real numbers. These show a preference, in line with finitism, for a recursive version of the continuum. (shrink)

Symposium of Oakeshott on religion, science and politics.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

The problem of the “identity of identity and nonidentity”, which haunted German idealism, has two closely related aspects. The first, epistemological aspect concerns the possibility of knowledge of an objective world. The second, transcendental aspect, concerns the question of how thoughts can be directed towards the world. Reconstructing McDowell’s Kantian account of intentionality as a purported resolution of the transcendental aspect of IINI, I pose the following dilemma for McDowell’s account: Either part ways with Kant’s purported resolution of IINI at (...) a crucial point, thereby being driven towards an approach that McDowell firmly opposes, indeed cannot accept, or follow Kant to the letter, and then face, head-on, a deep problem that Kant’s purported resolution of IINI faces. Parting ways, as I show, with Kant’s purported resolution of IINI, McDowell finds himself impaled upon the first horn of this dilemma. Were he, however, to respond by following Kant to the letter, McDowell would find himself impaled upon the second horn. Thus, I conclude, McDowell’s account of intentionality fails. (shrink)

A theory of relations is presented that provides a detailed account of the logical structure of relational complexes. The theory draws a sharp distinction between relational complexes and relational states. A salient difference is that relational complexes belong to exactly one relation, whereas relational states may be shared by different relations. Relational complexes are conceived as structured perspectives on states ‘out there’ in reality. It is argued that only relational complexes have occurrences of objects, and that different complexes of the (...) same relation may correspond to the same state. (shrink)

I analyze the relations of constituency or ``being in'' that connect different ontological items in the Tractatus logico-philosophicus by Wittgenstein. A state of affairs is constituted by atoms, atoms are in a state of affairs. Atoms are also in an atomic fact. Moreover, the world is the totality of facts, thus it is in some sense made of facts. Many other kinds of Tractarian notions -- such as molecular facts, logical space, reality -- seem to be involved in constituency relations. (...) How should these relations be conceived? And how is it possible to formalize them in a convincing way? I draw a comparison between two ways of conceiving and formalizing these relations: through sets and through mereological sums. The comparison shows that the conceptual machinery of set theory is apter to conceive and formalize Tractarian constituency notions than the mereological one. (shrink)

In a recent article in this journal, Joshua W. Seachris (2012) argues that the distinction I make between perspectives and standards in sub specie aeternitatis arguments for the meaninglessness of life does not hold for a salient component of the sub specie aeternitatis perspective: the ontological-normative component. In this article I suggest that Seachris’s argument is problematic in a number of ways and ought to be rejected.

The German physicist Heinrich Hertz played a decisive role for Wittgenstein's use of a unique philosophical method. Wittgenstein applied this method successfully to critical problems in logic and mathematics throughout his life. Logical paradoxes and foundational problems including those of mathematics were seen as pseudo-problems requiring clarity instead of solution. In effect, Wittgenstein's controversial response to David Hilbert and Kurt Gödel was deeply influenced by Hertz and can only be fully understood when seen in this context. To comprehend the arguments (...) against the metamathematical programme, and to appreciate how profoundly the philosophical method employed actually shaped the content of Wittgenstein's philosophy, it is necessary to make an intellectual biographical reconstruction of their philosophical framework, tracing the Hertzian elements in the early as well as in the later writings. In order to write Wittgenstein's biography, we have to take seriously the coherence of his thought throughout his life, and not let convenient philosophical ideologies be our guidance in drawing up a “Wittgensteinian philosophy”. To do so, we have to take a second look upon what he actually wrote, not only in the already published material, but in the entire Nachlass. Clearly, this is not easily done, but it is a necessary task in the historical reconstruction of Wittgenstein's life and work. (shrink)

This is a paper about the way language meshes with life. It focuses on Ludwig Wittgenstein’s later work, and compares it with Leo Tolstoy and Saint Augustine’s confessions. My aim is to better understand in this way what it means to have meaning in language, as well as meaning in life.

Careful readers of Wittgenstein tend to overlook the significance his engineering education had for his philosophy; this despite Georg von Wright’s stern admonition that “the two most important facts to remember about Wittgenstein were, firstly, that he was Viennese, and, secondly, that he was an engineer.” Such oversight is particularly tempting for those of us who come to philosophy late, having first been schooled in math and science, because our education tricks us into thinking we understand engineering by extension. But (...) we do not. I will illustrate this common tendency to misread Wittgenstein by examining three engineering concepts that have little significance for science but played important roles in Wittgenstein’s philosophical thinking. These are: method of projection, dynamical similarity, and satisfactoriness. The upshot of this analysis will be a strong challenge to the myth of his putative fideism because neither fideism nor its contrary simply would have occurred to Wittgensteinthe-engineer. (shrink)

Wittgenstein's insistence in his later philosophy that explanation comes to an end in the explication of what it is to follow a rule provides a locus for the awakening of wonder, analogous to the mystical awe referred to in the "Tractatus". While Wittgenstein did not explore this analogy, it provides a point of entry into the examination of the relevance of his work to religious concerns. Every regular practice is built on capacities of reaction, uptake, and response which are the (...) endpoints of explanation, whose sheer givenness in their relation to our physical and social environment can bring on amazement. This wonder at the end of explanation has been explored -- from quite a different perspective -- by Stephen Gould, whose conclusions complement Wittgenstein's own. (shrink)

It has been much debated whether Tractarian objects are what Russell would have called particulars or whether they include also properties and relations. This paper claims that the debate is misguided: there is no logical category such that Wittgenstein intended the reader of the Tractatus to understand his objects either as providing examples of or as not providing examples of that category. This is not to say that Wittgenstein set himself against the very idea of a logical category: quite the (...) contrary. However, where Russell presents his logical variety of particulars and the various types of universal, and Frege presents his of objects and the various types of function, Wittgenstein denies the propriety of such a priori expositions. Wittgenstein envisages a variety of logical types of entity but insists that the nature of these types is something to be discovered only through analysis. (shrink)

In this paper, we propose to analyze the phenomenon of Christian prayer by way of combining two different analytical frameworks. We start by applying Schutz’s theories of “intersubjectivity,” “inner time,” “politheticality,” and “multiple realities,” and then proceed by drawing on the ideas and insights of linguistic philosophers, notably, Wittgenstein’s “language-game,” Austin’s “speech act,” and Evans’s “logic of self-involvement”. In conjoining these accounts, we wish to demonstrate how their combination sheds new light on understanding the phenomenon of prayer. Prayer is a (...) complex phenomenon that involves two major dimensions: the private and the social, as Matthew and Acts, respectively, demonstrate. Schutz’s study of the phenomenon of “inner time” and the “polithetical” structure of consciousness, at both the subjective and intersubjective level, provides a useful lens to analyze these two dimensions. In addition, prayer, in following a specific set of rules, can also be considered as a specific, i.e., religious “language-game”. In the last analysis, however, we propose to analyze prayer within the Schutzian framework of “multiple realities,” “enclaves,” and “symbolic appresentation,” which permits accessing the “religious finite province of meaning” in the very midst of the paramount reality of everyday life. In a nutshell, we claim that Christian prayer is a practice of constructing and living within a “religious province of meaning” in the everyday world; it is a practice that revolves around self-involving language-activities such as praising, confessing, thanksgiving, or requesting to God, which enable the praying subject to transfigure the language of everydayness and “see through” the world of everyday life in order to let it appear in a different light, e.g., the light of grace, gift, and salvation. (shrink)

Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the (...) full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical. (shrink)

When it comes to Wittgenstein's philosophy of mathematics, even sympathetic admirers are cowed into submission by the many criticisms of influential authors in that field. They say something to the effect that Wittgenstein does not know enough about or have enough respect for mathematics, to take him as a serious philosopher of mathematics. They claim to catch Wittgenstein pooh-poohing the modern set-theoretic extensional conception of a real number. This article, however, will show that Wittgenstein's criticism is well grounded. A real (...) number, as an 'extension', is a homeless fiction; 'homeless' in that it neither is supported by anything nor supports anything. The picture of a real number as an 'extension' is not supported by actual practice in calculus; calculus has nothing to do with 'extensions'. The extensional, set-theoretic conception of a real number does not give a foundation for real analysis, either. The so-called complete theory of real numbers, which is essentially an extensional approach, does not define (in any sense of the word) the set of real numbers so as to justify their completeness, despite the common belief to the contrary. The only correct foundation of real analysis consists in its being 'existential axiomatics'. And in real analysis, as existential axiomatics, a point on the real line need not be an 'extension'. (shrink)

The first section of this paper introduces talk about absolutely everything -- the world as a totality -- as an integral element in the project of natural theology, as it has been presented by Fergus Kerr and Denys Turner respectively. The following section presents talk about the world as a totality of facts as a theme in philosophical logic and outlines a problem it has given rise to there. After confronting the solution originally suggested by Bertrand Russell and defended by (...) David Armstrong, the paper points to key elements of the solution presented by Wittgenstein in Tractatus Logico-Philosophicus. I show how Wittgenstein’s answer to the question of unrestricted quantification draws on his notion of showing and the inexpressible. Against this background, the concluding section draws attention to an important difference in ambition between Kerr’s and Turner’s description of the prospects for natural theology. (shrink)

Oxford: Oxford University Press, 2012. 264pp. £ 40.00 (hardcover). ISBN 978–0–19–969152–4.

ABSTRACTZalabardo argues that the Tractatus account of picturing is a direct and successful refutation of Russell’s ‘multiple relation’ theory of judgment, its role being ontological: Wittgenstein...

This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...) remarks on _Lebensformen_ is offered which factors in his reading of Alan Turing’s “On computable numbers, with an application to the _Entscheidungsproblem_“, as well as his discussions with Turing 1937-1939. An interpretation of the five occurrences of _Lebensform_ in the PI is then given in terms of a logical “regression” to _Lebensform_ as a fundamental notion. This regression characterizes Wittgenstein’s mature answer to the question, “What is the nature of the logical?”. (shrink)

ABSTRACT In her paper “On the Nature of Judgment”, published in 1919 in Mind, Dorothy Wrinch aimed at understanding how Russell’s multiple relation theory of judgement might be made to work. In this paper we will focus on Wrinch’s claim that on the theory it is impossible, as it should be, to judge nonsense. After having presented the prima facie objection to the theory created by nonsense and what we can take her solution to such a problem to imply, we (...) will show how Wrinch can resist the two main objections that have been moved to such a solution, whether as explicitly attributed to Wrinch or discussed without mentioning her. The conclusion will be, contrary to what one might be tempted to think, that even if there might be reasons to take the multiple relation theory as doomed, Wrinch was the first to show us that nonsense is not one of those reasons. (shrink)

This paper offers a novel interpretation of Wittgenstein’s early conception of ethics and the good ethical life. Initially, it critically examines the widespread view according to which Wittgenstein’s early conception of ethics and the good ethical life involves having a certain ethical attitude to the world. It points out that this reading incurs in some mistakes and shortcomings, thereby suggesting the need for an alternative reading that avoids and amends these inadequacies. Subsequently, it sets out to offer said reading. Specifically, (...) it is argued that the good ethical life is predicated on a good exercise of the ethical will and solving the riddle of life, both of which demand a certain view of, and not an attitude to, the world. This view is the view of the world sub specie aeterni. (shrink)

The Transcendental Reading of the Tractatus argues that Wittgenstein endorses, under the notion of ‘metaphysical subject’, the existence of a willing subject as a transcendental condition of ethics and representation. Tejedor aims to reject this reading resorting to three criticisms. The notion of ‘willing subject’ does not appear explicitly in, nor can it be deduced from, the Tractatus, the metaphysical subject and the willing subject are not synonymous or analogous notions and, finally, Wittgenstein abandons the notion of ‘willing subject’ at (...) the end of the Notebooks. The aim of this article is twofold. Firstly, it analyzes the critique introduced by Tejedor and presents three problems that demonstrate that Tejedor’s critique cannot adequately reject the Transcendental Reading. Secondly, it sets forth an alternative reading of the Tractatus that overcomes the issues that stem from the Transcendental Reading. This alternative reading conceives the metaphysical subject as an ethical subject and a willing subject. Additionally, it advances an alternative account of the transcendental character of ethics that does not defend the existence of a transcendental subject understood as a condition of ethics and representation in the Tractatus. (shrink)

Wittgenstein’s Tractatus construes the nature of reasoning in a manner which sharply conflicts with the conventional wisdom that logic is normative, not descriptive of thought. For although we sometimes seem to reason incorrectly, Wittgenstein denies that we can make logical mistakes (5.473). My aim in this paper is to show that the Tractatus provides us with good reasons to rethink some of the central assumptions that are standardly made in thinking about the relation between logic and thought. In particular, the (...) rejection of logical mistakes is to be understood in connection with Wittgenstein’s non-psychological approach to the thinking subject (5.641). On Wittgenstein's view, inference, understanding, and meaning are holistically related; cases of defective reasoning are to be explained in terms of a defective grasp of meaning which manifests in an indeterminate use of signs. Invalid reasoning therefore does not count for Wittgenstein as a species of reasoning, but rather as the mere illusion of reasoning. The rejection of logical mistakes thus gives voice to a radical disjunctivist approach. (shrink)

This dissertation investigates the origin, intellectual development and use of a semantic variant of the idea of logical space found implicitly in Kant and explicitly in early Wittgenstein and van Fraassen. It elucidates the idea of logical space as the idea of images or pictures representative of reality organized into a logico-mathematical structure circumscribing a form of all possible worlds. Its main claim is that application of these images or pictures to reality is through a certain conception of self. The (...) first chapter presents a novel interpretation of Kant’s semantic theory of schemata in the Critique of Pure Reason, showing that a structure of the imagination induced by the transcendental self informs an implicit idea of logical space. The second chapter offers an intellectual history of the idea through developments in the organization of images introduced by Helmholtz and Hertz. The third chapter reveals early Wittgenstein’s idea of logical space to be his notion of the self, demonstrating how this serves to unify propositions of the Tractatus Logico-Philosophicus concerning solipsism, realism, ethics, aesthetics and mysticism with those pertaining to the picture theory of meaning. The fourth chapter provides a historical overview of the development of van Fraassen’s empiricism in relation to his adaptation of logical space, and evaluates his recent proposal in Scientific Representation: Paradoxes of Perspective that the problem of coordination in the semantic view of theories is dissolved through self-location in logical space. After identifying a number of problems this proposal creates for his empiricism, a brief suggestion is made about how van Fraassen might improve upon his conception of logical space, and how an empiricist view of scientific representation might be understood as a result. (shrink)

Ethics was the major issue in Wittgenstein’s writings from 1916 to the time of publication of the Tractatus Logico-philosophicus. He explicates the notion of “good” in terms of “happiness” and the latter as “accepting the world as it is.” Nonetheless, this reductionistic philosophical program could not get off the ground unless there is a pretty clear conception of the notion of “accepting the world.” In this paper, I shall explore two alternative accounts of this concept. According to the first account, (...) which I dub “the actual world hypothesis,” Wittgenstein had meant accepting the actual world by the term “being good.” The alternative account, “the substance of the world hypothesis,” suggests accepting the substance of the world as the best reading of the Tractatus. Morris and Graver have endorsed the actual world hypothesis, as opposed to the substance of the world hypothesis. In this paper I try to show that they fail to provide good arguments for the former and against the latter. Additionally, I use ideas from McGuinness to illustrate “accepting the substance of the world” in a way that it avoids Graver’s objections. I argue that acceptance of the world ought to be interpreted as “accepting the fact that the world exists.” Finally, I shall point out that despite of his insight about the acceptance of the world, McGuinness misrepresents the relation between accepting the actual world and accepting its substance. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras comprise a materially adequate fragment of the language of thought, and endeavor to show how such algebras provide the resources necessary to resolve Russell's paradox of propositions. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are dually isomorphic. I examine, in particular, the virtues (...) unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are dual. I examine, in particular, the virtues unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast (...) to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

Undoubtedly, A Priori needs to be clarified if we are to understand the heart of Critique of Pure Reason; and Kant, precisely for this very reason, devoted a considerable part of Critique to explaining the epistemic status of A Priori, searching its origin, specifying its validity scope, and illustrating its instances. Although he, more or less, in both editions of Critique, put forward some characteristics intrinsic to A Priori since they have been also used in post-Kantian traditions, especially in a (...) meaning different from what Kant meant, so they may simply bring about some confusions cause failing to appropriately grasp the heart of Critique. With reference to such confusions the authors make an attempt to shed light on this point in part. Then, in part, based on the text of Critique and its commentators’ views, authors proceed to show that to evade such confusions one should re-define necessary to “what is emerged from the nature of the human mind”, strictly universal to “applicable just in the realm of phenomenon”, pure to “merely focused on the contribution of mind itself in collaboration with the objects themselves to form empirical knowledge”, clear to “what the scope of searching for is limited to within ourselves not outside of it” and certain to “what its scope is immutable –either regarding to its instances themselves or to their numbers”. In part, by scrutinizing the other characteristic, we shall show that this characteristic, besides of referring to mere structure, can refer to some kind of knowledge on which every possible experience is based; moreover, we shall determine the relation of above characteristic to pre-Kantian traditions. (shrink)

Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.

A close investigation of Wittgenstein’s MS 104, which contains the so-called Prototractatus, has shown that the manuscript originally contained an additional folio that was later cut out and is now missing. The content of this missing folio could be partly reconstructed by a faint inverse imprint that it has left behind on page 2. The paper discusses the consequences of this discovery for the interpretation of the beginning and early formation of the Prototractatus, including the introduction and role of the (...) numbering system. The paper also provides a transcription of the deepest visible textual layers of the first conception of the picture theory. (shrink)

This paper investigates Wittgenstein's "notorious" criticism of Russell's theory of judgment. Instead of advancing a further new interpretation of it, though, I analyze and discuss some of the most promising readings of the Russell/Wittgenstein dispute put forward in the secondary literature; I aim to show that, despite their alleged reciprocal opposition, they cohere with each other because they are, at bottom, different ways of highlighting the same question. I then connect Wittgenstein's criticism of Russell to the account of the nature (...) of the proposition presented in the Tractatus, arguing that the latter can be seen as a natural development of the former. Finally, I make a quick connection between Wittgenstein's criticism of Russell and the conception of the world as the totality of facts, as presented in the Tractatus. (shrink)

The aim of my paper is to describe and evaluate different conceptions of holism in Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. I distinguish three readings of holistic elements in this work: i) Minimal Holism (E. Anscombe, M. Black, D. Pears); ii) Moderate Holism (J. Conant, C. Diamond, G. Ryle); and iii) Radical Holism (G. Bar-Elli, M. Kremer, P. Livingston). The conclusion is that the most viable option is Moderate Holism since it embraces the logico-syntactical notion of use, rejects an anachronistic interpretation of (...) Tractatarian ontology and allows us to see that the holistic elements are complementary to the initial atomism of the work. Moreover, I point to the consequences of the topic for the overall reading of Wittgenstein’s early and late work. (shrink)

In this paper I pursue two goals. Firstly, I try to evaluate how Susan Haack receives and categorically rejects Rorty's anti-epistemological message from Philosophy and the Mirror of the Nature and some subsequent writings. I reconstruct Haack's counterarguments and Rorty's responses to these counterarguments. Secondly, I propose to deconstruct the theoretical position from which Haack orchestrates her attack on Rorty. On the one hand I show that she assumes a series of classical metaphysical presuppositions that are difficult to accept today, (...) which predisposes her to a lack of hermeneutical flexibility and clarity. On the other hand, at least some of Haack's arguments against Rorty are erroneous. Following Michael Williams, I point out that Rorty's position in Mirror is not against knowledge, since it raises questions about the legitimacy of epistemology. The challenge of my approach is not to defend Rorty, but rather to examine the mechanism of a charge against him in the name of a pretended philosophical correctness. I call this type of charge “hermeneutics of annihilation”. Haack's hermeneutics of annihilation is a pseudo-hermeneutics, since her goal is not to understand the stake of Rorty's philosophy exposed in Mirror. She only understood, from the point of view of an epistemologist ideology, that this work would be a threat to Truth, Knowledge, Epistemology, Science, and Reason. (shrink)

Classical theories of truth are monistic, since they fundamentally search for the essence of truth. The correspondence theory of truth is the most representative in this regard. There are several difficulties with the essentialist theories of truth, which led to the emergence of several alternatives. The purpose of this article is to critically evaluate three of them: the pragmatic theory of truth, the deflationary theory and the pluralistic approach. I argue for overcoming monism and for accepting pluralism in our understanding (...) of truth. At the same time, I argue – from a wittgensteinian point of view – for abandoning the attempt to build a general philosophical theory of truth. I plead for limiting the philosopher’s role to the clarification of the specific ways in which the concept of truth is used in various forms of life and areas of scientific investigation. Multiple uses of the concept of truth in different thematic areas cannot be synthesized, properly speaking, through a particular philosophical theory. (shrink)

I argue for the Wittgensteinian thesis that mathematical statements are expressions of norms, rather than descriptions of the world. An expression of a norm is a statement like a promise or a New Year's resolution, which says that someone is committed or entitled to a certain line of action. A expression of a norm is not a mere description of a regularity of human behavior, nor is it merely a descriptive statement which happens to entail a norms. The view can (...) be thought of as a sort of logicism for the logical expressivist---a person who believes that the purpose of logical language is to make explicit commitments and entitlements that are implicit in ordinary practice. The thesis that mathematical statements are expression of norms is a kind of logicism, not because it says that mathematics can be reduced to logic, but because it says that mathematical statements play the same role as logical statements. ;I contrast my position with two sets of views, an empiricist view, which says that mathematical knowledge is acquired and justified through experience, and a cluster of nativist and apriorist views, which say that mathematical knowledge is either hardwired into the human brain, or justified a priori, or both. To develop the empiricist view, I look at the work of Kitcher and Mill, arguing that although their ideas can withstand the criticisms brought against empiricism by Frege and others, they cannot reply to a version of the critique brought by Wittgenstein in the Remarks on the Foundations of Mathematics. To develop the nativist and apriorist views, I look at the work of contemporary developmental psychologists, like Gelman and Gallistel and Karen Wynn, as well as the work of philosophers who advocate the existence of a mathematical intuition, such as Kant, Husserl, and Parsons. After clarifying the definitions of "innate" and "a priori," I argue that the mechanisms proposed by the nativists cannot bring knowledge, and the existence of the mechanisms proposed by the apriorists is not supported by the arguments they give. (shrink)

This article analyses Wittgenstein’s conception of nonsense and, against resolute interpretations, defends that, perhaps influenced by Mauthner and Weininger, the Tractatus author conceived corrects ontological and ethical nonsenses like nearly to tautological senseless.

The paper considers one of the most enigmatic problems of Wittgenstein`s Tractatus - the problem of solipsism. The authorś task is to reveal how the discussion of solipsism illuminates Wittgenstein`s metaphysical view in this treatise. Wittgenstein`s method is considered as one through which the status of what cannot be said is demonstrated. Wittgenstein has not embrased solipsism or idealism in the Tractatus, and neither has he rejected metaphysics as a whole. His attack has been directed against dogmatic philosophy and ethics, (...) against the effort to say what cannot be said in true/false propositions. The discussion of solipsism brings into philosophy the importance of metaphysical "I" as a transcendental limit of the world and language. Wittgenstein`s aim in the Tractatus has been twofold: a) to show the nonsensicality of philosophical, ethical, aesthetical propositions , b) to emphasize, that the inexpresibility of the higher is the most important thing in our lives. (shrink)

In this paper we discuss the difference between (...) proliferations of logic systems, the questions of relativity and universality of logic and the position and interaction of logic with regards to other sciences such as physics, biology, mathematics and computer science. (shrink)

Words have meaning. Sentences also have meaning, but their meaning is different in kind from any collection of the meanings of the words they contain. I discuss two puzzles related to this difference. The first is how the meanings of the parts of a sentence combine to give rise to a unified sentential meaning, as opposed to a mere collection of disparate meanings (UP1). The second is why the formal ontology of linguistic meaning changes when grammatical structure is built up (...) (UP2). For example, the meaning of a sentence is a proposition evaluable for truth and falsity. In contrast, a collection of the meanings of its parts does not constitute a proposition and is not evaluable for truth. These two puzzles are closely related, since change in formal ontology is the clearest sign of the unity of meaning. The most popular strategy for answering them is taking the meanings of the parts as abstractions from primitive sentence meanings. However, I argue that, given plausible psychological constraints, sentence meanings cannot be taken as explanatory primitives. Drawing on recent work in Generative Grammar and its philosophy, I suggest that the key to both unity questions is to distinguish strictly between lexical and grammatical meaning. The latter is irreducible and determines how lexical content is used in referential acts. I argue that these referential properties determine a formal ontology, which explains why and how formal ontology changes when grammatical structure is built up (UP2). As for UP1, I suggest that, strictly speaking, lexical meanings never combine. Instead, whenever grammar specifies a formal ontology for the lexical meanings entering a grammatical derivation, further lexical (or phrasal) meanings can only specify aspects of this recursive grammatical process. In this way, contemporary grammatical theory can be used to address old philosophical problems. (shrink)

Pythagoras made the imperative “Man know thyself; then thou shalt know the Universe and God.” One of the Egyptian Luxor Temple proverbs is "Man, know thyself, and you are going to know the gods” and another is "The body is the house of God.” In some ways all classical literature addresses this question. Shakespeare’s asked the famous question, “To be, or not to be, that is the question,” which can be said, “To be, or not to be, that is the (...) question,” or Ǝ) V Ǝ) =?. Dispositive and probative facts for subsequent motions can be shown as proof of knowing God, which can be simply stated with logic and mathematics: know God therefore, ∴, know thyself, or cog ∴ cog, reducible to I ∴ X. Then, know self because, ∵, know God, or cog ∵ cog, reducible to X ∵ I. Human potential to know themselves can then represented as the set {cog + cog + glor } ⊂ {δt + δs}. (shrink)