The traditional model theory of first-order logic assumes that the interpretation of a formula can be given without reference to its deductive context. This paper investigates an interpretation which depends on a formula's location within a derivation. The key step is to drop the assumption that all quantified variables must have the same range and to require only that the ranges of variables in a derivation must be related in such way as to preserve the soundness of the inference rules. (...) With each (consistent) derivation there is associated a Buridan-Volpin (orBV) structure [M, {r(x)}] which is simply a Tarski structureM for the language and a map giving the ranger(x) of each variablex in the derivation. IfLK* is (approximately) the classical sequent calculusLK of Gentzen from which the structural contraction rules have been dropped, then our main result reads: If a set of first-ordered formulas has a Tarski modelM, then from any normal derivationD inLK* of can be constructed aBV modelM D=[M, {r(x)}] of where each ranger(x) is finite. (shrink)

This collection maintains a dialogue between the analytic and continental traditions, while aspiring to situate itself beyond the analytic-continental divide. It divides into four parts, Methodologies, Truth and Meaning, Metaphysics and Ontology, and Values, Personhood and Agency, though there is considerable overlap among the categories. History and temporality are recurrent themes, but there is a lot of metaphysics generally, with some philosophy of language, philosophy of social science, ethics, political philosophy and epistemology. Less prominent is a pragmatic, deflationary attitude, and (...) at a number of points I argue for the virtues of such an approach. (shrink)

On the point that, in practices of critical thinking, we respond spontaneously in concrete situations, this paper presents an account on behalf of Wittgenstein. I argue that the ‘seeing-things-aright’ model of Luntley's Wittgenstein is not adequate, since it pays insufficient attention to radically new circumstances, in which the content of norms is updated. While endorsing Bailin's emphasis on criteria of critical thinking, Wittgenstein would agree with Papastephanou and Angeli's demand to look behind criteriology. He maintains the primacy of the practical, (...) and yet contends that a reasonable person lets rules of rationality compel her. These rules are not mere heuristics. I further examine Burbules' conception of communicative reason, and, among others, his interpretation of Wittgenstein's sign-post example. (shrink)

David Hume’s and later Ludwig Wittgenstein’s views on concepts are generally presented as standing in stark opposition to each other. In a nutshell, Hume’s theory of concepts is taken to be subjectivistic and atomistic, while Wittgenstein is metonymic with a broadly pragmatistic and holistic doctrine that gained much attention during the second half of the 20th century. In this essay, I shall argue, however, that Hume’s theory of concepts is indeed much more akin to the views of Wittgenstein and his (...) epigones than many, including Wittgenstein himself, probably might have suspected. As I try to show, Hume anticipates many themes central to Wittgenstein’s writings on language and meaning, and actually takes initial steps towards both an anti-subjectivistic and anti-atomistic psychology and epistemology. (shrink)

The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am looking for (...) an explanation of this phenomenon. It is argued that the standard induction scheme plays a key role. (shrink)

ABSTRACT Classical and intuitionistic logic both validate Ex Contradictione Quodlibet, according to which any proposition whatsoever follows from a contradiction. Many philosophers have found ECQ counter-intuitive, but criticisms of the principle have almost universally been directed from a position of support for relevance or other orthodox paraconsistent logics, according to which some, but not necessarily all, propositions follow from a contradiction. This paper draws attention to the historically significant view that nothing whatsoever follows from a contradiction – Ex Contradictione Nihil. (...) It addresses the key arguments – model-theoretic, proof-theoretic, meaning theoretic and holist – deployed by proponents of ECQ against their standard opponents, and shows that each can be defeated from a position of support for ECN. In the course of answering these arguments, some understanding is developed of possible motivations for ECN and a solid case is built that ECN deserves further investigation. (shrink)

The aim of this paper is to discover whether or not a solitary individual, a human being isolated from birth, could become a rule-follower. The argumentation against this possibility rests on the claim that such an isolate could not become aware of a normative standard, with which her actions could agree or disagree. As a consequence, theorists impressed by this argumentation adopt a view on which the normativity of rules arises from corrective practices in which agents engage in a community. (...) However, it has been suggested that an isolated individual could engage in such a practice by herself. Three prospective examples of such cases are considered, and the possibility of solitary rule-following is vindicated. Furthermore, the nature of the goals at which rule-following practices generally aim is clarified. (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)

Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. (...) This paper explains the main complications involved and answers the main objections advanced in Batitsky's paper in this issue. (shrink)

At least since Descartes the epistemological turn derived its impetus from the sceptical challenge to provide a justification for all knowledge claims. According to a foundational view, a claim to know something is justified only when the justification refers to ultimate grounds in the form of self?supporting propositions. This paper's title suggests that justification may be seen from a different perspective, namely that of acting. Wittgenstein's examples show that the sceptic's maxim ? doubt everything ? breaks down because some beliefs (...) and judgments have to be accepted unconditionally if one is to believe or judge something else. Wittgenstein concludes that the certainty we are looking for is to be found in the very nature of the language?game. (shrink)

Throughout its history philosophy has been thought to be a member of a community of intellectual disciplines united by their common pursuit of knowledge. It has sometimes been thought to be the queen of the sciences, at other times merely their under-labourer. But irrespective of its social status, it was held to be a participant in the quest for knowledge – a cognitive discipline.

The phrase ‘Lebensform’ had a long and varied history prior to Wittgenstein’s use of it on a mere three occasions in the Philosophical Investigations. It is not a pivotal concept in Wittgenstein’s philosophy. But it is a minor signpost of a major reorientation of philosophy, philosophy of language and logic, and philosophy of mathematics that Wittgenstein instigated. For Wittgenstein sought to replace the conception of a language as a meaning calculus by an anthropological or ethnological conception. A language is not (...) a class of sentences that can be formed from a set of axioms, formation and transformation rules and the meanings of which is given by their truth-conditions, but an open-ended series of interlocking language-games constituting a form of life or way of living. Wittgenstein’s uses of ‘Lebensform’ and its cognates, both in the Investigations and in his Nachlass are severally analysed, and various exegetical misinterpretations are clarified. (shrink)

In Cavell (1994), the ability to follow and produce Austinian examples of ordinary language use is compared with the faculty of perfect pitch. Exploring this comparison, I clarify a number of central and interrelated aspects of Cavell's philosophy: (1) his way of understanding Wittgenstein's vision of language, and in particular his claim that this vision is "terrifying," (2) the import of Wittgenstein's vision for Cavell's conception of the method of ordinary language philosophy, (3) Cavell's dissatisfaction with Austin, and in particular (...) his claim that Austin is not clear about the nature and possible achievements of his own philosophical procedures, and (4) Cavell's notion that the temptation of skepticism is perennial and incurable. Cavell's reading of Wittgenstein is related to that of John McDowell. Like McDowell, Cavell takes Wittgenstein to be saying that the traditional attempt to justify our practices from an external standpoint is misguided, since such detachment involves losing sight of those conceptual and perceptual capacities in terms of which a practice is understood by its engaged participants. Unlike McDowell, however, Cavell consistently rejects the idea that philosophical clearsightedness can or should free us from that fear of groundlessness which motivates the traditional search for external justification. (shrink)

Although social scientists have been devoted to discovering specific realities of social life, many theorists devoted to critical judgment have turned to philosophy in search of universal grounds of truth and reality. They have, however, worried about the problem of relativism. Although Wittgenstein has often been characterized as a relativist, Cora Diamond, inspired by G. E. M Anscombe, argues that his work, despite internal tensions, provides rational grounds for external criticism of social practices. Her argument and her critique of the (...) work of Peter Winch and Ilham Dilman are, however, neither adequately supported by Wittgenstein’s texts nor sufficiently developed on their own terms. (shrink)

A mahāvidyā inference is used for establishing another inference. Its Reason is normally an omnipresent property. Its Target is defined in terms of a general feature that is satisfied by different properties in different cases. It assumes that there is no case that has the absence of its Target. The main defect of a mahāvidyā inference μ is a counterbalancing inference that can be formed by a little modification of μ. The discovery of its counterbalancing inference can invalidate such an (...) inference. This paper will argue that Cantor’s diagonal argument too shares some features of the mahāvidyā inference. A diagonal argument has a counterbalanced statement. Its main defect is its counterbalancing inference. Apart from presenting an epistemological perspective that explains the disquiet over Cantor’s proof, this paper would show that both the mahāvidyā and diagonal argument formally contain their own invalidators. (shrink)

In this article, a comparative analysis of Karl Popper’s falsifiability theory and Ludwig Wittgenstein’s theory of meaning in the context of the historical-philosophical approach to the problem of new knowledge formation and justification is undertaken. An assumption is made that the constellation of fact is connected with the possibility of the emergence of an epistemological field. Researchers have repeatedly addressed this issue; however, one important detail received no due attention: Popper’s counter-arguments regarding Wittgenstein’s view on semantic paradoxes show the fundamental (...) difference of these philosophers’ views on the sign and the signified, which contributes to the analysis of new knowledge formation. Arguments that concern both early and late periods of Wittgenstein’s philosophy are used in this study. The uncertainty of the demarcation criterion allowed analyzing Wittgenstein’s position as to how and why different rules of inference form different epistemological fields. (shrink)

Kalhat has forcefully criticised Wittgenstein's linguistic or conventionalist account of logical necessity, drawing partly on Waismann and Quine. I defend conventionalism against the charge that it cannot do justice to the truth of necessary propositions, renders them unacceptably arbitrary or reduces them to metalingustic statements. At the same time, I try to reconcile Wittgenstein's claim that necessary propositions are constitutive of meaning with the logical positivists’ claim that they are true by virtue of meaning. Explaining necessary propositions by reference to (...) linguistic conventions does not reduce modal to non‐modal notions, but it avoids metaphysical accounts, which are incapable of explaining how we can have a priori knowledge of necessity. (shrink)

The paper explicates a version of dispositionalism and defends it against Kripke's objections (in his "Wittgenstein on Rules and Private Language") that 1) it leaves out the normative aspect of a rule, 2) it cannot account for the directness of the knowledge one has of what one meant, and 3) regarding rules for computable functions of numbers, a) there are numbers beyond one's capacity to consider and b) there are people who are disposed to make systematic mistakes in computing values (...) of functions they understand perfectly well. (shrink)

This paper addresses a problem about aesthetic normativity raised by Kant. Can aesthetic experiences be appropriate or inappropriate to their objects? And, if so, how is that possible given that, according to Kant, aesthetic experience is not objective? Kant thought the answer to the first question was yes. But his official answer to the second question, in terms of the free play of the faculties, is obscure. The paper offers a clearer answer, inspired by Kant, which invokes Wittgenstein’s notion of (...) “knowing how to go on.” Aesthetic normativity is problematic only on the assumption that claims to the normativity of one’s responses to things must be based on the recognition of objective properties of those things. However, Wittgenstein’s discussion shows that we need not accept that assumption. There can be legitimate claims to the normativity of one’s responses which do not rely on those responses’ reflecting appreciation of objective facts. (shrink)

Suppose we were to ask some students of philosophy to imagine a typical book of classical German philosophy and describe its general style and character, how might they reply? I suspect that they would answer somewhat as follows. The book would be long and heavy, it would be written in a complicated style which employed only very abstract terms, and it would be extremely difficult to understand. At all events a description of this kind does indeed fit many famous works (...) of German philosophy. Let us take for example Hegel's Phenomenology of Spirit of 1807. The 1977 English translation published by Oxford has 591 pages, and as for style here is a typical passage: Self-consciousness found the Thing to be like itself, and itself to be like a Thing; i.e., it is aware that it is in itself the objectively real world. It is no longer the immediate certainty of being all reality, but a certainty for which the immediate in general has the form of something superseded, so that the objectivity of the immediate still has only the value of something superficial, its inner being and essence being self-consciousness itself. The object, to which it is positively related, is therefore a self-consciousness. It is in the form of thinghood, i.e. it is independent ; but it is certain that this independent object is for it not something alien, and thus it knows that it is in principle recognized by the object. It is Spirit which, in the duplication of its self-consciousness and in the independence of both, has the certainty of its unity with itself. This certainty has now to be raised to the level of truth; what holds good for it in principle , and in its inner certainty, has to enter into its consciousness and become explicit fork. (shrink)

This paper investigates the relation between what James Conant has called Kantian and Cartesian varieties of skepticism. It is argued that a solution to the most prominent example of a Kantian variety of skepticism, i.e. Kripkensteinian skepticism about rule-following and meaning, can be found in the works of Wilfrid Sellars. It is then argued that, on the basis of that very same solution to the Kantian problematic of rule-following and meaning, a novel argument against external world skepticism can be formulated. (...) This argument takes the shape of a transcendental argument, which is reminiscent of Hilary Putnam’s infamous argument against the brain-in-a-vat hypothesis, but is, as is argued, superior to it in certain respects. (shrink)

The present article aims at investigating the political aspects of Wittgenstein’s later philosophy, focusing mainly on the Philosophical Investigations. This theme remains rather marginal within Wittgensteinian scholarship, facing the key challenge of the sparsity of explicit discussions of political issues in Wittgenstein’s writings. Based on the broader anthropological and synecdochic character of Wittgenstein’s later philosophy, the main objective of the article is to make explicit the implicit political import of some of the main themes of the Philosophical Investigations. This is (...) done by correlating them with certain political concepts and issues, such as reification, mystification, emancipation, self-institution and the common. In such a way, a new light is shed on Wittgenstein’s influence on and his relevance to contemporary political theory, while at the same time the first steps are taken for the enrichment of the discussion regarding personal and social autonomy and the critique of late capit... (shrink)

Reification, a central theme in radical social/political theory from the 1920s onward, has started falling out of fashion since the 1970s, a period when a number of crucial alterations in the compo...

The later Wittgenstein’s perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein’s perspective on (...) mathematical language may appeal also to those who are not friends of or experts on Wittgenstein’s later philosophy of mathematics. (shrink)