Philosophy strives to give us a firmer hold on our concepts. But what about their hold on us? Why place ourselves under the sway of a concept and grant it the authority to shape our thought and conduct? Another conceptualization would carry different implications. What makes one way of thinking better than another? This book develops a framework for concept appraisal. Its guiding idea is that to question the authority of concepts is to ask for reasons of a special kind: (...) reasons for concept use, which tell us which concepts to adopt, adhere to, or abandon, thereby shoring up—or undercutting—the reasons for action and belief that guide our deliberations. Traditionally, reasons for concept use have been sought either in timeless rational foundations or in concepts’ inherent virtues, such as precision and consistency. Against this, the book advances two main claims: that we find reasons for concept use in the conceptual needs we discover when we critically distance ourselves from a concept by viewing it from the autoethnographic stance; and that sometimes, concepts that conflict, or exhibit other vices such as vagueness or superficiality, are just what we need. By considering not what concepts are absolutely best, but what concepts we now need, we can reconcile ourselves to the contingency of our concepts, determine the proper place of efforts to tidy up thought, and adjudicate between competing conceptions of things—even things as contested as liberty or free will. A needs-based approach separates helpful clarification from hobbling tidy-mindedness, and authoritative definition from conceptual gerrymandering. (shrink)

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

Extended Rationality: A Hinge Epistemology provides a novel account of the structure of epistemic justification. Its central claim builds upon Wittgenstein's idea in On Certainty that epistemic justifications hinge on some basic assumptions and that epistemic rationality extends to these very hinges. It exploits these ideas to address major problems in epistemology, such as the nature of perceptual justifications, external world skepticism, epistemic relativism, the epistemic status of basic logical laws, of the Principle of the Uniformity of Nature, of our (...) belief in the existence of the past and of other minds, and the nature of testimonial justification. Along the way, further technical issues, such as the scope of the Principle of Closure of epistemic operators under known entailment, the notion of transmission failure, and the existence of entitlements are addressed in new and illuminating ways. (shrink)

Peter Ludlow shows how word meanings are much more dynamic than we might have supposed, and explores how they are modulated even during everyday conversation. The resulting view is radical, and has far-reaching consequences for our political and legal discourse, and for enduring puzzles in the foundations of semantics, epistemology, and logic.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

This chapter argues that several aspects of Bernard Williams’s style, methodology, and metaphilosophy can be read as evolving dialectically out of Wittgenstein’s own. After considering Wittgenstein as a stylistic influence on Williams, especially as regards ideals of clarity, precision, and depth, Williams’s methodological debt to Wittgenstein is examined, in particular his anthropological interest in thick concepts and their point. The chapter then turns to Williams’s explicit association, in the 1990s, with a certain form of Wittgensteinianism, which he called ‘Left Wittgensteinianism’. (...) It is shown how this is not a sudden conversion, but the direct product of Williams’s longstanding critical engagement with Wittgenstein’s methodology and metaphilosophy: Williams arrives at this position by envisaging a Wittgensteinianism that thinks in concrete sociohistorical terms, embraces genuine explanation, and relinquishes its insistence on the purity of philosophy. When properly understood, moreover, this critique turns out to be continuous with Williams’s advocacy of a conception of philosophy as a humanistic discipline. Finally, it is shown that Williams inherits from Wittgenstein a certain understanding of how philosophy can help us to live, in particular the therapeutic ambition to liberate us from distortions in our self-understanding by assembling reminders. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

This paper seeks to widen the dialogue between the “epistemology of peer disagreement” and the epistemology informed by Wittgenstein’s last notebooks, later edited as On Certainty. The paper defends the following theses: not all certainties are groundless; many of them are beliefs; and they do not have a common essence. An epistemic peer need not share all of my certainties. Which response to a disagreement over a certainty is called for, depends on the type of certainty in question. Sometimes a (...) form of relativism is the right response. Reasonable, mutually recognized peer disagreement over a certainty is possible.—The paper thus addresses both interpretative and systematic issues. It uses Wittgenstein as a resource for thinking about peer disagreement over certainties. (shrink)

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...) different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake. (shrink)

In a famous passage from the Philosophical Investigations, Wittgenstein describes a pupil who has been learning to write out various sequences of numbers in response to orders such as “+1” and “+2”. He has shown himself competent for numbers up to 1000, but when we have him continue the “+2” sequence beyond 1000, he writes the numerals 1004, 1008, 1012. As Wittgenstein describes the case: We say to him, “Look what you’re doing!” — He doesn’t understand us. We say “You (...) should have added two; look how you began the series!” — He answers: “Yes! Isn’t it right? I thought that’s how I should [sollen] do it. — Or suppose he were to say, pointing to the series, “But I went on in the same way!”1The passage continues:— It would now be no use to us to say “But don’t you see…?” — and repeat for him the old explanations and examples. — In such a case, we might perhaps say: this person naturally understands our order, once given our explanations, as we would understand the order “Add 2 up to 1000, 4 up to 2000, 6 up to 3000, and so on.”. (shrink)

_ Source: _Volume 6, Issue 2-3, pp 97 - 119 In this paper, I briefly summarize the nature of Wittgenstein’s ‘hinge certainties,’ showing how they radically differ from traditional basic beliefs in their being nonepistemic, grammatical, nonpropositional, and enacted. I claim that it is these very features that enable hinge certainties to put a logical stop to justification, and thereby solve the regress problem of basic beliefs. This is a ground-breaking achievement—worthy of calling _On Certainty_ Wittgenstein’s ‘third masterpiece.’ As I (...) go along, I question some differing interpretations and respond to some objections from fellow-readers of _On Certainty_: Duncan Pritchard, Michael Williams, and Crispin Wright. (shrink)

ABSTRACT Contemporary relativists often see their view as contributing to a semantic/post-semantic account of linguistic data about disagreement and retraction. I offer an independently motivated metasemantic account of the same data, that also handles a number of cases and empirical results that are problematic for the relativist. The key idea is that the content of assertions and beliefs is determined in part by facts about other times, including times after the assertion is made or the belief is formed. On this (...) temporal externalist view, speaker behaviours such as retraction of previous assertions play a role in making it the case that a past utterance has a given meaning. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

Methodological reductionists practice ‘wannabe reductionism’. They claim that one should pursue reductionism, but never propose how. I integrate two strains in prior work to do so. Three kinds of activities are pursued as “reductionist”. “Successional reduction” and inter-level mechanistic explanation are legitimate and powerful strategies. Eliminativism is generally ill-conceived. Specific problem-solving heuristics for constructing inter-level mechanistic explanations show why and when they can provide powerful and fruitful tools and insights, but sometimes lead to erroneous results. I show how traditional metaphysical (...) approaches fail to engage how science is done. The methods used do so, and support a pragmatic and non-eliminativist realism. (shrink)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (shrink)

This is a short, and therefore necessarily very incomplete discussion of one of the great questions of modern philosophy. I return to a station at which an interpretative train of thought of mine came to a halt in a paper written almost 20 years ago, about Wittgenstein and Chomsky,[1] hoping to advance a little bit further down the track. The rule-following passages in the Investigations and Remarks on the Foundations of Mathematics in fact raise a number of distinct issues about (...) rules, meaning, objectivity, and reasons, whose conflation is encouraged by the standard caption, "the Rule-following Considerations".[2] So, let me begin by explaining my focus here. (shrink)

This paper seeks to defend, develop, and revise Edward Craig's “genealogy of knowledge”. The paper first develops the suggestion that Craig's project is naturally thought of as an important instance of “social cognitive ecology”. It then introduces the genealogy of knowledge and some of its main problems and weaknesses, suggesting that these are best taken as challenges for further work rather than as refutations. The central sections of the paper conduct a critical dialogue between Craig's theory and Wittgenstein's claim–familiar from (...) On Certainty–that common-sense certainties cannot be known. It turns out that Craig's distinction between different stages in the development of our concept of knowledge can illuminate and make plausible Wittgenstein's claim. But it can do so only if Craig's traditional commitment to a central “core” in our concept of knowledge is replaced with the idea of knowledge as a family-resemblance concept. (shrink)

The distinction between the a priori and the a posteriori is an old and influential one. But both the distinction itself and the crucial notion of a priori knowledge face powerful philosophical challenges. Many philosophers worry that accepting the a priori is tantamount to accepting epistemic magic. In contrast, this Element argues that the a priori can be formulated clearly, made respectable, and used to do important epistemological work. The author's conception of the a priori and its role falls short (...) of what some historical proponents of the notion may have hoped for, but it allows us to accept and use the notion without abandoning either naturalism or empiricism, broadly understood. This Element argues that we can accept and use the a priori without magic. (shrink)

The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...) a computer. In Emperor I go further than this and suggest that the outward manifestations ofconscious mental activity cannot even be properly simulated by calculation. To support this view, I use various arguments to show that the results of mathematical insight, in particular, do not seem to be obtained algorithmically. The main thrust ofthis work, however, is to present an overview ofthe present state of physical understanding and to show that an important gap exists at the point where, quantum and classical physics meet, as well as to speculate on how the conscious brain might be taking advantage ofwhatever new physics is needed to fill this gap to achieve its nonalgorithmic effects. (shrink)

Mathematical fictionalism (or as I'll call it, fictionalism) is best thought of as a reaction to mathematical platonism. Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. So, for instance, on the platonist view, the sentence ‘3 is prime’ provides a straightforward description of a certain object—namely, the number 3—in much the same way that the sentence ‘Mars is red’ provides a (...) description of Mars. But whereas Mars is a physical object, the number 3 is (according to platonism) an abstract object. And abstract objects, platonists tell us, are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 3 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects. This view has been endorsed by Plato, Frege (1884, 1893-1903, 1919), Gödel (1964), and in some of their writings, Russell (1912) and Quine (1948, 1951), not to mention numerous more recent philosophers of mathematics, e.g., Putnam (1971), Parsons (1971), Steiner (1975), Resnik (1997), Shapiro (1997), Hale (1987), Wright (1983), Katz (1998), Zalta (1988), and Colyvan (2001). (shrink)

This paper aims to distinguish Wittgenstein’s concept of ‘form of life’ from other concepts or expressions that have been confused or conflated with it, such as ‘language-game’, ‘certainty’, ‘patterns of life’, ‘ways of living’ and ‘facts of living’. Competing interpretations of Wittgenstein’s ‘form of life’ are reviewed, and it is concluded that Wittgenstein intended both a singular and a plural use of the concept; with, where the human is concerned, a single human form of life characterized by innumerable forms of (...) human life. (shrink)

[This Invited Paper will be published in December 2016.].

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 this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...) a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor inconsistency, and thus contradictions do not have any special status as a thing to be avoided. (shrink)

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and nonmental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the (...) term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893-1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951). (shrink)

This paper discusses the meta-ethical implications of Wittgenstein’s later moral philosophy. According to Lovibond and Brandhorst, Wittgenstein provided a novel conception of moral facts, properties and objects by adopting deflationism. Lovibond argues that Wittgenstein’s seamless conception of language together with his non-foundational epistemology and non-transcendent understanding of rationality involves a change of perspective towards a plausible and non-mystificatory moral realism. Meanwhile, Brandhorst argues that Wittgenstein’s provides a deflationist conception of moral truths from which we obtain a deflationist conception of moral (...) facts. This paper argues, on the contrary, that the attribution of deflationism does not do justice to Wittgenstein’s later work. It is concluded, therefore, that the appeal to deflationism does not afford or substantiate the exegetical claims made by Lovibond and Brandhorst. (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.

Discussions of the applicability of mathematics in the natural sciences have been flawed by failure to realize that there are multiple senses in which mathematics can be ‘applied’ and, correspondingly, multiple problems that stem from the applicability of mathematics. I discuss semantic, metaphysical, descriptive, and and epistemological problems of mathematical applicability, dwelling on Frege's contribution to the solution of the first two types. As for the remaining problems, I discuss the contributions of Hartry Field and Eugene Wigner. Finally, I argue (...) that there are epistemological problems concerning the applicability of mathematics that nobody in the philosophical community has yet confronted, though the problems are well known to physicists. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...) false. (shrink)

Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a (...) natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs. (shrink)

According to a standard criticism, Robert Brandom's “normative pragmatics”, i.e. his attempt to explain normative statuses in terms of practical attitudes, faces a dilemma. If practical attitudes and their interactions are specified in purely non-normative terms, then they underdetermine normative statuses; but if normative terms are allowed into the account, then the account becomes viciously circular. This paper argues that there is no dilemma, because the feared circularity is not vicious. While normative claims do exhibit their respective authors' practical attitudes (...) and thereby contribute towards establishing the normative statuses they are about, this circularity is not a mark of Brandom's explanatory strategy but a feature of social practice of which we theorists partake. (shrink)

This paper examines the view of ethical language that Wittgenstein took in later years. It argues that according to this view, ethics falls into place as a part of our natural history, while every sense of the mystical or supernatural that once surrounded it is irrevocably lost. Moreover, Wittgenstein argues that ethical language does not correspond to reality “in the way” in which a physical theory does. I propose an interpretation of this claim that shows how it sets his view (...) apart from a “realist” theory of ethics. The reality of which he speaks is the reality of human life. (shrink)

John Broome’s Rationality Through Reasoning is a trail-blazing study of the nature of rationality, the nature of reasoning and the connection between the two. But it may be somewhat misleading in two respects. First, his theory of reasoning is consistent with the meta-propositional view that he rejects; it develops a broadly similar theory but in much greater detail. And while his discussion of rule-following helps to explain the role of rules in reasoning, it does not constitute a response to the (...) classic problem associated with Wittgenstein and Kripke. (shrink)

The notion of the riddle plays a pivotal role in Wittgenstein’s Tractatus . By examining the comparisons he draws between philosophical problems and riddles, this paper offers a reassessment of the aims and methods of the book. Solving an ordinary riddle does not consist in learning a new fact; what it requires is that we transform the way we use words. Similarly, Wittgenstein proposes to transform the way philosophers understand the nature of their problems. But since he holds that these (...) problems are ultimately unsolvable, rather than attempting to solve the riddles of philosophy, he aims to dissolve them. (shrink)

According to the dominant view, the later Wittgenstein identified the meaning of an expression with its use in the language and vehemently rejected any kind of mentalism or intentionalism about linguistic meaning. I argue that the dominant view is wrong. The textual evidence, which has either been misunderstood or overlooked, indicates that at least since the Blue Book Wittgenstein thought speakers' intentions determine the contents of linguistic utterances. His remarks on use are only intended to emphasize the heterogeneity of natural (...) language. Taking into account remarks written after he finished the Investigations, I show how Wittgenstein anticipated the basic tenets of Gricean intention-based semantics. These are, in particular, the distinction between ‘natural’ and ‘non-natural’ meaning and the distinction between what a speaker means by an utterance and what the expression uttered means in the speaker’s natural language. Importantly, Wittgenstein also believed that only the meaning of the speaker determined the content of ambiguous expressions, such as ‘bank’, on a particular occasion of utterance. (shrink)

This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or (...) imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, the information thus displayed is not metrical and it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions. (shrink)