I focus on three preoccupations of recent writings on proof. -/- I. The role and possible effects of empirical reasoning in mathematics. Do recent developments (specifically, the computer-assisted proof of the 4CT) point to something essentially new as regards the need for and/or effects of using broadly empirical and inductive reasoning in mathematics? In particular, should we see such things as the computer-assisted proof of the 4CT as pointing to the existence of mathematical truths of which we (...) cannot have a priori knowledge? -/- 2. The role of formalization in proof. What are the patterns ofinference according to which mathematical reasoning naturally proceeds? Are they of 'local' character (i.e. sensitive to the subject-matter of the reasoning concerned) or 'global' character (i.e. invariant across all subject-matters)? Finally, what if any relationship is there (a) between the patterns of inference manifest in a proof and its explanatory capacity and (b) between explanatory capacity and rigor? -/- 3. Diagrams and their role in mathematical reasoning. What essentially is diagrammatic reasoning, and what is the nature and basis of its usefulness? Can it play a justificative role in the development of mathematical knowledge and, more particularly, in genuine proof? Finally, does the use of diagrammatic reasoning force an adjustment either in our conception of rigor or in our view of its importance? (shrink)

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this (...) paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples drawn from mathematical practice, and the account proposed here is compared to other accounts in the literature. The concept of a proof that explains is closely intertwined with other important concepts, such as a brute force proof, a mathematical coincidence, unification in mathematics, and natural properties. Ultimately, this paper concludes that the features of a proof that would contribute to its explanatory power would also contribute to its beauty, but that these two virtues are not the same; a beautiful proof need not be explanatory. (shrink)

This book is the first detailed study of Kant's method of 'transcendental reflection' and its use in the Critique of Pure Reason to identify our basic human cognitive capacities, and to justify Kant's transcendental proofs of the necessary a priori conditions for the possibility of self-conscious human experience. Kenneth Westphal, in a closely argued internal critique of Kant's analysis, shows that if we take Kant's project seriously in its own terms, the result is not transcendental idealism but realism regarding (...) physical objects. Westphal attends to neglected topics - Kant's analyses of the transcendental affinity of the sensory manifold, the 'lifelessness of matter', fallibilism, the semantics of cognitive reference, four externalist aspects of Kant's views, and the importance of Kant's Metaphysical Foundations for the Critique of Pure Reason - that illuminate Kant's enterprise in new and valuable ways. His book will appeal to all who are interested in Kant's theoretical philosophy. (shrink)

Public and professional debates have come to rely heavily on a special type of reasoning: the argument-from-ignorance, in which conclusions depend on the _lack_ of compelling information. "I win my argument," says the skillful advocate, "unless you can prove that I am wrong." This extraordinary gambit has been largely ignored in modern rhetorical and philosophical studies. Yet its broad force can be demonstrated by analogy with the modern legal system, where courts have long manipulated burdens of proof with skill (...) and subtlety. This legal, philosophical, and rhetorical study by Richard H. Gaskins provides the first systematic treatment of arguments-from-ignorance across a wide range of modern discourse—from constitutional law, scientific inquiry, and moral philosophy to organizational behavior, computer operation, and personal interaction. Gaskins reviews the historic shifts in constitutional proof burdens that have shaped public debate on fundamental rights and, by analogy, on the fundamental status of intellectual and cultural authority. He shows how similar shifts have dominated polemical battles between scientific and ethical modes of authority, affecting both academic and popular discussion. Finally, he discovers the philosophical roots of default reasoning strategies in the arguments of Kant and nineteenth-century Kantian schools. Concluding that shifting proof burdens are inescapable in a world of scientific and moral uncertainty, Gaskins emphasizes the common strategic ground shared by dogmatic and skeptical reasoning. Using Hegelian strategies, he describes a more pluralistic temper that can move critical thinking beyond polemics and strengthen our capacities for common discourse. (shrink)

If proofs are nothing more than truth makers, then there is no force in the standard argument against classical logic (there is no guarantee that there is either a proof forA or a proof fornot A). The standard intuitionistic conception of a mathematical proof is stronger: there are epistemic constraints on proofs. But the idea that proofs must be recognizable as such by us, with our actual capacities, is incompatible with the standard intuitionistic explanations of the (...) meanings of the logical constants. Proofs are to be recognizable in principle, not necessarily in practice, as shown in section 1. Section 2 considers unknowable propositions of the kind involved in Fitch''s paradox:p and it will never be known thatp. It is argued that the intuitionist faces a dilemma: give up strongly entrenched common sense intuitions about such unknowable propositions, or give up verificationism. The third section considers one attempt to save intuitionism while partly giving up verificationism: keep the idea that a proposition is true iff there is a proof (verification) of it, and reject the idea that proofs must be recognizable in principle. It is argued that this move will have the effect that some standard reasons against classical semantics will be effective also against intuitionism. This is the case with Dummett''s meaning theoretical argument. At the same time the basic reason for regarding proofs as more than mere truth makers is lost. (shrink)

Mathematical rigor is commonly formulated by mathematicians and philosophers using the notion of proof gap: a mathematical proof is rig­orous when there is no gaps in the mathematical reasoning of the proof. Any philosophical approach to mathematical rigor along this line requires then an account of what a proof gap is. However, the notion of proof gap makes sense only relatively to a given conception of valid mathematical reasoning, i.e., to a given conception of the (...) validity of mathematical inference. A proof gap can in particular be conceived as a failure in drawing a valid mathematical inference. The aim of this paper is to discuss two possible views of the validity of math­ematical inference with respect to their capacity to yield a plausible account of the intuitive notion(s) of proof gap present in mathematical practice. The first view is the one provided by the contemporary standards of mathematical rigor: a mathematical inference is valid if and only if its conclusion can be formally derived from its premises. We will argue that this conception does not lead to a plausible account of the intuitive notion(s) of proof gap. The second view is based on a new account of the validity of inference proposed by Prawitz: an inference is valid if and only if it consists in an operation that provides a ground for its conclusion given (previously obtained) grounds for its premises. We will first specify Prawitz's account to mathematical inference and we will then argue that the resulting ground-based account is able to capture various intuitive notions of proof gap as different types of failure in drawing valid mathematical inferences. We conclude that the ground-based account ap­pears of particular interest for the philosophy of mathematical practice, and we finally raise several challenges facing a full development of a ground-based account of the notions of mathematical rigor, proof gap and the validity of mathematical inference. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant’s Transcendental Proof of RealismBrandon C. LookKenneth R. Westphal. Kant’s Transcendental Proof of Realism. New York: Cambridge University Press, 2004. Pp. x + 299. Cloth, $80.00.Westphal's book is a rich and exciting contribution to the field of Kant studies. Its claims run counter to much contemporary discussion of Kant's theoretical philosophy and indeed challenge some of Kant's fundamental doctrines, but the arguments are very compelling and (...) therefore likely to force us to rethink both the Critique of Pure Reason [CPR] and Kant's relevance to contemporary epistemology.The central point of this work is that, if we follow Kant's injunction to engage in reflection on our cognitive capacities, then we will be led not to Kantian transcendental idealism but to an unqualified realism about objects and events in space and time. The book's first three chapters are devoted to analyzing Kant's methodology and the much-overlooked idea of transcendental affinity. Westphal focuses on the Kantian duty of engaging in "transcendental reflection," which is "the action through which I make the comparison of representations in general with the cognitive power in which they are situated, and through which I distinguish whether they are to be compared with one another as belonging to pure understanding or to sensible intuition" (CPR, A 261/B 317). And he adds to this the more general methodological obligation of "epistemic reflection," or the duty to determine precisely our cognitive capacities and incapacities. If, then, we reflect on our representations, their origins in sensibility and the understanding, and on our powers to know things of ourselves and the world in general, then certain puzzles arise—puzzles that were confronted by Kant (and Hume and Hegel) but that have not received the attention they have deserved. Chief among these puzzles is our ability to identify single objects and events and track them in space through time. But, as Westphal is keen to point out, identifying any particular over time requires that we be able to re-identify that particular. Now, while this puzzle is addressed by Kant in the Transcendental Deduction and Analogies of Experience, it is important to see that there is a material condition necessary for the possibility of self-conscious experience of the world that is not fleshed out in great detail by Kant and seems to be completely overlooked in the literature on Kant, namely, "the presupposition of diversity in nature" and the homogeneity of its objects among themselves (CPR, A 657/B 685). In other words, the fact that we are able to associate our various sensations with each other at all (and thereby identify and re-identify objects) is due to their "transcendental affinity." And it is Westphal's contention that "on Kant's own principles, the transcendental affinity of the manifold of sensory intuition can only be reconstructed, but not constructed, by intellectual syntheses of the understanding" (91). Therefore, pace Kant, who held that only his transcendental idealism could explain the possibility of experience, Westphal argues that transcendental idealism runs afoul of many of Kant's own arguments and observations in the Transcendental Aesthetic and Transcendental Analytic and, more important, that transcendental affinity provides grounds for "realism sans phrase" (the author's phrase) about objects and events in space and time, and for the view that our mental states are determined by external objects. As Westphal puts it in his conclusion: "Kant's analysis of transcendental affinity is in fact a transcendental argument for mental content externalism" (266). [End Page 665]The second part of Westphal's argument revolves around a detailed examination of Kant's theses about transeunt causality and the nature of matter as expressed not only in the Critique of Pure Reason, but also in the Metaphysical Foundations of Natural Science and the Opus postumum. Roughly the problem is this: in order to have an adequately grounded metaphysics of nature, Kant needs not only the results of the Analogies of Experience, the transcendental causal thesis that every event has a cause, but also the metaphysical causal thesis that every physical event has an external physical cause. But, according to Westphal, in the Metaphysical Foundations... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Nature of Proof in PsychiatryPaul Lieberman (bio)Keywordspsychotherapy process, knowledge and psychiatry, externalism, WittgensteinThis vivid clinical report illustrates recognizably, and provocatively, a number of routine, but often unexamined, clinical questions. In its few paragraphs, it depicts challenges that each practitioner confronts, and, in the flux of clinical work, addresses, however implicitly and imperfectly, every day: From what data, and by what processes, does a clinical formulation, or way (...) of understanding, come into being? How do we appraise its accuracy and adequacy? Of what value is even a well-substantiated understanding, in the mind of the therapist, to the patient? What is the power of empathy as a treatment tool? How do we assess someone's status as a “good candidate for therapy?” When, typically, only the outlines of a problem are visible, and its origins and implications are largely hidden, by what right do we recommend psychotherapy, and with what conception, at what level of detail, of what its outcome will be? These are among the questions that Dr. Bailey's story challenges us to address.They are clinical questions, of course, because they deal with empirical matters of fact—psychological processes, outcomes studies, and evidence. But they are also philosophical because, as Freud insisted and Dr. Bailey shows, information obtained in the clinical situation often has power and authority that lead us to believe we understand what is going on, understand the other person, even in the absence of scientifically tested hypotheses, or the clear application of research-based evidence. Interactions between people—including clinical interactions—have a life and ability to engage us. Their meanings can seem so transparent and convincing that no doubt or questioning may seem cogent. At their most powerful, such experiences can reawaken us to important realms of experience and feeling which we might, otherwise, forget, ignore, suppress, deny, or in other ways keep out of awareness; they have the potential to arouse us and reconnect us with truths that, once revived, can seem both valid and important—perhaps the kind of experience that we may derive from works of art or literature (in fact, Dr. Bailey's account could be seen as a clinical parable—meant to be neither true nor false, but instructive). But even less dramatic examples are commonplace: we do routinely claim to know and be able to interpret and understand the actions of other people from our everyday interactions with and observations of them.What is less clear is how to account for these convictions and how to appraise their value, because they do not derive from established scientific procedures. Clinical intuition has a role throughout medicine, but we usually expect it to be subjected later to more rigorous tests to establish the correct diagnosis. Yet, as Dr. Bailey's case illustrates, clinical intuition in the psychiatric encounter seems somehow different. When Colin [End Page 225] leads Dr. Bailey to the conclusion that a “painful lack of wounds” has made him depressed, we find this credible. It seems similarly credible that Dr. Bailey might be anxious about his own capacity to defend his young family, because he says he is, that he perceives Colin as testing his manhood or sincerity, because that seems to fit Colin's temperament, that being accurately understood is helpful, because most of us have had that experience and valued it, and that, most generally, an absence of challenge or of activity could be depressing. But suppose a patient believed that a painful lack of wounds produced diabetes instead of depression, or suppose he had developed epilepsy and attributed that to an absence of combat experience. We might see these as ‘pre-scientific’ or ‘hypothesis-generating’ (or worse). By contrast, it seems timid to consider psychiatric formulations to be always and only provisional or hypothetical.In what ways and to what extent should we expect psychiatry to be different, and why? Several considerations suggest that psychiatry's reasons are not, always and everywhere, the same as those of general medicine, nor are its objectives.In general medicine, we distinguish between signs and symptoms, on the one hand, and “underlying” disease processes, on the other. But in psychiatry, this distinction can be... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant and the Capacity to Judge; Sensibility and Discursivity in the Transcendental Analytic of the Critique of Pure Reason by Beatrice LonguenesseMichelle GreerBeatrice Longuenesse. Kant and the Capacity to Judge; Sensibility and Discursivity in the Transcendental Analytic of the Critique of Pure Reason. Translation by Charles T. Wolfe. Princeton, NJ: Princeton University Press, 1998. Pp. xv + 420. Cloth, $59.50.Kant and the Capacity to Judge is a translation (...) of Longuenesse’s Kant et Pouvoir de juger, although Longuenesse has revised and added to the original version. The central argument seeks to demonstrate the essential role played by the logical forms of judgment in the arguments of Kant’s first Critique. Longuenesse emphasizes straight away Kant’s efforts (in the Metaphysical Deduction) to deduce a set of pure concepts from the logical forms of judgment. Against many standard readings, she aims to reveal the very “tight” connection between this attempt and subsequent arguments in the Transcendental [End Page 372] Analytic. That Kant takes the functions of judgment to be relevant to these arguments is hardly a novel claim. The originality of Longuenesse’s work, however, stems both from the central and pervasive role she assigns to the logical forms of judgment, and from the impressive, painstaking effort she makes to sustain the close connection between these forms and Kant’s subsequent arguments. According to Longuenesse, any proper understanding of the arguments of the Transcendental Analytic absolutely depends upon relating these “down to the minutest details of their proofs,” to the role of the logical forms (5).These minute details do not escape Longuenesse in her subsequent elaboration on this original thesis. Given the length and detail of her work, I can only highlight a few of the central points and strategies. One should note from the outset, however, that the detail and the scholarship evinced to support her claims constitute much of what is of value in the book. Many of these “supporting arguments” and discussions, which include efforts to trace Kantian conceptions back to their historical/philosophical origins, stand in their own right as independent contributions to Kant scholarship and interpretation.The work is divided into three parts. The first part is essentially propaedeutic. Longuenesse begins by drawing a distinction between the potential or capacity to judge and judgement itself (i.e., the “actualization” of this judgmental capacity under [externally grounded] sensory stimulation) (7). Taking this distinction as her cue, Longuenesse seeks to reveal the way in which the line of argumentation in the transcendental analytic presents an extended investigation into the formal capacity (ibid). The centrality of the logical forms of judgment is secured early on by assigning them a substantive role in the very presentation of something in intuition “as” an “object.” Insofar as she assigns this role to the logical forms themselves, her account clearly undercuts the primary function of the categories in this regard. Relevant here is Longuenesse’s construal of “appearances” as the intentional correlates of our representational capacities and activities (cf. 20–21). Given this, the problem now motivating the transcendental deduction is how to make sense of the relation between this “internalized” object of (indeterminate) empirical intuition (the appearance) and the object corresponding to intuition which concepts allow one to think in a determinate way (the phenomenon). This ability to think the object in a determinate fashion appears to be the essential contribution made by judgement.These preliminary considerations ground Longuenesse’s efforts (in Part Two) to isolate and examine the discursive activity of judgment. Longuenesse stresses the reflective (and not simply the determinative) role of judgment and its forms. Indeed, she suggests that concepts (not merely empirical concepts, but also the pure concepts of the understanding themselves) are formed by reflecting (through acts of comparison, reflection, and abstraction) on the “sensible given.” Drawing extensively from the Logic, she interestingly argues that the form of judgment itself carries with it some inherent claim to objectivity. Thus, objectivity is folded into the formal activity of judging by being identified as a “normative propensity” inherent in every judgment by virtue of its form alone (87–88). Longuenesse accordingly eschews efforts to downplay the role of the logical use of the... (shrink)

In 1950, Alan Turing proposed his eponymous test based on indistinguishability of verbal behavior as a replacement for the question "Can machines think?" Since then, two mutually contradictory but well-founded attitudes towards the Turing Test have arisen in the philosophical literature. On the one hand is the attitude that has become philosophical conventional wisdom, viz., that the Turing Test is hopelessly flawed as a sufficient condition for intelligence, while on the other hand is the overwhelming sense that were a machine (...) to pass a real live full-fledged Turing Test, it would be a sign of nothing but our orneriness to deny it the attribution of intelligence. The arguments against the sufficiency of the Turing Test for determining intelligence rely on showing that some extra conditions are logically necessary for intelligence beyond the behavioral properties exhibited by an agent under a Turing Test. Therefore, it cannot follow logically from passing a Turing Test that the agent is intelligent. I argue that these extra conditions can be revealed by the Turing Test, so long as we allow a very slight weakening of the criterion from one of logical proof to one of statistical proof under weak realizability assumptions. The argument depends on the notion of interactive proof developed in theoretical computer science, along with some simple physical facts that constrain the information capacity of agents. Crucially, the weakening is so slight as to make no conceivable difference from a practical standpoint. Thus, the Gordian knot between the two opposing views of the sufficiency of the Turing Test can be cut. (shrink)

Since both berkeley and hume are committed to the view that a line is composed of finitely many fundamental parts, They must find responses to the standard geometrical proofs of infinite divisibility. They both repeat traditional arguments intended to show that infinite divisibility leads to absurdities, E.G., That all lines would be infinite in length, That all lines would have the same length, Etc. In each case, Their arguments rest upon a misunderstanding of the concept of a limit, And thus (...) are not successful. Berkeley, However, Adds a further ingenious argument to the effect that the standard geometrical proofs of infinite divisibility misread the unlimited representational capacity of geometrical diagrams as a substantive feature of the objects that these diagrams represent. The article concludes that berkeley is right on this matter, And that the traditional proofs of infinite divisibility do not show what they are intended to show. (shrink)

In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead (...) for an alternative account in which imagination, anticipation, and interpretations of natural language play roles in establishing mathematical rigor. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant’s Transcendental Proof of RealismBrandon C. LookKenneth R. Westphal. Kant’s Transcendental Proof of Realism. New York: Cambridge University Press, 2004. Pp. x + 299. Cloth, $80.00.Westphal's book is a rich and exciting contribution to the field of Kant studies. Its claims run counter to much contemporary discussion of Kant's theoretical philosophy and indeed challenge some of Kant's fundamental doctrines, but the arguments are very compelling and (...) therefore likely to force us to rethink both the Critique of Pure Reason [CPR] and Kant's relevance to contemporary epistemology.The central point of this work is that, if we follow Kant's injunction to engage in reflection on our cognitive capacities, then we will be led not to Kantian transcendental idealism but to an unqualified realism about objects and events in space and time. The book's first three chapters are devoted to analyzing Kant's methodology and the much-overlooked idea of transcendental affinity. Westphal focuses on the Kantian duty of engaging in "transcendental reflection," which is "the action through which I make the comparison of representations in general with the cognitive power in which they are situated, and through which I distinguish whether they are to be compared with one another as belonging to pure understanding or to sensible intuition" (CPR, A 261/B 317). And he adds to this the more general methodological obligation of "epistemic reflection," or the duty to determine precisely our cognitive capacities and incapacities. If, then, we reflect on our representations, their origins in sensibility and the understanding, and on our powers to know things of ourselves and the world in general, then certain puzzles arise—puzzles that were confronted by Kant (and Hume and Hegel) but that have not received the attention they have deserved. Chief among these puzzles is our ability to identify single objects and events and track them in space through time. But, as Westphal is keen to point out, identifying any particular over time requires that we be able to re-identify that particular. Now, while this puzzle is addressed by Kant in the Transcendental Deduction and Analogies of Experience, it is important to see that there is a material condition necessary for the possibility of self-conscious experience of the world that is not fleshed out in great detail by Kant and seems to be completely overlooked in the literature on Kant, namely, "the presupposition of diversity in nature" and the homogeneity of its objects among themselves (CPR, A 657/B 685). In other words, the fact that we are able to associate our various sensations with each other at all (and thereby identify and re-identify objects) is due to their "transcendental affinity." And it is Westphal's contention that "on Kant's own principles, the transcendental affinity of the manifold of sensory intuition can only be reconstructed, but not constructed, by intellectual syntheses of the understanding" (91). Therefore, pace Kant, who held that only his transcendental idealism could explain the possibility of experience, Westphal argues that transcendental idealism runs afoul of many of Kant's own arguments and observations in the Transcendental Aesthetic and Transcendental Analytic and, more important, that transcendental affinity provides grounds for "realism sans phrase" (the author's phrase) about objects and events in space and time, and for the view that our mental states are determined by external objects. As Westphal puts it in his conclusion: "Kant's analysis of transcendental affinity is in fact a transcendental argument for mental content externalism" (266). [End Page 665]The second part of Westphal's argument revolves around a detailed examination of Kant's theses about transeunt causality and the nature of matter as expressed not only in the Critique of Pure Reason, but also in the Metaphysical Foundations of Natural Science and the Opus postumum. Roughly the problem is this: in order to have an adequately grounded metaphysics of nature, Kant needs not only the results of the Analogies of Experience, the transcendental causal thesis that every event has a cause, but also the metaphysical causal thesis that every physical event has an external physical cause. But, according to Westphal, in the Metaphysical Foundations... (shrink)

We focus on the thesis that action understanding is a function of the mirror neuron system. According to our opinion, understanding is a process that runs through hermeneutic circles from the “Vorverständnis” (“previous understanding”) to steps of deeper understanding. Our critique relates to the narrow neuroscientific definition of action understanding as the capacity to recognize several movements as belonging to one action. After a reconstruction of the model's developments, we will challenge the claims of the model by Rizzolatti and Sinigaglia (...) (2010). By analyzing the relation between the experimental results and its interpretation, we will conclude that there is no proof that mirror neuron activity leads to action understanding. (shrink)

The paper provides a reconstruction of proof by contradiction in Kant’s pure general logic. A seemingly less-explored point of view on this topic is how apagogical proof can account for the formal truth of a judgement. Integrating the argument held by Kjosavik (2019), I intend to highlight how one can use proof by contradiction, conceived as a modus tollens, to establish the logical actuality (logical or formal truth) of a cognition. Although one might agree on the capacity (...) of the proof to prove formal falsity, the logical actuality of a judgement is assessable based on a logically grounded judgement and, as for transcendental logic, this cognitive operation has to presuppose the real possibility of an object. (shrink)

A new approach to informal rigorous mathematical proof is offered. To this end, algorithmic devices are characterized and their central role in mathematical proof delineated. It is then shown how all the puzzling aspects of mathematical proof, including its peculiar capacity to convince its practitioners, are explained by algorithmic devices. Diagrammatic reasoning is also characterized in terms of algorithmic devices, and the algorithmic device view of mathematical proof is compared to alternative construals of informal proof (...) to show its superiority. (shrink)

I challenge a claim that seems to be made when nominalists offer reformulations of the content of mathematical beliefs, namely that these reformulations are accessible to everyone. By doing so, I argue that these theories cannot account for the mathematical knowledge that ordinary people have. In the first part of the paper I look at reformulations that employ the concept of proof, such as those of Mary Leng and Ottavio Bueno. I argue that ordinary people don’t have many beliefs (...) about proofs, and that they are not in a position to acquire knowledge about proofs autonomously. The second part of the paper is concerned with other reformulations of content, such as those of Hartry Field and Stephen Yablo. There too, the problem is that people are not able to acquire knowledge of the reformulated propositions autonomously. Ordinary people simply do not have beliefs with the kind of content that the nominalists need, for their theory to account for the mathematical knowledge of ordinary people. All in all then, the conclusion is that a large number of theories that suggest reformulations of mathematical content yield contents that are inaccessible for most people. Thus, these theories are limited, in that they cannot account for the mathematical knowledge of ordinary people. (shrink)

Chomsky’s highly influential Syntactic Structures ( SS ) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs directly out of the work of the mathematical logician Emil Post on formalizing proof, but few linguists are (...) aware of this, because Post’s papers are not cited. Chomsky’s extensions to Post’s systems are not clearly defined, and the arguments for their necessity are weak. Linguists have also overlooked Post’s proofs of the first two theorems about effects of rule format restrictions on generative capacity, published more than ten years before SS was published. (shrink)

Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (...) (Knops, Piazza, Sengupta, Eger & Melcher, 2014; Sengupta, Surampudi & Melcher, 2014) suggest that mutual inhibition among neurons can explain both kinds of capacity limitations as well as why our ability to estimate the numerosity of larger sets is limited according to a Weber ratio signature. Based on simulations with a saliency map‐like network and mathematical proofs, we provide three results. First, mutual inhibition among neurons leads to catastrophic interference when items are presented simultaneously. The network can remember a limited number of items, but when more items are presented, the network forgets all of them. Second, if memory items are presented sequentially rather than simultaneously, the network remembers the most recent items rather than forgetting all of them. Hence, the tendency in WM tasks to sequentially attend even to simultaneously presented items might not only reflect attentional limitations, but also an adaptive strategy to avoid catastrophic interference. Third, the mean activation level in the network can be used to estimate the number of items in small sets, but it does not accurately reflect the number of items in larger sets. Rather, we suggest that the Weber ratio signature of large number discrimination emerges naturally from the interaction between the limited precision of a numeric estimation system and a multiplicative gain control mechanism. (shrink)

In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach (...) is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics. (shrink)

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned (...) class='Hi'>proof systems when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment. (shrink)

When people make sense of situations, illustrations, instructions and problems they do more than just think with their heads. They gesture, talk, point, annotate, make notes and so on. What extra do they get from interacting with their environment in this way? To study this fundamental problem, I looked at how people project structure onto geometric drawings, visual proofs, and games like tic tac toe. Two experiments were run to learn more about projection. Projection is a special capacity, similar to (...) perception, but less tied to what is in the environment. Projection, unlike pure imagery, requires external structure to anchor it, but it adds ‘mental’ structure to the external scene much like an augmented reality system adds structure to an outside scene. A person projects when they look at a chessboard and can see where a knight may be moved. Because of the cognitive costs of sustaining and extending projection, humans make some of their projections real. They create structure externally. They move the piece, they talk, point, notate, represent. Much of our interactivity during sense making and problem solving involves a cycle of projecting then creating structure. (shrink)

In the Critique of Pure Reason Kant introduced both transcendental idealism and transcendental arguments into philosophy. Transcendental arguments in general aim to establish conditions necessary for our having self-conscious experience at all. Transcendental idealism holds that such conditions do not hold independently of human subjects; those conditions obtain or are satisfied because they are generated or fulfilled by the structure or functioning of the subject’s cognitive capacities. Is transcendental idealism the only possible explanation of such conditions? I pursue this (...) question by exploring a widely neglected issue, the transcendental affinity of the manifold of intuition. I argue the following: (1) This issue remains vital to the second edition of the Critique, even though many passages on the topic were omitted from that edition. (2) Kant’s link between transcendental idealism and transcendental arguments is substantive, not methodological. (3) Kant’s views on transcendental affinity show that there are non-subjective, transcendental material conditions for the possibility of unified self-conscious experience. (4) These conditions and Kant’s arguments for them directly undermine Kant’s own arguments for transcendental idealism. This criticism of Kant’s arguments for transcendental idealism is entirely internal to the first Critique. (5) These points reveal some serious flaws in Henry Allison’s defense of Kant’s idealism. (6) Realists, naturalists, and pragmatists have much to learn and to borrow from Kant’s transcendental analysis of the conditions of unified self-conscious experience. (shrink)

Kant’s ‘Refutation of Idealism’ plainly has an anti-Cartesian conclusion: ‘inner experience in general is only possible through outer experience in general’ (B278). Due to wide-spread preoccupation with Cartesian skepticism, and to the anti-naturalism of early analytic philosophy, most of Kant’s recent commentators have sought to find a purely conceptual, ‘analytic’ argument in Kant’s Refutation of Idealism – and then have dismissed Kant when no such plausible argument can be reconstructed from his text. Kant’s argument supposedly cannot eliminate all relevant alternatives, (...) and so cannot justify its strong modal claims. Kant based his arguments on an inventory of our basic cognitive capacities to employ our forms of intuition and our forms of judgment. Kant provides a variety of considerations and arguments to determine what our cognitive capacities are. This involves ‘transcendental reflection’, which Kant held is absolutely crucial for judging matters a priori (A263/B319). I argue that there is a level of philosophical reflection on our own cognitive capabilities and their preconditions that is significantly richer than has been noticed by recent commentators, and that is a precondition of Kant’s transcendental reflection proper. I explicate certain thought experiments Kant proposes in order for us to recognize some our basic, characteristic cognitive capabilities, and the limits and requirements they entail for the nature and objects of human knowledge. These thought experiments involve a kind of reflection on who we as cognizant subjects are, on what our basic cognitive capabilities are. Engaging in this kind of reflection reveals that Kant’s transcendental arguments are significantly stronger and more persuasive than has been recognized in recent commentary. (shrink)

The concept of will to power is one of the most important Nietzsche’s theories, that deals with the capacity of a person to face death and the thought of his own sacrifice without any fear, in order to obtain one’s self-overcoming. The so called will to wreck is the most powerful objectification of will to power, and it is deep-rooted in European society, especially German popular ideology. Actually, it is possible to find this conception of will to wreck in connection (...) with will to power in Nibelungenlied, the greatest Nordic poem of 13th century, and, years and years later, in Nazi ideology (and of course Nietzsche himself), as a proof of the temporal continuity of this particular philosophy. A philosophy which is probably part of our psychology, and which is not likely to be easily forgotten though its terrible, destructive power. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Confronting Aristotle's EthicsDavid DepewConfronting Aristotle's Ethics by Eugene Garver Chicago: University of Chicago Press, 2006. Pp. ix + 290. $49.00, cloth.Readers of this journal are likely to be familiar with Eugene Garver's 1994 Aristotle's Rhetoric: An Art of Character. The main claim advanced in that important book is that for Aristotle rhetoric is an art because it has internal norms and ends. From this, it follows that although (...) any red-blooded rhetor probably does aim at winning a case, advancing a political career, getting rich, and other external goals, what is artful in rhetorical craft (technikos), and hence expressive of the distinctive human capacity for human rationality, is timely argumentation that binds premises to actionable conclusions through displays of good character and apt emotional response. This ordered combination of ethos, pathos, and logos recruits, or if you will interpellates, an audience that is uniquely capable of judging cases, proposals, and performances reasonably. In this way Aristotle defends rhetoric as a genuine art—an intellectual virtue—against Plato's Gorgias.To arrive at this conclusion Garver draws more widely on other parts of the Aristotelian corpus than rhetorical scholars normally do. In particular, he contrasts external with internal ends by using Aristotle's metaphysical distinction between movements, processes, or behaviors (kineseis), of which the world is chock-full, and actualizations or realizations (energeiai) of capacities, which are more rare. Because rhetorical art, qua artful, is an actualization, Garver infers that it is a "practical art" and so brushes up closely against ethical-political praxis. [End Page 184]How closely? To be sure, they are not identical. Praxis actualizes our rational capacities by issuing in deeds done for their own sake rather than in an ordered series of acts whose intelligibility and worth are, in the end, measured by their outcomes or products, as in arts (poiesis) (46). For this reason a rhetor or a doctor can display artfulness by consciously misbehaving as well as by doing his or her job well, whereas willful misbehavior on the part of a moral agent automatically disbars him or her from possessing practical wisdom (phronesis) at all (46; see Nicomachean Ethics [NE] 1140b22–25). Accordingly, even though moral virtues and technical skills are both acquired by slowly internalizing norms that at first aim only at external ends (29) and are both matched to their distinctive ends through their internal rational norms, Aristotle makes it abundantly clear that "the arts, including rhetoric, do not bring the soul into a good condition" (10). They are not the wellspring or protector of the intrinsically good actions that are constituents of happiness. that role is assigned to moral virtues such as prudence, courage, liberality, and, when these are practiced in relation to others, justice and friendship.Confronting Aristotle's Ethics begins by reviewing the above account of rhetorical art in Garver's earlier book. Precisely because that account posits a greater affinity between ethical virtue and craft knowledge than most contemporary analyses of Aristotle's Nicomachean Ethics, Garver feels a need to spell out more carefully than usual why Aristotle thinks that the arts, even at their best, cannot yield the intrinsically good acts that the moral virtues do and why for Aristotle the habitual performance of just such acts is constitutive of happiness (eudaimonia). To answer these questions is the aim of the book.Garver reports that satisfactory answers are surprisingly rare even in otherwise sophisticated contemporary Aristotelian studies (5–7). Now and again he points to one reason why this might be so. Since at least the eighteenth century, Aristotle's ethical theory has been commended by sloughing off its original political integument. Even Hannah Arendt, a devotee of Aristotle's conception of the public life if ever there was one, says that public figures must leave happiness to the private lives of little people. this depoliticization of ethics has allowed contemporary commentators to evade Aristotle's burden of proof. As good readers of Aristotle they may try to distance themselves from people who think that there might be an art of happiness by which one can technically realize one's desires. (Your local Barnes and Noble will... (shrink)

Those of us who enjoy certain products of the global industrial economy but also believe it is wrong to consume them are often so demoralized by the apparent inefficacy of our individual, private choices that we are unable to resist. Although he was a deontologist, Kant was clearly aware of this ‘consequent-dependent’ side of our moral psychology. One version of his ‘moral proof’ is designed to respond to the threat of such demoralization in pursuit of the Highest Good. That (...) version of the argument says that the capacity that faith and trust in God has to sustain our moral resolve licenses that faith and trust, from a practical point of view. My goal here is to argue that Kant’s proof has a contemporary, secular analogue in modern industrial contexts where the apparent “inefficacy” of an individual consumer’s choices in the face of massive insensitive supply-chains is a threat to her moral resolve. I conclude by suggesting that the Kantian approach may license us in adopting (as an item of defeasible moral faith) an evidential decision-theoretic principle regarding what it is to ‘make a difference.’ This in turn licenses trust -- if not in God then in other right-minded people. (shrink)

Notice that this paper has not claimed that all natural languages are CFL's. What it has shown is that every published argument purporting to demonstrate the non-context-freeness of some natural language is invalid, either formally or empirically or both.18 Whether non-context-free characteristics can be found in the stringset of some natural language remains an open question, just as it was a quarter century ago.Whether the question is ultimately answered in the negative or the affirmative, there will be interesting further questions (...) to ask. If it turns out that natural languages are indeed always CFL's, it will be reasonable to ask whether this helps to explain why speakers apparently recognize so quickly whether a presented utterance corresponds to a grammatical sentence or not, and to associate structural and semantic details with it. It might also be reasonable to speculate about the explanation for the universally context-free character of the languages used by humans, and to wonder whether evolutionary biological factors are implicated in some way (Sampson (1979) could be read in this light). And naturally, it will be reasonable to pursue the program put forward by Gazdar (1981, in press) to see to what extent CFL-inducing grammatical devices can be exploited to yield insightful descriptions of natural languages that capture generalizations in revealing ways.If a human language that is not a CFL is proved to exist, on the other hand, a different question will be raised: give the non-context-free character of human languages in general, why has this property been so hard to demonstrate that it has taken over twenty-five years to bring it to light since the issue was first explicitly posed? If human languages do not have to be CFL's, why do so many (most?) of them come so close to having the property of context-freeness? And, since the CFL's certainly constitute a very broad class of mathematically natural and computationally tractable languages, what property of human beings or their communicative or cognitive needs is it that has caused some linguistic communities to reach beyond the boundaries of this class in the course of evolving a linguistic system?Either way, we shall be interested to see our initial question resolved, and further questions raised. One cautionary word should be said, however, about the implications (or lack of them) that the answer will have for grammatical studies. Chomsky has repeatedly stated that he does not see weak generative capacity as a theme of central importance in the theory of grammar, and we agree. It is very far from being the case that the recent resurgence of interest in exploring the potential of CF-PSG or equivalent systems will, or should, be halted dead in its tracks by the discovery (if it is ever forthcoming) that some natural language is not a CFL. In the area of parsing, for instance, it seems possible that natural languages are not only parsed on the basis of constituent structure such as a CF-PSG would assign, but are parsed as if they were finite state languages (see Langendoen (1975) and Church (1980) for discussion along these lines). That is, precisely those construction-types that figure in the various proofs that English is not an FSL appear to cause massive difficulty in the human processing system; the sentences crucial to the proofs are for the most part unprocessable unless they are extremely short (yet the arguments for English not being and FSL only go through if length is not an issue). This means that in practice properties of finite state grammars are still of great potential importance to linguistic theory despite the fact that they do not provide the framework for defining the total class of grammatical sentences. The same would almost certannly be true of CF-PSG's if they were shown to be inadequate in a similar sense. It is highly unlikely that the advances made so far in far in phrase structure description could be nullified by a discovery about weak generative capacity. Moreover, there are known to be numerous ways in which the power of CF-PSG's can be marginally enhanced to permit, for example, xx languages to be generated without allowing anything like the full class of recursively enumerable or even context-sensitive languages (see Hopcroft and Ullmann (1979), Chapter 14) for an introduction to this topic, noting especially Figure 14.7 on p. 393. The obvious thing to do if natural languages were ever shown not to be CFL's in the general case would be to start exploring such minimal enhancements of expressive power to determine exactly what natural languages call for in this regard and how it could be effectively but parsimoniously provided in a way that closely modelled human linguistic capacities.In the meantime, it seems reasonable to assume that the natural languages are a proper subset of the infinite-cardinality CFL's until such time as they are validly shown not to be. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the (...) practitioners; and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

In this paper, we approach the idea of group cognition from the perspective of the “extended mind” thesis, as a special case of the more general claim that systems larger than the individual human, but containing that human, are capable of cognition (Clark, 2008; Clark & Chalmers, 1998). Instead of deliberating about “the mark of the cognitive” (Adams & Aizawa, 2008), our discussion of group cognition is tied to particular cognitive capacities. We review recent studies of group problem-solving and (...) group memory which reveal that specific cognitive capacities that are commonly ascribed to individuals are also aptly ascribed at the level of groups. These case studies show how dense interactions among people within a group lead to both similarity-inducing and differentiating dynamics that affect the group's ability to solve problems. This supports our claim that groups have organization-dependent cognitive capacities that go beyond the simple aggregation of the cognitive capacities of individuals. Group cognition is thus an emergent phenomenon in the sense of Wimsatt (1986). We further argue that anybody who rejects our strategy for showing that cognitive properties can be instantiated at multiple levels in the organizational hierarchy on a priori grounds is a “demergentist,” and thus incurs the burden of proof for explaining why cognitive properties are “stuck” at a certain level of organizational structure. Finally, we show that our analysis of group cognition escapes the “coupling-constitution” charge that has been leveled against the extended mind thesis (Adams & Aizawa, 2008). (shrink)

Educational theorists may be right to suggest that providing mindfulness training in schools can challenge oppressive pedagogies and overcome Western dualism. Before concluding that this training is liberatory, however, one must go beyond pedagogy and consider schooling’s role in enacting the educational neurofuture envisioned by mindfulness discourse. Mindfulness training, this article argues, is a biopolitical human enhancement strategy. Its goal is to insulate youth from pathologies that stem from digital capitalism’s economisation of attention. I use Bernard Stiegler’s Platonic depiction of (...) the ambiguousness of all attention channelling mechanisms as pharmaka—containing both poison and cure—to suggest that this training is a double-edged sword. Does the inculcation of mindfulness in schoolchildren empower them; or is it merely an exercise in pathology-proofing them in their capacity as the next generation of unpaid digital labourers? The answer, I maintain, depends on whether young people can use the Internet’s political potentialities to mitigate the exploitation of their unpaid online labour time. That is, on whether the exploitative ‘digital pharmakon’—the capitalistic Web—can at the same time be socio-politically curative. (shrink)

One of the most fruitful applications of substructural logics stems from their capacity to deal with self-referential paradoxes, especially truth-theoretic paradoxes. Both the structural rules of contraction and the rule of cut play a crucial role in typical paradoxical arguments. In this paper I address a number of difficulties affecting noncontractive approaches to paradox that have been discussed in the recent literature. The situation was roughly this: if you decide to go substructural, the nontransitive approach to truth offers a lot (...) of benefits that are not available in the noncontractive account. I sketch a noncontractive theory of truth that has these benefits. In particular, it has both a proof- and a model-theoretic presentation, it can be extended to a first-order language, and it retains every classically valid inference. (shrink)

One of America's foremost public intellectuals, Jean Bethke Elshtain has been on the frontlines in the most hotly contested and deeply divisive issues of our time. Now in Real Politics , Elshtain gives further proof of her willingness to speak her mind, courting disagreement and even censure from those who prefer their ideologies neat. At the center of Elshtain's work is a passionate concern with the relationship between political rhetoric and political action. For Elshtain, politics is a sphere of (...) concrete responsibility. Political speech should, therefore, approach the richness of actual lives and commitments rather than present impossible utopias. In her essays, Elshtain finds in the writings of Václav Havel, Hannah Arendt, and Albert Camus a language appropriate to the complexity of everyday life and politics, and she critiques philosophers and writers who distance us from a concrete, embodied world. She argues against those repressive strains within contemporary feminism which insist that families and even sexual differentiation are inherently oppressive. Along the way, she challenges an ideology of victimization that too often loses sight of individual victims in its pursuit of abstract goals. Elshtain reaffirms the quirky and by no means simple pleasures of small-town life as a microcosm of the human condition and considers the current crisis in American education and its consequences for democracy. Beyond exploring the details of political life over the past two decades, Real Politics advocates a via media politics that avoids unacceptable extremes and serves as a model for responsible political discourse. Throughout her diverse and insightful writings, Elshtain champions a civic philosophy that tends to the dignity of everyday life as a democratic imperative of the first order. "Jean Bethke Elshtain is a person of rare intellect. The moral wisdom that pervades these essays reminds us that when all is said and done politics is about the life and death of real people who are anything but abstractions. Her erudition is remarkable, but equally stunning is her eye for the significant. What she is so good at is helping us see the moral and political significance of the everyday."--Stanley Hauerwas, Duke University " Real Politics serves as a forceful reminder that Jean Elshtain has been dealing with the real world in twenty-five years of powerful essaying. Transcending ideological categories, she writes out of hope that human beings can enjoy those capacities of reason and faith which make them human. It is a pleasure to be reintroduced to her sustained intelligence."--Alan Wolfe, Boston University. (shrink)

In this work, we will try to state the opposition between two approaches to the problem of the overall reliability of human knowing capacities, and a possible solution to that conflict. On the one hand, as we will point out, there exist a number of approaches that fall under the broad term of “evolutionary reliabilism” and according to which the reasons that we have for believing in the reliability of human cognition are empirical in character. Namely, the adaptive success (...) of our species in a biological environment characterised by the survival of the fittest provides us with a reason to believe that our belief-forming mechanisms are truth-tracking; if they were not, we would have gone extinct. On the other hand, nevertheless, we find analyses—of which we will focus on the case of Ernest Sosa—according to which the tenet that our knowing capacities are reliable cannot be empirically based, and thus contingent; on the contrary, they point out that we need to presuppose—without need of a proof—that such capacities are trustworthy. Given this conflict between an “empirical” defence and a defence “in principle” of our knowing capacities, we will consider two possible objections against Sosa’s proposal and try to answer them. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

In this article we argue that idealizations and limiting cases in models play an exploratory role in science. Four senses of exploration are presented: exploration of the structure and representational capacities of theory; proof-of-principle demonstrations; potential explanations; and exploring the suitability of target systems. We illustrate our claims through three case studies, including the Aharonov-Bohm effect, the emergence of anyons and fractional quantum statistics, and the Hubbard model of the Mott phase transitions. We end by reflecting on how (...) our case studies and claims compare to accounts of idealization in the philosophy of science literature such as Michael Weisberg’s three-fold taxonomy. (shrink)

The question, 'Why is there something rather than nothing?', has a strong claim to be philosophy's central, and most perplexing, question; it has a capacity to set the head spinning which few other philosophical problems can rival. Bede Rundle challenges the stalemate between theistic and naturalistic explanations with a rigorous, properly philosophical approach, and presents some startlingly novel conclusions.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Confronting Aristotle's EthicsDavid DepewConfronting Aristotle's Ethics by Eugene Garver Chicago: University of Chicago Press, 2006. Pp. ix + 290. $49.00, cloth.Readers of this journal are likely to be familiar with Eugene Garver's 1994 Aristotle's Rhetoric: An Art of Character. The main claim advanced in that important book is that for Aristotle rhetoric is an art because it has internal norms and ends. From this, it follows that although (...) any red-blooded rhetor probably does aim at winning a case, advancing a political career, getting rich, and other external goals, what is artful in rhetorical craft (technikos), and hence expressive of the distinctive human capacity for human rationality, is timely argumentation that binds premises to actionable conclusions through displays of good character and apt emotional response. This ordered combination of ethos, pathos, and logos recruits, or if you will interpellates, an audience that is uniquely capable of judging cases, proposals, and performances reasonably. In this way Aristotle defends rhetoric as a genuine art—an intellectual virtue—against Plato's Gorgias.To arrive at this conclusion Garver draws more widely on other parts of the Aristotelian corpus than rhetorical scholars normally do. In particular, he contrasts external with internal ends by using Aristotle's metaphysical distinction between movements, processes, or behaviors (kineseis), of which the world is chock-full, and actualizations or realizations (energeiai) of capacities, which are more rare. Because rhetorical art, qua artful, is an actualization, Garver infers that it is a "practical art" and so brushes up closely against ethical-political praxis. [End Page 184]How closely? To be sure, they are not identical. Praxis actualizes our rational capacities by issuing in deeds done for their own sake rather than in an ordered series of acts whose intelligibility and worth are, in the end, measured by their outcomes or products, as in arts (poiesis) (46). For this reason a rhetor or a doctor can display artfulness by consciously misbehaving as well as by doing his or her job well, whereas willful misbehavior on the part of a moral agent automatically disbars him or her from possessing practical wisdom (phronesis) at all (46; see Nicomachean Ethics [NE] 1140b22–25). Accordingly, even though moral virtues and technical skills are both acquired by slowly internalizing norms that at first aim only at external ends (29) and are both matched to their distinctive ends through their internal rational norms, Aristotle makes it abundantly clear that "the arts, including rhetoric, do not bring the soul into a good condition" (10). They are not the wellspring or protector of the intrinsically good actions that are constituents of happiness. that role is assigned to moral virtues such as prudence, courage, liberality, and, when these are practiced in relation to others, justice and friendship.Confronting Aristotle's Ethics begins by reviewing the above account of rhetorical art in Garver's earlier book. Precisely because that account posits a greater affinity between ethical virtue and craft knowledge than most contemporary analyses of Aristotle's Nicomachean Ethics, Garver feels a need to spell out more carefully than usual why Aristotle thinks that the arts, even at their best, cannot yield the intrinsically good acts that the moral virtues do and why for Aristotle the habitual performance of just such acts is constitutive of happiness (eudaimonia). To answer these questions is the aim of the book.Garver reports that satisfactory answers are surprisingly rare even in otherwise sophisticated contemporary Aristotelian studies (5–7). Now and again he points to one reason why this might be so. Since at least the eighteenth century, Aristotle's ethical theory has been commended by sloughing off its original political integument. Even Hannah Arendt, a devotee of Aristotle's conception of the public life if ever there was one, says that public figures must leave happiness to the private lives of little people. this depoliticization of ethics has allowed contemporary commentators to evade Aristotle's burden of proof. As good readers of Aristotle they may try to distance themselves from people who think that there might be an art of happiness by which one can technically realize one's desires. (Your local Barnes and Noble will... (shrink)

Prefatory. The Logic of Theism .–Our world, the thing or complex of things, which is continuous and co-ordinate with our present perception, is self-transcendent. The proof is from observation, from our reactions, which are often more sensitive than our direct observations, from the testimony of philosophers, expert psychologists, and poets . To say that our world is self-transcendent is to say that it presents itself to our minds as indigent of some sort of supplement or complement having some sort (...) of ontological status which it implies in some capacity. The problem of the Logic of Theism is the problem of determining, assigning a definite value to, these “somes.” In other words, the proof of God is the proof that what “our world implies” when it is made determinate corresponds with the received conception of God in such a way as to justify the substitution of the name God for the indication “what our world implies.”. (shrink)

Drawing from our interdisciplinary qualitative study of LGBTI conservative Christians and their allies, we name an especially toxic form of shame—what we call sacramental shame—that affects the lives of LGBTI and other conservative Christians. Sacramental shame results from conservative Christianity's allegiance to the doctrine of gender complementarity, which elevates heteronormativity to the level of the sacred and renders those who violate it as not persons, but monsters. In dispensing shame as a sacrament, nonaffirming Christians require constant displays of shame as (...) proof that LGBTI church members love God and belong in the community. Part of what makes this shame so harmful is that parents and pastors often dispense it with sincere expressions of care and affection, compounding the sense that one's capacity to give and receive love is damaged. We foreground LGBTI Christian movements to overcome sacramental shame by cultivating nonhubristic pride, and conclude by discussing briefly their new understandings of love and justice that could have far‐reaching benefits. (shrink)

Kit Fine has replied to my criticism of a technical objection he had given to the version of Millianism that I advocate. Fine evidently objects to my use of classical existential instantiation in an object-theoretic rendering of his meta-proof. Fine’s reply appears to involve both an egregious misreading of my criticism and a significant logical error. I argue that my rendering is unimpeachable, that the issue over my use of classical EI is a red herring, and that Fine’s original (...) argument commits the straw-man fallacy. I argue further that contrary to Fine’s gratuitous attribution, what Kripke’s Pierre lacks and a typical bilingual has is not knowledge of a “manifest-making” premise, but the capacity to recognize London when it is differently designated. Fine’s argument refutes a preposterous theory no one advocates while leaving standard Millianism unscathed. The failure of his argument threatens to render Fine’s central notion of “coordination” redundant or empty. (shrink)

The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of the (...) notion of meaning is considered. (shrink)

As has often been observed, neither the thinkers of antiquity nor those of the Middle Ages exhibited a great theoretical interest in the social value or even the ethical significance of labour. Throughout this long period of history, the labour an individual had to carry out to make a living, and thus under compulsion, was understood more or less solely as a heavy burden. It signified daily toil and the state of personal dependency attaching to a lowly social rank. Consequently, (...) there was no cause to subject it to any kind of moral consideration. Indeed, as Moses Finley reports ‘[n]either in Greek nor Latin was there a word with which to express the general notion of ‘labour’ or the concept of labour as a general social function’. Famously, with the advent of modernity, the very opposite begins to become the case. In this period, in the wake of various intersecting processes of cultural revaluation and economic transformation, labour developed into a positive credential of free existence and a presupposition of social integrity: the Protestant ethic led to a gradual upgrading of the value of labour, because it was interpreted as a sign that one possessed a capacity for inner-worldly asceticism. In the course of the establishment of capitalist economic practices, the liberation of labour from personal dependency in legal terms gave rise to the idea that gainful work could henceforth be proof of a free decision, and it thus provided the precondition of individual independence. And over time, the more the intellectual union between these two revolutions was strengthened, the more it would go on to influence the cultural self-understanding of modern societies in the capitalist west: what was previously the sheer necessity of earning a daily crust was now understood as proof of social emancipation and freedom. Nobody provided a better conceptualisation of this transformed self-conception than Georg Wilhelm Friedrich Hegel, who devoted an entire chapter of his ‘Philosophy of Right’ of 1821 to the emancipatory value of labour; here, he tells us that every member of civil society ‘is somebody’ through ‘his competence’ and his ‘regular income and means of support’, i.e. possesses the social status of a full-fledged citizen, and will find ‘his honour’ in this recognised existence as a professional. (shrink)

In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s proof of (...) the validity of the categories in the objective deduction. I challenge this standard reading of the subjective deduction, arguing, first, that there is little textual evidence for it, and, second, that it encourages a problematic conception of how the deduction works. In its place, I present a new reading of the subjective deduction. Rather than being a broad investigation of our cognitive faculties, it should be seen as addressing a specific worry that arises in the course of the objective deduction. The latter establishes the need for a necessary connection between our capacities for thinking and being given objects, but Kant acknowledges that his readers might struggle to comprehend how these seemingly independent capacities are coordinated. Even worse, they might well believe that in asserting this necessary connection, Kant’s position amounts to an implausible subjective idealism. The subjective deduction ismeant to allay these concerns by showing that they rest on a misunderstanding of the relation between these faculties. This new reading of the subjective deduction offers a better fit with Kant’s text. It also has broader implications, for it reveals the more philosophically plausible account of our relation to the world as thinkers that Kant is defending – an account that is largely obscured by the standard reading of the subjective deduction. (shrink)