In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Judgement and Sense in Modern French Philosophy: A New Reading of Six Thinkers by Henry Somers-HallClayton CrockettSOMERS-HALL, Henry. Judgement and Sense in Modern French Philosophy: A New Reading of Six Thinkers. Cambridge: Cambridge University Press, 2022. 264 pp. Cloth, $99.99Henry Somers-Hall's book examines how French philosophers in the twentieth century develop a logic of thinking based on sense that is both influenced by but also counters Kant's paradigm (...) of thinking, which is based on judgment. Beginning with Kant and German idealism, including the German responses to Kant in the work of Hölderlin, Fichte, Schelling, and Hegel, this book then carefully draws out the ways that Bergson, Sartre, Merleau-Ponty, Derrida, Foucault, and Deleuze all work against this understanding of thinking as judging by showing how our experience and our thought precede the categories of judgment.In chapter 1, Somers-Hall carefully sets out Kant's model of thinking and shows how the categories of philosophical thought are fundamentally based on how we judge our sensible intuitions. Judgment is at the center of Kant's thought, and this is apparent in the Critique of Pure Reason, including the famous Transcendental Deduction. Our knowledge has a legislative function in relation to objects, and conscious synthesis takes the form of a judgment. Despite their criticisms of Kant, later German idealists do not fundamentally depart from this modality of judgment that takes place at the center of their philosophy. Even though they put Kant's concepts in motion, it remains a structure of judgment that is understood as dynamic.Chapter 2 turns to Bergson, to show how his emphasis on immediate experience precedes categorical judgement. Bergson distinguishes between temporal and spatial multiplicities, and argues that temporal multiplicities that are expressed in terms of duration underlie the spatial ones that contribute to judgment. Duration is a deeper experience of time that is associated with life. Somers-Hall in chapter 3 examines Sartre's writings on imagination to show how consciousness is a pure relation and an affective mode of thinking that underlies the categorial mode of judgment.Most of these French philosophers develop their accounts of noncategorial sense in either explicit or implicit relation to Kant's philosophy. Merleau-Ponty is no exception, and in chapter 4 we see how it is the organization of perception that gives sense to the world, and this precedes and generates "our reflective categories of judgement." Judgment emerges out of perception, although Merleau-Ponty grounds perception in the embodied person. Derrida does not ground sense or [End Page 365] thinking in a body, but looks for noncategorial grounds that make possible "surface structures of thinking." In chapter 5, Somers-Hall elaborates Derrida's famous nonconcept of différance, which underlies and makes possible our concepts of voice and writing that appear to be oppositions but in fact are not because they rely on each other. Différance is not a concept; it is prior to conceptual determination, and it "operates as an 'origin' that has none of the traits of the structure of judgement."Foucault relies on Kant for his three epistemes of resemblance, representation, and the human being, modern man. Chapter 6 shows how Foucault is concerned in both his archaeology and his genealogy with opening up the structures of power that make any juridical ordering possible. Here a productive biopower works beneath what we recognize more explicitly as "juridico-discursive power" in both positive and negative ways that escape the grasp of a philosophy that is solely based on judgment.In chapter 7 Somers-Hall shows how Deleuze's concept of intensity underlies all forms of representational judgment. Intensity operates according to a process of differentiation that produces a logic of sense, which we miss when we grasp onto a "dogmatic image of thought" that "prevents a genuine encounter with the world [that] conditions us to understand it in terms of unified subjects who make sense of the world in terms of judgements." We think in response to a shock or an encounter with something in the world that forces us to think and to make sense. We form judgments retroactively, by reducing differences to... (shrink)

According to a widely held view of science, scientific hypotheses are evaluated on the basis of observational data in accordance with the rules of inductive logic. Inductive logic, like deductive logic, is supposed to consist of a set of formal rules. These rules abstract from any details of the specific hypothesis under examination, the context in which the evaluation is taking place, and the individuals who carry out the evaluation. Observational data are also independent of the context or the observer (...) in the following sense: there may be individual and cultural limitations on what observations are undertaken, but the outcome of an observation procedure is presumably independent of the observer's preferences or peculiarities. Now, given impersonal data and a set of formal rules, the assessment of a hypothesis will be completely impersonal. The fact that a scientist thinks of a hypothesis and undertakes to evaluate that hypothesis may depend on individual features of that scientist and on the current state of science, but the resulting evaluation will be free of individual, historical, or cultural factors. Any two scientists who evaluate a hypothesis on the basis of the same observational evidence must arrive at the same evaluation of that hypothesis. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Concepts, Judgments, and Unity in Kant's Metaphysical Deduction of the Relational Categories CHARLES NUSSBAUM 1. INTRODUCTION TO ANY ATTENTIVEREADERof the section of the Critique of Pure Reason' known as the "Metaphysical Deduction of the Categories" (A67/B92-A83/B to9), one paragraph in that section stands out particularly by virtue of its special importance for Kant's developing argument: The same function Which gives unity to the various representations in ajudgment also gives (...) unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding. The same understanding, through the same operations by which in concepts, by means of analytical unity, it produced the logical form of a judgment, also introduces a transcendental content into its representations, by means of the synthetic unity of the manifold of intuition in general.... (CPR A79/B loS) The importance of this paragraph is, however, more than equaled by its difficulties, which center on the question of how the function which operates by means of analytical unity can be the same as one that operates by means of the synthetic unity of the manifold of intuition in general. Put shortly, the problem is this. If the functions are really the same, then how do we distinguish at all between analytic and synthetic operations? But if they are different, then how can these forms of judgment serve as a clue for the discovery of the categories? ' Immanuel Kant, Critiqueof Pure Reason, trans. Norman KempSmith (London: Macmillan and Co., Ltd., 1963).Hereafter CPR. [89] 9~ JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 1990 The results of this dilemma which can be observed in the literature are not surprising: commentators tend to grasp one horn or the other. They either emphasize the difference between analysis and synthesis, and reject or dilute the claims as to sameness of function; or they take seriously Kant's argument concerning sameness of functions, and try to minimize the difference between analysis and synthesis. The major twentieth-century representant of the former approach is Kemp Smith," and of the latter, Paton. 3 This latter approach has found a formidable contemporary champion in the person of Henry Allison. By Allison's own admission,4 however, his position on this controversial topic was suggested (in part) by arguments first put forward over fifty years ago by Klaus Reich in a most remarkable book entitled Die Volls~ndigkeit der Kantischen Urteilstafel, 5 a book, by the way, also greatly admired by Paton. 6 In the first section of this paper I will try to show that Reich's arguments are rather more subtle than Allison apparently takes them to be, and that Reich is one commentator who attempts to go between the horns of the dilemma described above, and who essays an interpretation of our crucial paragraph that unifies its seemingly divergent tendencies. In the second section of the paper I will introduce some interpretive elements of my own. 2. Let us begin by reacquainting ourselves with Kant's notion of analytical unity, one aspect of this debate which is not particularly controversial and is largely agreed upon by all parties. For Kant, analytical unity is the sort of unity achieved by all general concepts (conceptus communes) insofar as they abstract from all differences that subsist between the objects under them, or the lower concepts subordinated to them. 7 A general concept unifies these objects or concepts by means of a common mark or set of marks. Thus Kant's example at CPR A69/B94 of the unification of bodies under the concepts 'body' and 'divisible' is a perfectly representative instance of unification via analytical unity, as the function upon which such concepts "rest." Let us note that the " Norman KempSmith,A CommentarytoKant's "Cr/t~rueofPureReason"(NewYork:HumanitiesPress, 196~). 3 H.J. Paton, Kant's MetaphysicofExperience, 2 vols.(London:George Allenand Unwin,Ltd., 1936). 4 Henry Allison,Kant's TranscendentalIdealum (NewHaven:YaleUniversityPress, 1983), 144 n. 3o. Hereafter KTI. 5 KlausReich,Die Vollst~ndigkeitderKantischenUrteilstafel,3rd. ed. (Hamburg: Meiner, 1986). Hereafter VKU. 6 Paton, Kant's Metaphysic, 1:302. Kant, we should note, does not makethis important logicaldistinctionbetweensubordination... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 40.3 (2002) 406-408 [Access article in PDF] Book Review Kant's Theory of Taste: A Reading of the Critique of Aesthetic Judgment Henry E. Allison. Kant's Theory of Taste: A Reading of the Critique of Aesthetic Judgment. New York: Cambridge University Press, 2001. Pp. xvi + 424. Cloth, $69.95. Paper, $24.95. In his new book, Henry Allison provides a study of the two introductions (...) and the first half of Kant's Critique of the Power of Judgment to stand alongside his previous books on Kant's theoretical and practical philosophy, Kant's Transcendental Idealism (1983) and Kant's Theory of Freedom (1990). Those books showed Allison's commitment to the unity and coherence of Kant's thought, and it is the aim of the present book to demonstrate the connections between the two halves of Kant's third Critique, that is, Kant's aesthetics and his teleology, as well as to demonstrate the connections between Kant's aesthetic theory and both his theoretical and his practical philosophy. In order to defend the unity of the third Critique, Allison defends Kant's characterization of the judgment of taste as a species of reflective judgment, and argues that our judgments of beauty depend upon the principle of the purposiveness of nature that is also the basis for judgments about the systematicity of natural laws. To display the connections between Kant's aesthetics and his theoretical philosophy, [End Page 406] Allison uses the first Critique's distinction between the quid facti and the quid juris to explicate the relation between Kant's "analytic of the beautiful" and his "deduction of pure aesthetic judgment"; he then defends the success of Kant's strategy for the deduction of judgments of taste by grounding them in the general conditions of the possibility of cognition. Finally, in order to explain Kant's connection between aesthetics and morality, Allison interprets Kant's theory of the "intellectual interest" in the beautiful as evidence of nature's amenability to our achievement of the ends of morality, an assurance that we need not be motivated in the first place to act as morality requires, but rather to prevent our motivation to be moral from being undermined by our own predisposition to radical evil. He then defends Kant's thesis that all beauty, and thus natural as well as artistic beauty, can be seen as an expression of aesthetic ideas, and specifically of the morally requisite idea of nature's amenability to the achievement of our moral objectives.There is much in this approach with which I can agree, and some with which I cannot. I agree that there is much in Kant's general conception of reflective judgment that illuminates his conception of judgments of beauty, yet I do not think that the principle of taste is analogous to the principle of the purposiveness of nature, because it does not play a role in making particular judgments of taste analogous to the role the latter principle plays in the conduct of scientific inquiry. My own interpretation of Kant's model for making particular judgments of taste is not fundamentally different from that which Allison offers under the rubric of the quid facti, although we disagree about which of the four "moments" of the "Analytic of the Beautiful" are part of the meaning of a judgment of beauty and which function more as grounds for making judgments with such a meaning. But I am not persuaded by Allison's defense of Kant's deduction of pure judgments of taste, that is, his answer to the quid juris, from the objections that I and others have raised to it. Finally, although there are large areas of agreement between our interpretations of Kant's theory of intellectual interest in the beautiful, the claim that aesthetic experience is evidence of nature's amenability to the realization of the ends that we adopt in the name of morality is only part of the story that Kant develops in the Critique of Aesthetic... (shrink)

This chapter contains sections titled: I II III IV References.

We can formalize judgments as logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow’s impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. As (...) an example of derivation, a formal proof of Arrow’s impossibility theorem is given. (shrink)

Equivalent deductive systems were introduced in [4] with the goal of treating 1-deductive systems and algebraic 2-deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if and only if their lattices of theories are isomorphic via an isomorphism that commutes with substitutions. Deductive equivalence of π-institutions [14, 15] generalizes the notion of equivalence of deductive systems. In [15, Theorem 10.26] this criterion for the equivalence (...) of deductive systems was generalized to a criterion for the deductive equivalence of term π-institutions, forming a subclass of all π-institutions that contains those π-institutions directly corresponding to deductive systems. This criterion is generalized here to cover the case of arbitrary π-institutions. (shrink)

In this paper, it is argued that only in the section on dialectic in the Critique of Judgment does Kant reach a definitive and conclusive version of deduction, after discovering the concept of the supersensible. In the section on the deduction of pure aesthetic judgments, Kant does not satisfactorily explain the critical distinction between the sensible nature of humanity and the supersensible nature of human reason presupposed in the concept of universal communicability. While the concept of the supersensible illustrates this (...) distinction, it is only through this concept that Kant that can justify the specific possibility of claiming subjective validity in taste. The priority of the solution found in the dialectic is illustrated not only by a comparative analysis of the two sections, but also by a historical reconstruction of the process of the formation of the work, which shows that the first formulation of the concept of validity coincides with the use of the concept of the supersensible. (shrink)

Given a π -institution I , a hierarchy of π -institutions I is constructed, for n ≥ 1. We call I the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I of I is also called the “Gentzenization” of I . In the main result of the paper, it (...) is shown that I is strongly Gentzen , i.e. it is deductively equivalent to its Gentzenization via a special deductive equivalence, if and only if it has the deduction-detachment property. (shrink)

Equivalent deductive systems were introduced in [4] with the goal of treating 1‐deductive systems and algebraic 2‐deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if and only if their lattices of theories are isomorphic via an isomorphism that commutes with substitutions. Deductive equivalence of π‐institutions [14, 15] generalizes the notion of equivalence of deductive systems. In [15, Theorem 10.26] this criterion for the equivalence (...) of deductive systems was generalized to a criterion for the deductive equivalence of term π‐institutions, forming a subclass of all π‐institutions that contains those π‐institutions directly corresponding to deductive systems. This criterion is generalized here to cover the case of arbitrary π‐institutions. (shrink)

In this paper, it is argued that only in the section on dialectic in the Critique of Judgment does Kant reach a definitive and conclusive version of deduction, after discovering the concept of the supersensible. In the section on the deduction of pure aesthetic judgments, Kant does not satisfactorily explain the critical distinction between the sensible nature of humanity and the supersensible nature of human reason presupposed in the concept of universal communicability. While the concept of the supersensible illustrates this (...) distinction, it is only through this concept that Kant that can justify the specific possibility of claiming subjective validity in taste. The priority of the solution found in the dialectic is illustrated not only by a comparative analysis of the two sections, but also by a historical reconstruction of the process of the formation of the work, which shows that the first formulation of the concept of validity coincides with the use of the concept of the supersensible. (shrink)

This chapter contains section titled: The Metaphysical Deduction.

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on (...) budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way . Heterogeneous fibring, allowing the original logics to have different presentations , has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus (...) and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated. (shrink)

Abstract: This paper traces a Kantian and pragmatist line of thinking that connects the ideas of conceptual content, object cognition, and modal constraints in the form of counterfactual sustaining causal laws. It is an idea that extends from Kant’s Critique of Pure Reason through C. I. Lewis’s Mind and the World-Order to the Kantian naturalism of Wilfrid Sellars and the analytic pragmatism of Robert Brandom. Kant put forward what I characterize as a modal conception of objectivity, which he developed as (...) an extended argument stretching from the transcendental deduction through the analogies of experience to the regulative maxims of reason and reflective judgment. In related ways in Lewis and Sellars, the very idea of an object of knowledge (and of intentionality more generally) is connected with a certain lawfulness or modal constraint the necessary representation of which, they argue, is an achievement of conceptualization. While Sellars agreed with the spirit of Lewis’s famous pragmatic conception of the a priori, Sellars’s conception of meaning and conceptual content differed in crucial ways with important consequences for this issue. I argue furthermore that a certain phenomenalist temptation threatens to spoil this insight both among some of Kant’s interpreters and in Lewis’s thought. Finally, I point out that Brandom’s “Kant-Sellars thesis” provides new support for this line of thought. Although questions concerning idealism continue to raise controversies for neo-Kantians and pragmatists, the line of thought itself represents a distinctive and still promising approach to questions concerning intentionality and conceptual content. (shrink)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of (...) rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

We give a correction to the paper [2] mentioned in the title.

The article offers an account of the constructivist methodology in ethics and political philosophy as 1) deriving from an agnostic moral ontology and 2) proposing intersubjective justifiability as the criterion of justification for normative principles. It then asks whether constructivism, conceived in this way, can respond to the challenge of “content skepticism about practical reason”, namely whether it can provide sufficiently precise normative guidance whilst remaining faithful to its methodological commitment. The paper critically examines to alternative way of meeting this (...) challenge, namely John Rawls's original position and O'Neill's Kantian constructivism, analyses what is problematic about both, and endorses a third, possibly intermediate model. Within such a model, the basic features of the original position are accepted, but in a flexible and heuristic manner, thereby accommodating some of O'Neill's concerns. (shrink)

Bioethics became applied ethics when it was assimilated to moral philosophy. Because deduction is the rationality of moral philosophy, subsuming facts under moral principles to deduce conclusions about what ought to be done became the prescribed reasoning of bioethics, and bioethics became a theory comprised of moral principles. Bioethicists now realize that applied ethics is too abstract and spare to apprehend the specificity, particularity, complexity and contingency of real moral issues. Empirical ethics and contextual ethics are needed to incorporate these (...) features into morality, not just bioethics. The relevant facts and features of problems have to be identified, investigated and framed coherently, and potential resolutions have to be constructed and assessed. Moreover, these tasks are pursued and melded within manifold contexts, for example, families, work and health care systems, as well as societal, economic, legal and political backgrounds and encompassing worldviews. This naturalist orientation and both empirical ethics and contextual ethics require judgment, but how can judgment be rational? Rationality, fortunately, is more expansive than deductive reasoning. Judgment is rational when it emanates from a rational process of deliberation, and a process of deliberation is rational when it uses the resources of non-formal reason: observation, creative construction, formal and informal reasoning methods and systematic critical assessment. Empirical ethics and contextual ethics recognize that finite, fallible human beings live in complex, dynamic, contingent worlds, and they foster creative, critical deliberation and employ non-formal reason to make rational moral judgments. (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to the literature.

The paper aims to show how by elaborating the Peircean terms used in the title creativity in learning processes and in scientific discoveries can be explained within a semiotic framework. The essential idea is to emphasize both the role of external representations and of experimenting with those representations , and to describe a process consisting of three steps: First, looking at diagrams "from a novel point of view" offers opportunities to synthesize elements of these diagrams which have never been perceived (...) as connected before. Second, by forming those observed syntheses to "new objects" of thinking, and by signifying these objects through new signs , new means of thinking and acting are created . And finally, by applying these new means – in proofs, for instance – the "intelligibility" of new discoveries and their power to explain problematic facts must be tested. (shrink)

ABSTRACT Critical realist thought has theorised convincingly that epistemic relativism is constellationally embedded in ontological realism which in turn necessitates judgemental rationality. In social science, judgemental rationality involves acting upon plausible decisions about competing points of view. However, the tools for doing this are, as yet, under-articulated. This paper addresses this absence by articulating triangulation and depth-reflexivity as two tools for doing judgemental rationality in empirical research. It draws on the experiences of a diverse team working on an international comparative (...) research project on conversion to Islam in prisons. It demonstrates how epistemic and relational gaps between researchers and research subjects can be bridged by mobilising the ‘laminated’ properties and personal attributes of a diverse research team that factors in attributes that are absent as well as those present. The biographical experiences of the team are analyzed in a variety of intersecting dimensions: faith, ethnicity/ethno-culture, gender, class and professionality. (shrink)

Abstract In this paper I undertake an in-depth examination of an oft mentioned but rarely expounded upon state: suspended judgment. While traditional epistemology is sometimes characterized as presenting a “yes or no” picture of its central attitudes, in fact many of these epistemologists want to say that there is a third option: subjects can also suspend judgment. Discussions of suspension are mostly brief and have been less than clear on a number of issues, in particular whether this third option should (...) be thought of as an attitude or not. In this paper I argue that suspended judgment is (or at least involves) a genuine attitude. Content Type Journal Article Pages 1-17 DOI 10.1007/s11098-011-9753-y Authors Jane Friedman, St Catherine’s College, University of Oxford, Oxford, OX1 3UJ UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

An important part of the theory of algebraizable sentential logics consists of studying the algebraic semantics of these logics. As developed by Czelakowski, Blok, and Pigozzi and Font and Jansana, among others, it includes studying the properties of logical matrices serving as models of deductive systems and the properties of abstract logics serving as models of sentential logics. The present paper contributes to the development of the categorical theory by abstracting some of these model theoretic aspects and results from the (...) level of sentential logics to the level of π-institutions. (shrink)

ABSTRACT Real-time graphical interval logic is a modal logic for reasoning about time in which the basic modality is the interval. The logic differs from other logics in that it has a natural intuitive graphical representation that resembles the timing diagrams drawn by system designers. We have developed an automted deduction system for the logic, which includes a theorem prover and a user interface. The theorem prover checks the validity of proofs in the logic and produces counterexamples to invalid proofs. (...) The user interface includes a graphical editor that enables the user to create graphical formulas on a workstation display, and a database and proof manager that tracks proof dependencies and allows graphical formulas to be stored and retrieved. In this paper we describe the logic, the automated deduction system, and an application to robotics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Hegel's Concept of Life: Self-Consciousness, Freedom, Logic by Karen NgMarina F. BykovaKaren Ng. Hegel's Concept of Life: Self-Consciousness, Freedom, Logic. Oxford: Oxford University Press, 2020. Pp. iii + 319. Hardback, $85.00.In her insightful book, Karen Ng defends the fundamental significance of Hegel's concept of life, which she considers "constitutive" not merely of his dynamic account of reason but also of his "idealist program" itself (3–4), the very core (...) structure that grounds his idealism (151, 291). Integrating this concept into his philosophy allows Hegel to resolve three systematic problems indicated in the subtitle of the book: self-consciousness, freedom or self-determination, and logical form.The book offers a systematic account of the logical concept of life by defending three interconnected claims, helpfully summarized in chapter 1. The first, rather general claim clarifies Ng's interpretive point of departure. She maintains that the "core tenets" of Hegel's philosophy can be understood through the "purposiveness theme" inherited from Kant's a priori principle of purposiveness in his Critique of Judgment (5, 43). Ng advances this claim in chapter 2, where she argues that it is working through Kant's concept of inner purposiveness of natural ends from the teleological power of judgment that leads Hegel to develop his own account of Concept, which is foundational for his entire philosophical system (61–64).Chapter 3 continues the examination of Hegel's immediate predecessors in relation to the interpretation of his "speculative identity thesis" (8), which constitutes the second claim. According to Ng, Hegel first introduces this thesis—which remains central to all his works—in the Differenzschift. In this work, Hegel, siding with Schelling, criticizes Fichte's subjective version of idealism, more specifically for his explanation of the relation between subject and object as constructed and facilitated by subjective consciousness itself, thus rendering "nature lifeless and dead" (88). Opposing this approach, in the Phenomenology of Spirit, Hegel interprets the identity of object and subject as facilitated by the relation and opposition between self-consciousness and life. Thus, the speculative identity thesis assumes a fundamental significance of life for self-consciousness. Unfolding this thesis is at the core of Hegel's absolute method in the Science of Logic as well. On Ng's reading, Hegel's speculative thesis along with his account of self-consciousness also have their roots in the purposiveness theme inherited from Kant. What is at work here is Kant's claim that the principle of purposiveness is a necessary condition for judgment, which Hegel develops into a claim about the concept of life as being constitutive for self-consciousness.In the rest of the book (chapters 4–8), devoted to a close analysis of Hegel's Science of Logic, Ng advances her third and perhaps most original claim: understanding Hegel's [End Page 527] Subjective Logic "as his own version of a 'critique of judgment'" (18). She demonstrates that this part of the Logic offers a positive account of the concept of life that Hegel develops in his critical interaction with Kant. The most illustrative in this respect is the "Subjectivity" section of the Logic, in which the form of life is presented as the ground and presupposition of Hegel's theory of concepts and judgments. According to Ng, such a reading makes evident that "life opens up the space of reasons" (234, 281).Chapter 4 takes up Hegel's immanent deduction of the Concept argument, revealing that the key to understanding it is the concept of reciprocity (Wechselwirkung) (127), most fully recognizable as an internal purposiveness of the Concept itself.Ng traces the purposiveness theme through the entirety of the Subjective Logic, establishing its significance for understanding the deduction of the Concept and for the transition to the Idea. In her analysis, she closely follows Hegel's division of the Subjective Logic and addresses Subjectivity, Objectivity, and the Idea in chapters 5–8, respectively. With chapter 5, Ng moves to a discussion of how Hegel finds judgment to arise from the "original judgement of life," the initial unity and division of subject and object within life (172). Chapter 6 extends this discussion by elucidating the tension Hegel... (shrink)

Richard Arthur’s _Natural Deduction_ provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.

I argue, contrary to Dennis Schulting inKant’s Radical Subjectivism, that the main reasoning of Kant’s transcendental deduction of the categories is progressive, not regressive. Schulting is right, however, to emphasize that the deduction takes the object cognized to be constituted in an idealism-entailing way. But his reasoning has gaps and bypasses Kant’s most explicit deduction argument, independent of the Transcendental Aesthetic, for idealism. Finally, Schulting’s claim that Kantian discursivity itself requires idealism overlooks the fact that Kantian general judgements can be (...) true in a domain of objects without being specificallyofor about any particular ones of those objects. (shrink)

We present an algebraic proof of the theorem stating that there are continuum many axiomatic extensions of global consequence associated with modal system E that do not admit the local deduction detachment theorem. We also prove that all these logics lack the finite frame property and have exactly three proper axiomatic extensions, each of which admits the local deduction detachment theorem.

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which all reality can (...) emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

Rationality in medicine is frequently construed as hypotheticodeductive. This article argues that such a model gives a distorted view of the rational character of an enterprise that makes judgments about individual human well-being. Medicine as a science is a practical human science. Seen as such, its rational orientation is one that applies general knowledge to particular situations. It is argued that such an orientation is not deductive but interpretative. The Aristotelian concept of practical wisdom (‘phron sis’) is used as a (...) model of the rational orientation of clinical judgment. Keywords: clinical judgment, rationality, human sciences CiteULike Connotea Del.icio.us What's this? (shrink)

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. (...) In their abstract form, thus,deductive relationsare defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic. (shrink)

In focusing on the systematic deduction of the categories from a principle, Schulting takes up anew the controversial project of the eminent German Kant scholar Klaus Reich, whose monograph “The Completeness of Kant's Table of Judgments” made the case that the logical functions of judgement can all be derived from the objective unity of apperception and can be shown to link up with one another systematically. -/- Common opinion among Kantians today has it that Kant did not mean to derive (...) the functions of judgement, and accordingly the categories, from the principle of apperception. Schulting challenges this standard view and aims to resuscitate the main motivation behind Reich’s project. He argues, in agreement with Reich’s main thesis about the derivability of the functions of judgement, that Kant indeed does mean to derive, in full a priori fashion, the categories from the principle of apperception. -/- Schulting also shows that, given the general assumptions of the Critical philosophy, Kant's derivation is successful and that absent an account of the derivation of the categories from apperception, the B-Deduction cannot really be understood. -/- New edition. First published 2012 as „Kant’s Deduction and Apperception. Explaining the Categories" (Palgrave Macmillan). (shrink)

The injective version of Cantor’s theorem appears in full second-order logic as the inconsistency of the abstraction principle, Frege’s Basic Law V (BLV), an inconsistency easily shown using Russell’s paradox. This incompatibility is akin to others—most notably that of a (Dedekind) infinite universe with the Nuisance Principle (NP) discussed by neo-Fregean philosophers of mathematics. This paper uses the Burali–Forti paradox to demonstrate this incompatibility, and another closely related, without appeal to principles related to the axiom of choice—a result hitherto unestablished. (...) It discusses both the general interest of this result, its interest to neo-Fregean philosophy of mathematics, and the potential significance of the Burali–Fortian method of proof. (shrink)

A proof of ‘correctness’ for a mathematical algorithm cannot be relevant to executions of a program based on that algorithm because both the algorithm and the proof are based on assumptions that do not hold for computations carried out by real-world computers. Thus, proving the ‘correctness’ of an algorithm cannot establish the trustworthiness of programs based on that algorithm. Despite the (deceptive) sameness of the notations used to represent them, the transformation of an algorithm into an executable program is a (...) wrenching metamorphosis that changes a mathematical abstraction into a prescription for concrete actions to be taken by real computers. Therefore, it is verification of program executions (processes) that is needed, not of program texts that are merely the scripts for those processes. In this view, verification is the empirical investigation of: (a) the behavior that programs invoke in a computer system and (b) the larger context in which that behavior occurs. Here, deduction can play no more, and no less, a role than it does in the empirical sciences. (shrink)