In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well (...) as the one of Gödel 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. -/- From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to first-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained. (shrink)

Fichte assigns ‘intellectual intuition’ a new meaning after Kant. But in 1799, his doctrine of intellectual intuition is publicly deemed indefensible by Kant and nihilistic by Jacobi. I propose to defend Fichte’s doctrine against these charges, leaving aside whether it captures what he calls the ‘spirit’ of transcendental idealism. I do so by articulating three problems that motivate Fichte’s redirection of intellectual intuition from being to acting: (1) the regress problem, which states that reflecting on empirical facts of consciousness leads (...) only to further facts and so cannot yield a first principle; (2) the rhapsody problem, which states that the categories form a haphazard set and so lack necessity unless they derive from a first principle; and (3) the nihilism problem, which states that a first principle cannot lie outside our cognition of it, lest it be the cause of our cognition and, being first, the cause of all our actions, reducing us to machines. Crucially, Fichte’s three motivating problems are in fact aspects of a single problem. Leaving any aspect unsolved spoils putative solutions to the other two. Consequently, Fichte requires a single unified solution to all three, which his doctrine of intellectual intuition provides. (shrink)

This chapter intervenes in recent debates in Kant scholarship about the possibility of a general logical alien. Such an alien is a thinker whose laws of thinking violate ours. She is third-personal as she is radically unlike us. Proponents of the constitutive reading of Kant’s conception of general logic accordingly suggest that Kant rules out the possibility of such an alien as unthinkable. I add to this an often-overlooked element in Kant’s thinking: there is reason to think that he (...) grants—and in fact presupposes—the possibility of a transcendental logical alien. Such an alien is a knower whose laws of experience purport to violate ours. She is first-personal as she is radically like us. In other words, she is us, insofar as we are alienated from ourselves and our experience. I go on to draw an analogy between her, a dogmatist, and another transcendental alien, an evil agent. Just as a dogmatist is alienated from her (our) experiential laws, an evil agent is alienated from her (our) moral law. These forms of theoretical and practical self-conceit require self-knowledge in the form of a critique of speculative or practical reason. In bringing this point out, I aim to shift from the question of whether logical laws constitute our thinking to the question of whether grasping our experiential and moral laws as our laws constitutes our reason. (shrink)

The history of philosophy risks a self-opacity whereby we overestimate or underestimate our proximity to prior modes of thinking. This risk is relevant to assessing Hegel’s appropriation by McDowell and Priest. McDowell enlists Hegel for a quietist answer to the problem with assuming that concepts and reality belong to different orders, viz., how concepts are answerable to the world. If we accept Hegel’s absolute idealist view that the conceptual is boundless, this problem allegedly dissolves. Priest enlists Hegel for a dialetheist (...) answer to the problem with assuming that truth and falsity are mutually exclusive, viz., how certain sentences are both true and false. If we accept Hegel’s dialectical view that certain contradictions are necessary, this problem allegedly dissolves. For both McDowell and Priest, we find a true friend in Hegel. I argue that McDowell’s and Priest’s appropriations of Hegel overestimate Hegel’s affinity with quietism and dialetheism. McDowell reads Hegel as a quietist who silences metaphysical claims and the skeptical questions they raise against commonsense, but neglects Hegel’s adaptation of ancient skepticism against commonsense. Priest reads Hegel as a dialetheist who subordinates formal logic to dialectical logic by affirming the truth of certain contradictions, but neglects Hegel’s commitment to resolving contradictions for the sake of truth qua whole. I diagnose their misreadings in terms of what Hegel regards as the three moments of logic and argue that while McDowell jumps to its third moment, Priest stalls at its second moment. According to Hegel’s Encyclopedia Logic, logic has three “moments”: the abstractive moment of the understanding, which “stops short” at fixed categories; the negative moment of dialectic, which discovers the “genuine nature” of the categories, viz., that each “passes over, of itself, into its opposite”; and the positive moment of speculation, which grasps the “unity” of categories through the “dissolution” of their inner opposition. Hegel warns that if these moments are “kept separate from each other […] they are not considered in their truth”. I suggest that quietist and dialetheist readings of Hegel fail to consider truthfully the unified moments of his logic. In his quietist critique of metaphysics, McDowell enlists Hegel to dissolve the problem with assuming the duality of concept and reality. But McDowell helps himself directly to the third moment of logic, where the unity of the categories, and hence the boundlessness of the conceptual, would be fully articulated. Since he arrives at the third moment prematurely, ignoring its prior moments, he obscures its truth (§1). In his dialetheist critique of formal logic, Priest enlists Hegel to dissolve the problem with assuming the duality of truth and falsity. But Priest restricts himself gratuitously to the second moment of logic, where contradictions within the categories are not yet resolved. Since he stalls at the second moment, severed from its final moment, he obscures its truth (§2). I argue we can extricate Hegel from quietist and dialetheist misreadings only if we grasp the truth of the three moments of logic. (shrink)

In the Vocation of Man, Fichte makes the striking claim that life is eternal, rational, our true being, and the final cause of nature in general and of death in particular. How can we make sense of this claim? I argue that the public lectures that compose the Vocation are a popular expression of Fichte’s pre-existing commitment to what I call immortalism, the view that life is the unconditioned condition of intelligibility. Casting the I as an absolutely self-active or living (...) power enables his philosophical account of both the intelligibility of objects and of what it means to die. This explains his characterization of the Wissenschaftslehre as a system in which ‘all is act, movement, and life’. In Sect. 1, I explain the context of Jacobi’s use of ‘caput mortuum’ as a term for the thing in itself. In Sects. 2 and 3, I reconstruct two immortalist arguments from Fichte’s Jena period. The first is that the I’s self-activity rules out the existence of the thing in itself and thereby vanquishes ‘death’s head’. The second is that, insofar as the I charges us with the moral perfection of nature, it is the final cause of our entire life, including its end. This is to say that the I puts our every moment into question, even our last. In Sect. 4, I use these immortalist arguments to interpret the striking claim from the Vocation. (shrink)

The concept of facticity denotes conditions of experience whose necessity is not logical yet whose contingency is not empirical. Although often associated with Heidegger, Fichte coins ‘facticity’ in his Berlin period to refer to the conclusion of Kant’s metaphysical deduction of the categories, which he argues leaves it a contingent matter that we have the conditions of experience that we do. Such rhapsodic or factical conditions, he argues, must follow necessarily, independent of empirical givenness, from the I through a process (...) of ‘genesis.’ I reconstruct Fichte’s argument by tracing the origin of his neologism, presenting his Jena critique of Kant’s rhapsodic appeal to the forms of judgment, and illustrating the Jena period’s continuity with the Berlin period’s genetic method, while noting a methodological shift whereby Fichte directs his critique against his own doctrine of intellectual intuition in order to eliminate its ‘factical terms.’. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree (...) logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

Scholars agree that Schelling’s critique of Hegel consists in charging reason with an inability to account for its own possibility. This is not an attack on reason’s project of constructing a logical system, but rather on the pretense of doing so with complete justification and so without presuppositions, as if it were obvious why there is a logical system or why there is anything meaningful at all. Scholars accordingly cite the question ‘why is there something rather than nothing’ as emblematic (...) of Schelling’s critique and the source of his claim against Hegel that reason is bounded by something other than itself. But what sort of claim is this? For what sort of argument could it be the conclusion? On these questions, the literature is lacking. I propose that the question ‘why something’ motivates Schelling to give a transcendental argument to the effect that past and future are a priori conditions of the possibility of reason. As I reconstruct it from the Weltalter, this argument construes the past as the pre-rational decision to construct a logical system, while the future represents the purpose that guides the construction of the same. Schelling’s claim against Hegel that reason is bounded by something other is thus the discovery of inescapable presuppositions that condition the possibility of reason as such. (shrink)

Despite F. W. J. Schelling’s relative exclusion from the ongoing German idealist renaissance in Anglophone scholarship, recent critical and historical engagement with idealist texts affords an unprecedented opportunity to discover the richness and value of his thinking. This volume provides a wide-ranging presentation of Schelling’s original contribution to and internal critique of the basic insights of German idealism, his role in shaping the course of post-Kantian thought, and his sensitivity and innovative responses to questions of lasting metaphysical, epistemological, ethical, aesthetic, (...) and theological importance. The contributing authors offer compelling reasons to regard Schelling as one of Kant’s most incisive interpreters, a pioneering philosopher of nature, a resolute philosopher of human finitude and freedom, a nuanced thinker of the bounds of logic and self-consciousness, and perhaps Hegel’s most effective critic. (shrink)

While the idea that philosophy requires self-transformation is historically pervasive, it exerts considerable influence on the post-Kantians who first aim to systematize Kant’s idealism by grounding it on a first principle. In the 1790s, Fichte and Schelling offer competing accounts of the self-transformation that they regard as essential to positing a first principle. Their accounts raise two central questions. First, what makes this kind of self-transformation possible? Second, are there different possible expressions of philosophical self-transformation? In what follows, I will (...) articulate the Fichtean and Schellingian answers to these central questions. For Fichte, the one who summons me to posit a first principle makes possible my philosophical self-transformation, although the latter has an exclusively idealist expression in that I can only genuinely posit the I as first principle, which is to say that philosophical self-transformation depends on mutual recognition and vindicates precisely one philosophical system (Section 1). For Schelling, a brute act of will makes possible my philosophical self-transformation, although the latter has either an idealist or a realist expression in that I can genuinely posit either the I or the not-I as first principle, which is to say that philosophical self-transformation does not depend on mutual recognition and vindicates one of two possible philosophical systems (Section 2). Thus, whereas Fichtean self-transformation is recognitive and non-pluralistic, Schellingian self-transformation is pluralistic and non-recognitive. I conclude with a discussion of how Jacobi poses a challenge to Fichte’s and Schelling’s answers to the two central questions (Section 3). (shrink)

This paper addresses debates in German idealism that arise in response to the modal shift in logic, proposed by Kant, from a logic of thinking to a logic of experience. With the Kantian logic of experience arises a problem of radical contingency or 'rhapsodic determination' for logic. While Fichte and Hegel attempt to resolve the problem of contingency by constructing rational systems aimed at established the grounds for logic, I show how Schelling brings into (...) view, in a proto-existentialist movement, the way in which the indeterminacy of the will undergirds rational system construction and, thereby, presents a limiting problem for the question of the value of system-building itself. (shrink)

Does Kant’s restriction of knowledge to phenomena undermine objectivity? Jacobi argues that it does, daring the transcendental idealist to abandon the thing in itself and embrace the “strongest idealism”. According to Bruno, McDowell and Meillassoux adopt a similar critique of Kant’s conception of objectivity and, more significantly, echo Jacobi’s dare to profess the strongest idealism – what McDowell approvingly calls “consistent idealism” and Meillassoux disparagingly calls “extreme idealism”. After exposing the Cartesian projection on which Jacobi’s critique rests, Bruno shows that (...) McDowell’s and Meillassoux’s critiques make the same projection. He argues that whereas McDowell offers an inconsistent alternative to Kant’s idealism, Meillassoux begs the question against it. Finally, Bruno sketches the account of objectivity that follows from Kant’s distinction between general and transcendental logic. (shrink)

A number of cases involving self-locating beliefs have been discussed in the Bayesian literature. I suggest that many of these cases, such as the sleeping beauty case, are entangled with issues that are independent of self-locating beliefs per se. In light of this, I propose a division of labor: we should address each of these issues separately before we try to provide a comprehensive account of belief updating. By way of example, I sketch some ways of extending Bayesianism in order (...) to accommodate these issues. Then, putting these other issues aside, I sketch some ways of extending Bayesianism in order to accommodate self-locating beliefs. Finally, I propose a constraint on updating rules, the "Learning Principle", which rules out certain kinds of troubling belief changes, and I use this principle to assess some of the available options. (shrink)

While philosophers are often concerned with the conditions for moral knowledge or justification, in practice something arguably less demanding is just as, if not more, important – reliably making correct moral judgments. Judges and juries should hand down fair sentences, government officials should decide on just laws, members of ethics committees should make sound recommendations, and so on. We want such agents, more often than not and as often as possible, to make the right decisions. The purpose of this paper (...) is to propose a method of enhancing the moral reliability of such agents. In particular, we advocate for a procedural approach; certain internal processes generally contribute to people’s moral reliability. Building on the early work of Rawls, we identify several particular factors related to moral reasoning that are specific enough to be the target of practical intervention: logical competence, conceptual understanding, empirical competence, openness, empathy and bias. Improving on these processes can in turn make people more morally reliable in a variety of contexts and has implications for recent debates over moral enhancement. (shrink)

The prospect of consumable meat produced in a laboratory setting without the need to raise and slaughter animals is both realistic and exciting. Not only could such in vitro meat become popular due to potential cost savings, but it also avoids many of the ethical and environmental problems with traditional meat productions. However, as with any new technology, in vitro meat is likely to face some detractors. We examine in detail three potential objections: 1) in vitro meat is disrespectful, either (...) to nature or to animals; 2) it will reduce the number of happy animals in the world; and 3) it will open the door to cannibalism. While each objection has some attraction, we ultimately find that all can be overcome. The upshot is that in vitro meat production is generally permissible and, especially for ethical vegetarians, worth promoting. (shrink)

This paper examines the debate between permissive and impermissive forms of Bayesianism. It briefly discusses some considerations that might be offered by both sides of the debate, and then replies to some new arguments in favor of impermissivism offered by Roger White. First, it argues that White’s (Oxford studies in epistemology, vol 3. Oxford University Press, Oxford, pp 161–186, 2010) defense of Indifference Principles is unsuccessful. Second, it contends that White’s (Philos Perspect 19:445–459, 2005) arguments against permissive views do not (...) succeed. (shrink)

Even when they are defined with precision, one can often read and hear judgments about the vagueness of heuristics in debates about heuristic reasoning. This opinion is not just frequent but also quite reasonable. In fact, during the 1990s, there was a certain controversy concerning this topic that confronted two of the leading groups in the field of heuristic reasoning research, each of whom held very different perspectives. In the present text, we will focus on two of the papers published (...) in Psychological Review, wherein the arguments of each of these groups were presented:. (shrink)

Cushman, Young, & Greene (2010) urge the consolidation of moral psychology around a dual-system consensus. On this view, a slow, often-overstretched rational system tends to produce consequentialist intuitions and action-tendencies, while a fast, affective system produces virtuous (or vicious) intuitions and action-tendencies that perform well in their habituated ecological niche but sometimes disastrously outside of it. This perspective suggests a habit-corrected-by-reason picture of moral behavior. Recent research, however, has raised questions about the adequacy of dual-process theories of cognition and behavior, (...) which tend to distinguish categorically between fast, affect-laden, automatic, sometimes-unconscious, nearly-incorrigible mental processes and slow, rational, effortful, conscious, corrigible mental processes. Processes of one alleged type often have properties associated with the contrary type. For instance, rational processes can be emotional, and fast thinking can perform logical operations. In addition, the fast-slow binary transforms a continuous temporal scale into a dichotomous one, losing potentially important information along the way. While these problems are beginning to be addressed in some subfields of psychology, moral psychology has yet to grapple with them. In this theoretical paper, we argue that moral psychology needs a framework that accounts for our knowledge of both temporal and spatial (anatomical) dimensions of the brain basis of moral cognition and virtuous decision-making. We argue that methodologies with very fine-grained temporal granularity, such as electroencephalography (EEG), should be used to complement more frequently used methodologies such as functional magnetic resonance imaging (fMRI). We outline how this might be accomplished using generosity, gratitude, and integrity as a case study. (shrink)

The paper proposes an anthropocentric argument for veganism based on a speciesistic premise that most carnists likely affirm: human flourishing should be promoted. I highlight four areas of human suffering promoted by a carnistic diet: (1) health dangers to workers (both physical and psychological), (2) economic dangers to workers, (3) physical dangers to communities around slaughterhouses, and (4) environmental dangers to communities-at-large. Consequently, one could ignore the well-being of non-human animals and nevertheless recognize significant moral failings in the current standard (...) system of meat production. (shrink)

Meillassoux seeks knowledge of transcendental reality, blaming Kant for the ‘correlationist’ proscription of independent access to either thought or being. For Meillassoux, correlationism blocks an account of the meaning of ‘ancestral statements’ regarding reality prior to humans. I examine three charges on which Meillassoux’s argument depends: (1) Kant distorts ancestral statements’ meaning; (2) Kant fallaciously infers causality’s necessity; (3) Kant’s transcendental idealism cannot grasp ‘the great outdoors’. I reject these charges: (1) imposes a Cartesian misreading, hence Meillassoux’s false assumption that, (...) for Kant, objects don’t exist without subjects; (2) misreads Kant, who infers causality’s necessity from the possibility of experience; (3) casts Kant’s idealism as subjective, ignoring his perspectival portrayal of it. (shrink)

Schelling scholars face an uphill battle. His confinement to the smallest circles of ‘continental’ thought puts him at the margins of what today counts as philosophy. His eclipse by Fichte and Hegel and inheritance by better-read thinkers like Kierkegaard and Heidegger tend to reduce him to a historical footnote. And the sometimes obscure formulations he uses makes the otherwise difficult writings of fellow post-Kantians seem comparatively more accessible. For those seeking to widen these circles, see through this eclipse and elucidate (...) these formulations, a deeper internal challenge is to make sense of the appearance and disappearance of intellectual intuition in Schelling’s work. The term’s apotheosis is often attributed to the height of German idealism and especially to Schelling’s identity philosophy, outside which he subjects the term to a radical critique. The identity philosophy aims to cognize the absolute ground of the system of knowledge and the system of nature, for which cognition Schelling enlists intellectual intuition. While the identity philosophy falls between a Fichtean debut and a late attack on Hegel, it is difficult to determine its exact parameter. I propose that a necessary condition for doing so is to clarify the explanatory role of intellectual intuition—that is, the specific problem to which it is the intended solution—on which the identity philosophy depends. To this end, I will trace a nexus of problems that Schelling’s use of intellectual intuition is meant to solve. Doing so will not only help to delineate the identity philosophy, but show it to be continuous with Schelling’s earlier and later periods. In §1, I account for the nexus of the problems of grounding, freedom and meaning. These problems demand, respectively, a principle by which cognition forms a system rather than an aggregate, a principle by which a system of cognition is compatible with freedom rather than incompatible and a principle by which a system of freedom can show why there is meaning rather than none. In §2, I reconstruct Schelling’s argument in the identity philosophy for why intellectual intuition can resolve this nexus of problems and, in §3, his arguments during other periods of his thought for why it cannot. I conclude in §4 by suggesting why the identity philosophy is continuous with these periods. Beyond fulfilling the interpretive task of making sense of intellectual intuition in Schelling’s sprawling corpus, my aim is thus to contribute to a unified reading of the latter. (shrink)

Materialism in the philosophy of mind — materialismPM — is the view that everything mental is material (or, equivalently, physical). Consciousness — pain, emotional feeling, sensory experience, and so on — certainly exists. So materialismPM is the view that consciousness is wholly material. It has, historically, nothing to do with denial of the existence of consciousness. Its heart is precisely the claim that consciousness — consciousness! — is wholly material. [2] ‘Physicalism’, the view introduced by members of the Vienna Circle (...) in the late 1920s, also has nothing to do with denial of the existence of consciousness. [3] Recently the words ‘materialism’ and ‘physicalism’ have come to be treated as synonymous, and as names for a position in the philosophy of mind that does involve denial of the existence of consciousness. They’ve been used to name a position that (i) directly rejects the heart of materialism (materialismPM) and (ii) is certainly false. This is a pity, because they’re good terms for a view that is very likely true. (shrink)

An attempt at a Montague-style reconstruction of the semantics of Buridan's logic on a regimented fragment of Latin.

In the literature on supervaluationism, a central source of concern has been the acceptability, or otherwise, of its alleged logical revisionism. I attack the presupposition of this debate: arguing that when properly construed, there is no sense in which supervaluational consequence is revisionary. I provide new considerations supporting the claim that the supervaluational consequence should be characterized in a ‘global’ way. But pace Williamson (1994) and Keefe (2000), I argue that supervaluationism does not give rise to counterexamples to familiar inference-patterns (...) such as reductio and conditional proof. (shrink)

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists (...) of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

This work is about current theories concerning the application of the constitutional rules, on the approach of the efficacy and effectiveness of the fundamental rights. It also suggests an alternative way of logical analysis of the problem, mainly taking in account the phenomena of the application-efficacy-effectiveness of the rules. Therefore, it discusses the dogmatic rules and proposes the logical separation between its applicability and its effectiveness, considering the effectiveness as the potential power to realize the fundamental rights.

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

This chapter defends the account of metaphysical indeterminacy of Barnes and Williams against Eklund's objections.

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic (...) in the number of truth values, and it is shown that this bound is tight. (shrink)

German idealism stems in large part from Fichte’s response to a dilemma involving the concepts of pantheism, freedom and time: either time is the form of the determination of modes of substance, as held by a pantheistic or ‘dogmatic’ person, or the form of acts generated by human freedom, as held by an idealistic person. Fichte solves the dilemma by refuting dogmatism and deducing time from idealism’s first principle. But his diagnosis is more portentous: by casting the lemmas in terms (...) of person-types, he unintentionally invites Schelling’s philosophical rethinking of personality. In his middle period, Schelling argues for the consistency of the concepts of pantheism, freedom and time, claiming that it depends on a ‘good’ as opposed to ‘evil’ personality. However, since on his view personality is an absolute or originally undecided capacity for good and evil, the trio’s consistency is entirely contingent. In §1, I trace Fichte’s resolution of the dilemma. In §§2-3, I reconstruct Schelling’s arguments for consistency from the Freiheitsschrift and Weltalter, texts written just a few years apart. In §4, I allay a Kantian worry that this consistency relies problematically on the liberty of indifference or Willkür. (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value (...) and the exclusion of the opposite truth value describe the same situation.). (shrink)

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for (...) postulating this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)

A close look at Frege's proof in "Foundations of Arithmetic" that every number has a successor. The examination reveals a surprising gap in the proof, one that Frege would later fill in "Basic Laws of Arithmetic".

This study determined the cognitive skills achievement in mathematics of elementary pre-service teachers as a basis for improving problem-solving and critical thinking which was analyzed using Piaget's seven logical operations namely: classification, seriation, logical multiplication, compensation, ratio and proportional thinking, probability thinking, and correlational thinking. This study utilized an adopted Test on Logical Operations (TLO) and descriptive research design to describe the cognitive skills achievement and to determine the affecting factors. Overall, elementary pre-service teachers performed with sufficient understanding in dealing (...) with the TLO. However, in each logical operation, students were found to have insufficient understanding of probability thinking and correlational thinking. These insufficiencies in other logical operations were attributed to their misconceptions on some mathematical terms, misinterpretation of the problems, poor comprehension skills, poor problem-solving skills, and poor performance in mathematics in general. (shrink)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

This paper defends a novel account of how to determine the intrinsic value of possible worlds. Section 1 argues that a highly intuitive and widely accepted account leads to undesirable consequences. Section 2 takes the first of two steps towards a novel account by clarifying and defending a view about value-contribution that is based on some of W. D. Ross’ claims about the value of pleasure. Section 3 takes the second step by clarifying and defending a view about value-suppression that (...) is based on Ross’ claims about the interplay between prima-facie duties. Section 4 states and defends the account that I call Rossian Totalism. According to this account, the atoms of intrinsic value within a world only sometimes contribute their intrinsic value to the value of that world. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. (...) The essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

Skeptical puzzles and arguments often employ knowledge-closure principles . Epistemologists widely believe that an adequate reply to the skeptic should explain why her reasoning is appealing albeit misleading; but it’s unclear what would explain the appeal of the skeptic’s closure principle, if not for its truth. In this paper, I aim to challenge the widespread commitment to knowledge-closure. But I proceed by first examining a new puzzle about failing to know—what I call the New Ignorance Puzzle . This puzzle resembles (...) to the Old Ignorance Puzzle , although it does not involve a closure principle. It instead centers on the standard view of ignorance, a highly intuitive principle stating that ignorance is merely a failure to know. In Sects. 2 and 3, I argue that the best way to solve the New Ignorance Puzzle is to reject the standard view of ignorance and to explain away its appeal via conversational implicature. I then use this solution to the New Ignorance Puzzle as a way of explaining why knowledge-closure principles would seem true, and why abominable conjunctions would seem abominable, even if such principles were false . The upshot is a new way of explaining why the skeptic’s reasoning is appealing albeit misleading. (shrink)

Many accounts of structural rationality give a special role to logic. This paper reviews the problem case of clear-eyed logical uncertainty. An account of rational norms on belief that does not give a special role to logic is developed: doxastic probabilism.

The Gettier problem has stymied epistemologists. But, whether or not this problem is resolvable, we still must face an important question: Why does the Gettier problem arise in the first place? So far, philosophers have seen it as either a problem peculiar to the concept of knowledge, or else an instance of a general problem about conceptual analysis. But I would like to steer a middle course. I argue that the Gettier problem arises because knowledge is a thick concept, and (...) a Gettier-like problem is just what we should expect from attempts at analyzing a thick concept. Section 2 is devoted to establishing the controversial claim that knowledge is thick, and, in Sect. 3, I show that there is a general problem for analyzing thick concepts of which the Gettier problem is a special instance. I do not take a stand on whether the Gettier problem, or its general counterpart, is resolvable. My primary aim is to bring these problems into better focus. (shrink)

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines a (...) dutch book, but we only have a partial converse. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:This Universalism Which Is Not OneLinda M. G. Zerilli (bio)Ernesto Laclau. Emancipation(s). London: Verso, 1996.Judging from the recent spate of publications devoted to the question of the universal, it appears that, in the view of some critics, we are witnessing a reevaluation of its dismantling in twentieth-century thought. One of the many oddities about this “return of the universal” 1 is the idea that contemporary engagements with it are (...) more or less of a piece, and that they reflect a growing consensus that poststructuralist political theories are incapable of generating a viable alternative to the collective fragmentation that characterizes late modernity. 2 The putative return to the universal marks, on this view, both a homecoming to Enlightenment ideals—purified of their more poisonous elements, of course—and a reconciliation of sorts between those who refuted these ideals and those who sought to realize them. Now that “we” all know and agree that poststructuralism is critically valuable but politically bankrupt; now that we all know and agree that the “old universal” was indeed a “pseudo-universal,” so the homecoming narrative goes; we can get on with the project of constructing a “new universal.” 3 This authentic universal would really be inclusive of all people, regardless of race, class, gender, sexuality, ethnicity, nationality, and whatever else attaches to the “embarrassing etcetera” that, as Judith [End Page 3] Butler reminds us, inevitably accompanies such gestures of acknowledging human diversity.Before signing on to this felicitous agreement about “the necessity of universalism,” we may wish to know whether we have anything like a minimal agreement in language, that is, whether we who speak of this universal are even speaking about the same thing. Apart from the not insignificant problem of translating from a philosophical to a political idiom, the whole question of this agreement is virtually occluded by the rush to rescue politics from the virulent particularisms that admit no common ground or sense of collective belonging. Presented in terms of the familiar binary couple, the choice between universalism and particularism seems settled by merely pointing to global and domestic political realities. Universalism is the only alternative to social fragmentation, wild child of the collapse of communism, the rise of deadly nationalisms, and the multiculturalist romance with particularism. To invoke the name of the universal in any affirmative sense is already to sign on to the political diagnosis and its solution.One of the many virtues of Ernesto Laclau’s Emancipation(s) is that it offers both an alternative to the binarisms spawned by the “return” to the universal (for example, false universalism/true universalism) and a trenchant critique of the original binary couple itself (universalism/ particularism). Demonstrating the imbrication of the universal and the particular, Laclau shows why it is a matter not of choosing one over the other but of articulating, in a scrupulously political sense, the relation between the two. He thus explicitly rejects the notion that this relation is one of mutual exclusion, and shows that the tendency to see it as just that has led to the impasse of the contemporary debate, an impasse that is glossed over in some highly visible academic cases by proclaiming the necessary return to the universal. Although the language of universalism as spoken by Laclau searches for some common ground between particularists and universalists, it is more by way of articulating their mutual contamination, that is, how each is rendered impure by the irreducible presence of the other.The Problem of UniversalsLaclau situates his collection of essays in the context of the increasingly polarized debate over multiculturalism, a debate in which the classical universalism of the philosophical tradition has come under serious question. Reading his essays, one comes to see the deep dependence of the entire contemporary discussion on this tradition, even when its metaphysical assumptions are explicitly rejected (as, say, in the work of Seyla Benhabib) or insufficiently comprehended (as in most of the popularized political discourse). Laclau’s book can help us to see that the political question of universalism cannot be posed properly as long as it remains tethered to the classical philosophical “problem of universals.” At stake in sorting out the affinities and... (shrink)

Hartry Field has suggested that we should adopt at least a methodological deflationism: [W]e should assume full-fledged deflationism as a working hypothesis. That way, if full-fledged deflationism should turn out to be inadequate, we will at least have a clearer sense than we now have of just where it is that inflationist assumptions ... are needed. I argue here that we do not need to be methodological deflationists. More pre-cisely, I argue that we have no need for a disquotational truth-predicate; (...) that the word true, in ordinary language, is not a disquotational truth-predicate; and that it is not at all clear that it is even possible to introduce a disquotational truth-predicate into ordinary language. If so, then we have no clear sense how it is even possible to be a methodological deflationist. My goal here is not to convince a committed deflationist to abandon his or her position. My goal, rather, is to argue, contrary to what many seem to think, that reflection on the apparently trivial character of T-sentences should not incline us to deflationism. (shrink)

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified - the strength of (...) the connection and its multiplicity. (shrink)