It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial Π10 subset of Cantor space. We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability. As for nonempty Π10 subsets of Cantor space, we show the existence of a finite-Δ20-piecewise degree containing infinitely many finite-2-piecewise degrees, and a finite-2-piecewise degree containing infinitely many finite-Δ20-piecewise degrees 2 denotes the difference of two Πn0 (...) sets), whereas the greatest degrees in these three “finite-Γ-piecewise” degree structures coincide. Moreover, as for nonempty Π10 subsets of Cantor space, we also show that every nonzero finite-2-piecewise degree includes infinitely many Medvedev degrees, every nonzero countable-Δ20-piecewise degree includes infinitely many finite-piecewise degrees, every nonzero finite-2-countable-Δ20-piecewise degree includes infinitely many countable-Δ20-piecewise degrees, and every nonzero Muchnik degree includes infinitely many finite-2-countable-Δ20-piecewise degrees. Indeed, we show that any nonzero Medvedev degree and nonzero countable-Δ20-piecewise degree of a nonempty Π10 subset of Cantor space have the strong anticupping properties. Finally, we obtain an elementary difference between the Medvedev degree structure and the finite-Γ-piecewise degree structure of all subsets of Baire space by showing that none of the finite-Γ-piecewise structures is Brouwerian, where Γ is any of the Wadge classes mentioned above. (shrink)

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded learnability is equivalent to finite View the MathML source2-piecewise computability 2 denotes the difference of two View the MathML sourceΠ10 sets), error-bounded learnability is equivalent to finite View (...) the MathML sourceΔ20-piecewise computability, and learnability is equivalent to countable View the MathML sourceΠ10-piecewise computability . Second, we introduce disjunction-like operations such as the coproduct based on BHK-like interpretations, and then, we see that these operations induce Galois connections between the Medvedev degree structure and associated Medvedev/ Muchnik-like degree structures. Finally, we interpret these results in the context of the Weihrauch degrees and Wadge-like games. (shrink)

A mass problem is a set of functions $\omega \to \omega $. For mass problems ${\mathcal {C}}, {\mathcal {D}}$, one says that ${\mathcal {C}}$ is Muchnik reducible to ${\mathcal {D}}$ if each function in ${\mathcal {C}}$ is computed by a function in ${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For $p \in [0,1]$ let (...) ${\mathcal {D}}$ be the mass problem of infinite bit sequences y such that for each computable bit sequence x, the bit sequence $ x {\,\leftrightarrow\,} y$ has asymptotic lower density at most p = y$ ). We show that all members of this family of mass problems parameterized by a real p with $0 p$ for each computable set x. We prove that the Medvedev complexity of the mass problems ${\mathcal {B}}$ is the same for all $p \in $, by showing that they are Medvedev equivalent to the mass problem of functions bounded by ${2^{2}}^{n}$ that are almost everywhere different from each computable function.Next, together with Joseph Miller, we obtain a proper hierarchy of the mass problems of type $\text {IOE}$ : we show that for any order function g there exists a faster growing order function $h $ such that $\text {IOE}$ is strictly above $\text {IOE}$ in the sense of Muchnik reducibility.We study cardinal characteristics in the sense of set theory that are analogous to the highness properties above. For instance, ${\mathfrak {d}} $ is the least size of a set G of bit sequences such that for each bit sequence x there is a bit sequence y in G so that $\underline \rho >p$. We prove within ZFC all the coincidences of cardinal characteristics that are the analogs of the results above. (shrink)

We prove that the first-order theory of the Medvedev degrees, the first-order theory of the Muchnik degrees, and the third-order theory of true arithmetic are pairwise recursively isomorphic (obtained independently by Lewis, Nies, and Sorbi [7]). We then restrict our attention to the degrees of closed sets and prove that the following theories are pairwise recursively isomorphic: the first-order theory of the closed Medvedev degrees, the first-order theory of the compact Medvedev degrees, the first-order (...) theory of the closed Muchnik degrees, the first-order theory of the compact Muchnik degrees, and the second-order theory of true arithmetic. Our coding methods also prove that neither the closed Medvedev degrees nor the compact Medvedev degrees are elementarily equivalent to either the closed Muchnik degrees or the compact Muchnik degrees. (shrink)

This is a contribution to the study of the Muchnik and Medvedev lattices of non-empty Π01 subsets of 2ω. In both these lattices, any non-minimum element can be split, i. e. it is the non-trivial join of two other elements. In fact, in the Medvedev case, ifP > MQ, then P can be split above Q. Both of these facts are then generalised to the embedding of arbitrary finite distributive lattices. A consequence of this is that both lattices have (...) decidible ∃-theories. (shrink)

Let w and M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Π1 0 subsets of 2ω, under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of w . We show that many countable distributive lattices are lattice-embeddable below any non-zero element of M.

We extend results of Harizanov and Barker. For a relation R on a recursive structure /oA, we give conditions guaranteeing that the image of R in a recursive copy of /oA can be made to have arbitrary ∑α0 degree over Δα0. We give stronger conditions under which the image of R can be made ∑α0 degree as well. The degrees over Δα0 can be replaced by certain more general classes. We also generalize the Friedberg-Muchnik Theorem, giving conditions on (...) a pair of relations R and S under which the images of R and S can be made ∑α0 and independent over Δα0 in a recursive copy of /oA. (shrink)

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.

We introduce a hierarchy of degree structures between the Medvedev and Muchnik lattices which allow varying amounts of nonuniformity. We use these structures to introduce the notion of the uniformity of a Muchnik reduction, which expresses how uniform a reduction is. We study this notion for several well-known reductions from algorithmic randomness. Furthermore, since our new structures are Brouwer algebras, we study their propositional theories. Finally, we study if our new structures are elementarily equivalent to each other.

§1. Introduction. Natural sets that can be enumerated by a computable function always seem to be either actually computable or of the same complexity as the Halting Problem, the complete r.e. set K. The obvious question, first posed in Post [1944] and since then called Post's Problem is then just whether there are r.e. sets which are neither computable nor complete, i.e., neither recursive nor of the same Turing degree as K?Let be the r.e. degrees, i.e., the r.e. sets (...) modulo the equivalence relation of equicomputable with the partial order induced by Turing computability. This structure is a partial order with least element 0, the degree of the computable sets, and greatest element 1 or 0′, the degree of K. Post's problem then asks if there are any other elements of.The solution of Post's problem by Friedberg [1957] and Muchnik [1956] was followed by various algebraic or order theoretic results that were interpreted as saying that the structure was in some way well behaved:Theorem 1.1. Every countable partial ordering or even uppersemilattice can be embedded into.Theorem 1.2. For every nonrecursive r.e. degreeathere are r.e. degreesb, c < asuch thatb ∨ c = a.Theorem 1.3. For every pair of nonrecursive r.e. degreesa < bthere is an r.e. degreecsuch thata < c < b. (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and (...) PAC reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

We investigate the notion of hyperimmunity with respect to how it can be applied to Π{\sp 0}{\sb 1} classes and their Muchnik degrees. We show that hyperimmunity is a strong enough concept to prove the existence of Π{\sp 0}{\sb 1} classes with intermediate Muchnik degree—in contrast to Post's attempts to construct intermediate c.e. degrees.

Let $\mathcal{P}_w$ be the lattice of Muchnik degrees of nonempty $\Pi^0_1$ subsets of $2^\omega$. The lattice $\mathcal{P}$ has been studied extensively in previous publications. In this note we prove that the lattice $\mathcal{P}$ is not Brouwerian.

The property of smallness for Π01 classes is introduced and is investigated with respect to Medvedev and Muchnik degree. It is shown that the property of containing a small Π01 class depends only on the Muchnik degree of a Π01 class. A comparison is made with the idea of thinness for Π01 classesmsthm.

We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.

The property of smallness for Π0 1 classes is introduced and is investigated with respect to Medvedev and Muchnik degree. It is shown that the property of containing a small Π0 1 class depends only on the Muchnik degree of a Π0 1 class. A comparison is made with the idea of thinness for Π0 1 classesmsthm.

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

We formulate an abstract version of the finite injury method in the form of the Baire category theorem. The theorem has the following corollaries: The Friedberg-Muchnik pair of recursively enumerable degrees, the Sacks splitting theorem, the existence of a minimal degree below 0′ and the Shoenfield jump theorem.

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our first (...) main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices. However, they only formalised this for propositional logic, while Kolmogorov also discussed the universal quantifier. We extend the work of Medvedev to first-order logic, using the notion of a first-order hyperdoctrine from categorical logic, to a structure which we will call (...) the hyperdoctrine of mass problems. We study the intermediate logic that the hyperdoctrine of mass problems gives us, and we study the theories of subintervals of the hyperdoctrine of mass problems in an attempt to obtain an analogue of Skvortsova’s result that there is a factor of the Medvedev lattice characterising intuitionistic propositional logic. Finally, we consider Heyting arithmetic in the hyperdoctrine of mass problems and prove an analogue of Tennenbaum’s theorem on computable models of arithmetic. (shrink)

There is a perfect thin class whose upward closure in the Turing degrees has full measure . Thus, in the Muchnik lattice of classes, the degree of 2-random reals is comparable with the degree of some perfect thin class. This solves a question of Simpson [S. Simpson, Mass problems and randomness, Bulletin of Symbolic Logic 11 1–27].

Kant infamously claimed that all human beings, without exception, are evil by nature. This collection of essays critically examines and elucidates what he must have meant by this indictment. It shows the role which evil plays in his overall philosophical project and analyses its relation to individual autonomy. Furthermore, it explores the relevance of Kant's views for understanding contemporary questions such as crimes against humanity and moral reconstruction. Leading scholars in the field engage a wide range of sources from which (...) a distinctly Kantian theory of evil emerges, both subtle and robust, and capable of shedding light on the complex dynamics of human immorality. (shrink)

In this paper, I develop a quasi-transcendental argument to justify Kant’s infamous claim “man is evil by nature.” The cornerstone of my reconstruction lies in drawing a systematic distinction between the seemingly identical concepts of “evil disposition” (böseGesinnung) and “propensity to evil” (Hang zumBösen). The former, I argue, Kant reserves to describe the fundamental moral outlook of a single individual; the latter, the moral orientation of the whole species. Moreover, the appellative “evil” ranges over two different types of moral failure: (...) while an “evil disposition” is a failure to realize the good (i.e., to adopt the motive of duty as limiting condition for all one’s desires), an “evil propensity” is a failure to realize the highest good (i.e., to engage in the collective project of transforming the legal order into an ethical community). This correlation between units of moral analysis and types of obligation suggests a way to offer a deduction of the universal propensity on behalf of Kant. It consists in tracing the source of radical evil to the same subjective necessity that gives rise to the doctrine of the highest good. For, at the basis of Kant’s two doctrines lies the same natural dialectic between happiness and morality. While the highest good brings about the critically acceptable resolution of this dialectic, the propensity to evil perpetuates and aggravates it. Instead of connecting happiness and morality in an objective relation, the human will subordinatesmorality to the pursuit of happiness according to the subjective order of association. If this reading is correct, it would explain why prior attempts at a transcendental deduction have failed: interpreters have looked for the key to the deduction in the body of Kant’s text, where it is not to be found, for it is tucked, instead, in the Preface to the first edition. (shrink)

An Essay on Kant’s Theory of Evil shows the centrality of the doctrine of radical evil within Kant's critical philosophy. Combining textual accuracy with systematic ethical theory, it fills the gaps Kant left open in his own doctrine, and provides a non-mystifying account of human immorality, which shows the pertinence of the Kantian view to our moral concerns.

The main purpose of these introductory remarks is to give the reader a sense of Philip Rossi’s philosophical project and its importance. I will then advance an interpretation of what motivates Kant’s commitment to community, and, on its basis, object to Rossi’s views on radical evil –a point which affects how one should conceive the moral vocation of humanity and the role that politics and religion play within it. My reconstruction concludes with a sketch of how the five contributions to (...) this Symposium fit together and deepen our understanding of Rossi’s overall project. (shrink)

This Guide is designed to restore the theological background that informs Kant’s treatment of grace in Religion to its rightful place. This background is essential not only to understand the nature of Kant’s overall project in this book, namely, to determine the “association” or “union” between Christianity (as a historical faith) and rational religion, but also to dispel the impression of “internal contradictions” and conundrums” that contemporary interpreters associate with Kant’s treatment of grace and moral regeneration. That impression, we argue, (...) is the result of entrenched interpretative habits that can be traced back to Karl Barth’s reading of the text. Once we realize that such a reading rests on a mistake, much of the anxiety and confusion that plague current discussions on these issues can be put to rest. (shrink)

The aim of Kant’s Sources in Translation is to retrieve the rich intellectual world that influenced Kant’s philosophical development. In its first stage, the series makes available the most important textbooks Kant used throughout his long teaching career. Many of these textbooks are in Latin or in German and remain inaccessible to Anglophone readers. Lacking this material, however, it is difficult to appreciate Kant’s originality and process of philosophical maturation, for readers are unable to understand what prompted Kant to introduce (...) a distinction, offer a qualification, attack a position, or develop a new thesis. This background is essential to understand the genesis of Kant’s thought. -/- This volume provides a translation of Georg Friedrich Meier’s Auszugaus der Vernunftlehre, the textbook that serves not only as the basis for Kant’s lectures on logic and related Reflexionen but is also crucial for studying the so-called Jäsche Logic of 1800, which is redacted from the marginal and interleave notes found in Kant’s personal copy of Meier’s book. Given the recent growth in scholarship on Kant’s logic, normative epistemology, and the psychology of belief, this volume makes a major contribution to contemporary debates in the field. (shrink)

The aim of Kant’s Sources in Translation is to retrieve the rich intellectual world that influenced Kant’s philosophical development. In its first stage, the series makes available the most important textbooks Kant used throughout his long teaching career. Many of these textbooks are in Latin or in German and remain inaccessible to Anglophone readers. Lacking this material, however, it is difficult to appreciate Kant’s originality and process of philosophical maturation, for readers are unable to understand what prompted Kant to introduce (...) a distinction, offer a qualification, attack a position, or develop a new thesis. This background is essential to understand the genesis of Kant’s thought. -/- This volume provides a translation of Georg Friedrich Meier’s Auszugaus der Vernunftlehre, the textbook that serves not only as the basis for Kant’s lectures on logic and related Reflexionen but is also crucial for studying the so-called Jäsche Logic of 1800, which is redacted from the marginal and interleave notes found in Kant’s personal copy of Meier’s book. Given the recent growth in scholarship on Kant’s logic, normative epistemology, and the psychology of belief, this volume makes a major contribution to contemporary debates in the field. (shrink)

The complete Hebrew text illuminated by English transliteration and commentary in an illustrated gift edition.

In recent years, there has been a growing interest in Kant's doctrine of radical evil, arising from as diverse quarters as philosophy, psychoanalysis and the social sciences. This interest has contributed to the revival of the notion of evil, which had been displaced from the center of philosophical discussion in the 20th century. A common trait in the recent literature is that it takes the relevance of the use of the concept of evil for granted. Yet, before understanding what Kant (...) really means by radical evil, it seems appropriate to ask first whether the notion of evil as such is necessary. For, given its religious background, this notion elicits expectations that may be incompatible with the secular concerns of moral philosophy. Such misgivings are aggravated by additional doubts about the concept's explanatory function in the first place. The pertinence of reviving a concept so allegedly flawed cannot be taken at face value. Thus, the task I set for myself here is to show the necessity of the concept of evil as it lies at the core of Kant's moral philosophy already in the Groundwork, far before he actually coins the notion of “radical evil” in the Religion. Whether this latter account is defensible or not, we will at least be sure that talk about an evil which is said to be radical is not in vain. (shrink)

Publications in the Kant-Studien have a dual focus: firstly contributions to the interpretation, history and editorial questions of Kant’s philosophy, and secondly systematic debates on transcendental philosophy. In addition, there are investigations on Kant’s precursors and on the effects of his philosophy. The journal also contains a documentation section, in which the current state of research is indicated by means of a continually updated bibliography with reviews and references.

This paper analyzes the system of inferences Kant uses to determine whether an agent is evil.

ABSTRACT: Kant and Mendelssohn published almost simultaneously influential essays on the Enlightenment. I use this historical contingency as occasion to reflect on the presuppositions and implications their views have with respect to philosophy and politics. In the first part, I compare Mendelssohn's discursive strategy with that of traditional liberalism. A contradiction emerges from this contrast, which, in the second part, I interpret in Kantian terms as an antinomy of modern political reason. Kant's notion of “autonomy,” I suggest, is an attempt (...) to overcome this very antinomy. Putting things this way allows us to better appreciate the originality of Kant's defense of the free use of public reason and his contribution to the liberal tradition. (shrink)

This paper reflects on the exchange that took place in a session organized by the North American Kant Society at the Eastern Division Meeting of the American Philosophical Association in Washington, DC (January, 2016). The session, “New Perspectives in Kant’s Psychology,” marked a rare occurrence: the almost simultaneous publication in 2014 of two important new books on this topic, Corey Dyck’s Kant and Rational Psychology (Oxford University Press) and Patrick Frierson’s Kant’s Empirical Psychology (Cambridge University Press). At first glance, these (...) books have little in common. While the bulk of Dyck’s project is devoted to interpreting Kant’s Paralogisms in light of 18th century German discussions of rational psychology, Frierson shows how Kant’s conception of human beings as objects of empirical investigation is essential to understanding his theory of action, cognition, and moral motivation. If one looks more closely, however, these projects share a fundamental assumption, namely, that in order to understand what motivates and shapes the development of Kant’s transcendental philosophy, one must grapple with the implications of his empirical psychology. (shrink)

Against the impression that Rousseau is an eclectic thinker, this paper is an attempt to reconstruct the systematic core of his anthropology. First, I discuss the methodological starting-point. Second, I develop the structural framework required to make the concept of nature operative as an ideal within social contexts. Finally, I interpret Rousseau's genetic account in terms of this framework. Such a procedure allows me to solve two interpretative problems, the aporia of the origin of wickedness and the question of man's (...) natural isolation. A twofold notion of logic is introduced to integrate the demands of history and structure, which overlap with those of freedom and necessity in Rousseau's thought. This organizes my argument in a mirror-like way. I call this undertaking an essay, for it is the endeavor to think what Rousseau must have thought in order to write what he wrote. Key Words: amour de soi • amour propre • bourgeois • ego sentio • human make-up • human nature • natural as ideal • other-centered • savage • self-centered • totalities of feeling • totalities of needs. (shrink)

This paper provides a defense of the ethical/political dimensions of Kant’s liberalism by gauging the strength of the critique of one of its most acerbic contemporary critics, Richard Rorty. Rorty’s dissatisfaction with Kant’s position can be traced back to a narrative of the coming to age of our culture, which bears surprising similarities to Kant’s account of the Enlightenment. Yet, in Rorty’s version of the story, Kant’s philosophy is mistakenly assimilated to a form of “Platonism.” This is due, I argue, (...) to the fact that Rorty confuses the “transcendental” with the “transcendent” in Kant. To set the score straight, I present a “de-Platonized” reading of Kant’s 1784 Enlightenment essay, whose goal is to protect the achievements of liberalism against Rorty’s poetic excesses. (shrink)

In a note introduced into the second edition of Religion within the Boundaries of Mere Reason (1794), Kant assigns a systematic role to the General Remarks at the end of each Part of his book. He calls those Remarks, “as it were, parerga to religion within the boundaries of pure reason; they do not belong within it yet border on it” (RGV 6:52). As Kant sees them, the parerga are only a “secondary occupation” that consists in removing transcendent obstacles. This (...) paper is skeptical of Kant's view. It proposes an alternative account, according to which the parerga are essential to our moral education, since they force human reason to confront its own limitations and resist the urge to take refuge in spurious religious beliefs. That urge, I argue, is linked to the propensity to evil, and uses religious orthodoxy to undermine moral religion. By clipping our dogmatic wings, the parerga encourage reason to face its own dialectical tendencies and direct its speculative interest to immanent practical use. This redirection counteracts the debilitating effects of the propensity to evil and plays a key role in our moral regeneration. To consider the parerga “derivative,” as Kant himself does, is therefore a grave mistake. (shrink)

In a note introduced into the second edition of Religion within the Boundaries of Mere Reason (1794), Kant assigns a systematic role to the General Remarks at the end of each Part of his book. He calls those Remarks, “as it were, parerga to religion within the boundaries of pure reason; they do not belong within it yet border on it” (RGV 6:52). As Kant sees them, the parerga are only a “secondary occupation” that consists in removing transcendent obstacles. This (...) paper is skeptical of Kant's view. It proposes an alternative account, according to which the parerga are essential to our moral education, since they force human reason to confront its own limitations and resist the urge to take refuge in spurious religious beliefs. That urge, I argue, is linked to the propensity to evil, and uses religious orthodoxy to undermine moral religion. By clipping our dogmatic wings, the parerga encourage reason to face its own dialectical tendencies and direct its speculative interest to immanent practical use. This redirection counteracts the debilitating effects of the propensity to evil and plays a key role in our moral regeneration. To consider the parerga “derivative,” as Kant himself does, is therefore a grave mistake. (shrink)

Au moment où Le Nouvel Observateur célèbre son vingtième anniversaire, voici le portrait, la musique, le style de cet hebdomadaire à travers ceux qui ont fait le paysage intellectuel de notre temps. « Copyright Electre ».

Let μ be a universal lower enumerable semi-measure . Any computable upper bound for μ can be effectively separated from zero with a constant . Computable positive lower bounds for μ can be nontrivial and allow one to construct natural examples of hypersimple sets.

This article offers a short biography of Kant and explains why his work was so important.

Immanuel Kant’s Religion within the Boundaries of Mere Reason (1793) is a formidably difficult book, which since its very inception was ripe for controversy. Part of the difficulty in understanding Kant’s text is thematic: in the idea of God and the questions surrounding faith in God’s existence, all interests of reason seem to converge –metaphysics, epistemology, morality, politics, the purposiveness of nature, and the destiny of the human species all unite in Kant’s view of religion and give it a distinctive (...) polyphonic tone. Part of the difficulty is ideological: Kant’s treatment of religious matters—relying on the assumption that a rational a priori core (identical to the principles of his morality) underlies and shapes all historical revelations—distances itself from both dogmatism and atheism. Those who accept religious orthodoxy, no less than those who are committed to a purely secular view of human affairs, are doomed to be displeased with the ambiguities of Kant’s approach, which preserves religion but subverts the meaning of this term so drastically as to make it unrecognizable in its traditional understanding. James DiCenso’s Commentary, “the first complete English language commentary on the work” (according to the dust-jacket), is thus a daring philosophical undertaking: it required not only comprehensive knowledge of Kant’s corpus but also the intellectual versatility to appreciate Kant’s innovative view. (shrink)

This paper suggests a general interpretative strategy for reading Religion within the Boundaries of Mere Reason namely, as an attempt to find a middle ground between what Kant considers two forms of excess: the appeal to a transcendent conception of God and the denial of any claim that presupposes God’s existence. To make my case, I use the example of two contemporary thinkers (Wolterstorff and Rorty) and trace their dispute to the antinomic character of “religious reason.” Putting things this way (...) underscores the originality of Kant’s view: the wake-up call of an antinomy serves us to motivate Kant’s solution to the problem raised by dogmatic religious claims, as well as to capture what is the distinctive ethical function he reserved for religion in the critical system, i.e., the support of the non-individualistic virtues involved in shared undertakings and common pursuits. Throughout the discussion, I show the importance that radical evil had in Kant’s “constructing” the idea of God. (shrink)

The series Rethinking Kant, now in its fourth volume, has become a mirror of Kantian studies in North America. It gathers papers presented at the various study groups of the North American Kant Society, along with contributions from hosts, session chairs, and keynote speakers. Because of its broad and unique composition, it offers a sample of a whole generation of Kantian thought, ranging from recent PhDs, to up and coming young scholars, to some well-established and influential players in the field. (...) Contributions are subjected to strenuous peer review and are, without exception, examples of the most innovative and cutting-edge research done in this area. Anyone interested in taking the pulse of contemporary Kantian scholarship and engaging in the humbling but rewarding task of rethinking Kant, should consider it. (shrink)

The series Rethinking Kant, now in its fifth volume, has become a mirror of Kantian studies in North America. It gathers papers presented at the various study groups of the North American Kant Society, along with contributions from hosts, session chairs, and keynote speakers. Because of its broad and unique composition, it offers a sample of a whole generation of Kantian thought, ranging from recent Ph.Ds, to up and coming young scholars, to some well-established and influential players in the field. (...) Contributions are subjected to strenuous peer review, and are, without exception, examples of the most innovative and cutting-edge research done in this area. Any one interested in taking the pulse of contemporary Kantian scholarship and engage in the humbling, but rewarding task of rethinking Kant, should consider it. (shrink)