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.

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)

The foundation scheme in set theory asserts that every nonempty class has an ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in $$\end{document}-minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory. We take KP set theory without foundation as the base theory. We show that KP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document} + Π1\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _1$$\end{document}-Foundation + V=L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V=L$$\end{document} is enough to carry out finite injury arguments in α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. (shrink)

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called “microscopic theory”, applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which (...) serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen–Specker–Bell theorem and Gleason’s theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory. (shrink)

§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)

We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional complexity and total conditional complexity, Epstein–Levin theorem and some (yet unpublished) result of Muchnik and Vyugin.

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)

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where (...) α * = λ = ω. (shrink)

In [2], Jockusch and Shore have introduced a new hierarchy of sets and operators called the REA hierarchy. In this note we prove analogues of the Friedberg Jump Theorem and the Sacks Jump Theorem for many REA operators. MSC: 03D25, 03D55.

Working in the language of first-order arithmetic we consider models of the base theory P - . Suppose M is a model of P - and let M satisfy induction for σ 1 -formulas. First it is shown that the Friedberg-Muchnik finite injury argument can be performed inside M, and then, using a blocking method for the requirements, we prove that the Sacks splitting construction can be done in M. So, the "amount" of induction needed to perform the known finite (...) injury priority arguments is Σ 1 -induction. (shrink)

We consider implicit definability over the natural number system $\mathbb{N},+,\times,=$. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of $\mathbb{N}$ which are not explicitly definable from each other. The second theorem says that there exists a subset of $\mathbb{N}$ which is not implicitly definable but belongs to a countable, explicitly definable set of subsets of $\mathbb{N}$. Previous proofs of these theorems have used finite- or infinite-injury (...) priority constructions. Our new proof is easier in that it uses only a nonpriority oracle construction, adapted from the standard proof of the Friedberg jump theorem. (shrink)

Khutoretskii's Theorem states that the Rogers semilattice of any family of c.e. sets has either at most one or infinitely many elements. A lemma in the inductive step of the proof shows that no Rogers semilattice can be partitioned into a principal ideal and a principal filter. We show that such a partitioning is possible for some family of d.c.e. sets. In fact, we construct a family of c.e. sets which, when viewed as a family of d.c.e. sets, has (...) (up to equivalence) exactly two computable Friedberg numberings ¼ and ν, and ¼ reduces to any computable numbering not equivalent to ν. The question of whether the full statement of Khutoretskii's Theorem fails for families of d.c.e. sets remains open. (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)

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)

There is a family of questions in relativized complexity theory--weak analogs of the Friedberg Jump-Inversion Theorem--that are resolved by 1-generic sets but which cannot be resolved by essentially any weaker notion of genericity. This paper defines aw2-generic sets. i.e., sets which meet every dense set of strings that is r.e. in some incomplete r.e. set. Aw2-generic sets are very close to 1-generic sets in strength, but are too weak to resolve these questions. In particular, it is shown that for (...) any set X there is an aw2-generic set G such that $\mathbf{NP}^G \cap co-\mathbf{NP}^G \nsubseteq \mathbf{P}^{G \oplus X}$ . (On the other hand, if G is 1-generic, then $\mathbf{NP}^G \cap co-\mathbf{NP}^G \subseteq \mathbf{P}^{G \oplus \mathrm{SAT}}$ . where SAT is the NP-complete satisfiability problem [6].) This result runs counter to the fact that most finite extension constructions in complexity theory can be made effective. These results imply that any finite extension construction that ensures any of the Friedberg analogs must be noneffective, even relative to an arbitrary incomplete r.e. set. It is then shown that the recursion theoretic properties of aw2-generic sets differ radically from those of 1-generic sets: every degree above O' contains an aw2-generic set: no aw2-generic set exists below any incomplete r.e. set; there is an aw2-generic set which is the join of two Turing equivalent aw2-generic sets. Finally, a result of Shore is presented [30] which states that every degree above 0' is the jump of an aw2-generic degree. (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)

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)

Do we have free will? Can we trust our memories? How well do you know yourself? Felix Friedberg answers these questions in Caveat Homo Sapiens, arguing that humanity, while limited by the non-existence of free will, gains salvation in the ability to respond. Subjectivity, memory, psychotropic drugs, and the existence of the subconscious mind are explored, especially concerning their impact on self-knowledge and perception. Accessible to the general educated reader, the book will also be of interest to psychiatrists, sociologists and (...) philosophers. (shrink)

The advent of the post-Stalin "thaw," particularly the period after 1956, was marked by a spectacular expansion in the publishing of translated Western writing and also, on occasion, of editions in the original languages: the virtual ban on import of Western books was, as of 1975, never relaxed. The more permissive political atmosphere favored the publication of a vastly larger variety of Western authors and titles and provision for the Soviet public of much larger quantities of such books in the (...) country's bookstores and libraries. While the improvement was very impressive in itself, abundant data attest that it was far from adequate to satisfy reader demand.1 Among the beneficiaries, books by American authors stood out the more prominently since it was these that were most discriminated against during the years immediately preceding.2 Decades of neglect, to say nothing of politically inspired selectivity, resulted in such incongruities as the first Russian translation of Melville's Moby Dick in 1961—more than a century after the novel's appearance—and the first Soviet publication of any work by Henry James in 1973. It was not until the 1960's that Russians had an opportunity to read Faulkner—but then, the same was true of Kafka. However unevenly, the range of American literature, both old and new, now made available to Soviet readers is gradually expanding. · 1. The overall problem is discussed in detail in this writer's forthcoming book, A Decade of Euphoria: Western Literature in Post-Stalin Russia, 1954-64 . · 2. For a thorough and illuminating discussion of the fate of American literature in the U.S.S.R. from the Revolution until the early post-Stalin years, see Deming Brown, Soviet Attitudes toward American Writing . Interesting statistical data on the first post-Stalin years may also be found in Melville J. Ruggles, "American Books in Soviet Publishing," Slavic Review 20, n.3 : 419-35. A useful, very brief list of selected works of American writing published by 1968, though not entirely as complete as it purports to be, may be found in M.O. Mendel'son, A.N. Nikolyukin, R.M. Samarin, eds., Problemy literature S. Sh. A. XX. veka , pp. 391-517. Unfortunately, the Soviet bibliography contains no information on press runs of the books listed. Maurice Friedberg, head of the Department of Slavic Languages and Literatures at the University of Illinois, is the author of numerous essays and articles on Soviet literature. Professor Friedberg's most recent book, A Decade of Euphoria: Western Literature in Post-Stalin Russia, 1954-1964, will be published this year. (shrink)

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

A commentary on “Patient-Satisfaction Surveys on a Scale of 0 to 10: Improving Health Care, or Leading It Astray?,” byAlexandra Junewicz and Stuart J. Youngner in the May-June 2015 issue.

This article is intended to emphasize several ethical issues relating to the activities of the internal auditor. The points of view expressed relate mainly to the public sector of Israel. Beyond the discussion of the specific issues against its unique Israeli background (Internal Audit Law), the discussion throws light on general problems that have not yet been solved.

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)

Eukaryotic cells are able to mount several genetically complex cellular responses to DNA damage. The yeast Saccharomyces cerevisiae is a genetically well characterized organism that is also amenable to molecular and biochemical studies. Hence, this organism has provided a useful and informative model for dissecting the biochemistry and molecular biology of DNA repair in eukaryotes.

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)