The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on (...) meaning-theoretic considerations. The second is that the intuitionist's chief objection to the classical mathematician's use of logic does not center on the use of particular logical principles (in particular, the law of excluded middle and its ilk). Rather on the role the classical mathematician assigns (or at least extends) generally (i.e. regardless of the particular principles used) to the use of logic in the production mathematical proofs. Thus, the intuitionist critique of logic that we shall be presenting is far more radical than that which has commonly been presented. -/- Concerning the second, more general, theme, my claim is this: some restriction of the role of logical inference in mathematical proof such as that mentioned above is necessary if one is to account for the seeming difference in the epistemic conditions of provers whose reasoning is based on genuine insight into the subject-matter being investigated, and would-be provers whose reasoning is based not on such insight, but rather on principles of inference which hold of every subject-matter indifferently. (shrink)

The work of the French Lithuanian Jewish philosopher, Emmanuel Levinas, describes a perceptive rethinking of the possibility of concrete acts of goodness in the world, a rethinking never more necessary than now, in the wake of the cruel realities of the twentieth century—ten million dead in the First World War, forty million dead in the Second World War, Hiroshima, Nagasaki, the Soviet gulags, the grand slaughter of Mao’s “Great Leap Forward,” the pointless and gory Vietnam War, the Cambodian self-genocide (...) and many an attempted extermination from the face of the earth of entire nations of indigenous peoples. The list of horrors goes on and on—daily holocausts that do not distinguish between the civilian and the soldier, the guilty and the innocent, those deserving of life and those less deserving. (shrink)

Two sources of possible disagreement in bioethics may be associated with pessimism about what bioethics can achieve. First, pluralism implies that bioethics engages with interlocutors who hold divergent moral beliefs. Pessimists might believe that these disagreements significantly limit the extent to which bioethics can provide normatively robust guidance in relevant areas. Second, the interdisciplinary nature of bioethics suggests that interlocutors may hold divergent views on the nature of bioethics itself—particularly its practicality. Pessimists may suppose that interdisciplinary disagreements could frustrate (...) the goals of bioethics. In this article, I explore how wonder may alleviate the concerns of the first group of pessimists regarding problems associated with pluralism, provided that we are willing to accept some interdisciplinary frustrations. Then, I invite readers of this issue of The Journal of Medicine & Philosophy to test these intuitions by considering the role of wonder in these articles. (shrink)

Attributed to Alexander of Aphrodisias -the leading ancient commentator on Aristotle -the Quaestiones exemplify the process through which Aristotle's thought was organized and came to be interpreted as "Aristotelianism." This volume of R.W. Sharples's translation, together with his earlier translation of Quaestiones 1.1-2.15, makes the Quaestiones available in its entirety for the first time in a modern language. The Quaestiones are concerned with problems of physics and metaphysics, psychology and divine providence. Readers interested in Aristotle's psychological views will find (...) the second half of the Quaestiones particularly valuable. Ten of the problems discussed involve issues raised in Aristotle's On the Soul, including the unity of apperception and the transition from first to second actuality in the act of contemplation. An additional twelve problems relate to aspects of physical theory such as infinity, necessity, and potentiality. Quaestio 2.21 concerns divine providence and helps supplement our knowledge of Alexander's position. A study of the Quaestiones also suggests how interpretations of Aristotle were influenced by doctrines of Hellenistic philosophy. Translated first into Arabic and then into Latin, excerpts from the Quaestiones played a significant role in the transmission of ancient Greek philosophy to the medieval world. (shrink)

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

On 11 September 2019, the verdict was read in the first prosecution of a doctor for euthanasia since the Termination of Life on Request and Assisted Suicide Act of 2002 was installed in the Netherlands. The case concerned euthanasia on the basis of an advance euthanasia directive for a patient with severe dementia. In this paper we describe the review process for euthanasia cases in the Netherlands. Then we describe the case in detail, the judgement of the Regional Review (...) Committees for Termination of Life on Request and Euthanasia and the judgement of the medical disciplinary court. Both the review committees and the disciplinary court came to the conclusion there were concerns with this case, which mainly hinged on the wording of the AED. They also addressed the lack of communication with the patient, the absence of oral confirmation of the wish to die and the fact that the euthanasia was performed without the patient being aware of this. However, the doctor was acquitted by the criminal court as the court found she had in fact met all due care criteria laid down in the act. We then describe what this judgement means for euthanasia in the Netherlands. It clarifies the power and reach of AEDs, it allows taking conversations with physicians and the testimony of the family into account when interpreting the AED. However, as a practical consequence the prosecution of this physician has led to fear among doctors about prosecution after euthanasia. (shrink)

We investigate the logical structure of intuitionistic Kripke-Platek set theory , and show that the first-order logic of is intuitionistic first-order logic IQC.

Is there, today," asks Jacques Derrida, "another 'question of religion'?" Derrida's writings on religion situate and raise anew questions of tradition, faith, and sacredness and their relation to philosophy and political culture. He has amply testified to his growing up in an Algerian Jewish, French-speaking family, to the complex impact of a certain Christianity on his surroundings and himself, and to his being deeply affected by religious persecution. Religion has made demands on Derrida, and, in turn, the study of religion (...) has benefited greatly from his extensive philosophical contributions to the field. Acts of Religion brings together for the first time Derrida's key writings on religion, along with two new essays translated by Gil Anidjar that appear here for the first time in any language. These texts are organized around the secret holding of links between the personal, the political, and the theological. In these texts, Derrida's reflections on religion span from negative theologyto the limits of reason and to hospitality. Acts of Religion will serve as an excellent introduction to Derrida's remarkable contribution to religious studies. (shrink)

Acts of Religion, compiled in close association with Jacques Derrida, brings together for the first time a number of Derrida's writings on religion and questions of faith and their relation to philosophy and political culture. The essays discuss religious texts from Jewish, Christian, and Muslim traditions, as well as religious thinkers such as Kant, Levinas, and Gershom Scholem, and comprise pieces spanning Derrida's career. The collection includes two new essays by Derrida that appear here for the first time (...) in any language, as well as a substantial introduction by Gil Anidjar that explores Derrida's return to his own "religious" origins and his attempts to bring to light hidden religious dimensions of the social, cultural, historical, and political. (shrink)

This paper constructs models of intuitionistic set theory in suitable categories. First, a Basic Intuitionistic Set Theory (BIST) is stated, and the categorical semantics are given. Second, we give a notion of an ideal over a category, using which one can build a model of BIST in which a given topos occurs as the sets. And third, a sheaf model is given of a Basic Intuitionistic Class Theory conservatively extending BIST. The paper extends the results in [2] by introducing (...) a new and perhaps more natural notion of ideal, and in the class theory of part three. (shrink)

In this paper we will develop a first-order anti-intuitionistic logic withoutand with paraconsistent apartness. We will give a system of Hilbert-type counteraxioms, that we show to be correct and complete with respect to a deictic Kripkesemantics. Also we will illustrate some examples about objects being apart and notapart in some possible world.

Let us define the intuitionistic part of a classical theory T as the intuitionistic theory whose proper axioms are identical with the proper axioms of T. For example, Heyting arithmetic HA is the intuitionistic part of classical Peano arithmetic PA. It's a well-known fact, proved by Heyting and Myhill, that ZF is identical with its intuitionistic part. In this paper, we mainly prove that TT, Russell's Simple Theory of Types, and NF, Quine's "New Foundations," are not equal to their intuitionistic (...) part. So, an intuitionistic version of TT or NF seems more naturally definable than an intuitionistic version of ZF. In the first section, we present a simple technique to build Kripke models of the intuitionistic part of TT (with short examples showing bad properties of finite sets if they are defined in the usual classical way). In the remaining sections, we show how models of intuitionistic NF 2 and NF can be obtained from well-chosen classical ones. In these models, the excluded middle will not be satisfied for some non-stratified sentences. (shrink)

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is (...) equivalent to a standard translation of an intuitionistic propositional formula over the class of intuitionistic Kripke models iff it is invariant with respect to asimulations between intuitionistic models. (shrink)

This is Dr. Roberto Assagioli's second book on the psychological system he formulated known as Psychosynthesis. It continues where his first book left off and delves into the important process of willing as a psychological function based on a higher self rather on guilt or determination as in the Victorian concept of the will.

This contribution reconstructs and assesses Gideon Yaffe’s claims in his book Attempts about what constitutes an attempt, what can count as evidence that an attempt has been made, whether abandonment is a genuine defense, and whether attempts should be punished less severely than completed crimes. I contrast Yaffe’s account of being motivated by an intention and the completion of an attempt in terms of the truth of the completion counterfactual with an alternative picture of attempts as temporally extended decision trees (...) that are complete insofar as the agent has progressed toward the final act in the tree. I suggest that this alternative scalar conception of attempt may provide a more plausible account of the defense of abandonment. I also raise questions about whether Yaffe has provided an adequate justification of his mix of luck skepticism about censure and luck realism about punishment. (shrink)

ABSTRACT In 1933 Gödel introduced an axiomatic system, currently known as S4, for a logic of an absolute provability, i.e. not depending on the formalism chosen ([God 33]). The problem of finding a fair provability model for S4 was left open. The famous formal provability predicate which first appeared in the Gödel Incompleteness Theorem does not do this job: the logic of formal provability is not compatible with S4. As was discovered in [Art 95], this defect of the formal (...) provability predicate can be bypassed by replacing hidden quantifiers over proofs by proof polynomials in a certain finite basis. The resulting Logic of Proofs enjoys a natural arithmetical semantics and provides an intended provability model for S4, thus answering a question left open by Gödel in 1933. Proof polynomials give an intended semantics for some other constructions based on the concept of provability, including intuitionistic logic with its Brouwer- Heyting- Kolmogorov interpretation, ?-calculus and modal ?-calculus. In the current paper we demonstrate how the intuitionistic propositional logic Int can be directly realized by proof polynomials. It is shown, that Int is complete with respect to this proof realizability. (shrink)

This paper discusses the thesis defended by Edith Stein that certain acts can be attributed to the State. According to Stein, the State is a social structure characterized by sovereignty. As such, it is responsible for the production, interpretation, and application of law. These tasks require the performance of acts, most of which are what Stein calls “social acts” like enactments and orders. For Stein, the acts in question are made by the organs of the State, but in the name (...) of the State, and are thus attributed to the State via a relation of representation. In the first section, the paper presents Stein’s thesis that the sovereignty of the State entails a series of legal prerogatives, which in turn result in various social acts being ascribed to the State through its representatives. In the second section, the paper critically discusses Stein’s views, notably her theory of representation, and her account of the nature of the State, while emphasizing its most interesting aspects, namely, its fine-grained analyses of the various acts that are attributed to the State. (shrink)

Speaker’s meaning is the act at the core of meaning shift, where meaning can be the very act or its output. What are its conditions, which intentions direct it? What’s its mechanics? I will give a first answer to the first question. Then, I will discuss the mechanics of speaker’s meaning, as well as meaningful links different from speaker’s meaning. This will bring me to surmise a second answer to the first question. Along the way, I will (...) compare the act of meaning with other acts. In closing, I will try a limited elucidation of the notion of intention, which I use throughout. On these issues there is the conspicuous tradition of studies, originating from the late Paul Grice, to confront us with. Rather naturally, I will move from it. But I am interested in the notion of speaker’s meaning and its place in an analysis of meaning, and not in that tradition as such. The notion of speaker’s meaning, I think, is relevant even for those who do not subscribe to a Gricean approach to meaning, as I don’t. (shrink)

On the base of the classical logic the connectives of necessity and possibility have the equivalent positions in this sense that each of them is definable by the other one. The consequence of this fact is the possibility to define of the both modalities using the connective of identity. Thus, the connective of propositional identity defining the congruence of the propositional language has become the base of the reconstruction of necessity operator in some modal systems. Already in 1957 Greniewski [9] (...) obtained system S5 on the base of the propositional calculus with identity. Next, Cresswell [3], [4] reconstructed S4 and S5 in a similar way. Systematic investigations of this problem were undertaken by Suszko within the broader frame of SCI programme [16], [17], [18]. The connections between modal connectives and the connective of identity settle some philosophical sense of both modalities. Something is necessary, if it is identical with a logical truth. If something is different from the negation of some logical truth, it is possible. It is however, the “ontological” characteristics typical for modalities defined on the base of the classical logic. The settling of similar connections between intuitionistic identity and intuitionistic modalities uncover the philosophical sense of the “epistemic” necessity and possibility. Unfortunately, the symmetry between the classical and intuitionistic case is not entire. The acceptance of both equalities: = ¬ ¬ and = ¬ ¬, in the intuitionistic logic yields the classical versions of both modalities . Thus, there is a problem with defining the connective of intuitionistic possibility by the connective of identity. In Sections 2 and 3 two “partial” solutions of the mentioned problem are presented. They are “partial” because the connective of possibility has undesirable properties. The second solution yields the strengthening of the necessity connective, too. The main aim of this paper is obtained in Section 5, where a definition of the intuitionistic possibility is given. This definition uses the new connective of nonidentity, presented in Section 4. The new approach bases on the idea that some connectives like implication, negation, identity, necessity are “Heyting's” ones. The case of possibility is different. Together with coimplication, weak negation, and nonidentity, possibility belongs to the so-called “Brouwerian” connectives. The connectives of the first kind have such property that in Kripke's style semantics their interpretations in each point of this semantics are related to the interpretations in next points. In the case of the “Brouwerian” connectives the interpretations in each point depend on the interpretations in previous points. In this sense, “Heyting's” connectives are interpreted from the point of view of the future, while the interpretations of the “Brouwerian” connectives are from the point of view of the past. The relations between nonidentity and possibility connectives allow to say that in temporal semantics something is possible in the moment a, if before a there was such moment b in which it was different from the contradiction. Thus, “something is possible” does not mean that it held once in the past. A broader philosophical remarks about the nature of intuitionistic possibility are contained in two Comments in the last Section. (shrink)

The paper proves refined feasibility properties for the disjunction property of intuitionistic propositional logic. We prove that it is possible to eliminate all cuts from an intuitionistic proof, propositional or first-order, without increasing the Horn closure of the proof. We obtain a polynomial time, interactive, realizability algorithm for propositional intuitionistic proofs. The feasibility of the disjunction property is proved for sequents containing Harrop formulas. Under hardness assumptions for NP and for factoring, it is shown that the intuitionistic propositional calculus (...) does not always have polynomial size proofs and that the classical propositional calculus provides a superpolynomial speedup over the intuitionistic propositional calculus. The disjunction property for intuitionistic propositional logic is proved to be P-hard by a reduction to the circuit value problem. (shrink)

This volume explores African philosophies’ expression of transitional acts where thought interacts with history and proposes solutions to problems. Influential thinkers from both sides of the Atlantic engage with the realm of criticism and imagination, public spaces in Africa, and the relationship between historical politics and poetics.

This essay explores the historiographic and ethnographic valence of video in Indonesia since 1998, against the backdrop of transition from an authoritarian to a neoliberal regime, and the concurrent renewal of the country’s public sphere. The first section takes Joshua Oppenheimer’s controversial film The Act of Killing (2012) as exemplary of the moving image’s purchase on national trauma, emphasizing its role in the production (and perversion) of official history. The second section concerns the state of video discourse in Indonesia (...) as reflected in a conference held in Yogyakarta in 2011, addressing the diversity of contemporary video practices and situating them in local art and media histories. In a third and final section, we return to the epistemological quandaries raised by Oppenheimer’s film, mooting video’s capacity as a means of reconciliation with the past – a reconciliation that would seem to require both the documentary and a ‘revelatory’ function of the image. (shrink)

In this article I discuss T. Wartenberg’s claim that the film The Act of Killing, which has as protagonists and quasi co-authors perpetrators of the 1965–66 Indonesian massacre, ‘confirms’ and ‘supplements’ Arendt’s ‘banality of evil’ thesis. I argue for a more moderate version of the first part of this claim and expand upon the second. Thus, I suggest that the film gives us clues to articulate Arendt’s thesis with theories of alienation, hence also with Marxist theorizing. Central here is (...) the idea that deficient sensibility, which, according to Wartenberg’s claim, supplements Arendt’s idea of ‘thoughtlessness’, is related to an alienating process within which cinema plays a prominent role. Thus, my argument revolves around the premise that in the film the question of mass evil-doing is intertwined with positing its own medium as an object of reflection, revealing cinema as carrying a contradictory potential. The critical upholding of Arendt’s thesis that the film enables also concerns the relationship of ‘banality’ to ideological motivation, a rather problematic issue in Arendt’s thesis. The film, I argue, suggests that ‘banality’ does not necessarily exclude ideological zealotry. (shrink)

Odysseus’ Apologue, Books 9 to 12 of the “Odyssey”, is characterized by a substantial repetition of acts/scenes of eating/feasting. The following analysis serves, firstly, as a structural indication of the pervasiveness of eating acts to several episodes in Odysseus’ internal narrative, observing parallels between certain episodes which have not as yet been noticed. Secondly, I illustrate how acts of eating come to connote secondary associations in the Apologue, oscillating between the danger of destruction and of delay for the Ithacan travellers. (...) These connotations of eating ultimately respond both to Odysseus’ situation in Scheria and to the threat of the suitors in Ithaca. (shrink)

We use the language of categorical logic to construct generic saturated models of intuitionistic theories. Our main technique is the thorough study of the filter construction on categories with finite limits, which is the completion of subobject lattices under filtered meets. When restricted to coherent or Heyting categories, classifying categories of intuitionistic first-order theories, the resulting categories are filtered meet coherent categories, coherent categories with complete subobject lattices such that both finite disjunctions and existential quantification distribute over filtered meets. (...) Such categories naturally embed into Grothendieck toposes which then contain saturated models of the theory we started with. (shrink)

Some say that consent is essentially just a state of mind. Others say it is essentially just a communication. Many say it is both. I say it is neither. Instead it is an act, or rather a pair of acts—an internal mental act in the first instance, an external performative act in the second. Each of those acts is an act of commitment, intrapersonally in the first case and interpersonally in the second. The content of the commitment is, (...) familiarly enough, to give permission to someone else to do something that it would be wrong for them to do without your permission. The novelty lies in seeing consent as an act of commitment in those two dimensions and in seeing those as commitments that persist until and unless undone by an act of a similar sort. (shrink)

The concept of negation is the central operator in distinguishing between historical change and natural evolution, which is constitutive of modern thinking. The crisis of this distinction is therefore the »crisis of negation « (Alain Badiou). The text examines this crisis by first considering Hegel’s concept of »determinate negation« and its impact on the modern understanding of revolution and then discusses two possible alternative understandings of negation: abstract negation (Luhmann) and infinite negation (Agamben).

Das Konzept der Negation ist der zentrale Operator bei der Unterscheidung zwischen historischem Wandel und natürlicher Evolution, welche grundlegend für das moderne Denken ist. Die Krise dieser Abgrenzung ist somit auch eine »Krise der Negation« (AlainBadiou). Der vorliegende Text untersucht die Krise, indem er zuerst Hegels Konzept der »bestimmten Negation« und deren Auswirkungen auf das moderne Verständnis von Revolution beleuchtet und erörtert im Anschluss zwei mögliche Alternativen, wie Negation noch verstanden werden kann: als abstrakte Negation (Luhmann) und als endlose Negation (...) (Agamben). The concept of negation is the central operator in distinguishing between historical change and natural evolution, which is constitutive of modern thinking. The crisis of this distinction is therefore the »crisis of negation « (Alain Badiou). The text examines this crisis by first considering Hegel’s concept of »determinate negation« and its impact on the modern understanding of revolution and then discusses two possible alternative understandings of negation: abstract negation (Luhmann) and infinite negation (Agamben). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Oberlin's First Philosopher* EDWARD H. MADDEN ASA MAHANWAS THE FroST president of Oberlin College (1835-50) and professor of moral philosophy--the usual pattern during these years of "academic orthodoxy" when Christianity was purveyed in American colleges as the philosophy.1 The orthodox professors argued philosophical points very little but rather "presented" and "illustrated" their basic truths. 2 In some ways Mahan fit the stereotype. He did not always probe deeply (...) into questions or always offer reasons for his conclusions. His books are full of phrases like "it could not be otherwise", "no one, it is presumed, will deny that", "it is intuitively evident", "everyone cannot but know", and so on. And he frequently cited other philosophers, as well as the Scriptures, as "authorities." He even cited lengthy passages from Jonathan Edwards whenever he could, even though he differed with Edwards on almost every major point f In more important ways Mahan, however, does not fit the stereotype. Unlike Francis Wayland and most of the other academic orthodoxy before 1850, he had read, and been influenced by, German and French philosophers as well as the Scottish realists. Mahan was particularly influenced by Kant and Cousin. An astute contemporary reviewer remarked that Mahan, like Cousin, was an eclectic. "His eclecticism degenerates sometimes into the merely aggressive, and he delights occasionally in strange and incongruous combinations of Kant, Coleridge, Cousin and himself, but showing here and there great vigor and acuteness, and very considerable philosophical ability." a The aggressiveness of Mahan also sets him apart from the rest of the orthodoxy. He was too fiery by temperament to pass up polemics and hence got to the heart of some basic philosophical problems. He attacked the Edwardian doctrine of determinism and was led, by the vigor of his attack, into what many nineteenth-century Christians considered heresy3 He attacked utilitarianism in all its forms, including Paley's, in a far more consistent and thorough fashion than Francis Wayland and the other followers of Scottish realism and English intuitionism. And first and foremost he vigorously attacked the moral philosophy of his colleague Charles Grandison Finney, famous evangelist, professor of theology, and president-to-be of Oberlin. The spiritedness of his criticisms frequently aroused the ire of his Oberlin colleagues, but the spirited- *Research for some of the material in this paper was made possible by a grant from the Penrose Fund of the AmericanPhilosophicalSociety. ~Cf. Herbert W. Schneider, A History o] American Philosophy (2nd ed.; New York: Columbia University Press, 1963),pp. 195-220; and Joseph L. Blau, Men and Movements in American Philosophy (New York: Prentice-Hall, Inc., 1952). 2Cf. E. H. Madden, "Francis Wayland and the Limits of Moral Responsibility," Proceedings o] the American Philosophical Bociety, Vol. 106 (1962),pp. 348-359. *Quoted by R. S. Fletcher in his History o] Oberlin College (Oberlin, Ohio, 1943),II, 701. 4Fletcher, I, 223-231. [57] 58 HISTORY OF PHILOSOPHY hess fortunately was accompanied by a "considerable philosophical ability" that merits close attention. I Mahan's critique of Edwards appears in his Doctrine o] the Will, first published in 1844. According to Mahan, "Edwards stands convicted of a fundamental error in philosophy, an error which gives form and character to his whole workmthe confounding of the Will with the Sensibility, and thus confounding the characteristics of the phenomena of the former faculty with those of the phenomena of the latter." 5 The trouble is that the whole of Edwards' work "is constructed without an appeal to Consciousness, the only proper and authoritative tribunal of appeal in the case." 8 If we attend carefully to consciousness, said Mahan, we can distinguish volition from the strongest desire and hence must distinguish between the separate faculties of will as personal activity and sensation as mere passive impression. The latter does not "act," it merely "suffers." The will is the moving force in life and unless it can be shown that there is some necessary connection between will and sensation--which, in fact, cannot be done--then it follows that the will is free, that is, the source of "personal activity." Mahan's rejection of universal determinism, of course, entailed the rejection of the Calvinistic doctrine of election... (shrink)

This essay concerns Heidegger’s assertion that the biography of the poet is unimportant when interpreting great works of poetry. I approach the question in three ways. First, I consider its merits as a principle of literary interpretation and contrast Heidegger’s view with those of other Trakl interpreters. This allows me to clarify his view as a unique variety of non-formalistic interpretation and raise some potential worries about his approach. Second, I consider Heidegger’s view in the context of his broader (...) philosophical project. Viewed this way, Heidegger’s decision to neglect the poet’s biography seems quite reasonable and consistent with his inquiry into the being of language. Finally, I consider Heidegger’s suggestion that Trakl is a kind of mad genius. I recast this paradigmatic figure in terms of what I call the ‘wretched prophet’ and consider some ways in which its appeal sheds light on the crisis of modernity and the aestheticization of politics. (shrink)

We define a class of first-order formulas $\mathsf{P}^{\ast }$ which exactly contains formulas $\varphi$ such that satisfaction of $\varphi$ in any classical structure attached to a node of a Kripke model of intuitionistic predicate logic deciding atomic formulas implies its forcing in that node. We also define a class of $\mathsf{E}$-formulas with the property that their forcing coincides with their classical satisfiability in Kripke models which decide atomic formulas. We also prove that any formula with this property is an (...) $\mathsf{E}$-formula. Kripke models of intuitionistic arithmetical theories usually have this property. As a consequence, we prove a new conservativity result for Peano arithmetic over Heyting arithmetic. (shrink)

Transcription is a fundamental cellular process and the first step in gene regulation. Although RNA polymerase (RNAP) is highly processive, in growing cells the progression of transcription can be hindered by obstacles on the DNA template, such as damaged DNA. The authors recent findings highlight a trade‐off between transcription fidelity and DNA break repair. While a lot of work has focused on the interaction between transcription and nucleotide excision repair, less is known about how transcription influences the repair of (...) DNA breaks. The authors suggest that when the cell experiences stress from DNA breaks, the control of RNAP processivity affects the balance between preserving transcription integrity and DNA repair. Here, how the conflict between transcription and DNA double‐strand break (DSB) repair threatens the integrity of both RNA and DNA are discussed. In reviewing this field, the authors speculate on cellular paradigms where this equilibrium is well sustained, and instances where the maintenance of transcription fidelity is favored over genome stability. (shrink)

We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers.

Most philosophers assume (often without argument) that belief is a mental state. Call their view the orthodoxy. In a pair of recent papers, Matthew Boyle has argued that the orthodoxy is mistaken: belief is not a state but (as I like to put it) an act of reason. I argue here that at least part of his disagreement with the orthodoxy rests on an equivocation. For to say that belief is an act of reason might mean either (i) that it’s (...) an actualization of its subject’s rational capacities or (ii) that it’s a rational activity (hence, a certain kind of event). And, though belief is not an act of reason in the second sense, it may nonetheless be one in the first: it may be a static actualization of its subject’s rational capacities. (shrink)

It is one of the crucial insights of pragmatism that our judging is itself a discursive practice. Our judgments are normatively determined performances for which we are responsible. Therefore, judgments are a species of action. For in both actions and judgments, we subject ourselves and others to justifiable norms. Since these insights can already be found in Hegel, Hegel is now often interpreted as a champion of pragmatism. Hegel’s logic is thereby mainly understood as the continuation of the Kantian project (...) of transcendental philosophy. Based upon this pragmatist interpretation of Hegel, the paper reads F. H. Jacobi’s philosophy as an alternative pragmatism which is explicitly founded on our life praxis rather than our practice of judgment. (shrink)

We consider formal theories synonymous with various free categories . Their Lindenbaum algebras may be described as the lattices of subobjects of a terminator. These theories have intuitionistic logic. We show that the Lindenbaum algebras of second order and higher order arithmetic , and set theory are not isomorphic to the Lindenbaum algebras of first order theories such as arithmetic . We also show that there are only five kernels of representations of the free Heyting algebra on one generator (...) in these Lindenbaum algebras. (shrink)

We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and (...) formal logics, respectively. We also show that, for most “natural” first-order modal logics, the two-variable fragment with a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable, regardless of whether we consider semantics with expanding or constant domains. These include all sublogics of QKTB, QGL, and QGrz—among them, QK, QT, QKB, QD, QK4, and QS4. (shrink)

We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of practically all standard modal logics like K, K4, GL, S4, S5, K4.1, S4.2, GL.3, etc.). For many quantified modal (...) logics, including those in the standard nomenclature above, even the monadic two-variable fragments turn out to be undecidable. (shrink)

Research on future-oriented mental time travel (FMTT) is highly active yet somewhat unruly. I believe this is due, in large part, to the complexity of both the tasks used to test FMTT and the concepts involved. Extraordinary care is a necessity when grappling with such complex and perplexing metaphysical constructs as self and time and their co-instantiation in memory. In this review, I first discuss the relation between future mental time travel and types of memory (episodic and semantic). I (...) then examine the nature of both the types of self-knowledge assumed to be projected into the future and the types of temporalities that constitute projective temporal experience. Finally, I argue that a person lacking episodic memory should nonetheless be able to imagine a personal future by virtue of (a) the fact that semantic, as well as episodic, memory can be self-referential, (b) autonoetic awareness is not a prerequisite for FMTT, and (c) semantic memory does, in fact, enable certain forms of personally-oriented FMTT. (shrink)

Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, (...) and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. (shrink)