We first discuss some technical questions which arise in connection with the construction of undecidable propositions in analysis, in particular in connection with the notion of the normal form of a function representing a predicate. Then it is stressed that while a function f(x) may be computable in the sense of recursive function theory, it may nevertheless have undecidable properties in the realm of Fourier analysis. This has an implication for a conjecture of Penrose's which states that classical physics is (...) computable. (shrink)

We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elementary operations.

The emergence of modern sciences in the seventeenth century profoundly renewed our understanding of Nature. For the last three centuries new ideas of Nature have been continuously developed by theology, politics, economics, and science, especially the sciences of the material world. The situation is even more unstable today, now that we have entered an ecological mutation of unprecedented scale. Some call it the Anthropocene, but it is best described as a new climatic regime. And a new regime it certainly is, (...) since the many unexpected connections between human activity and the natural world oblige every one of us to reopen the earlier notions of Nature and redistribute what had been packed inside. So the question now arises: what will replace the old ways of looking at Nature? This book explores a potential candidate proposed by James Lovelock when he chose the name "Gaia" for the fragile, complex system through which living phenomena modify the Earth. The fact that he was immediately misunderstood proves simply that his readers have tried to fit this new notion into an older frame, transforming Gaia into a single organism, a kind of giant thermostat, some sort of New Age goddess, or even divine Providence. In this series of lectures on "natural religion", Bruno Latour argues that the complex and ambiguous figure of Gaia offers, on the contrary, an ideal way to disentangle the ethical, political, theological, and scientific aspects of the now obsolete notion of Nature. He lays the groundwork for a future collaboration among scientists, theologians, activists, and artists as they, and we, begin to adjust to the new climatic regime. (shrink)

Giordano Bruno.--La cena de le ceneri.--De la causa, principio e uno.--De l'infinito, universi e mondi.--Spaccio de la bestia trionfante.--De gli eroici furori.--Accusa e condanna di Bruno.--Nota bibliografica (p. 313-315).

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

A precursor to the hard problem of consciousness confronts nihilism. Like physicalism, nihilism collides with the first-personal fact of what perception and action are like. Unless this problem is solved, nature’s inclusion of conscious experience will remain, as Chalmers warns the physicalist, an “unanswered question” and, as Jacobi chides the nihilist, “completely inexplicable". One advantage of Kant’s Copernican turn is to dismiss the question that imposes this hard problem. We need not ask how nature is accompanied by the first-person standpoint (...) because “I think” is an apperceptive form of thinking that must be able to accompany any cognition of nature. Kant’s formal conception of apperception worries Fichte in his Nova Methodo lectures. This conception arguably cannot exhaust the ground of experience, for it does not show why we posit objects “at all". For Fichte, it is our agency that first opens a world of objects, viz., as subjects, means, ends, and obstacles. In what follows, I argue that, for Fichte, the I poses no hard problem because it collides exclusively with nihilistic views like Spinozism, which are refuted by a properly transcendental idealist conception of apperception, according to which the first-person standpoint is the absolute ground of our experience of nature. If transcendental idealism refutes nihilism, nature is no more explicable than that there is something it is like for me to perceive and act. In Section 1, I show why Kantian apperception is necessary for possible experience. In Section 2, I reconstruct Fichte’s argument that a modified conception of apperception refutes guises of nihilism, thereby solving the hard problem of consciousness. In Section 3, I suggest that transcendental idealism undermines Chalmers’ proposed solution to and Dennett’s dismissal of this problem. (shrink)

Ontological pluralism is the view that there are different ways to exist. It is a position with deep roots in the history of philosophy, and in which there has been a recent resurgence of interest. In contemporary presentations, it is stated in terms of fundamental languages: as the view that such languages contain more than one quantifier. For example, one ranging over abstract objects, and another over concrete ones. A natural worry, however, is that the languages proposed by the pluralist (...) are mere notational variants of those proposed by the monist, in which case the debate between the two positions would not seem to be substantive. Jason Turner has given an ingenious response to this worry, in terms of a principle that he calls ‘logical realism’. This paper offers a counter-response on behalf of the ‘notationalist’. I argue that, properly applied, the principle of logical realism is no threat to the claim that the languages in question are notational variants. Indeed, there seems to be every reason to think that they are. (shrink)

This chapter challenges Cantor’s notion of the ‘power’, or ‘cardinality’, of an infinite set. According to Cantor, two infinite sets have the same cardinality if and only if there is a one-to-one correspondence between them. Cantor showed that there are infinite sets that do not have the same cardinality in this sense. Further, he took this result to show that there are infinite sets of different sizes. This has become the standard understanding of the result. The chapter challenges this, arguing (...) that we have no reason to think there are infinite sets of different sizes. It begins with an initial argument against Cantor’s claim that there are infinite sets of different sizes and then proceeds, by way of an analogy between Cantor’s mathematical result and Russell’s paradox, to a more direct argument. (shrink)

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

Throughout his career, Schelling assigns knowledge of the absolute first principle of philosophy to intellectual intuition. Schelling's doctrine of intellectual intuition raises two important questions for interpreters. First, given that his doctrine undergoes several changes before and after his identity philosophy, to what extent can he be said to “hold onto” the same “sense” of it by the 1830s, as he claims? Second, given that his doctrine of intellectual intuition restricts absolute idealism to what he calls a “science of reason”, (...) which he says cannot prove the absolute’s existence, what other doctrine does he require in order to prove this? I will answer these questions by tracing the shifts in Schelling’s doctrine of intellectual intuition from the 1790s to the 1830s and drawing out its evolving methodological role within his science of intelligibility. (shrink)

Kant’s critique/doctrine distinction tracks the difference between a canon for the understanding’s proper use and an organon for its dialectical misuse. The latter reflects the dogmatic use of reason to attain a doctrine of knowledge with no antecedent critique. In the 1790s, Fichte collapses Kant’s distinction and redefines dogmatism. He argues that deriving a canon is essentially dialectical and thus yields an organon: critical idealism is properly a doctrine of science or Wissenschaftslehre. Criticism is furthermore said to refute dogmatism, by (...) which Fichte means Spinozism. Schelling repudiates Fichte’s position in his Philosophical Letters by reviving Kant’s distinction. First, ‘critique’ for Schelling names a canon that is valid for all systems—including Spinozism—and thus favours none—not even the Wissenschaftslehre. Second, Schelling coins ‘dogmaticism’ to refer to what Kant calls ‘dogmatism’: reason’s uncritical claim to doctrine. Hence, he says all systems—even Fichte’s—are susceptible to the ‘enthusiasm’ of mistaking themselves for doctrines or ‘objects of knowledge’, instead of subjectively valid ‘objects of freedom’. I reconstruct Schelling’s argument for reviving Kant’s distinction, while noting two consequences for German idealism. First, if criticism favours no system, a system’s origin cannot be an act of knowledge, e.g., intellectual intuition, but only an act of endorsement. Second, if dogmaticism entails enthusiasm, a system’s goal cannot be absolute knowledge, but only infinite striving. Hence, by retrieving Schelling’s notion of dogmaticism, we can both gain a better understanding of the Letters and register the impact of a core Kantian distinction on the German idealist project. (shrink)

In Intuition et idéalités: Phénoménologie des objets mathématiques (2020), Dominique Pradelle questioned the nature of mathematical knowledge–the status of math.

Which entities should be accepted as part of the furniture of the world, and which not? What are pseudo-objects, if they are not properly objects? This collection explores the answers given to these questions by some key philosophers throughout the 20th century. It brings together essays by leading scholars on a subject of central importance to both metaphysics and the history of philosophy.".

In the last years, a theological turn had a pervasive influence in the reception of Carl Schmitt’s writings. According to this view, his thought has a strong, substantial religious foundation. With regards to understanding not only Schmitt’s position but also his current influence in authoritarian countries, this essay argues that this interpretation is misleading and proposes a different and comprehensive analysis of Schmitt’s concept of political theology that replaces it in a political-legal framework. Against the theological reading, it argues that (...) Schmitt’s concept of “political theology” refers to his own conception of legal theory as an attempt to relegitimize authority in a secular context. As “political theology,” this legal theory is designed to overcome normativism and parliamentarism by “substantializing” the legal form. Using Schmitt’s post-1933 works as an example, the essay shows that, as theology translates faith into a written doctrine, legal theory must, according to Schmitt, substantialize the legal form by translating the political idea into jurisprudence. Hence, this article concludes that Schmitt’s theory might be described as “political theology” but only in a formal, ideological sense. It is part of an authoritarian theory that is not religious but uses theology to revive an appearance of absolute legitimacy. (shrink)

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

Fichte argues that the conclusion of Kant’s transcendental deduction of the categories is correct yet lacks a crucial premise, given Kant’s admission that the metaphysical deduction locates an arbitrary origin for the categories. Fichte provides the missing premise by employing a new method: a genetic deduction of the categories from a first principle. Since Fichte claims to articulate the same view as Kant in a different, it is crucial to grasp genetic deduction in relation to the sorts of deduction that (...) Kant offers. I propose to interpret genetic deduction as the simultaneous fulfillment of two tasks: answering the question quid facti by deriving the categories from the I and answering the question quid juris by establishing our entitlement to the categories as conditions of experience. While the second task represents Fichte’s agreement with Kant’s transcendental deduction, the first reflects his correction of Kant’s metaphysical deduction. (shrink)

In the Freedom essay, Schelling charges that (1) idealism fails to grasp human freedom’s distinctiveness and that (2) this failure undermines idealism's attempt to refute pantheism, as exemplified by Spinoza. This raises two questions, which I will answer in turn: what, for Schelling, is distinctive of human freedom; and how does the idealists’ failure to grasp it render them unable to refute pantheism? To answer these questions, I will reconstruct Schelling’s argument that freedom has the distinctness of being the unconditioned (...) condition of the world’s intelligibility. My reconstruction will illustrate how Schelling’s notion of freedom as primal will grounds the alleged primacy of practical reason as Kant and Fichte conceive it. I will then consider three objections to Schelling’s argument. Throughout, I will develop the Schellingian idea that freedom is enacted in an unprethinkable decision that cannot be anticipated by any law or principle. (shrink)

General-elimination harmony articulates Gentzen’s idea that the elimination-rules are justified if they infer from an assertion no more than can already be inferred from the grounds for making it. Dummett described the rules as not only harmonious but stable if the E-rules allow one to infer no more and no less than the I-rules justify. Pfenning and Davies call the rules locally complete if the E-rules are strong enough to allow one to infer the original judgement. A method is given (...) of generating harmonious general-elimination rules from a collection of I-rules. We show that the general-elimination rules satisfy Pfenning and Davies’ test for local completeness, but question whether that is enough to show that they are stable. Alternative conditions for stability are considered, including equivalence between the introduction- and elimination-meanings of a connective, and recovery of the grounds for assertion, finally generalizing the notion of local completeness to capture Dummett’s notion of stability satisfactorily. We show that the general-elimination rules meet the last of these conditions, and so are indeed not only harmonious but also stable. (shrink)

In some of the Aristotelian accounts, Parmenides’ thesis is construed in opposition to the philosophy of nature; on the other hand, he is also depicted, in a different context, as a cosmologist, to whom the Stagirite (and a long tradition afterwards, ending with Simplicius) ascribes a theory of becoming and its principles. In this paper, I exhibit and analyse the relevant passages from Physics I 1-3, Metaphysics I 3 and 5 and On generation and corruption I 3, providing an interpretation (...) that aims to solve the apparent paradox, making sense of the information we can gather from Aristotle’s and Simplicius’ testimonies. Eventually, I propose a construal of the Two Ways of fr. 2 with an emphasis on the predicative reading of einai, which could hint at the Parmenidean approach to cosmology that runs in parallel with the argument on Being. (shrink)

This vibrant bilingual edition, annotated by celebrated Bruno scholar Ingrid D. Rowland, features the text in its original Italian alongside an elegant, accurate English translation.

When reading contemporary theories of distributive justice, one could easily get the impression that questions of fiscal design are normatively speaking merely instrumental for realizing the distributive ideal. Once the overall conception of justice is settled upon, questions of how the state should arrange its institutions and policies are settled if they effectively and efficiently promote the preferred distribution. I argue that such pure instrumentalism is mistaken in the context of fiscal policy. As a result, there is nothing problematic or (...) morally arbitrary about accepting domain-specific principles of fiscal justice. (shrink)

Der soziotechnische Wandel bringt neue Phänomene des Zufalls hervor, die sich den üblichen Strategien des Umgangs mit Risiken und Unsicherheit entziehen. Diese Akzidenzphänomene sind prinzipiell unvorhersehbar und in ihrer komplexen Effektgesamtheit jenseits von Kalkulation und Antizipation. Eine allgemeine Verzukünftigung unseres Weltbezuges mit spezifischen weitreichenden Problemen ist die Folge und lässt klassische Agenturen des Risikomanagements und der Unsicherheitsbewältigung an ihre Leistungsgrenzen stoßen. Bruno Gransche zeigt, dass Philosophie und Zukunftsforschung gemeinsam großes Potenzial aufweisen, hier zu helfen.

Disagreements about scientific ontology have frequently been reconstructed as the result of a dispute between rival epistemic stances. In this paper, (i) we characterize some of these disagreements as deep disagreements. In addition, we show that deep disagreements about scientific ontology can arise not only from the adoption of different epistemic stances, but also between positions that fall within the same stance. The development of this point allows us, in turn, to establish a distinction between types of deep disagreement and (...) to explore the possibility that there are differences of degree between them. (shrink)

... Le figure del terzo legislatore e del terzo giudice costituiscono la garanzia che la tutela dei deboli non renda debole né il dovere né il diritto, ma ne fortifichi la consapevolezza responsabile in ognuno di noi, mostrando il significato giuridico del ‘dono di senso’, nucleo, nella mia interpretazione dell’intenso magistero di Bruno Romano. (Dalla Presentazione di L. Avitabile).

This paper argues that we should solve paradoxes for propositions (such as the Russell–Myhill paradox) in essentially the same way that we solve Russellian paradoxes for sets. That is, the standard, iterative approach to sets is extended to include properties, and then the resulting hierarchy of sets and properties is used to construct propositions. Propositions on this account are structured in the sense of mirroring the sentences that express them, and they would seem to serve the needs of philosophers of (...) language and metaphysicians who rely on such propositions. The resulting account has limitations, comparable to those faced by the iterative approach to sets, but it is argued to be in important ways preferable to others that have been proposed. (shrink)

In a series of papers, 137–158; 1994, Midwest Studies in Philosophy, 23, 61–74, 1999) Fine develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points (...) in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the second-order quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine’s principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine’s various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki’s main objection to Fine’s theory. In the appendix we present proofs of the inexpressibility results of Section 6. (shrink)

It is commonly assumed that blameworthiness is epistemically constrained. If one lacks sufficient epistemic access to the fact that some action harms another, then one cannot be blamed for harming. Acceptance of an epistemic condition for blameworthiness can give rise to a worry, however: could agents ever successfully evade blameworthiness by deliberately stunting their epistemic position? I discuss a particularly worrisome version of such epistemic shirking, in which agents pre-emptively seek to avoid access to potentially morally relevant facts. As Roy (...) Sorensen and Jan Willem Wieland have argued, we seem to be faced with a potentially troubling regress when trying to explain what goes wrong in such situations. I argue that the solution to this so-called Shirker Problem is not to be found in complicated and demanding anti-shirking-principles with universal scope and potentially self-reflexive content. Instead, careful consideration of the necessary motivational make-up of genuine shirkers reveals their ignorance to lack the necessary depth to be exculpatory. Since shirkers by definition react to the possibility of the revelation of morally relevant facts with acts of epistemic self-limitation, they necessarily prove guilty of a form of culpable moral recklessness. Epistemic shirking thus does not pose a worrisome problem for ethical theory. (shrink)