A young scientist and mathematician explores the mystery and complexity of human thought processes from an interdisciplinary point of view.

We investigate the “unprovability of unprovability”. Given a sentence P and a fixed base theory T, the unprovability of P is the sentence “\ ”. We show that the unprovability of an unprovable true sentence can be “hard to prove”.

The problem of eternal separation is the problem of explaining how someone could be happy in heaven while knowing that his beloved is in hell. Some argue that this problem is insoluble, while others try to solve it through the lover, the beloved, or the love between them. I argue that the problem of eternal separation is really three problems, namely, of suffering, separation, and regret. I show that no existing reply solves these problems simultaneously. I then present (...) a new approach through theodicy. I argue that, if we reflect on what it would take to defeat the suffering from losing one’s beloved to hell, a regress emerges, and an adequate solution to the problem of eternal separation is a solution to this regress. I articulate five replies to the regress and evaluate their prospects. The upshot is a roadmap to defending the traditional Christian view of heaven and hell. (shrink)

In this essay, I suggest that Spinoza acknowledges a distinction between formal reality that is infinite and timelessly eternal and formal reality that is non-infinite (i. e., finite or indefinite) and non-eternal (i. e., enduring). I also argue that if, in Spinoza’s system, only intelligible causation is genuine causation, then infinite, timelessly eternal formal reality cannot cause non-infinite, non-eternal formal reality. A denial of eternal-durational causation generates a puzzle, however: if no enduring thing – not (...) even the sempiternal, indefinite individual composed of all finite, enduring things – is caused by the infinite, eternal substance, then how can Spinoza consistently hold that the one infinite, eternal substance is the cause of all things and that all things are modes of that substance? At the end of this essay, I sketch how Spinoza could deny eternal-durational causation while still holding that an infinite, eternal God is the cause of all things and that all things are modes. I develop the interpretation more in the companion essay.1 1 In “Spinoza’s Monism II,” in the next issue of this journal. (shrink)

Several scholars align Nietzsche’s philosophy with Stoicism because of their naturalist approaches to ethics and doctrines of eternal recurrence. Yet this alignment is difficult to reconcile with Nietzsche’s criticisms of Stoicism’s ethical ideal of living according to nature by dispassionately accepting fate—so much so that some conclude that Nietzsche’s rebuke of Stoicism undermines his own philosophical project. I argue that affinities between Nietzsche and Stoicism belie deeper disagreement about teleology, which, in turn, yields different understandings of nature and human (...) flourishing, so that Nietzsche’s objections to Stoicism support his commitments to ethical naturalism and to affirming life’s eternal recurrence. (shrink)

Descartes argued that the eternal truths, most prominently the truths of mathematics, are created by God. He was not explicit, however, about the ontological status of these truths. Interpreters have proposed interpretations ranging from Platonism and conceptualism. I argue for an intermediate interpretation: Descartes held they have objective being in God’s mind. In this regard his view was line with a prominent view in Aristotelian scholasticism. I defend this interpretation against objections based on divine simplicity and concerns about causation. (...) I raise questions about the philosophical merit of these objections, but in addition I argue that there is good reason to think that Descartes himself did not think they were problems for the view. Seemingly conceptualist passages in the Principles, I argue, in fact address issues different from the ontological status of the eternal truths. (shrink)

Atheist philosophers Jean-Paul Sartre and Kurt Baier, though from different philosophical traditions, shared a common concern about the traditional Judeo-Christian-Muslim doctrine that human beings are the creations of a Supreme Being. For Sartre, in “Existentialism is a Humanism” (1946), a God who designed us would thereby detract from our freedom and dignity. For Baier, in “The Meaning of Life” (1957), the idea that God designs us to serve his own purposes was deeply offensive in treating us as artifacts, domestic animals, (...) or slaves. Indeed, Baier said explicitly what was implicit in Sartre: that the divine creation of humans as would violate Immanuel Kant’s respect for persons principle. But this Kantian objection is badly flawed in ignoring the crucial role of human free will in traditional Abrahamic theism. Still, if we focus not on the divine-creation doctrine but on the doctrine of eternal torment for non-worshippers of God, then traditional Abrahamic theism does arguably undermine human freedom and dignity. For the threat of eternal torment is extraordinarily coercive. Keywords: theism, artifacts, free will, eternal torment, coercion. (shrink)

The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has (...) persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields. (shrink)

Jerry L. Walls argues that the doctrine of heaven is ripe for serious reconsideration. He contends not only that the orthodox view of heaven can be defended from objections commonly raised against it, but also that heaven is a powerful resource for addressing persistent philosophical problems, not the least of which concern the ground of morality and the meaning of life. Walls shows how heaven is integrally related to central Christian doctrines, particularly those related to salvation, and tackles the difficult (...) problem of why faith in Christ is necessary to save us from our sins. In addition, heaven is shown to illumine thorny problems of personal identity and to be an essential component of a satisfactory theodicy. Walls goes on to examine data from near-death experiences from the standpoint of some important recent work in epistemology and argues that they offer positive evidence for heaven. He concludes that we profoundly need to recover the hope of heaven in order to recover our very humanity. (shrink)

This book examines the significantly similar, yet finally different, thinking of two nineteenth-century existentialist thinkers, Soren Kierkegaard and Friedrich Nietzsche. Its focus is on the different ways each envisioned a joyful acceptance of life - a concern they shared. Each strove to give a place to this acceptance in his picture of life, but their conceptions of it are far apart.

This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.

While it seems to be evident that the vision of the eternal return of the same is the solution to the riddle mentioned in "On the vision and the riddle," exactly what constitutes the riddle is anything but clear. Li ke all good riddles the solution demands a paradigm shift. Nietzsche's riddle is solved by a radical rethinking of the concept of time, from a straight line to a circle. I give a detailed account of how Nietzsche's riddle is (...) formulated in such a way tha t the eternal return of the same is the only possible solution. (shrink)

Samuel R. Buss and Aleksandar Ignjatović. Unprovability of Consistency Statements in Fragments of Bounded Arithmetic.

The famous passage from Descartes' Sixth Meditation (54), proving that I am distinct from my body, is analysed in a way that it presupposes the following argument: (1) God can make X and Y distinct. (2) I f God can make X and Y distinct, then X and Y are distinct. (3) Therefore, X and Y are distinct. (2) is shown up as the crucial premise, several objections to it and possible ways out are discussed with the result that Descartes (...) needs to avoid references to God within the argument for the real distinctness of mind and body. (shrink)

This paper considers two different kinds of philosophical interpretations of the movie Eternal Sunshine of the Spotless Mind. On the one hand, Eternal Sunshine as a thought experiment that can function as an argument against utilitarianism. On the other hand, Eternal Sunshine as an instance of the genre of the remarriage comedy. I will argue that these two kinds of interpretations are in conflict. More specifically, Eternal Sunshine, understood as a comedy of remarriage, cannot function as (...) an argument against utilitarianism, at least in the sense specified by Grau and Wartenberg. Finally, I will suggest a different way in which Eternal Sunshine, understood as a comedy of remarriage, might function as an argument against utilitarianism. (shrink)

Post-anarchism poses a profound challenge to the fundamental tenets of traditional anarchism, particularly its veneration of science and reason, its overarching narrative of human emancipation, and its reliance on a sanguine conception of innate human goodness. However, this challenge inadvertently erodes the utopian aspirations inherent in traditional anarchism, leaving a conspicuous absence of a tangible alternative. Yet, a sense of utopia remains integral to the impetus for political engagement. This article seeks to address the implicit quandary of political engagement within (...) post-anarchism by examining the works of Max Stirner through the lens of existentialism. By juxtaposing Stirner's notions of involuntary egoism, ownness, the un-man, and insurrection with the philosophical perspectives of Sartre, Camus, and De Beauvoir, we discover that, despite its anti-political inclination, post-anarchism finds solace in the tragic and ceaseless nomadic pursuit of societal amelioration. (shrink)