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)

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”.

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.

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

We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U.

For a function $f$ with domain $[X]^{n}$, where $X\subseteq\mathbb{N}$, we say that $H\subseteq X$ is canonical for $f$ if there is a $\upsilon\subseteq n$ such that for any $x_{0},\ldots,x_{n-1}$ and $y_{0},\ldots,y_{n-1}$ in $H$, $f=f$ iff $x_{i}=y_{i}$ for all $i\in\upsilon$. The canonical Ramsey theorem is the statement that for any $n\in\mathbb{N}$, if $f:[\mathbb{N}]^{n}\rightarrow\mathbb{N}$, then there is an infinite $H\subseteq\mathbb{N}$ canonical for $f$. This paper is concerned with a model-theoretic study of a finite version of the canonical Ramsey theorem with a largeness (...) condition and also a version of the Kanamori–McAloon principle. As a consequence, we produce new indicators for cuts satisfying $\operatorname{PA}$. (shrink)

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

This note is part of the implementation of a programme in foundations of mathematics to find exact threshold versions of all mathematical unprovability results known so far, a programme initiated by Weiermann. Here we find the exact versions of unprovability of the finite graph minor theorem with growth rate condition restricted to planar graphs, connected planar graphs and graphs embeddable into a given surface, assuming an unproved conjecture : ‘there is a number a>0 such that for all k≥3, (...) and all n≥1, the proportion of connected graphs among unlabelled planar graphs of size n omitting the k-element circle as minor is greater than a’. Let γ be the unlabelled planar growth constant . Let P be the following first-order arithmetical statement with real parameter c: “for every K there is N such that whenever G1,G2,…,GN are unlabelled planar graphs with Giunprovability thresholds in the general case of the finite graph minor theorem. (shrink)

Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.

This chapter surveys the Greek background in Plato’s Timaeus, Aristotle’s Physics and De Caelo, and the dispute between late Greek thinkers, especially Proclus and Philoponus. Against this background, al-Kindī’s arguments that only God can be eternal and that creation must be finite in time as well as space are explored. It is suggested that al-Kindī’s interest in this topic can be explained in terms of the contemporary ’Abbāsid dogma that the Koran is not eternal, but created.

In this paper we prove general exact unprovability results that show how a threshold between provability and unprovability of a finite well-quasi-orderedness assertion of a combinatorial class is transformed by the sequence-construction, multiset-construction, cycle-construction and labeled-tree-construction. Provability proofs use the asymptotic pigeonhole principle, unprovability proofs use Weiermann-style compression techniques and results from analytic combinatorics.

I don’t remember if I got as high as 2-390, but I distinctly remember taking my first logic course - as a Freshman - with Hartley Rogers, in Fall 1964 - here in 2-190. Or was it in 2-290?

Paul Helm presents a new, expanded edition of his much praised 1988 book Eternal God, which defends the view that God exists in timeless eternity. Helm argues that divine timelessness is grounded in the idea of God as creator, and that this alone makes possible a proper account of divine omniscience.

Nietzsche’s Eternal Return (ER) is interpreted in many ways, including by him. I present it as a hermeneutic device, a way of reading texts, especially those whose influence threatens one’s authorial autonomy and/or are later difficult to take ownership of due to philosophical growth. It returns past texts with new interpretations, similar to the way ER leads one to embrace one’s past without changing anything, which radically changes everything from a resented painful burden into a celebrated enhancement of freedom (...) and power. I show how he could have derived the idea from Schopenhauer, his own embarrassing past, by performing the technique on Schopenhauer. The same attitude toward past texts of recreating them according to one’s present interests and concerns simultaneously releases one’s present texts for future readers to impose their readings onto them, just as Zarathustra tells his followers not to follow him. Heidegger takes the idea up in a far more nuanced account than he is usually given credit for and applies it, among other places, to the history of philosophy. All philosophers say the same as it keeps returning. Derrida then recreates this as iterability, the deconstruction of the no/change dichotomy that Nietzsche began. (shrink)

This paper addresses the question: given some theory T that we accept, is there some natural, generally applicable way of extending T to a theory S that can prove a range of things about what it itself (i.e. S) can prove, including a range of things about what it cannot prove, such as claims to the effect that it cannot prove certain particular sentences (e.g. 0 = 1), or the claim that it is consistent? Typical characterizations of Gödel’s second incompleteness (...) theorem, and its significance, would lead us to believe that the answer is ‘no’. But the present paper explores a positive answer. The general approach is to follow the lead of recent (and not so recent) approaches to truth and the Liar paradox. (shrink)

This book provides an account of the nature of time, especially time's arrow and the role of entropy, at a semi-popular level. Special attention is given to statistical mechanics, the past hypothesis, and possible cosmological explanations thereof.

Modernity seemed to be the autumn of eternity. The secularization of European culture provided little sustenance to the concept of eternity with its heavy theological baggage. Yet, our hero would not leave the stage without an outstanding performance of its power and temptation. Indeed, in the first three centuries of the modern period – the subject of the third chapter by Yitzhak Melamed - the concept of eternity will play a crucial role in the great philosophical systems of the period. (...) The first part of this chapter concentrates on the debate about the temporality of God. While most of the great metaphysicians of the seventeenth century – Suarez, Spinoza, Malebranche, and Leibniz – ascribed to God eternal, non-temporal, existence, a growing number of philosophers conceived God as existing in time. For Newton, God’s eternity was simply the fact that “He was, he is, and is to come.” A similar view of God as being essentially in time was endorsed by Pierre Gassendi, Henry More, Samuel Clarke, Isaac Barrow, John Locke, and most probably Descartes as well. In the second part of the chapter we study the concept of eternal truth, and its relation to the emerging notion of Laws of Nature. The third part of the chapter explicates Spinoza’s original understanding of eternity as a modal concept. For Spinoza, eternity is a unique kind of necessary existence: it is existence that is self-necessitated (unlike the existence of other things whose necessity derives from external causes). Eternity is the existence of God or the one substance. Yet, Spinoza claims that if we conceive finite things adequately - “sub specie aeternitatis” – as nothing but modes flowing from the essence of God, even finite things (like our minds) can take part in God’s eternity. The fourth and final part of the chapter is mostly focused on the reception of Spinoza’s original conception of eternity by Leibniz and other eighteenth century philosophers. (shrink)

Metaphysics as an independent discipline has a surprisingly short history. Until the early eighteenth century, many, perhaps even most, writers on “metaphysics” primarily had the eponymous work of Aristotle in mind. In the writings of the early eighteenth-century German rationalists—Christian Wolff and Alexander Baumgarten—we find a conception of metaphysics that is no longer necessarily tied to Aristotle’s great work. But metaphysics as a discipline was not blessed with longevity, as a dozen years or so before Louis XVI it was condemned (...) to the guillotine by Kant’s first critique. The fate of metaphysics after the Kantian revolution is a story that still needs to be told, but it would be fair to say, I think, that for the past two centuries engagement with heavy metaphysical concepts such as eternity has been taken to be either a form of backwardness (religious or otherwise) or a kind of eccentricity. Luckily, things seem to have changed somewhat over the past twenty years. Suddenly, for example, we are seeing debates about monism appear in mainstream journals. (This could hardly be imagined in the 1970s or 1980s.) The emergence of interest in metaphysical monism as well as the persistent engagement with the philosophy of modality may open a window of opportunity through which eternity could again take her rightful seat as a fundamental notion of metaphysics. (shrink)

The story of eternity is not as simple as a secularization narrative implies. Instead it follows something like the trajectory of reversal in Kant’s practical proof for the existence of god. In that proof, god emerges not as an object of theoretical investigation, but as a postulate required by our practical engagement with the world; so, similarly, the eternal is not just secularized out of existence, but becomes understood as an entailment of, and somehow imbricated in, the conditions of (...) our practical existence. -/- The sections that follow discuss some of those central figures in modern European philosophy whose views prominently feature some consideration of eternity. I start with Kant in section I. Kant’s critique of speculative theology is well-known, and this hostility would appear to make it unlikely that the eternal, with all its theological baggage, would feature prominently in Kant’s critical philosophy. But in fact Kant’s transcendental idealism endorses no fewer than three different concepts of the eternal, including what turns out to be the most historically influential idea: that practical reason involves a kind of eternal, non-temporal action. Kant shifts this notion of a non-temporal act from its original theological context of god’s actus purus to a practical context, setting the stage for Schelling’s and Kierkegaard’s later development of this theme. Before detailing this trajectory however, section II is devoted to Hegel, the philosopher whose radical historicism is perhaps more than any other thinker responsible for making “the nineteenth century preeminently the historical century.”4 Hegel is not fertile soil for the concept of the eternal, but his historicism does turn out, at a crucial moment in the philosophy of nature, to presuppose a certain conception of eternity as an eternal present. Perhaps more importantly for the further development of eternity in nineteenth century thought however is that both Schelling and Kierkegaard situate their views of the eternal in the context of a collective rejection of Hegel. Section III discusses Schelling, who returns to Kant’s conception of non-temporal choice, seeing human capacities for free eternal self-creation as rivaling god’s. Such powers are required, Schelling argues, to resist the sublimation of the individual human person into the blankness of the Absolute. Section IV briefly consider Schopenhauer’s view that the in-itself of everything is an endlessly striving will. Section V concerns Kierkegaard who is strongly committed to the eternal, and indeed criticizes Hegel for compromising his conception of the eternal by thinking it temporally; but he is obsessed by the paradoxical question of our practical “access” to the eternal within a particular temporal moment: the decisive moment, imbued with significance that can turn life around and create a new person, pushing Schelling’s concerns even further. The remaining, shorter sections, present briefer accounts of more recent figures who make important use of some conception of the eternal: Nietzsche’s eternal return (section VI), Agamben’s (1942-) theory of sovereignty (section VII) and finally Alain Badiou’s unapologetic attempt to resuscitate eternity as the condition of revolutionary political change (Section VIII). I end with a concluding meditation (Section IX). (shrink)

In an excellent article that traces the logical structure of Maimonides’ Guide of the perplexed and his arguments on the existence of God, William Lane Craig (1988 122-147), concludes that most of the Guide’s impact rests precisely on its rigorous method of deduction. Perhaps, in Craig’s view, this is one of the things that makes Maimonides a model for further conciliating attempts between theology and philosophy. However, despite his careful analysis, there is one idea that Craig mentions and leaves undeveloped, (...) namely, that a certain notion of eternity of time underlies Maimonides’ argumentative scheme. Trying to go beyond the examples Craig offered in his article, my method toward a final solution to the question is divided in three steps. The first one is a reconstruction of Craig’s statements and its interpretation as supporting material for his conclusion. Then, I present three alternative views about Maimonides’ beliefs on the creation of the world, an issue strongly attached to his idea of time. Finally, I use the material of the two former sections to support an answer to my question. (shrink)

This article aims to provide an explication of the Christian doctrine of eternal generation. A model of the doctrine is formulated within the ground-theoretic framework of Jonathan Schaffer and E. Jonathan Lowe, which enables it to be explicated clearly and consistently, and two often raised objections against the doctrine can be successfully answered.

In eternally inflating cosmology, infinitely many pocket universes are seeded. Attempts to show that universes like our observable universe are probable amongst them have failed, since no unique probability measure is recoverable. This lack of definite probabilities is taken to reveal a complete predictive failure. Inductive inference over the pocket universes, it would seem, is impossible. I argue that this conclusion of impossibility mistakes the nature of the problem. It confuses the case in which no inductive inference is possible, with (...) another in which a weaker inductive logic applies. The alternative, applicable inductive logic is determined by background conditions and is the same, non-probabilistic logic as applies to an infinite lottery. This inductive logic does not preclude all predictions, but does affirm that predictions useful to deciding for or against eternal inflation are precluded. (shrink)

Are the laws of nature among the eternal truths that, according to Descartes, are created by God? The basis of those laws is the immutability of the divine will, which is not an eternal truth, but a divine attribute. On the other hand, the realization of those laws, and in particular, the quantitative consequences to be drawn from them, depend upon the eternal truths insofar as those truths include the foundations of geometry and arithmetic.

This ambitious book looks into the reasons for the exceptional durability of the Chinese empire, which lasted for more than two millennia (221 B.C.E. - 1911 C.E.). Yuri Pines identifies the roots of the empire's longevity in the activities of thinkers of the Warring States period (453-221 B.C.E.), who, in their search for solutions to an ongoing political crisis, developed ideals, values, and perceptions that would become essential for the future imperial polity. In marked distinction to similar empires worldwide, the (...) Chinese empire was envisioned and to a certain extent 'preplanned' long before it came into being. As a result, it was not only a military and administrative construct, but also an intellectual one. Pines makes the argument that it was precisely its ideological appeal that allowed the survival and regeneration of the empire after repeated periods of turmoil. "Envisioning Eternal Empire" presents a panoptic survey of philosophical and social conflicts in Warring States political culture. By examining the extant corpus of preimperial literature, including transmitted texts and manuscripts uncovered at archaeological sites, Pines locates the common ideas of competing thinkers that underlie their ideological controversies. This bold approach allows him to transcend the once fashionable perspective of competing 'schools of thought' and show that beneath the immense pluralism of Warring States thought one may identify common ideological choices that eventually shaped traditional Chinese political culture. The result is a refreshingly novel look at the foundational period in Chinese intellectual history. (shrink)

Considers four apparent problems of eternal life--is heaven a mystical or social reality, is it other-worldly or this-worldly, is it static or dynamic, is it boring?--and shows how the teachings of Thomas Aquinas support more satisfying solutions than many contemporary philosophical and theological approaches.

The Eternal Coin is a fair coin has existed forever, and will exist forever, in a region causally isolated from you. It is tossed every day. How confident should you be that the Coin lands heads today, conditional on (i) the hypothesis that it has landed Heads on every past day, or (ii) the hypothesis that it will land Heads on every future day? I argue for the extremely counterintuitive claim that the correct answer to both questions is 1.

This article considers Descartes? doctrine of eternal truths, in connection with the status of the principle of no contradiction. It is shown that the rear created and uncreated eternal truths; the former are eternal truths about creatures and the se truths are the object of divine will, while the latter are the truths about God him self, which are founded in his existence, so he can not change them. Concerning the question whet her the principle of no (...) contradiction is a created or a no created eternal truth, different Descartes? claims on this subject, potentially incongruent, are pointed out. Based on the fact that this principle does not have absolute validity, the conclusion is that in Descartes? metaphysics the status of the principle of no contradiction is not relevant, because God?s infinite power is in different to ward it. U tekstu je razmatrana Dekartova doktrina o vecnim istinama, s obzirom na status principa neprotivrecnosti. Pokazano je da kod Dekarta postoje stvorene i nestvorene vecne istine; prve jesu vecne istine o stvorevinama i jesu objekat Bozje volje, druge jesu vecne istine o Bogu samom, temelje se u njegovoj egzistenciji i on ih ne moze menjati. U vezi sa pitanjem da li je princip neprotivrecnosti stvorena ili nestvorena vecna istina, ukazano je na razlicite, potencijalno nesaglasne Dekartove tvrdnje o ovom problemu. Na osnovu cinjenice da on ne vazi vise apsolutno, izveden je zakljucak da u Dekartovoj metafizici njegov status jeste irelevantan, zato sto je Bozja beskonacna moc prema njemu indiferentna. (shrink)

It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...) the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)

Does it make sense to think of eternal life not as an unending continuation of life subsequent to death but as fully actualized in one’s present mortal and finite life? After outlining conceptual and moral reasons for being troubled by the notion of an endless life, this article draws upon the thought of major Christian theologians and philosophers of religion to expound the idea of eternal life as a possession exclusively of the life one is presently living. Supplementing (...) the claims of religious thinkers with notions of four-dimensionalism and eternalism from theoretical physics and the philosophy of time, and considering important objections to the conception of eternal life in question, I argue for both the conception’s intelligibility and its ethical and spiritual profundity. (shrink)

The present piece focuses on the influence of Plotinus' understanding of time and eternity as articulated in Plotinus' third and fifth Enneads upon Mīr Dāmād's (d. 1631–2) conception of eternity, perpetuity, and time found in his Book of Blazing Brands (Kitab al‐Qabasāt). Although Mīr Dāmād's conception of eternity, perpetuity, and time resembles that of Plotinus' cosmology and ontology, he departs from Plotinus' hypostases in establishing strict parameters for each domain. Unlike Plotinus, Mīr Dāmād argues that the realm of eternity is (...) reserved for God alone, while the realm of Perpetuity contains the Platonic Forms. For Mīr Dāmād, the realm of time is an effect of the realm of Perpetuity and a tool for human beings to understand how to measure events in the temporal world. Unlike many other Shī'ite philosophers, Mīr Dāmād's articulation of these three cosmological realms incorporates thought found in the works of both prominent Sunni and Shī'ite scholars such as Ibn Sīnā, Abū Ḥāmid al‐Ghāzālī, Suhrawardī, and Naṣīr al‐Dīn Ṭūsī. Although his most successful student, Mullā Ṣadrā Shirazī, had ultimately disagreed with his teacher's cosmological doctrine, he remained influenced by the multitude of sources that his teacher had used. (shrink)

Published in PoMo Magazine vol. 2, nr. 1 (Spring/Summer 1996) during my years as a grad student at the New School. I examine Nietzsche's presentation of the eternal recurrence, and discuss its interpretations by Heidegger, Bataille, Derrida, Klossowski, Stambaugh, and Vattimo. I will be returning to Nietzsche in the future.

In this paper I defend the eternity solution to the problem of human freedom and divine foreknowledge. After motivating the problem, I sketch the basic contours of the eternity solution. I then consider several objections which contend that the eternity solution falsely implies that we have various powers (e.g., to change God’s beliefs, or to affect the past) which, according to the objector, we do not in fact have.

Eternity is a unique kind of existence that is supposed to belong to the most real being or beings. It is an existence that is not shaken by the common wear and tear of time. Over the two and half millennia history of Western philosophy we find various conceptions of eternity, yet one sharp distinction between two notions of eternity seems to run throughout this long history: eternity as timeless existence, as opposed to eternity as existence in all times. Both (...) kinds of existence stand in sharp contrast to the coming in and out of existence of ordinary beings, like hippos, humans, and toothbrushes: were these eternally-timeless, for example, a hippo could not eat, a human could not think or laugh, and a toothbrush would be of no use. Were a hippo an eternal-everlasting creature, it would not have to bother itself with nutrition in order to extend its existence. Everlasting human beings might appear similar to us, but their mental life and patterns of behavior would most likely be very different from ours.The distinction between eternity as timelessness and eternity as everlastingness goes back to ancient philosophy, to the works of Plato and Aristotle, and even to the fragments of Parmenides' philosophical poem. In the twentieth century, it seemed to go out of favor, though one could consider as eternalists those proponents of realism in philosophy of mathematics, and those of timeless propositions in philosophy of language. However, recent developments in contemporary physics and its philosophy have provided an impetus to revive notions of eternity due to the view that time and duration might have no place in the most fundamental ontology.The importance of eternity is not limited to strictly philosophical discussions. It is a notion that also has an important role in traditional Biblical interpretation. The Tetragrammaton, the Hebrew name of God considered to be most sacred, is derived from the Hebrew verb for being, and as a result has been traditionally interpreted as denoting eternal existence. Hence, Calvin translates the Tetragrammaton as 'l'Eternel', and Mendelssohn as 'das ewige Wesen' or 'der Ewige'. Eternity also plays a central role in contemporary South American fiction, especially in the works of J.L. Borges. The representation of eternity poses a major challenge to both literature and arts. The current volume aims at providing a history of the philosophy of eternity surrounded by a series of short essays, or reflections, on the role of eternity and its representation in literature, religion, language, liturgy, science, and music. Thus, our aim is to provide a history of philosophy as a discipline that is in constant commerce with various other domains of human inquisition and exploration. (shrink)

This book, the author tells us, is "about some of the ways in which the techniques of modal logic may be used to study concepts of proof theory first studied in Gödel's famous paper on the incompleteness of arithmetic." Those who, with Quine and others, think that modal logic was conceived in sin, may well doubt that its techniques will throw anything but more Dunkel on proof theory. The author attempts to show otherwise and construes "☐A", where " ☐" is (...) the symbol for modal necessity, in terms of Gödel's arithmetical predicate "Bew" for provability. The formulae in which this latter occurs are perfectly well-defined, we are told, and thus no sin can be attached to this identification. But are such formulae perfectly well-defined? Syntactically, yes; but semantically? It is usually assumed that they are, but the full array of semantical principles needed to carry out Gödel's arithmetization seems never to have been given in full detail. And it is just possible that a fallacy of ambiguity lies concealed in such formulae, as F. Rivetti-Barbò has contended and Lesniewski appears to have hinted at. In any case, not all is happy philosophically and to everyone's satisfaction, at the very foundation of Gödel's method. Although the author purports to have proved here a number of seemingly interesting and sophisticated theorems, the real semantical issues involved seem to have been skirted.--R.M.M. (shrink)

Eleonore Stump and Katherin Rogers have recently defended the doctrine of divine timelessness in separate essays, arguing that the doctrine is consistent with libertarian free will and that timeless divine knowledge is providentially useful. I show that their defenses do not succeed; a doctrine of eternity having these features cannot be saved.

The methods of intellectual history have not yet been applied to studying the invention of technology for printing texts and images ca. 1375–ca. 1450. One of the several conceptual developments in this period refl ecting the possibility of mechanical replication is a view of the relationship of eternity to durational time based on Gregory of Nyssa’s philosophy of time and William of Ockham’s. Th e article considers how changes in these ideas helped enable the conceptual possibilities of the dissemination of (...) ideas. It describes a direct connection of human perceptual knowledge to divine knowledge that enhanced the authority of printed production to transfer and reproduce the true and the good. (shrink)

(Version 2.4) I have argued elsewhere for ascribing an error theory about all normative and evaluative judgements to Nietzsche. Such a nihilism brings with it a puzzle: how could we—or at least the select few of us being addressed by Nietzsche—continue in the face of this nihilism? This is a philosophical puzzle and so, defeasibly, an interpretive puzzle. If there is no theory it would make sense for Nietzsche to have about how the select few could go on, then this (...) is some evidence against the proposed interpretation of him as a nihilist. I defended the interpretation by arguing that Nietzsche’s declarations about creating values point to a practice of generating honest evaluative illusions. Such honest evaluative illusions are tricky things, though, and, precisely because they are honest, one might worry that they lack the motivational power of genuine evaluative belief. Can they truly play the role that evaluative beliefs play in our psychological economies? I suspect that Nietzsche does not want the honest illusions to play exactly the role that evaluative beliefs played. The cheerfulness, the playfulness, the lightness that Nietzsche hopes for are, I have suggested, a function of the shift from belief to pretence, from illusion to honest illusion. The question, nonetheless, is whether the resulting picture is too light. Can I go through life merely acting, as a critic might put it? My suggestion in this essay will be that the thought of eternal recurrence is meant to add weight to the lightness of acting—“acting”, obviously, in both the here relevant senses of the word. (shrink)

It is the laws of nature, among other things, that allow for the periodic processesthat underlie isochronic clocks. Is God in any Measured Time? If not, does our Measured Time measure the eternity of God? I will argue that God is not in any ...

Truth Eternal and the Adversity of Diversity Law sheds new light on the problem of truth, and its power to create, sustain, and account for all things. It also seeks to convey some new insights into how truth inconspicuously pervades every element of creation. Silent and unseen, it grounds time and the flow of events within it.

Nietzsche believed in the horror of existence—in a world filled with meaningless suffering. He also believed in eternal recurrence—that our lives will repeat infinitely and that in each life every detail will be exactly the same. Furthermore, it was not enough that eternal recurrence simply be accepted—Nietzsche demanded that it be loved. Thus the philosopher who introduces eternal recurrence is the very same philosopher who also believes in the horror of existence—a paradox that is completely overlooked by (...) commentators (who thus fail to adequately understand Nietzsche). All of this demands careful explanation. (shrink)

The paper argues that two apparently attractive conceptions of an eternal sentence are defective. An alternative conception is presented which the authors think allows greater insight into the nature of semantic concepts.

In this essay I argue that the film Eternal Sunshine of the Spotless Mind eloquently and powerfully suggests a controversial philosophical position: that the harm caused by voluntary memory removal cannot be entirely understood in terms of harms that are consciously experienced. I explore this possibility through a discussion of the film that includes consideration of Nagel and Nozick on unexperienced harms, Kant on duties to oneself, and Murdoch on the requirements of morality.