Many recent writers have developed a rich system of theological concepts inspired by computers. This is digital theology. Digital theology shares many elements of its eschatology with Christian post-millenarianism. It promises a utopian perfection via technological progress. Modifying Christian soteriology, digital theology makes reference to four types of immortality. I look critically at each type. The first involves transferring our minds from our natural bodies to superior computerized bodies. The second and third types involve bringing into being a previously living (...) person, or person who has never existed, within an artificial digital environment. The fourth involves promotion of our lives into some higher level computational reality. (shrink)

I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural (...) numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals. (shrink)

1000 time-travelers travel back in time, each with the intention of killing their own infant-self. If there is no branching time, then on pain of bringing about a logical contradiction, all must fail. But this seems inexplicable: what is to ensure that the time-travelers are stopped? For a time, this inexplicability objection was thought to provide evidence that there is something incoherent about the possibility of backwards time travel in a universe without branching time. There is now near-consensus, however, that (...) the objection has no bite: there is nothing inexplicable about the mass failure. Lewis, Sider and Ismael independently argue that since it is built into the description of the class of cases considered that the time-travelers must fail – and so we consider only unsuccessful attempts – there is no mystery. Smith argues that the absence of possible worlds at which auto-infanticide is committed suffices as a complete explanation for the failures. And Baron and Colyvan maintain that available causal and logical explanations jointly account for everything that needs accounting for. I argue that these are wrong. There is remaining, problematic inexplicability. For backwards time travel not to lead to logical contradiction, something would need to do logic’s bidding, after all. (shrink)

After rejecting substance dualism, some naturalists embrace patternism. It states that persons are bodies and that bodies are material machines running abstract person programs. Following Aristotle, these person programs are souls. Patternists adopt four-dimensionalist theories of persistence: Bodies are 3D stages of 4D lives. Patternism permits at least six types of life after death. It permits quantum immortality, teleportation, salvation through advanced technology, promotion out of a simulated reality, computational monadology, and the revision theory of resurrection.

ABSTRACT The apparent consistency of Sobel sequences famously motivated David Lewis to defend a variably strict conditional semantics for counterfactuals. If Sophie had gone to the parade, she would have seen Pedro. If Sophie had gone to the parade and had been stuck behind someone tall, she would not have seen Pedro. But if the order of the counterfactuals in a Sobel sequence is reversed—in the example, if is asserted prior to —the second counterfactual asserted no longer rings true. This (...) is the Heim sequence problem. That the order of assertion makes this difference is surprising on the variably strict account. Some argue that this is reason to reject the Lewis-Stalnaker semantics outright. Others argue that the problem motivates a contextualist rendering of counterfactuals. Still others maintain that the explanation for the phenomenon is merely pragmatic. I argue that none of these is right, and I defend a novel way to understand the phenomenon. My proposal avoids the problems faced by the alternative analyses and enjoys independent support. There is, however, a difficulty for my view: it entails that many ordinarily accepted counterfactuals are not true. I argue that this cost is acceptable. (shrink)

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There (...) are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

You can survive after death in various kinds of artifacts. You can survive in diaries, photographs, sound recordings, and movies. But these artifacts record only superficial features of yourself. We are already close to the construction of programs that partially and approximately replicate entire human lives (by storing their memories and duplicating their personalities). A digital ghost is an artificially intelligent program that knows all about your life. It is an animated auto-biography. It replicates your patterns of belief and desire. (...) You can survive after death in a digital ghost. We discuss a series of digital ghosts over the next 50 years. As time goes by and technology advances, they are progressively more perfect replicas of the lives of their original authors. (shrink)

Neoplatonism is alive and well today. It expresses itself in New Thought and the mind-cure movements derived from it. However, to avoid many ancient errors, Neoplatonism needs to be modernized. The One is just the simple origin from which all complex things evolve. The Good, which is not the One, is the best of all possible propositions. A cosmological argument is given for the One and an ontological argument for the Good. The presence of the Good in every thing is (...) Spirit. Spirit sits in the logical center of every body; it is surrounded by the regulatory forms of that body. Striving for the Good, Spirit seeks to correct the errors in its surrounding forms. To correct the errors in biological texts, modern Neoplatonists turn to the experimental method. This Neoplatonism is pantheistic not because of some theoretical definition of God but rather because of its practical focus on the shaping of Spirit. (shrink)

A powerful argument against the resurrection of the body is based on the premise that all resurrection theories violate natural laws. We counter this argument by developing a fully naturalistic resurrection theory. We refer to it as the revision theory of resurrection (the RTR). Since Hick’s replica theory is already highly naturalistic, we use Hick’s theory as the basis for the RTR. According to Hick, resurrection is the recreation of an earthly body in another universe. The recreation is a resurrection (...) counterpart. We show that the New Testament supports the idea of resurrection counterparts. The RTR asserts that you are a node in a branching tree of increasingly perfect resurrection counterparts. These ever better counterparts live in increasingly perfect resurrection universes. We give both theological arguments and an empirical argument for the RTR. (shrink)

This article suggests a change of perspective on philosophy’s engagement with its past. It argues that rather than the putative purport of giving life to the past philosopher’s work, philosophical engagement with the past gives life to one’s own. Drawing on the neo-pragmatist thesis of Robert Brandom, it suggests looking to what philosophers do when they attribute meaning to concepts and considering their engagement with the past as appropriation in consequence. By scrutinizing Robert Pippin’s opposing thesis of philosophical engagement with (...) the past as dialogue, and carefully examining Brandom’s, the article suggests an account for appropriation that shows it to be non-dialogical, and hence unable to yield the fruits associated with this conception, but also insightful and rich with other philosophical values. Brandom and John McDowell’s dispute over the interpretation of Wilfrid Sellars provides an illustration of the proposed perspective and of those values. (shrink)

If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. They (...) have infinitely complex bodies. Transfinite games anchor their social relations. (shrink)

I go deep into the biology of the human organism to argue that the psychological features and functions of persons are realized by cellular and molecular parallel distributed processing networks dispersed throughout the whole body. Persons supervene on the computational processes of nervous, endocrine, immune, and genetic networks. Persons do not go with brains.

Robert Brandom’s notion of historical rationality seeks to supplement his inferentialism thesis by providing an account for the validity of conceptual contents. This account, in the shape of a historical process, involves the same self-integration of Brandom’s earlier inferentialism and is similarly restricted by reciprocal recognition of others. This article argues that in applying the synchronic social model of normative discourse to the diachronic axis of engaging the past, Brandom premises a false analogy between present community and past tradition, which (...) obscures the important differences between the two axes. This is explored by looking closely at how Brandom’s own engagements with the past exemplify his historical rationality. Taking its cue from Brandom’s critics, the article shows that Brandom’s own discourse with tradition is not, and cannot be, dialogical and, in accordance, that historical rationality is not, and cannot be, governed by the same social structure of inferentialism. The article concludes with the implications of such a claim on Brandom’s thesis as a whole and on the role of tradition in the process of normative change, in light of it. (shrink)

Just as knowledge contextualism offers a way out of knowledge skepticism in the face of powerful skeptical arguments, counterfactual contextualism purports to answer the many compelling arguments for the skeptical thesis that most ordinary counterfactuals of the form ‘if A had happened, C would have happened’, are false. In this article I review a few of the arguments for counterfactual skepticism, before surveying the various types of contextualist responses. I then discuss some of the recent objections to counterfactual contextualism, with (...) an eye toward weighing contextualism's costs with the costs of accepting skepticism. I conclude by remarking on some of the implications that skepticism and contextualism each has for many disputes in metaphysics. (shrink)

The structural theory of metaphor (STM) uses techniques from possible worlds semantics to generate and interpret metaphors. STM is presented in detail in The Logic of Metaphor: Analogous Parts of Possible Worlds (Steinhart, 2001). STM is based on Kittay’s semantic field theory of metaphor (1987) and ultimately on Black’s interactionist theory (1962, 1979). STM uses an intensional calculus to specify truth-conditions for many grammatical forms of metaphor. The truth-conditional analysis in STM is inspired in part by Miller (1979) and (...) Hintikka & Sandu (1994). STM is by no means a toy theory. It has been successfully tested on dozens of large texts taken from real authors. Its methods can be applied in very large linguistic databases like WordNet or MindNet. (shrink)

Nietzsche has a surprisingly significant and strikingly positive assessment of mathematics. I discuss Nietzsche's theory of the origin of mathematical practice in the division of the continuum of force, his theory of numbers, his conception of the finite and the infinite, and the relations between Nietzschean mathematics and formalism and intuitionism. I talk about the relations between math, illusion, life, and the will to truth. I distinguish life and world affirming mathematical practice from its ascetic perversion. For Nietzsche, math is (...) an artistic and moral activity that has an essential role to play in the joyful wisdom. (shrink)

Nick Bostrom’s Simulation Argument (SA) has many intriguing theological implications. We work out some of them here. We show how the SA can be used to develop novel versions of the Cosmological and Design Arguments. We then develop some of the affinities between Bostrom's naturalistic theogony and more traditional theological topics. We look at the resurrection of the body and at theodicy. We conclude with some reflections on the relations between the SA and Neoplatonism (friendly) and between the SA and (...) theism (less friendly). (shrink)

Many religions and religious philosophies say that ultimate reality is a kind of primal energy. This energy is often described as a vital power animating living things, as a spiritual force directing the organization of matter, or as a divine creative power which generates all things. By refuting older conceptions of primal energy, modern science opens the door to new and more precise conceptions. Primal energy is referred to here as ‘spirit’. But spirit is a natural power. A naturalistic theory (...) of spirit is developed using ideas from information theory and thermodynamics, such as the maximum entropy production principle. Spirit drives the evolution of complexity at all levels of existence. (shrink)

Pantheism claims: (1) there exists an all-inclusive unity; and (2) that unity is divine. I review three current and scientifically viable ontologies to see how pantheism can be developed in each. They are: (1) materialism; (2) Platonism; and (3) class-theoretic Pythagoreanism. I show how each ontology has an all-inclusive unity. I check the degree to which that unity is: eternal, infinite, complex, necessary, plentiful, self-representative, holy. I show how each ontology solves the problem of evil (its theodicy) and provides for (...) salvation (its soteriology). I conclude that Platonism and Pythagoreanism have the most divine all-inclusive unities. They support sophisticated contemporary pantheisms. (Published Online February 17 2004). (shrink)

Teilhard is among the first to seriously explore the future of human evolution. He advocates both bio-technologies (e.g. genetic engineering) and intelligence technologies. He discusses the emergence of a global computation - communication system (and is said by some to have been the first to have envisioned the Internet). He advocates the development of a global society. He is almost surely the first to discuss the acceleration of technological progress to a Singularity in which human intelligence will become super-intelligence. He (...) discusses the spread of human intelligence into the universe and its amplification into a cosmic-intelligence. His work has been taken up by Barrow and Tipler; Tipler; Moravec; and Kurzweil. Of course, Teilhard's Omega Point Theory is deeply Christian. For secular transhumanists, this may be difficult. But transhumanism cannot avoid a fateful engagement with Christianity. Christian institutions may support or oppose transhumanism. Since Christianity is an extremely powerful cultural force in the West, it is imperative for transhumanism to engage it carefully. A serious study of Teilhard can help that engagement and will thus be rewarding to both communities. (shrink)

At the end of the 19th century, Josiah Royce participated in what has come to be called the great debate (Royce, 1897; Armour, 2005).1 The great debate concerned issues in metaphysical theology, and, since metaphysics was primarily idealistic, it dealt considerably with the relations between the divine Self and lesser selves. After the great debate, Royce developed his idealism in his Gifford Lectures (1898-1900). These were published as The World and the Individual. At the end of the first volume, Royce (...) added a Supplementary Essay. The Essay, continuing themes from the great debate, developed an intriguing mathematical model of the relations between the divine Self and lesser selves. The second volume went on to.. (shrink)

A god is a cosmic designer-creator. Atheism says the number of gods is 0. But it is hard to defeat the minimal thesis that some possible universe is actualized by some possible god. Monotheists say the number of gods is 1. Yet no degree of perfection can be coherently assigned to any unique god. Lewis says the number of gods is at least the second beth number. Yet polytheists cannot defend an arbitrary plural number of gods. An alternative is that, (...) for every ordinal, there is a god whose perfection is proportional to it. The n -th god actualizes the best universe(s) in the n -th level of an axiological hierarchy of possible universes. Despite its unorthodoxy, ordinal polytheism has many metaphysically attractive features and merits more serious study. (shrink)

Many writers advocate the development of new and more naturalistic religions.1 Perhaps these new religions will emerge from religious naturalism. Peters believes that religious naturalism “could lead to a new significant form of organized religion with a structured community, ritual practices, and ways of moral living.”2 However, at the present time, religious naturalism is not a nature-centered religion. The features mentioned by Peters are mainly missing.3 At the present time, the most significant effort to derive a nature-centered religion from religious (...) naturalism is found in Crosby. Over the course of several books, Crosby lays out his metaphysical theory of nature.4 He uses that theory to develop a... (shrink)

Skeptical atheism is deeply concerned with the development of a true atheistic belief-system which competes with allegedly false theistic belief-systems. Spiritual atheists are concerned with building a successful atheistic culture to compete with an allegedly dysfunctional theistic culture. These atheisms are compared in terms of their epistemologies, metaphysics, axiologies, eschatologies, soteriologies, prosocial activities, and individual practices. Skeptical atheism is likely to remain a perpetually marginal community. Spiritual atheism may become a significant alternative to theism.

Ordinal polytheism is motivated by the cosmological and design arguments. It is also motivated by Leibnizian–Lewisian modal realism. Just as there are many universes, so there are many gods. Gods are necessary concrete grounds of universes. The god-universe relation is one-to-one. Ordinal polytheism argues for a hierarchy of ranks of ever more perfect gods, one rank for every ordinal number. Since there are no maximally perfect gods, ordinal polytheism avoids many of the familiar problems of monotheism. It links theology with (...) counterpart theory, mathematics and computer science. And it entails that the system of universes has an attractive axiological structure. (shrink)

Metaphors have computable semantics. A program called NETMET both generates metaphors and produces partial literal interpretations of metaphors. NETMET is based on Kittay's semantic field theory of metaphor and Black's interaction theory of metaphor. Input to NETMET consists of a list of literal propositions. NETMET creates metaphors by finding topic and source semantic fields, producing an analogical map from source to topic, then generating utterances in which terms in the source are identified with or predicated of terms in the topic. (...) Given a metaphor, NETMET utilizes if-then rules to generate the implication complex of that metaphor. The literal leaves of the implication complex comprise a partial literal interpretation. (shrink)

It has often been said that metaphors are based on analogies, but the nature of this relation has never been made precise. This article rigorously and formally specifies two semantic relations that do obtain between some metaphors and analogies. We argue that analogies often provide conditions of meaningfulness and truth for metaphors. An analogy is treated as an isomorphism from a source to topic domain. Metaphors are thought of as surface structures. Formal analogical conditions of meaningfulness and truth are fully (...) and rigorously worked out for several grammatical classes of metaphors. By providing analogical meaningfulness and truth conditions for metaphors, this article shows that truth-conditional semantics can be extended to metaphors. (shrink)

Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. That series (...) rises to an absolutely infinite degree of that perfection. God has that absolutely infinite degree. We focus on the perfections of knowledge, power, and benevolence. Our model of divine infinity thus builds a bridge between mathematics and theology. (shrink)

Before a fair, indeterministic coin is tossed, Lucky, who is causally isolated from the coin-tossing mechanism, declines to bet on heads. The coin lands heads. The consensus is that the following counterfactual is true: (M:) If Lucky had bet heads, he would have won the bet. It is also widely believed that to rule (M) true, any plausible semantics for counterfactuals must invoke causal independence. But if that’s so, the hope of giving a reductive analysis of causation in terms of (...) counterfactuals is undermined. Here I argue that there is compelling reason to question the assumption that (M) is true. (shrink)

I gather and constructively criticize Nietzsche’s writings on identity. Nietzsche treats identity as a logical fiction. He denies that there are any enduring things (no substances); he denies that there are any indiscernible things in any respect (no universals, no bare particulars). For Nietzsche, the world consists of durationless events bearing non-universal properties and standing to one another in non-universal relations. Events are bundles of tropes. Nietzsche even denies self-identity. His events are self-differing trope-bundles. I link Nietzsche’s denial of self-identity (...) with modern treatments of paradox. (shrink)

Infinite machines (IMs) can do supertasks. A supertask is an infinite series of operations done in some finite time. Whether or not our universe contains any IMs, they are worthy of study as upper bounds on finite machines. We introduce IMs and describe some of their physical and psychological aspects. An accelerating Turing machine (an ATM) is a Turing machine that performs every next operation twice as fast. It can carry out infinitely many operations in finite time. Many ATMs can (...) be connected together to form networks of infinitely powerful agents. A network of ATMs can also be thought of as the control system for an infinitely complex robot. We describe a robot with a dense network of ATMs for its retinas, its brain, and its motor controllers. Such a robot can perform psychological supertasks - it can perceive infinitely detailed objects in all their detail; it can formulate infinite plans; it can make infinitely precise movements. An endless hierarchy of IMs might realize a deep notion of intelligent computing everywhere. (shrink)

Structural idealism uses formal and computational techniques to describe an idealist ontology composed of God and a set of finite minds. A finite mind is a system of private intentional worlds. An intentional world is a connectionist hierarchy of intentional objects (propositions, concepts, sensible things, sensations). Intentional objects, similar to Leibnizian monads, are computing machines. To escape the egocentric predicament, Leibnizian relations of (in)compossibility exist between finite minds, linking them together into a constraint-satisfaction network, thereby coordinating their private intentional worlds.

An Omega Point Theory says that reality is making progress from some initial state to some final state. It moves from some Alpha Point (the initial state) to some Omega Point (the final state). The progress is an increase in some quality. For example, reality is making progress from the chaotic to the orderly; or it is making progress from the simple to the complex; or from the mindless to the mental; or from evil to good. Here we focus on (...) the Omega Point theory of Peirce. An Omega Point Theory is an evolutionary cosmology – it says that the universe is evolving from the Alpha Point to the Omega Point. Peirce refers to his evolutionary cosmology as a Cosmogonic Philosophy would suppose that in the beginning – infinitely remote – there was a chaos of unpersonalized feeling, which being without connection or regularity would properly be without existence. This feeling, sporting here and there in pure arbitrariness, would have started the germ of a generalizing tendency. Its other sportings would be evanescent, but this would have a growing virtue. Thus the tendency to habit would be started; and from this, with the other principles of evolution, all the regularities of the universe would be evolved. At any time, however, an element of pure chance survives and will remain until the world becomes an absolutely perfect, rational, and symmetrical system, in which mind is at last crystallized in the infinitely distant future. (Peirce, Collected Papers , 6.33). (shrink)

Thought about the singularity intersects the philosophy of mind in deep and important ways. However, thought about the singularity also intersects many other areas of philosophy, including the history of philosophy, metaphysics, the philosophy of science, and the philosophy of religion. I point to some of those intersections. Singularitarian thought suggests that many of the objects and processes that once lay in the domain of revealed religion now lie in the domain of pure computer science.

The game of life is an excellent framework for metaphysical modeling. It can be used to study ontological categories like space, time, causality, persistence, substance, emergence, and supervenience. It is often said that there are many levels of existence in the game of life. Objects like the glider are said to exist on higher levels. Our goal here is to work out a precise formalization of the thesis that there are various levels of existence in the game of life. To (...) formalize this thesis, we develop a set-theoretic construction of the glider. The method of this construction generalizes to other patterns in the game of life. And it can be extended to more realistic physical systems. The result is a highly general method for the set-theoretical construction of substances. (shrink)

A model of analogical mapping is proposed that uses five principles to generate consistent and conflicting hypotheses regarding assignments of elements of a source domain to analogous elements of a target domain. The principles follow the fine conceptual structure of the domains. The principles are: (1) the principle of proportional analogy; (2) the principle of mereological analogy, (3) the principle of chain reinforcement; (4) the principle of transitive reinforcement; and (5) the principle of mutual inconsistency. A constraint-satisfaction network is used (...) to find the set of assignments that preserves the greatest relational structure of the source. In contrast to the model proposed here, most models of analogical mapping use only the principle of proportional analogy. The use of many principles is shown to be superior in that it permits smoother integration of pragmatic factors and results in a more efficient mapping process. (shrink)

I discuss the view, increasingly common in physics, that the foundational level of our physical reality is a network of computing machines (so that our universe is ultimately like a cellular automaton). I discuss finitely extended and divided (discrete) space-time and discrete causality. I examine reasons for thinking that the foundational computational complexity of our universe is finite. I discuss the emergence of an ordered complexity hierarchy of levels of objects over the foundational level and I show how the special (...) sciences study these emergent objects. (shrink)

Plotinus resolved the paradox of the immanent transcendence, characterizing the relation between the One and the universe, through his theory of the two energeiai. According to this doctrine, all existents have an internal activity and an external activity: the internal activity comprises the true essence and substance of each being; the external activity is emitted outwards as its image. The source of the emission is thus present in the lower layer of being by virtue of its manifold images. The prominence (...) given to light in elucidating this solution led to a distinction between two types of lights: an original light, corresponding to the internal energeia of every existent, and a secondary light, which is the outflow and image of the first light, existing outside of the luminous body.This paper demonstrates the striking similarity between these two Plotinian lights and the concepts of lux and lumen developed by two thirteenth-century philosophers: Robert Grosseteste and Albertus Magnus. Moreover, the paper contends that the purpose of these two medieval concepts of light was identical to what Plotinus had in mind when he first made the distinction: to account for the relation between the one and the many.Keywords: Plotinus; Albertus Magnus; Robert Grosseteste; Light; Lux; Lumen. (shrink)

(in lieu of abstract, first paragraphs here) For philosophers, reading Richard Dawkins is often a frustrating experience. Many of Dawkins’ writings treat important philosophical topics, such as the existence of God, the meaning of life, the relationship of randomness to order. Dawkins has original ideas, but he lacks the philosophical training and vocabulary to articulate these ideas properly and to develop them coherently. In Believing in Dawkins, Eric Steinhart sets himself an ambitious task: to use the writings of Dawkins (...) to present a coherent, naturalistic alternative to religious metaphysics, specifically to Christian theism. Using an architectural metaphor, he summarizes the project of Believing in Dawkins as follows -/- It is helpful to think of the Dawkinsian texts in architectural terms. His fragmentary sketches for spiritual naturalism are like architectural drawings. Sometimes they depict little windows, while other times they portray enormous spires reaching towards the stars. The edifice is vast. But these architectural diagrams are often unclear, incomplete, and inconsistent. I want to clarify them, fill in their missing parts, and resolve their conflicts. So I’m using his writings to construct a novel building. … To fit his fragmentary plans into a coherent and self-supporting structure, I will add some large-scale frameworks (10). -/- Steinhart’s wide-ranging book covers many topics: complexity, ontology, possibility, humanity, spirituality, among many others. He does not sneak theism into Dawkins’ writings. In fact, Steinhart argues that many practices and ideas that he uses to construct the edifice of Dawkins’ spiritual naturalism have been hijacked by theism, such as the notion of an afterlife, sacredness, holiness, and even the notion of gratitude. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

Durante los últimos treinta años, los nacionalistas liberales han defendido la idea según la cual del mismo modo que el liberalismo necesita delnacionalismo para lograrmejor sus objetivos centrales, las diferentes expresiones delnacionalismo deben ser limitadas por los principios liberales.Yael Tamir ha sidouna de las figuras clave de esta singular articulación. En su obra Liberal Nationalism(1993), como en sus trabajos posteriores,no sólo defendió que era posible conciliar los valores liberales con ciertos aspectos fundamentales de la tradición nacionalista, sino también que (...) era necesario fundar una alianza entre el liberalismo y el multiculturalismocon el propósito de hacerjusticia a los miembros de las minorías culturales y religiosas. En Why Nationalism, su más reciente libro,Tamirse proponeenumerar las ventajas que el nacionalismo aporta al discurso político y examinar una variedad de reivindicaciones nacionales juzgándolas por sus propios méritos. (shrink)