This is the second volume of philosophical essays by one of the most innovative and influential philosophers now writing in English. Containing thirteen papers in all, the book includes both new essays and previously published papers, some of them with extensive new postscripts reflecting Lewis's current thinking. The papers in Volume II focus on causation and several other closely related topics, including counterfactual and indicative conditionals, the direction of time, subjective and objective probability, causation, explanation, perception, free will, and rational (...) decision. Throughout, Lewis analyzes global features of the world in such a way as to show that they might turn out to supervene on the spatiotemporal arrangement of local qualities. (shrink)

I Physics of Information Information, Physics, Quantum: The Search for Links John Archibald Wheeler Information from Quantum Measurements Benjamin Schumacher Local Accessibility of Quantum States William K. Wootters The Entropy of Black Holes V. F. Mukhanov Some Simple Consequences of the Loss of Information in a Spacetime with a Horizon Shin Takagi Why is the Physical World so Comprehensible? P. C. W. Davies II Laws of Physics and Laws of Computation Algorithmic Information Content, Church-Turing Thesis, Physical Entropy, and Maxwell’s Demon (...) W. E. Zurek Entropy and Information: How Much Information is Needed to Assign a Probability? Carlton M. Caves Complexity of Models J. Rissanen Laws and Boundary Conditions C. H. Woo How to Define Complexity in Physics, and Why Charles H. Bennett III Complexity and Evolution Requirements for Evolvability in Complex Systems: Orderly Dynamics and Frozen Components Stuart A. Kauffman Valuable Information Seth Lloyd Non-Equilibrium Polymers, Entropy, and Algorithmic Information Dilip K. Kondepudi The Dynamics of Complex Computational Systems Tad Hogg Computation at the Onset of Chaos James P. Crutchfield and Karl Young IV Physics of Computation Parallel Quantum Computation Norman Margolus Information Processing at the Molecular Level: Possible Realizations and Physical Constraints W. G. Teich and G. Mahler How Cheap Can Mechanics’ First Principles Be? Tommaso Toffoli Intermittent Fluctuations and Complexity Xiao-Jing Wang Information Processing in Visual Perception A. Zee V Probability, Entropy, and Quantum Thermodynamic Constraints on Quantum Axioms Asker Peres Entropy and Quantum Mechanics M. Hossein Páriovi Einstein Completion of Quantum Mechanics Made Falsifiable O. E. Rossler Quantum Mechanics and Algorithmic Complexity J. W. Barrett Probability in Quantum Theory E. T. Jaynes Quantum Measurements and Entropy H. D. Zeh VI Quantum Theory and Measurement Quantum Mechanics in the Light of Quantum Cosmology Murray Gell-Mann and James B. Hartle Information Dissipation in Quantum Cosmology and the Emergence of Classical Spacetime Jonathan J. Halliwell The Quantum Mechanics of Self-Measurement David Z. Albert The Quantum-Classical Correspondence in Light of Classi- cal Bell’s and Quantum Tsirelson’s Inequalities X. A. Khalfin Some Progress in Measurement Theory: The Logical Inter- pretation of Quantum Mechanics Roland Omnes. (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)

What happens when machines become more intelligent than humans? One view is that this event will be followed by an explosion to ever-greater levels of intelligence, as each generation of machines creates more intelligent machines in turn. This intelligence explosion is now often known as the “singularity”. The basic argument here was set out by the statistician I.J. Good in his 1965 article “Speculations Concerning the First Ultraintelligent Machine”: Let an ultraintelligent machine be defined as a machine that can far (...) surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an “intelligence explosion”, and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make. The key idea is that a machine that is more intelligent than humans will be better than humans at designing machines. So it will be capable of designing a machine more intelligent than the most intelligent machine that humans can design. So if it is itself designed by humans, it will be capable of designing a machine more intelligent than itself. By similar reasoning, this next machine will also be capable of designing a machine more intelligent than itself. If every machine in turn does what it is capable of, we should expect a sequence of ever more intelligent machines. This intelligence explosion is sometimes combined with another idea, which we might call the “speed explosion”. The argument for a speed explosion starts from the familiar observation that computer processing speed doubles at regular intervals. Suppose that speed doubles every two years and will do so indefinitely. Now suppose that we have human-level artificial intelligence 1 designing new processors. Then faster processing will lead to faster designers and an ever-faster design cycle, leading to a limit point soon afterwards. The argument for a speed explosion was set out by the artificial intelligence researcher Ray Solomonoff in his 1985 article “The Time Scale of Artificial Intelligence”.1 Eliezer Yudkowsky gives a succinct version of the argument in his 1996 article “Staring at the Singularity”: “Computing speed doubles every two subjective years of work.. (shrink)

This paper examines the relationship between the classical theistic conception of God and modal realism. I suggest that realism about possible worlds has unwelcome consequences for that conception. First, that modal realism entails the necessity of divine existence eludes explanation in a way congenial to a commitment to both modal realism and classical theism. Second, divine knowledge is dependent on worlds independent of the creative role and action of God, thereby suggesting a limitation on the nature of divine knowledge and (...) on the nature of God's creative role. Third, modal realism indicates the existence of real, albeit non-actual, worlds of appalling evil threatening the classical conception of divine omnipotence and benevolence. (Published Online July 10 2006). (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)

The structure of the second, Or so-Called modal version of anselm's ontological argument is discussed in relation to various systems of alethic modal logic. It is argued that there are three current problems standing in the way of acceptance of the argument, Each related to its modal structure, And each an analogue of a traditional objection to anselm's original argument. Two of these problems can probably be solved, But the third remains recalcitrant.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

Are there really beliefs? Or are we learning (from neuroscience and psychology, presumably) that, strictly speaking, beliefs are figments of our imagination, items in a superceded ontology? Philosophers generally regard such ontological questions as admitting just two possible answers: either beliefs exist or they don't. There is no such state as quasi-existence; there are no stable doctrines of semi-realism. Beliefs must either be vindicated along with the viruses or banished along with the banshees. A bracing conviction prevails, then, to the (...) effect that when it comes to beliefs (and other mental items) one must be either a realist or an eliminative materialist. (shrink)

Instead of simply defending a denial of God's existence Le Poidevin presents instead a way of interpreting religious discourse which allows us to make sense of the role of religion in our spiritual and moral lives.

This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

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)

The tape is divided into squares, each square bearing a single symbol—'0' or '1', for example. This tape is the machine's general-purpose storage medium: the machine is set in motion with its input inscribed on the tape, output is written onto the tape by the head, and the tape serves as a short-term working memory for the results of intermediate steps of the computation. The program governing the particular computation that the machine is to perform is also stored on the (...) tape. A small, fixed program that is 'hard-wired' into the head enables the head to read and execute the instructions of whatever program is on the tape. The machine's atomic operations are very simple—for example, 'move left one square', 'move right one square', 'identify the symbol currently beneath the head', 'write 1 on the square that is beneath the head', and 'write 0 on the square that is beneath the head'. Complexity of operation is achieved by the chaining together of large numbers of these simple atoms. Any universal Turing machine can be programmed to carry out any calculation that can be performed by a human mathematician working with paper and pencil in accordance with some algorithmic method. This is what is meant by calling these machines 'universal'. (shrink)

Abstract Charles Darwin, in his discussions with Asa Gray and in his published works, doubted whether God could so arrange it that exactly the desired contingent events would occur to cause particular outcomes by natural selection. In this paper, I argue that even a limited or neo-Leibnizian deity could have chosen a world that satisfied some arbitrary set of goals or functions in its outcomes and thus answer Darwin's conundrum. In more general terms, this supports the consistency of natural selection (...) with providentialism, and makes “theistic evolutionism” a coherent position to hold. (shrink)

We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. This allows the following characterization of computable sets: a set of ordinals is ordinal register (...) computable if and only if it is an element of Gödel’s constructible universe L. (shrink)

Some wag reported the following story: Scholars have recently established that the Iliad and the Odyssey were not, after all, written by Homer. They were actually written by another author, of the same name.The majority of current theories of naming and reference, including ones as divergent in other respects as those of Russell and Searle, would rule this story impossible. They would do so on roughly these grounds: the sense and reference of the name ‘Homer’ is determined, given the absence (...) of other reliable testimony, by the sole description: ‘Author of the Iliad and the Odyssey’. ‘Homer is the author of the Iliad and the Odyssey’ is therefore known a priori, hence necessarily true. There could not be another author of that name and claim to fame.In lectures delivered at Princeton in the Winter of 1970, Saul Kripke offered a lucid alternative to such theories. (shrink)

At least some of these commentators have then, rather naturally, taken a step which it will be the business of this essay to criticize. They have suggested that Leibniz’s "counter-part theory" can be understood as providing an interpretation of counter-factuals and certain forms of modal discourse within his system. For example, Mondadori writes.

Kyburg proposes the following test for the simplicity of a theory: the complexity of a theory is measured by the number of quantifiers that occur in the set of statements comprising the theory. (staff).

I. The argument from design or ‘teleological argument’ purports to be an inductive proof for the existence of God, proceeding from the evidence of the order exhibited by natural phenomena to the probable conclusion of a rational agent responsible for producing that order. The argument was severely criticized by David Hume in his Dialogues Concerning Natural Religion , and it was widely conceded that Hume's objections had cast serious doubt on the adequacy of the teleological argument, if not destroyed its (...) credibility entirely. However, there has been a recent reappraisal of this claim by R. G. Swinburne, who maintains that none of Hume's criticisms have any validity against a ‘carefully articulated version of the argument’. Using an analogical argument based on temporal regularities rather than on spatial regularities , Swinburne claims to have shown that the teleological argument is a legitimate inference to the best explanation whose force depends only on the strength of the analogy and on the degree to which the resulting theory makes explanation of empirical matters simpler and more coherent. Moreover, he claims to have shown that the argument provides support for the Christian monotheistic hypothesis and not merely for the weak claim that the universe was designed . This is an important claim since it has long been thought that Hume's most devastating blow was dealt when he showed that the teleological argument provides just as much support for the negation of certain propositions considered essential to Christian monotheism as it does for their affirmation. (shrink)

Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.

This paper argues for the proposition that there is fundamental incoherence in the idea of a divine designer. Such a being would have to have intentions and thoughts prior to designing and making a world. But it is a necessary truth that thought – of the complex and articulated kind necessary for the design of a cosmos – presupposes possession of language. It is further necessarily true that language is impossible, save for beings who inhabit a public world containing other (...) linguistic subjects. The divine designer would be the impossible exemplar of the private language, whose incoherence was demonstrated by Wittgenstein. Objections to this line of argument are noted and rebutted. Even God can't whisper in His own ear.Isaak Babel (Published Online February 17 2004). (shrink)

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Paul Sheehy has argued that the modal realist cannot satisfactorily allow for the necessity of God's existence. In this short paper I show that she can, and that Sheehy only sees a problem because he has failed to appreciate all the resources available to the modal realist. God may be an abstract existent outside spacetime or He may not be: but either way, there is no problem for the modal realist to admit that He exists at every concrete possible world.