Eric Steinhart

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.

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.

The Logic of Metaphor uses techniques from possible worlds semantics to provide formal truth-conditions for many grammatical classes of metaphors. It gives logically precise and practically useful syntactic and semantic rules for generating and interpreting metaphors. These rules are implemented in a working computer program. The book treats the lexicon as a conceptual network with semantics provided by an intensional predicate calculus. It gives rules for finding analogies in such networks. It shows how to syntactically and semantically analyze texts containing metaphors and how to use structural similarities between parts of possible worlds to provide truth-conditions for metaphors. Meanings for metaphors are linked to the modal logics of identity and indiscernibility. The book shows how to extend deductive and abductive inference systems to handle metaphors. It shows how to handle novel metaphorical word-senses. The Logic of Metaphor will be useful to philosophers, logicians, linguists, and computer scientists.

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.

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.

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.

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.

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.