Eric Steinhart

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.

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)

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.

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...

On Nietzsche aims to present Nietzsche's thought as a coherent and reasonable system rather than as a collage of prophetic or poetic aphorisms. Nietzsche is a thinker who gives reasons and makes arguments. At the core of Nietzsche's thought is radical world- and life-affirmation. It is that affirmation than which there is none greater. It is an affirmation ultimately based on the classical Greek principle of plenitude: it is better to be than not to be. On Nietzsche lays out his views on the human condition, religion, language, knowledge, science, truth, the will to power, the herd and the individual, and the eternal return. On Nietzsche shows how he develops ideas from Plotinus, Anselm, Leibniz, Kant, Schopenhauer, and others. It also aims to show how the contemporary Anglo-American tradition has adopted many Nietzschean ideas.

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.

I use concepts from Foucault's analysis of the human condition to investigate how we recognize or fail to recognize ourselves in machines like computers. Human beings are traditionally defined as "rational animals" or as "thinking things". I examine how this self-conception determines our use of computing machines as logical mirrors in which we both hope and fear to see our truest selves. I examine two analogies: (1) how we think of computers as if they were human (self-projection) and (2) how we think of humans as if they were computers (self-reflection). I interpret the humanization of computers and the computerization of humans as ways that thought tries to master its own freedom by thinking of itself metaphorically in terms of something else.