Eric Steinhart

The many kinds of naturalism fall into two main types. Dogmatic naturalists define naturalness using some rule. Progressive naturalists define naturalness in terms of a research program. This research program, illustrated by the sciences, progressively defines things ever more precisely using mathematics. Most traditional religious concepts fail to be natural on any type of naturalism. But progressive naturalists are open to naturalistic revisions of traditional concepts. They do not tie religion to the past, but welcome novel religious and spiritual naturalisms.

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.

_More Precisely_ is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.

My dissertation aims to provide a formal semantic theory for metaphors and a computational model of that theory. A computer program, NETMET, implements the ideas presented in the dissertation. Working in a thoroughly cognitive manner, my dissertation is both rigorously mathematical and psychologically well-informed. The dissertation is scientific in method. The reasoning is primarily abductive, and each proposed hypothesis is validated against large, detailed examples from the history of philosophy and science. ;The dissertation begins by sketching a formal theory of conceptual knowledge. Conceptual knowledge is modeled as a semantic network of concepts: concepts are modeled as network nodes, propositions as structures containing such nodes. A semantic field is characterized as a cluster of densely interrelated concepts. ;The core of the dissertation is a formal theory of analogy. It is argued that analogies serve as the primary basis for the generation of metaphors. Analogies are viewed as approximate homomorphisms from a source semantic field to a target field. Constraint-satisfaction algorithms are presented for computing analogies and for transfering knowledge from the source to the target by means of an underlying analogy; particular care is taken to transfer the implicative structure of the source field. Such analogical transference produces metaphorical propositions. Rules are given for generating several syntactical forms of metaphorical utterances. ;The dissertation then proceeds to the analysis and interpretation of metaphors. Logical deep structures are provided for several syntactic forms of metaphors. For instance, copula metaphors are shown to be class-inclusion statements . A forward-chaining inference algorithm is presented that deduces literal propositions from metaphorical propositions. It is then shown how such literal entailments can be incorporated into abductive argument schema which confirm or disconfirm metaphors. In this respect, at least, metaphorical propositions are analogous to theoretical statements. Since arguments can be provided for metaphorical propositions, it is argued that they carry truth-values, and so are cognitively meaningful

In this article I discuss identity and indiscernibility for person‐stages and persons. Identity through time is not an identity relation (it is a unity relation). Identity is carefully distinguished from persistence. Identity is timeless and necessary. Person‐stages are carefully distinguished from persons. Theories of personal persistence are not theories of identity for persons. I deal not with the persistence of persons through time but with the timeless and necessary identity and indiscernibility of persons. I argue that it is possible that there are non‐identical but indiscernible temporally whole persons. I discuss the biographies of persons and develop the type or token distinction for persons. Twins in symmetrical or eternally recurrent universes are examples of indiscernible persons. I discuss temporal and modal branching, and I end with survival for person‐tokens and eternity for person‐types.

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.

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).

_More Precisely_ provides a rigorous and engaging introduction to the mathematics necessary to do philosophy. It is impossible to fully understand much of the most important work in contemporary philosophy without a basic grasp of set theory, functions, probability, modality and infinity. Until now, this knowledge was difficult to acquire. Professors had to provide custom handouts to their classes, while students struggled through math texts searching for insight. _More Precisely_ fills this key gap. Eric Steinhart provides lucid explanations of the basic mathematical concepts and sets out most commonly used notational conventions. Furthermore, he demonstrates how mathematics applies to many fundamental issues in branches of philosophy such as metaphysics, philosophy of language, epistemology, and ethics.

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.

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).

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.

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

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.

Philosophical concepts are easier to teach and to learn if students can directly manually and visually manipulate the objects instantiating them. What is needed is a philosophy laboratory in which students learn by experimenting. Games are highly idealized yet concrete structures able to instantiate abstract concepts. I show how to use the Game of Life (a computerized cellular automaton "game") to teach concepts like: individuation; supervenience; the phenomena / noumena distinction; the physical / design / and intentional stances; the argument from design; and models for Leibnizian monads. Such formal games are good ways to use computers to teach philosophy.

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.

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.

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.