Abstracts of Steinhart Articles

Philosophy of Mathematics

ABSTRACT: 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.

Philosophy of Religion

Steinhart, E. (2010) Theological implications of the simulation argument. Ars Disputandi: The Online Journal for Philosophy of Religion 10, 23-37.

ABSTRACT: 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).
 

Steinhart, E. (2009) A mathematical model of divine infinity. Theology and Science 7 (3), 261 - 274.

ABSTRACT: 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.
 

Steinhart, E. (2008) Teilhard and Transhumanism. Journal of Evolution and Technology 20 (1), 1 - 22.

ABSTRACT: 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, Teilhards 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.
 

Steinhart, E. (2008) The revision theory of resurrection. Religious Studies 44 (1), 1 - 19.

ABSTRACT: 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.
 

Steinhart, E. (2004) Pantheism and current ontology. Religious Studies 40 (1), 1 - 18.

ABSTRACT: 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.
 

Metaphysics

Steinhart, E. (2007) Infinite machines.  In A. Schuster (Ed.), Intelligent Computing Everywhere. New York: Springer, 25 - 43.

ABSTRACT: I examine the computational foundations of possible physical systems. I analyze physical laws in terms of algorithms. I analyze the complexity of physical systems into (1) universes founded on finite recursion; (2) universes founded on transfinite recursion; and (3) universes with non-recursive foundations.
 

Steinhart, E. (2002) Logically possible machines. Minds and Machines 12 (2), 259 - 280.

ABSTRACT: 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.
 

Steinhart, E. (1999) Emergent values for automatons. Ethics and Information Processing 1(2), 1-6.

ABSTRACT: The infrastructure is becoming a network of computerized machines regulated by swarms of self-directing software agents. Complexity encourages the emergence of new values in software agent societies. Interdependent human societies and software societies cohabitate and coevolve in a symbiotic cooperation of freedoms.
 

Steinhart, E. (1998) Philosophy laboratory. Teaching Philosophy 21 (4), 315-326.

ABSTRACT: 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.
 

Steinhart, E. (1998) Digital metaphysics. In T. Bynum & J. Moor (Eds.), The Digital Phoenix: How Computers are Changing Philosophy . New York: Basil Blackwell, 117-134.

ABSTRACT: 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.
 

Steinhart, E. (1997) Leibniz's palace of the fates: A 17th century virtual reality system. Presence: Teleoperators and Virtual Environments 6 (1), 133-135.

ABSTRACT: One way to think logically about virtual reality systems is to think of them as interactive depictions of possible worlds. Leibniz's "Palace of the Fates" is probably the earliest description of an interactive virtual reality system. Leibniz describes a system for the simulation of possible worlds by a human user in the actual world. He describes a user-interface for interacting multiple possible worlds and their histories.
 

Steinhart, E. (1994) Structural idealism. Idealistic Studies 24 (1), 77-105.

ABSTRACT: 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.

Metaphysics of Persons

ABSTRACT: 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 your self. 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 fifty years. As time goes by and technology advances, they are progressively more perfect replicas of the lives of their original authors.
 

ABSTRACT: If the computational theory of mind is right, then minds are realized by computers. There is an ordered complexity hierarchy of computers. Some finite state machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible computers 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.
 

Steinhart, E. (2002) Indiscernible persons. Metaphilosophy 33 (3), 300 - 320.

ABSTRACT: I discuss identity and indiscernibility for person-stages and persons. Identity-through-time is not an identity relation (it's a unity relation). Identity is carefully distinguished from persistence. 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 / token distinction for persons. Twins in symmetrical or eternally recurrent universes are examples of indiscernible persons. I discuss temporal and modal branching. I end with survival for person-tokens and eternity for person-types.
 

Steinhart, E. (2001) Persons vs. brains: Biological intelligence in the human organism. Biology and Philosophy 16 (1) (January), 3-27.

ABSTRACT: 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.

Steinhart, E. (1989) Self-recognition and countermemory. Philosophy Today , Vol. 33, No. 4, 302-317

ABSTRACT: 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 beingas 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.

Nietzsche

ABSTRACT OF BOOK: 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.
 

Steinhart, E. (1999) Nietzsche's philosophy of mathematics. International Studies in Philosophy 31 (3), 19 - 27.

ABSTRACT: 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.
 

Steinhart, E. (1999) The will to power as parallel distributed processing. In B. Babich & R. Cohen (Eds.), Nietzsche's Epistemological Writings . Boston Studies in the Philosophy of Science Series. Dordrecht: Kluwer Academic, 313-322.

ABSTRACT: The will to power has non-trivial physical models taken from the class of parallel distributed processing systems, specifically wave-mechanical discrete dynamical systems with cyclical entropy. The will to power is thus linked to research in non-linear self-organizing dynamical systems, including oscillons, cellular automata, spin-glasses, Ising systems, and connectionist networks.
 

Steinhart, E. (1997) Fragments of the Dionysian Body: The Will to Power as Dynamical System . (Interactive Electronic Text) Watertown, MA: Eastgate Systems.

ABSTRACT: This electronic text (originally implemented in Hypercard for Macintosh computers) is a systematic and detailed analysis of Nietzsche's metaphors, symbols, and ideas in The Gay Science. The Gay Science is structured by a large-scale networks of metaphors (e.g. ship, sailor, sea, island, mountain, volcano, tree, sky, bird, storm, sun). Hypertext allows distant aphorisms to be joined for analysis according to their symbols. The Gay Science also contains many of Nietzsche's central themes (e.g. the death of God, the eternal return, the herd and the individual). These themes are joined with the metaphors by analyzing Nietzsche's thought of becoming in terms of dynamical systems.

Analogy and Metaphor

ABSTRACT OF BOOK: 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.
 

Steinhart, E. (1995) NETMET: A program for generating and interpreting metaphors. Computers and Humanities 28 (6), 383-392.

ABSTRACT: 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.
 

Steinhart, E. (1994) Beyond proportional analogy: A structural model of analogy. Pragmatics and Cognition 2 (1), 95-130.

ABSTRACT: 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.
 

Steinhart, E. (1994) Analogical truth-conditions for metaphors. Metaphor and Symbolic Activity 9 (3), 161-178.

ABSTRACT: 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.
 

Steinhart, E. & Kittay, E. (1994) Generating metaphors from networks. In J. Hintikka (Ed.), Approaches to Metaphor. Synthese Library. Dordrecht: Kluwer Academic, 41-94.

ABSTRACT: We describe a computational model (NETMET) of the semantic field theory of metaphor (SFTM). The interactionist approach to metaphor, recently refined as the semantic field theory of metaphor, asserts that metaphors are grammatically well-formed utterances combining terms from distinct but analogous semantic fields. NETMET encodes literal input texts as semantic networks of interconnected concept nodes. NETMET uses clustering algorithms to find densely interconnected knots of concepts; these are fields. The user selects a target field. NETMET then finds several potentially analogous source fields. The user selects one. NETMET then uses constraint-satisfaction algorithms to find the most coherent system of structure-preserving correspondences between the source and target fields. The correspondences are used to move concepts from the source to the target so that the target is analogically extended to more closely structurally resemble the source. NETMET then generates propositions mixing both original target concepts and concepts transferred from the source. NETMET thereby generates many grammatically different kinds of metaphors from literal input texts.

Steinhart, E. & Kittay, E. (1993) Metaphor. Encyclopedia of Language and Linguistics. Oxford: Pergamon Press, 2452-6.

ABSTRACT: We review the main theories of metaphor, particularly from a semantical point of view concerned with meaning, truth, and reference. We outline the semantic field theory of metaphor and explain its semantic advantages over competing theories.