Philosophical Writing

The Resurrection of the Body

Steinhart, E. (Forthcoming) Digital theology: Is the resurrection virtual? In M. Luck (Ed.) (Forthcoming) A Philosophical Exploration of New and Alternative Religious Movements. Farnham, UK: Ashgate.

ABSTRACT: 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.
 

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.
 

Philosophy of Religion

Steinhart, E. (Forthcoming) On the Number of Gods. International Journal for the Philosophy of Religion.

ABSTRACT: 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.
 

Steinhart, E. (2010) Platonic Atheism. Research Report.

ABSTRACT: Platonic atheism is an affirmative atheism. It affirms modern analytic metaphysics and ethics. The platonic atheist is a metaphysical and moral realist. Reality is lawful. The Law includes the laws of logic, mathematics, actuality, and morality. All things fall under the Law. Gods exist only if the Law permits them to exist. The existence of any god is a scientific question. And if any gods do exist, they are subject to the Law. Hence science decides what the gods can and cannot do. Any actions of any gods can be evaluated using the moral laws. Platonic atheism allows the soul to be defined as the form of the body. It allows for life after death via lawful resurrection in other universes. Since all persons are equal before the law, platonic atheists are committed to justice. For the platonic atheist, the Law is divine. The projection of any King above the Law is idolatry. The platonic atheist has a rich system of atheological concepts (piety, impiety, eschatology, soteriology, etc.). Platonic atheism liberates religion from theism.
 

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. (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.
 

Absolute Affirmation

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. (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.

Persons

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

Translation into Bulgarian by Albert Ward.

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.
 

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. (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. (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. (1989) Self-recognition and countermemory. Philosophy Today 33 (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 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.
 

Steinhart, E. (1988) Two principles of moral performance in the thought of Thomas Hobbes. Graduate Paper. Boston College Philosophy Masters Program.

ABSTRACT: Hobbes is a dualist, presenting both an inertial and non-inertial theory of motion. Hobbes advocates a principle of inertial motion in his physics, including his physics of the human body. This view gives rise to a mechanistic theory of the emotions, a theory which would lead to a peculiarly non-Hobbesian political philosophy. In fact, Hobbes abandons the inertial theory of motion as he proceeds into his politics. Instead of being governed strictly by a principle of inertia, motion in the human body occurs in accordance with a will to power: a person has a "perpetual and restless desire of power after power". The will to power leads to a potency theory of the emotions, which Hobbes represents as a race in which every contestant has a "desire to be foremost". The race is the familiar "war of all against all", upon which Hobbes bases his politics.
 

Biology

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. (2004) The Soul. Research Report.

ABSTRACT: We review three theories of the soul. The astral body theory disagrees with science. It is false. The Cartesian theory disagrees with science and is also false. The Aristotelian theory of the soul as the form of the body is consistent with science. Hence the soul is the form of the body. As Aquinas argues, the soul has a part-whole structure. It is functionally divisible - the soul is the community of functions of the body. The parts of the soul are the functions of the parts of the body. The best way to think of the soul is to think of it in computational terms: the soul is to the body as a program is to a computer. The body runs a program; the body-program is a community of organ-programs; the organ-programs are communities of cell-programs.
 

Analogy and Metaphor

Steinhart, E. (2005) Generating and interpreting metaphors with NETMET. APA Newsletter on Computing and Philosophy 4 (2). (Electronic publication).

ABSTRACT: We review the structural theory of metaphor and the computer program NETMET.  According to this theory, metaphors are based on analogies.  Analogies establish counterpart relations between approximately homomorphic structures.  The truth-conditions for metaphors are based on these counterpart relations.  NETMET takes as input a description of a source structure and a target structure.  It finds analogies between them, generates counterpart relations, and uses them to generate metaphors.  The entailments of the metaphors are generated to specify the meanings (the literal senses) of the metaphors.
 

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.

Mechanics

Steinhart, E. (Forthcoming) Ontology in the Game of Life. Axiomathes.

Steinhart, E. (2006) The Existence of Software. Invited talk at 2006 meeting of the Society of Machines and Mentality at Eastern American Philosophical Association meeting. Washington DC.

ABSTRACT: Many ontologies posit levels of existence. A whole exists at a level above its parts; a set exists at a level above its members. Hardware objects are at the lowest level in a computational ontology. Software objects exist at higher levels. The game of life illustrates a stratified computational ontology. The cells in the life grid are the hardware objects. An event is a function from cells to values 0 or 1. A process is a series of events. A process contains a software object iff its content is generated by some rule that is independent of the rule for cells. We give a precise existence axiom for software objects. As expected, blinkers, gliders, puffer trains, and so on are software objects. Software objects satisfy traditional conceptions of materiality. Our conception of software objects has intriguing links to modern conceptions of material particles in terms of symmetry groups and topological invariants. Software objects are not abstract.
 

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. (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. (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.
 

Computation

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

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. (2002) Ordinal machines Research Report.

ABSTRACT: I aim to extend the concepts of algorithms and machines arbitrarily far into the set-theoretic hierarchy of mathematical objects. I work within the universe V of sets defined by Von Neumann - Bernays - Godel class theory (VBG) and the von Neumann theory of ordinal numbers developed in VBG. Since the theory of ordinals is essential to the theory of these machines, I refer to them as ordinal machines.
 

Steinhart, E. (1995) Computational monadology. Computers and Philosophy Conference, Carnegie-Mellon University, Pittsburgh PA, August 1995.

I use computational techniques (mainly from object-oriented programming) to model several systems of coordinated monads. I thus model parts of Leibniz's Monadology.
 

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. (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.

More Precisely

Steinhart, E. (2009) More Precisely: The Math You Need To Do Philosophy Vancouver, BC: Broadview Press.

More Precisely is a mathematics book for philosophers. It introduces the formal tools used in philosophy, and illustrates the applications of those tools with examples from both classical and contemporary philosophy. More Precisely is illustrated with many examples taken from many branches of philosophy - including metaphysics, philosophy of mind, philosophy of language, epistemology, ethics, and philosophy of religion. It shows how the mathematics is directly applied to philosophy.

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.
 

Steinhart, E. (2007) Infinity. In J. Lachs & R. Talisse (Eds.) Encyclopedia of American Philosophy. New York: Rougledge.

ABSTRACT: I review the evolution of the concept of infinity in the work of classical American philosophers, primarily Charles Sanders Peirce and Josiah Royce.
 

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.
 

Logic