Pantheism and current ontology

r (HN TUE «So Religious Studies 40, 63-80 © 2004 Cambridge University Press DOI: 10.1017/S0034412503006814 Printed in the United Kingdom ET Pantheism and current ontology ERIC STEINHART Department of Philosophy, William Paterson University, Wayne, NJ 07470 Abstract: Pantheism claims: (1) there exists an all-inclusive unity; and (2) that unity is divine. 1 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. Introduction A pantheist claims that (1) all existing things are unified; and (2) the P\Aa&kASRVETNE. >2 maximally-inclusive unity is divine (see Macintyre 1967, 34; Levine 1994; Oppy 1997, 320). Much pantheism has been developed in the context of seventeenthand nineteenth-century monisms and idealisms. However, Levine (1994, 217) correctly points out that these ontologies ‘are no longer generally taken to be philosophically defensible’. I aim to extend the history of pantheism into the twenty-first century. I therefore examine three contemporary ontologies to show each permits the development of pantheism. Each of these ontologies is very much alive in current philosophical, mathematical, and scientific thought. The ontologies are: (1) materialism; (2) Platonism; and (3) class-theoretic Pythagoreanism. I will conclude that sophisticated contemporary pantheisms can be developed within Platonism and class-theoretic Pythagoreanism. As might be expected, each ontology is deeply controversial. Each ontology has vocal critics. It would be pointless to try to settle disputes among these ontologies. Such a project would be enormous and would shed no light on pantheism. I am concerned only with how pantheism can be developed within each ontology. For each ontology, I will first illustrate ways it can satisfy the claim that some

Pantheism and Current Ontology Source: Religious Studies, Vol. 40, No. 1 (Mar., 2004), pp. 63-80 Published by: Cambridge University Press Stable URL: http://www.jstor.org/stable/20008510 . Accessed: 05/02/2011 10:55 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=cup. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Cambridge University Press is collaborating with JSTOR to digitize, preserve and extend access to Religious Studies. http://www.jstor.org

Religious Studies 40, 63-80 ?) 2004 Cambridge University Press DOI: 10.1017/S0034412503006814 Printed in the United Kingdom Pantheism and current ontology ERIC STEINHART Department of Philosophy, William Paterson University, NJ Wayne, 07470 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 towhich 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 themost divine all-inclusive unities. They support sophisticated contemporary pantheisms. Introduction A pantheist claims that maximally-inclusive unity is divine 1997, 320). Much pantheism and nineteenth-century correctly points out (1) all existing (see Maclntyre has been monisms things are unified; and 1967, 34; Levine in the context developed and idealisms. that these ontologies 'are no 1994; Oppy of seventeenth Levine However, (2) the (1994, 217) longer generally taken to be philosophically defensible'. I aim to extend fore examine ment the history of pantheism. philosophical, terialism; of pantheism three contemporary Each of these and contemporary and class-theoretic Pythagoreanism. As might be expected, vocal critics. Itwould each ontology be pointless Such a project would be enormous concerned how only with For each ontology, pantheisms Iwill is very much thought. (3) class-theoretic that sophisticated controversial. pantheism within Platonism Each ontology among within it can satisfy (1)ma conclude has these ontologies. shed no light on pantheism. can be developed first illustrate ways are: Iwill can be developed is deeply in current alive Pythagoreanism. I there the develop The ontologies to try to settle disputes and would century. to show each permits ontologies and scientific mathematical, (2) Platonism; into the twenty-first ontologies I am each ontology. the claim that some

unity inclusive maximally is divine or is God. Pantheism requires a concept to severe leads logical problems.' So I consider only unities A whole or membership. clusive unity contains an ontology's I always other Inclusion is thus itself as an im as proper parthood interpret in itself.3 I refer to as its maximum.4 unity inclusive that contain members.2 it does not include things as parts; all other maximally a universal or as a part. Any maximally itself as a member contains No unity parthood. over said to include is sometimes this can be confusing, part. Since proper parts or as a class contains (i) one universal unity with inclusive contains three (3) one class over many the maximally things as awhole parthood are: and to identify Any attempt recognize ontologies These parts; the claim it can satisfy how Current over many (2) one whole particulars; members. of unity. is a one over many. Each kind kinds of unities. many then examine Iwill exists; that its unity Divinity Pantheology each version of each ontology, traditionally attributes how well with divinity. perfect being. However, I do not consider is a person.5 sonal each Iwill relations.6 ontology consider stand with to: respect plenitude; (4) self-representativeness; ontologies can support theodicies Some ontological attributes some spatio-temporal-causal natural otherwise. The ontologies (the objects objects inclusive system non-physical of pure mathematics contains in any space-time. Such an object traditionally more is not simplicity. complex in or ident It is super non-scientific objects are either abstract objects and logic) or possible contained particular these iff it is included do not admit I review Their object (2) Simple/complex. (3) show how also (i.e. it is physical). is natural supernatural mally (2) complexity; with divinity associated ical with souls). I will by posited and soteriologies. An object (1)Natural/supernatural. (e.g. Platonic-Cartesian (1) supernaturalness; (5) holiness. are or per properties the various maxima how specifically a agree with the maximum whether it has any personal whether certain satisfies can the theist and pantheist I do not consider likely to agree on the perfections. not its maximum A pantheist For maxima. different that define I consider associated is a maximally theist that God versions has different ontology Each objects. A maxi and is not is 'eternal'. Supernaturalness is An object is a unit all existing space-times divine. Unity thing. An object is simple iff it has no parts or members. iff it has some parts or members. Theists sometimes iff it is one An object say God is simple.

Pantheism and current ontology A pantheist reject this: a maximally must inclusive unity number of its parts or members. The complexity of an object finite cardinals are just o, 1, 2, 3 and so on. An object is the cardinal of its parts or members the number is some is technical informally like this: an object has infinite complexity is the same cardinality The can define cardinals subclass whose has finite finite cardinal. 1982). We (see Hamilton is maximally complex. The complexity iff theory of infinite infinite complexity iff it has some proper part or as its own. Greater is greater complexity inclusiveness; hence, for the pantheist, it is greater divinity. (3) Poverty/plenitude. Theists say that God's existence is necessary. One popular says that necessary definition the only possible However, world). unities. A unity inclusive istic God includes at all possible this definition all possible seems worlds in all possible exists it includes worlds; worlds. the actual world may (of course, it is hard to apply that merely all possible is existence worlds that includes than one kind of existence existence in all possible So the theistic God exists be to maximally to have a greater The panthe worlds. all necessary Its exist beings. ence therefore exceeds necessity. of amaximally The divinity A unity by necessity. variation of that object possible universes includes that contains is also is closed in the system. that an object X ismaximally plentiful x P. A better that x such maximally instantiates plentiful plentiful and mathematical plentiful. is not Plenitude impoverished An possibilities. object may to make complexity. every model as a plentiful some X is of that of every consistent all physical insofar logic of the infinite The be as complex is to say an object God contains is impoverished object plentiful P, X contains that every model plentiful of all the system this precise theory, X contains contains unity is closed kind any consistent A maximally is to say way theory. A maximally or mathematical physical variations. iff, for every property iff, for every consistent theory. So a maximally in the system, One way all logical possibilities.7 of possibilities of some For example: all physical under than by plenitude some system all possibilities of that kind - for any object all variations object is better measured unity insofar as it contains is plentiful (Kane 1976, 1986). A unity under inclusive as it is not shows that an object.8 Plenitude ismore divine. (4) Self-representation. Since the impersonal pantheistic a mind, it is not to have intentionality or knowledge. It follows that no pantheistic God it is possible to define the core than psychological terms. If God likely is literally omniscient. of omniscience concept in logical However, rather God is not likely to be is maximally inclusive, then omniscience is just God's own self-knowledge. Self knowledge is mental self-representation. of omniscience is that God contains representative system' within England is the classic same form as God. (Royce The We 1927, 506-507). example. theory can drop a representation So God the mentality. of God. The So God core is a 'self Royce's perfect map of England contains a structure that has the is highly developed of self-representation

mathematics (e.g. via reflection principles and elementary embeddings).9 We need not go into the technical details. More perfect self-representation ismore divine. I consider (5) Holiness. 1958) or sublime to which the degree so on. The holiness is what of the object is numinous each maximum Such objects (Kant 1790, secs 23-29). evokes (Otto glorious, are excessive, responses emotional and of awe, terror,admiration,worship, and so forth.Greater holiness ismore divine. The soul and personal immortality A scientifically-minded pantheist can easily adopt theAristotelian theory that the soul is the form of the body theory coheres well with modern Its soul living and thinking machine. versal, property, or structure. many physical particular program idea that the soul The resurrection computations the same program). does not strictly naturalistic. pantheists Each Hick's 150-154; Steinhart 2003). Hick eschatology. body nor any personal and more powerful, possibilities (Moravec can further that (1976, ch. 22) argues to a final union with God. For the pantheist, For each ontology, or eschatology. more divine. A naturalistic I will itsmaximum Any ontology examine version adopt the series (1976, more thus allowing 1988, 102-108, like something of resurrections the series of resurrections of Hick's eschatology can serve salvation. how it conceives has the resources whose in progressively more A pantheist Hick pareschatology. times to the maximum. examine whether Computational God. They can be immortality.10 body becomes of personal of are thus able to provide theories converges doctrine of its pro that resurrection identity'. 'personal converges as a pantheistic compu the guidance (under (2001) have argued many to realize more the soul-program 2000, the guidance (under like Hick's resurrection to develop The are resurrected that humans worlds. used 1985, something ch. 20) argues is failures need not end computations. resurrection of personal can easily adopt soul that the form of 1997; Polkinghorne about Computational A pantheist complex been recently (1983) and Hudson a doctrine with has require neither miracles theories 1994, 124-128). The (Hick 1976, ch. 15;Mackay from naive worries suffer resurrection by as a computer be stressed later by a new resurrection Dilley that can be instantiated Itmust by the old earthly body performed be continued gram) may uni res cogitans. is software theories is a kind of is a very complex can be analysed 1988, 116-122, Tipler 1988, ch. 4). Hardware 180-181; Moravec The body soul pattern pattern is to hardware. as software is not any sort of Cartesian the body tational It is an abstract The Aristotelian 412a5-412b2l). and psychology. is its form. The things. This 1967, Moravec (Putnam thus to the body (De Anima, biology maximum of the soul; to realize Hick's allows for personal I will also pareschatology immortality

Pantheism and current ontology Theodicy spite A maximum is more the fact that it contains inclusive maximally greater being; is greater The tradition and this is to argue being is greater first step would third steps are that seem to derive is perfection little justification. an Aristotelian-Thomistic by in terms of perfection goodness (3) greater to require justified from goodness inclusiveness (i) greater and de good to say that some wants perfection; The that defines who good will have to do (2) greater goodness. second evil.1" A pantheist is maximally unity One way inclusiveness. to be maximally if it can be shown divine and Kretzmann (Stump 1988). A thing is perfect insofar as it realizes or actualizes I am concerned nature. here only with of any living thing is its soul. On the body, deeply ecological in my to humans) (Levine 1994, 218-239). I reflect A career is a possible each soul has many of the a soul is like a library in which biographies. possible careers of one soul may share skills). Each state or less. functional excellences that corresponds (talents, to the degree of the soul are realized by that state. Example: but not at chess; But of pages. of the same soul start out the biographies The distinct its own specific Bill is talented states are more Bob, piano-playing career Hence possible states and overlap more excellences Each is a series of the soul has a degree of perfection specific to death. book diverge. at the piano of all just like a biographical same but gradually soul has souls or career of that soul. history from conception biography of states careers. All possible Each is souls. Pantheism this by including of the soul is some possible the books describe many have calculations. full potentiality is a series theory that the soul is the form of (from bacteria Each soul in its found of living things. The nature the perfections the biological things all living living things the potentialities at chess but not than chess-playing perfect to which the is talented Bob the piano; so for for Bill, the states; opposite holds. A soul-state greater S: a change better); x is better than (worse than) a soul-state than (less than) that of y. A change (x, y) is good for S iff x is worse it is evil for S iff x is better than y (it is a change than y; it is neutral an orange with a knife; a good change is to cut yourself. An evil change is typically physically you're working a good change A natural way y iff the perfection of x is is any pair (x, y) of states. For any soul from worse for S otherwise. is to peel to Example: it; an evil change or psychologically painful; is pleasurable.12 to define the degree to let it be the sum of the perfections any career of some soul of perfection of any career of the soul is just of its component is the extent to which states. So the perfection its specific talents during that career. The distinct verses. For any soul, we may career of that soul."3 For any soul S, if no career of S is realized careers suppose of souls are actualized that any universe are exercised at distinct contains of at most in U, then uni

a set of careers of distinct universe contains souls. Soul X co-operates with soul such that what is good for the one entangled competes with is good for the one a wolf the wolf starves is eaten W2 is evil for and a rabbit. and Y W1: In universe dies. W2: is evil for the rabbit but good careers are Soul X such that what two possible universes are entangled the rabbit escapes from the wolf; the wolf the catches rabbit; the for the rabbit but evil for the wolf; W1 is good and dies. Universe their in for the other. is good Consider the other. In universe and non-human) (human iff changes in their careers soul Y iff changes involving of of S. Any rabbit in U, then the goodness of U for S is nil; if one career X of S is realized goodness U for S is the perfection for the wolf. Hence the wolf and the rabbit of all souls (McCabe compete. occur and competition Co-operation among all careers 1981,618-619).Much moral evil (good) is analysable as competition (co-operation) humans. among as human competition include entanglement and oppressed. Much natural with (co-operation) forces or as non-human and inorganic ganisms competitive and slave, oppressor either is analysable of moral Examples and victim, master competition criminal evil (good) non-human or (co-operation) with non-humans. Examples of natural competitive entanglements include: predator and prey; infector and infected; A career in other universes. goods and host. parasite in one universe due to lost competitions Evils suffered sated by a career that contains a good that contains career of S inW inW that contains the coin tails you win; U2. Your universe comes set W some of M of W for any set Z of souls A maximum tails in up loss in U2 is in the set {U1, U2} is com suffer for S is the goodness M contains of W for S. is the sum over all z in Z of the goodness in amaximum whose S is the of Wfor of w for S. Each maximum the goodness for z. So there is goodness or ecosystem. comes in U2; my and for any soul S, the goodness of the goodness of universes; The goodness of W in W all w Iwin, for myself. For any set W of universes, sum over by a career of S is tossed: heads U1 but by your win in U1. So the evil you in that set; likewise pensated a coin in universe up heads loss in U1 is compensated by my win compensated (x, z). For example, a good change inW insofar as each is compensated (x, y) is compensated an evil change that contains by (x, y) is compen (x, z). For any set W of universes, change and for any soul S, the evil suffered by S inW can be compensated an evil change goodness for a family, is greater town, nation, for more souls species, is more divine. For any set W of universes, to which the evil suffered contains some for S. The justice of W and for any soul S, the justice of Wfor set W of universes; justice of W M the justice of M for soul S is the justice of W is compensated for any set Z of souls for z. So there is justice S is the degree in W. Each maximum by S in W is the sum over all z in Z of the in a maximum for a family, town, nation,

species, A maximum or ecosystem. whose justice current Pantheism and is greater for more 69 ontology souls is more divine. Materialism itsmaximum Materialism and Materialists typically affirm only (2) the concrete properties ticulars; and existence and universals). 'x exists says It seems =df x belongs can advance is just the whole as parts It includes all actual and possibilia is often denoted physical '@'. I use (e.g. math objects when one only things sort of maximally universe (at all places of the maximum. inclusive (Oppy 1997, 328). and times). Abstract The actual We that abbreviation. he that is our world'. system actual physical are not parts objects verse par deny (1985, 35) typifies materialism to the space-time-causal that a materialist the maximum unity: among (4) abstract objects; Aune concrete them. They of: (i) actual and relations of (3) possible the independent ematical objects the existence uni physical can evaluate the divinity of@. The divinity For the materialist, consider actual physical @. I universe of this maximum: @ has both (1)Natural/supernatural. object is the whole the maximum of divinity the degree It is a natural maxima of the materialistic spatial extension and temporal duration. So it is less divine. and not supernatural. (2)Simple/complex. Current cosmology suggests that @ is both spatially and finite temporally (it is only a few billion years old). Its spatio-temporal volume estimated to be finite. The complexity finiteness of @ is not certain, is finite. The number of basic particles is of @ is likely to be finite. Although the plausible. decreases the that @ is plentiful; after it is highly A materialist (3) Poverty/plenitude. all, the materialist thesis about notion). example: one it is only a few billion Such finiteness of @. divinity order' light years wide; will want says that @ contains the instantiation There the property fail to have models of properties are obviously many of being a unicorn to argue all that exists. However, or models of theories properties not is not instantiated plenitude is a (it is a 'second instantiated at @. For in @. All theories but in @. The actual universe is impoverished. Any thing It is therefore less divine. (4) Self-representation. its brain) contains representation intelligent some mental of the whole of @ are representations model physical of @. Such (e.g. a human a mental of @ by a part of @. Although of @ within @, they are partial body with model of @ is a human mental and inaccurate. models More

of @ more intelligent species may to believe that any part of @ has the same complexity any part of @ exactly to see how representative system. (5) Holiness. emotional The size responses and associated sublime when infinite structures The to any It is therefore objective. (6) Soul and The immortality. It endures terialist, resurrection requires physical medium. human for such One A materialist souls that all presently pareschatology one career y of the soul of x is just the perfection of y. of any soul suffers from the fact in @ (Mann 1991). Evil changes lost in @ is not won in @ else. The anywhere is low or zero. that @ is the best universe. However there simply is a kind of fatalism. This new assert of any soul. For any soul, the goodness are fictions try to argue is for any soul or set of souls, goodness. in some nor any good argu Hick's of @ for that soul is therefore it is the only possible because simulate neither It is a less divine. thing x, exactly living future will realizes is therefore form. (1994, 220) any good evidence Materialism A competition can is not For the ma endures. of the old body and Tipler in the distant that all but one of its potentialities justice of @ for many ap ma Its holiness is a substantial is likely to be low or zero. Every actual compensated. laws and cannot So @, as conceived holiness. as long as the body (1988, 116-124) career does not realize much are not is abstract. the reconstruction Its maximum For any single universe The mathematical from abstract A strict materialist ontology. Yet there is neither speculations. in @. The goodness realized and inspire @ does not seem very of @ come form of the body computers bodies. and It is 'dynamically of other ontologies. glory exactly Moravec nor his eschatology. (7) Theodicy. and awe less divine. universal. powerful other 1999). However, For such order concrete extremely evokes It is glorious. to have at best amind-dependent seems difficult a self of @ tend toward divinity the maxima 'natural order'. it is hard of @. @ is not the whole holiness. (Harrison beauty However, as @. It is therefore of @ easily aspects in the materialist's not found terialistically, existing with with compared is missing. accurately. less divine. complexity as 'nature worship' pantheism ment represents It is therefore (Kant 1790, sec. 28). These sublime' peal represent more of all possible universes just low the justice or goodness of @ does not exist any greater justice or is at best of Stoic or Its theodicy a kind Nietzschean amorfati. Such fatalism non-actual viously suffers from serious defects. The non-actual careers are counterfactual stories told in @. Many of these stories souls) portray better every counterfactual lives for the souls story of some does not exist any thing equate of good theodicy. career of some that career. soul, materialism If the account is right, then this failure of existence terms of perfection The absence that realizes involved. Yet these stories is itself an evil. It is a privation. So @ is thus less divine. (of actual or ob are false. For says there of goodness in is a failure of perfection. Fatalism is hardly an ad

(the actual physical of materialism The maximum to be divine to have much claim pantheism identify does and universe @) does not seem or to be God. Although it seems with God, this maximum current Pantheism much 71 ontology traditional to be a poor divinity. Platonism The addition of abstract A materialist affirms only jects (i.e. physical particulars the materialist's ontology. Platonism and possible and universals). There adds only abstract Abstract particulars functions. Abstract objects of a system of actual concrete A Platonist adds various the existence are many kinds are mathematical as numbers, such 4 and universals). particulars objects to A thin kind of of Platonism. (i.e. abstract objects ob objects and sets, among those ab stract particulars. Leibniz is a classical example of a thin Platonist: only one concrete exists; other possible universes are merely objects universe God's mind of and relations abstract 1976). A thick kind of Platonism (see also Plantinga I do not consider as well. possibles are properties universals adds concrete - so 'Platonism' thin Platonism in means thick Platonism. of Platonism The ontology for any science of any possible realism - all possible modal verse @ is only one of abstract example: propositions universes towers over are sets of possible needed it here) entails exist.15 Our actual physical uni universes the system universes. (Miller 2001). The of possible Lewis universes. For (1986) is probably the of this Platonism.16 Platonism and the great chain of being Platonism portrays mathematics is an iterative parti physical or universal (as I construe alternative Classical 1971). Each (1) all possible particular Platonism these many objects example 1936). Modern ality universe. physical among hierarchy best modern includes: therefore and (2) at least every abstract culars and universals, gives of being' (Lovejoy a logically precise meaning: this metaphor An hierarchy. level can be thought reality as a 'great chain iterative hierarchy of as something re is a series of levels (Boolos like a link in the classical great chain of being. Each level is indexed by a number. on. Each higher contains level is formed all combination tells us that for any endless every number endlessly So there are levels numbered the levels below it. For example: of all objects on levels o and 1.Modern series of numbers, in the series. For example: increasing so on is an endlessly series; o, 1, 2, 3, and so from its limit number increasing series; there is a limit number level 2 mathematics greater than the series 1/2, 3/4, 7/8, and so on is an is 1.Likewise: its limit number the series o, 1, 2, 3, and is w. w is the least infinite

number (it is greater than every hierarchy is defined by four rules: VO= all physical objects; V? 1= all combinations V=the V= of all objects of all objects on all lower levels on all V, for every number that occur on the various and collections hierarchy are proper formally classes; known as classes. The all the other on the first level V1 is the empty likely to admit. Classes For instance: can always include all the pure classes all physical to identify and their maxima There versions (1) First version: The hierarchy to contains will want. two versions and examine (amaximum): is all possible all that exists physical and just enough objects abstract objects the needs of all possible sciences. suggests there is some upper bound on the possible sizes of space-times. on physical If Lewis is right, then there will be some objects needed an upper bound upper bound One good to serve pure objects with can be extended hierarchy I state unity have the mathematicians. all mathematical of Platonism. or not each has an all-inclusive is standardly philosophers to go with the Platonist objects that as pure classes. mathematicians by any mathematics. needed Two Platonisms are many of the classes that no materialist class are known to V,. The Platonic and mathematical at the top of any are sets. One 1965), I think it best add them n. levels of Platonic classes are pure classes. Although objects does not want who classes if k is a limit number; {}. It is an object {{}} and {{}, {{}}} are pure classes. Modern this (cf. Benacerraf A philosopher classes class built up from the empty that all mathematical whether on all lower levels; of all objects are more disputed form of a Platonic collection The combinations assert The generic the collection hierarchies occurs finite number). complexity. on the hierarchy for this hierarchy candidate Neumann-Bernays of abstract hierarchy of abstract (the VNB hierarchy; (1986, 103) This for all possible sciences. is known as the Von objects see Hamilton as the little totality. 1991, ch. 2).17 I'll refer to this hierarchy Lewis is 1982, ch. 4; Devlin It is defined by these four rules: VO= all possible physical V +1= all combinations things; of all objects V>= the set of all objects on all lower levels science infinity needed for all possible The little totality= the proper on all lower levels; if X is less than the biggest (e.g. numbers class of all objects definable in VNB); on all Vn for every number n. (2) Second the abstract version: system the concrete includes system all possible includes mathematical all possible objects. physical objects; Every consistent

Pantheism and current ontology mathematical theory describes a part of the abstract refers to this as 'full-blooded and the abstract achieve mathematical Platonism' are both systems logically possible levels. To do this, start with every consistent 'large cardinal' cludes all possible abstract systems.18 The concrete is defined totality It is arguable is to extend plenitude axiom objects. to FBP, the concrete (FBP). According plentiful. (1998, ch. 3) system. Balaguer that the best way the iterative hierarchy through standard VNB class-theory (Drake 1974). The It includes resulting all models system plus the abstract to all and add in hierarchy of all consistent axiom is the big totality. The big system by these four rules: VO= all possible physical 1= all combinations V things; of all objects Vk= the set of all objects on all lower levels if k is any logically possible on all lower levels; limit number (including every consistent largecardinal); The big totality= The divinity I now the proper of the Platonic examine class of all objects on all Vn for any number n. maxima how well the maxima defined by the two versions of Platonism satisfy the pantheistic criteria of divinity. Each version of Platonism avoids the charge an extra name (see Levine that the identification to something of the maximum (e.g. the universe) I look at the degree 1994, 26-28). totality and the big totality with God is just adding which is already properly to which the attributes named of the little tend to divinity: (1)Natural/supernatural. The little totality includes all possible space-times. It is therefore not in any space-time. supernatural. includes Since the basis universe, infinitely many totality the big totality Analogously, (2) Simple/complex. physical All space-times are in it. So the little totality is is supernatural. there are infinitely many of the little totality levels; however, it is bounded the little totality. Its infinity variations is infinite. The of the actual little totality has by the limits of science. is not scientifically The big constrained. Its infinity contains every logically possible cardinal number. Its complexity is maximal. (3)Poverty/plenitude. The little totality has as its urelemente (its objects on level VO) all possible However, needs, possible since physical things. This set of urelemente the abstract part of the little totality it is not mathematically universes as well plentiful. The big totality as all mathematically is physically is constrained possible plentiful. by scientific includes all physically universes. It is maxi are each sufficiently mally plentiful. (4) Self-representation. The little totality and big totality complex to instantiate all sorts of powerful reflection principles. However, the completeness of any self-representation is blocked by the existence of physical urelemente. So both totalities fail to be maximally self-representative.

physically is mathematically while totality all the other maxima cardinals. There has a far greater therefore abstract entity. has tions. Platonism affirms needed that (i) the earthly universe each human there resurrection is some resurrection Platonism allows of Hick's pareschatology. tied to physicality, it is not possible Platonic maximum. for any and since series So Platonism the Platonic maxima of resurrection cannot the It permits the bodies realize Hick's are not physical, to either to converge bodies of into is extended the resurrection since However, career into the transfinite, of resurrections. for a very rich system transfinite. remain that career in which universe (4) @, @*, @** and finite earthly that career can be extended realization always universes exist. For each universes (3) since U*; U* does exist; universe series of resurrection soul, for every way universe in a larger resurrection that U is embedded exist, for every U, the next resurrection there exists an endless (2) for any universe @ exists; all possibilities therefore: theory of serial resurrec to support Hick's U, it is possible so on. All possible existing of any or all of its instances. the death after form exists The The big totality is an eternally The soul (the form of the body) the resources the big totality as a that grasps than any other maximum. to holiness claim (6) Soul and immortality. Platonism Y, then X ismore (Rucker 1995, 202-218). intuition be a kind of mystical whole must can that the big totality has the kind of by divinity. Any cognition required transcendence large is ineffable. We for any levels X and Y, ifX includes than Y. It is thus arguable like the big totality all possible to specify the big totality in which is a very real sense it analogically: only describe way is no complete is no axiomatic there definitions, axiomatic have of the big totality. There way. Moreover, in a truly awesome infinite definition qualification. It is sublime without or mathematically. not constrained The is The big totality sublime. of the mathematically rule out any full instantiation big limits on the little totality of the little totality. The scientific or glory or sublimity any awesomeness to negate seems This constraint possibility. of scientific notion by the is constrained of the little totality The size and complexity (5) Holiness. Its totalities eschatology. are thus less divine. (7) Theodicy. is best for S iff for every career W For any soul S, a set of universes that career is realized. For any set X of of S, there is some universe inW at which souls, a set of universes W is best for that set iff for every career of every soul in X, contains whole It is therefore maximally includes big) of Platonism maximally good. Evil occurs is perfectly best (perfectly) all possible only So any maximum that soul and for the for every possible is that than which good. universes, no better either totality each totality of Platonism in the parts of the totality; but is (little or Since is the totality as a good. For every possible change is both is realized. souls. Any such maximum set of all possible possible. whole universes all possible that career inW at which there is some universe that happens soul, for every possible to X in some universe, career X of that soul, there is a variant for every evil in which some

Pantheism and current ontology compensatory universes event good of X. Consider and the rabbit. They are predator the wolf from the wolf; rabbit escapes to a counterpart happens the wolf involving starves and dies. for the rabbit but evil the rabbit; the rabbit is eaten and dies. Universe W1 is good for the wolf. evil; if both then there is an uncompensated pensated by good. Modal an appropriate humans between conflicts among people; (3)misfortunes. by some good, the whole system occurs If only one universe then each evil is com that attack or infect universes of possible (2) moral them; evil is compensated ismaximally the maximum (1) natural covers: Since every possible in the parts of the maximum; only exist, compensation and organisms conflicts catches In W2, the wolf for the wolf; W2 is evil for the rabbit but good exists, the again and prey. InW1, the just. Injustice is perfectly as a whole just. The totalities are both better of Platonism candidates for God than the actual physical universe. The little totality suffers from conceptual constraints thatmake it a poor for a pantheistic candidate these constraints. is the best candidate The big totality suffer from God. The big totality does not for a pantheistic God so far.Nevertheless, class-theoretic Pythagoreanism provides a better candidate. Class-theoretic Pythagoreanism The purification of physical objects Platonists put physical things on the bottom level of their hierarchies. Quine classes has frequently observed things can be identified that physical with 1969, 147-152; 1976; 1978; 1981, 15-18; see also Harman (Quine pure 1967 and Gottlieb 1976,63). If all physical things are pure classes, if all mathematical and pure classes, then all that exists are pure classes class-theoretic Pythagoreanism. Rucker is a set. I am a set, my thoughts This result is and their properties. (1995) puts If reality is physics, if physics ismathematics, everything things are also it like this: and ifmathematics are sets, my emotions is set theory, then are sets .... The whole physical universe could be a single large set U .... If the universe is completely finite, then U in V,, is a set somewhere .... And so very far out - surely U must lie inV+,,, universes would be sets in V. (200-202) even if it is infinite, we wouldn't expect it to be .... Under this viewpoint, all the possible It should be obvious that class-theoretic Pythagoreanism is controversial. How ever, it is not my purpose concerned with The pantheism how either to defend the ontology of modern or to criticize permits Pythagoreanism any ontology. the development I am only of pantheism. shares no theology with the ancient Pythagorean religion. Pythagoreanism is like the full-blooded version of Platonism. However, the bottom level of the hierarchy identified with pure classes is empty. on higher It is empty because levels. There the urelemente are no empirical are all or physical

all consistent It rises through hierarchy. of the Pythagorean limits on the height large cardinals: 1= all combinations Vn on all lower levels; of all objects V, = the set of all objects if k is any logically possible on all lower levels limit number (including any consistent largecardinal); V=the proper For Pythagoreanism, class of all objects on all Vn for any number as for full-blooded Platonism, theory Every consistent how well the plenum The plenum ismuch like the big totality totality, the plenum is supernatural, the same It has ways. First, the plenum a function adding the ideal of divine approximates No greater degree any other maximum. ismore the plenum Hence contains two kinds relations. The plenum the plenum of things contains ogy and his eschatology. there of concrete than any physical worlds time, perfectly than is logically possible. are all pure clas c. The big totality relation structured and mathematical) as more perfectly unified is the plenum relations, by many by many relation. So than the big totality. It is by one one kind of thing structured For the Platonist, There universe. These One However, are concrete systems of both Hick's there is an upper universes). (physical bound. and causality. is to conceive for the realization provides systems is no such upper of space, more divine. Third, Pythagoreanism plexity self-representation the membership (physical can be regarded therefore more of set theory by are of the same kind. They relation: one by exactly structured maximal with hold the language of self-representation are structured all other maxima ses. While totality. Reflection than the big totality. divine in the plenum all objects Second, in three axiom that says that j: V-+V is a j; (2) add a wholeness of V into itself (Corazza 2000). The function j embedding system. The itself. It shows that V is a self-representative reveals how V mirrors plenum totality symbol elementary non-trivial embeddings (1) extend plentiful, maximally than the big elementary For example: in the plenum. strength Just like the big the big from It differs self-representative about theorems and principles is more complex, criteria of pantheistic of Platonism. maximally theodicy. various satisfies Inow examine important as the plenum. maximum divinity. and holy. part of V. I some describes Pythagoreanism of the Pythagorean The divinity plenitudinous. V ismaximally or mathematical) (physical of class-theoretic refer to the maximum n. bound of them as infinite games. on the com for the Pythagorean, systems far more involve mathematical good way pareschatol complex generalizations to think of such For the Pythagorean, super-physical the series of

Pantheism and current ontology resurrections goes on through concrete systems of arbitrarilyhigh complexity (thus realizing Hick's timately converges there soul, The Pythagorean is a better plenum totalities of Platonism. the best candidate maximum. is a series within for the pantheistic It satisfies that career divine. criteria than the God I've reviewed, It is the greatest God. the pantheistic For every in which for the pantheistic candidate all the ontologies Among limit, it ul eschatology). the plenum is therefore more itself. The plenum to the plenum rises without (thus realizing Hick's to the maximum converges of every career the series Since pareschatology). the plenum for divinity more is unified and most than any other maximum. Conclusion Pantheism an all-inclusive (i) there exists asserts: unity; and (2) the all inclusive unity is divine (isGod). Ihave reviewed three contemporary ontologies to see how pantheism fares with alism; (3) class-theoretic (2) Platonism; an all-inclusive ontology has satisfies certain pantheistic Materialism to each. The ontologies respect and (i)materi (1) how each any such maximum (2) how well criteria of divinity. at best a maximum provides that is a poor candidate I showed Pythagoreanism. maximum are: (the whole It is therefore for God. actual physical universe) that so many pantheists surprising identify God with the whole actual physical universe. Platonism provides (at least) two maxima: various (1) the little totality, for God candidate than the materialist's attributes and (2) the big totality. Each maximum. of God very well. However, is a better The big totality the Platonic dualism satisfies the on which it is based undercuts its self-representation, its unity, and its soteriology. Class theoretic Pythagoreanism posits one maximum: the plenum. The plenum has all the advantages of the big totality. However, the plenum has greater self representation, greater uniformity, and better soteriology. It is thereforemore divine. The plenum is an excellent candidate for a pantheistic God. Notes 1. If the maximally inclusive unity it is arguable such'. However, or 'being as such'. then itwill be something is a universal, is not a property that existence It is further arguable that 'to be is to be the value of a bound that our best current variable'; like 'pure being' so there are no universals theory of existence but no logic has variables or 'being as like 'pure being' is the Quinean that range over theory 'pure being' or 'being as such'. 2. It is sometimes argued has one kind of unity; seriously that there are different an organism or mind argue that reality is an organism the unity of all things kinds of unity: has a more perfect or that it is a mind. is the unity of life or thought. nineteenth-century monisms of which all other things are parts or a class of which criticizes such unity as merely and idealisms. Such views For my purposes, all other 'formal unity'. He points a heap of sand (amere A scientific pantheism today can the maximally out (30) that Plotinus's affirm that cannot are relics of seventeenthinclusive things are members. or sum) aggregate kind of unity. Nobody and unity is a whole Levine (1994, 29-30) One, Hegel's geist, and

Lao Tzu's Levine tao are not formal unities; says however, and member-class scientifically I see no way is (i) even richer than the obsolete theories includes itself as a proper part or member, discovered by Russel and Burali-Forti. proper parts or members, 4. Ontological arguments is superior' 'that than which ordered typical make no greater ordered maximally (where ontological hierarchy but it does not believe God asserts typically familial, moral, objective arguments can be made variations. through all variations. (as a person) God So a collection o is as complex possible finite combination contain every member plentiful than u. 9. A whole satisfies may of its urelemente. the existence if and only that is also infinite. An elementary universe V to a part M of the universe through all from V to M, then M immortality'. of u. HFS is infinite, it very roughly) is a kind of logical mirror of the whole, a function truths about V. So if of V. is arguably who pantheist ismore then there is some all (first-order) Yet Plotinus every of ; but o does not for every property is (to put (2001) is amodern likewise Leslie is invariant of x is also in U. is plenitude. variations is not a subclass that preserves deny personal order or an are a society. every member embedding 'Pantheists is a in the collection if the whole embedding lays finite sets (HFS). But HFS contains if (to put it roughly) For example: God legal: God moral is invariant all logically possible of HFS but HFS from the whole immortality; of an objective ifmembership of hereditarily part of the whole affirms personal unity, So God has is a father; political: God keeps his promises; So HFS contains there is some part that also has that property. (1994, 248) says God that God and humans under system of the to the all-inclusive in social relations. persons Familial: if and only to closure. Closure interpret complex at the top of an = for every x, if x is in U, then every variation as the whole a reflection principle identical is to say that its existence of HFS. So (u)is a subclass there is an elementary human admit worlds is necessary Ifwe for the existence is an object or from any than' or 'ismore into arguments or benevolent; will not admit Say U is necessary is thus equivalent engages is virtuous reasons like a person'. relations with humans. a pantheist Necessity inclusive in one God, a God or anything is 'that to which no greater can be conceived' Fourth Way 1936). that God 8. The ordinal God (a great chain of being - Lovejoy exists at all possible possible For Augustine, things as or less, there is a most). than' as 'ismore is a person justice. However, objects. there are degrees more or rewards. A pantheist 7. To say that an object io. Levine and is (2) like those all existing is 'that than which 'is greater 'is the belief paradoxes includes unity legal, and political judge; God punishes unity inclusive laws and is a king; moral: down by current part-whole by Levine, thing. to maximal God unity. The maximally (1994, 3) says that pantheism 6. Theism discussed (1077, chs 2 and 3). Aquinas's to' and inclusive complexity inferences is possible' 'is superior then the traditional 5. Levine unities inclusive be an existing for Anselm, to an upper bound series than', sense of such unities. we get self-referential If the maximally then it cannot (1993, 40-64); the order relations pantheist's scientific of unity offered viable. 3. If the unity nothing to make (30). I reply that the notion 'Formal unity will not do' a pantheist who affirms personal immortality. does not face the traditional is. Pantheism therefore not have a theodicy that the maximum are metaphysical 12. Pain ismaximally concepts of the organ's functional doing some organs include The organs of health, property, family, or friends 13. For each career of each soul, we ought but we can get by with 14. Thin Platonism sort of Leibnizian is painful; has the actual physical universe of thin Platonism it is only capable of partial lots of abstract is natural; of thin Platonism signals the loss on it for on which the other persons artificial, or social. Hence P the loss is pleasurable. volume that contains that career; objects. Its maximum is the one career. it is less than maximally self-representation; 'best-of-all-possible-worlds' 1979, 1997). So the maximum @ plus of these space-time contains it therefore the parts of P's body; P's artificial include be natural, the recovery to refer to smallest (i) that good and evil is an organ of X iff X depends include organs P's social organs the idea that one universe sum of all these. The maximum impoverished; of some organ: in good or evil changes may involved evil. Note will to argue both of right and wrong. concepts the destruction P, P's natural P depends; still want may contains skill, or talent. Say an object excellence, the tools on which depends. to the moral evil. Pain signals For any person function. (Levine 1994, i96-218). A pantheist a pantheist sense. However, (2) that the maximum good; and orthogonal is not evil; pain signals 'problem of evil' theistic in any theistic theodicy without it is not sublime. the personal is only slightly more divine complex; Its theodicy Leibnizian God it is is at most (see Leslie than @. It is a poor God.

Pantheism and current ontology 15. Forrest (1997, 312) says: universes 'Positing many would that all mereological sums or sets have exactly are farmore that the mere complex replace pantheism seem be a god but the sum of them would universe would to be God.' required the same kind of unity. Moreover, sum or set of possible For our by polytheism. to lack the unity universes. Modal Platonism's I reply maxima realism does not entail polytheism. See his (1986), 3-4, 50, n. 37. Lewis i6. I read Lewis as believing in sets and classes. but I'm just using Lewis as a close exemplar. 17. A strictly set-theoretical be any maximum are by now theoretic so widely Platonists i8. It is arguable founded is likely to deny hierarchy that one there will not hence classes; 1996, 127). However, like VNB class-theories is not likely to find many things; strictly set today. through all consistent extended It contains theories. all mathematically of non-well-founded (Aczel 1988). The universe contains models large cardinals set-theoretic possible it includes well-founded 1982, sec. 4.5). For example: (Hamilton universes that there are any proper (see Bigelow among mathematicians accepted that an iterative hierarchy of all mathematical universes Platonist of any set-theoretic (1991) complicates and class-theoretic universes and non-well as a graph sets appears in the hierarchy. References Sets, CSLI Lecture Notes ACZEL,P. (1988) Non-Well-Founded tr.M. J.Charlesworth ANSELM (1077/1965) Proslogion, AUGUSTINE (1993) On the Free Choice of the Will, AUNE, B. (1985)Metaphysics: M. BALAGUER, The Elements (1998) Platonism of Mathematics tr. T. Williams University Press), of set', in Benacerraf (eds) Press). (1984) Philosophy 272-295. 84, 127-154. Studies, and Putnam 2nd edn (New York NY: Cambridge axiom and Laver sequences', 'The wholeness Press). and H. Putnam BOOLOs,G. (1971) 'The iterative conception CORAZZA,P. (2000) of Minnesota in P. Benacerraf Philosophical Selected Readings, Press). (New York NY: Oxford University BIGELOW,J. (1996) 'God and the new math', Mathematics: of Notre Dame IN: Hackett). inMathematics could not be', (New York NY: Cambridge IN: University (Indianapolis MN: University (Minneapolis and Anti-Platonism BENACERRAF, P. (1965) 'What numbers 14 (Stanford CA: CSLI Publications). (Notre Dame Annals (eds) (1996) Philosophy University of Press), 486-502. of Pure and Applied Logic (October), 157-260. DEVLIN,K. (1991) The Joy of Sets: Fundamentals of Contemporary DILLEY,F. (1983) 'Resurrection objection" and the "replica DRAKE,F. (1974) Set Theory: An Introduction to Large Cardinals FORREST,P. (1997) 'Pantheism The Monist, and science', D. (1976) 'Ontological GOTTLIEB, M. HALLETT, HAMILTON,A. (1982) Numbers, University reduction', Journal Sets, and Axioms: (New York NY: Springer-Verlag). Studies, 19, 459-474. (New York NY: American Elsevier). 80, 307-319. 73 (3), 57-76. of Philosophy, Set Theory and Limitation (1988) Cantorian Set Theory ',Religious of Size (New York NY: Oxford University The Apparatus Press). (New York NY: Cambridge of Mathematics Press). HARMAN,G. (1967) 'Quine on meaning HARRISON,P. (1999) The Elements (Boston MA: Element HICK, J. (1976) Death Books II', Review Metaphysics pantheism', LEWIS,D. (1986) On the Plurality (1991) Parts of Classes The Monist, of Worlds Philosophical Quarterly, (New York NY: Macmillan). (Totowa NJ: Rowman A Non-Theistic (1994) Pantheism: the Universe (Ithaca NY: Cornell University 24, 115-136. Concept & Littlefield). 80, 218-231. (New York NY: Oxford University M. LEVINE, and & Row). Person reason', American tr. J.Bernard of Judgment, LESLIE,J. (1979) Value and Existence (2001) Infinite Minds of the Human and sufficient of reason', Erkenntnis, (1997) 'ANeoplatonist's 21, 343-367. inNature Inc.). KANE,R. (1976) 'Nature, plenitude KANT, I. (1790/1951) Critique of Metaphysics, the Divinity Understanding and Eternal Life (New York NY: Harper HUDSON, H. (2001) A Materialist (1986) 'Principles and existence of Pantheism: Press). of Divinity (New York NY: Routledge). (Cambridge MA: Blackwell). (Cambridge MA: Blackwell). Press),

LovEjoy, A. (1936) The Great Chain MAcDONALD, S. (ed.) Theology of Being (Cambridge MA: Harvard University (i99i) Being and Goodness: (Ithaca NY: Cornell University MACINTYRE,A. (1967) 'Pantheism', The Concept of the Good Press). inMetaphysics and Philosophical Press). in P. Edwards (ed.) The Encyclopedia of Philosophy, vol. 6 (New York NY: Macmillan). MACKAY,D. (1997) 'Computer Prometheus Books), software and life after death', MCCABE, H. (i981) 'God, evil, and divine responsibility', (New York NY: Oxford University ch. 56. MANN, W. in P. Edwards Press), (199i) 'The best of all possible in B. Davies inMacDonald worlds', realism', MORAVEC,H. (1988) Mind The Future of Robot and Human Children: (ed.) (2000) Philosophy (2000) Robot: Mere Machine 28, 3-38. Philosophia, to Transcendent quantification, OTTO, R. (1958) The Idea of the Holy, A. (1976) 'Actualism PLANTINGA, Intelligence tr. J.W. Harvey 253-273. PUTNAM,H. (1967) 'The nature of mental states', vol. in M. Loux in N. Block 1 (Cambridge MA: Harvard University QUINE,W. V. (1969) Ontological (1976) 'Whither physical (ed.) (1980) Readings in the Philosophy (1978) 'Facts of the matter', Southwestern Journal of Philosophy, (i981) Theories and Things (Cambridge MA: Harvard University Pittsburgh (1991) G. W. Leibniz's Monadology: of of Science, University Press). 39, 497-504. 9, 155-169. Press). Philosophy An Edition the Actual and Phenomenological for Students (Pittsburgh Research, PA: University of Press). ROYCE,J. (1927) The World Macmillan universalism', and in Philosophy (New York NY: Columbia Studies of mereological Press). 223-231. Boston (1998) 'In defense Press). 80, 320-336. (ed.) (1979) The Possible Press), and Other Essays Relativity objects?', The Monist, (New York NY: Oxford University worlds', Press), 347-360. RESCHER,N. (Cambridge MA: Harvard (New York: Oxford University Mind and mereology', and possible (Ithaca NY: Cornell University REA,M. of Religion Press). Oppy, G. (1997) 'Pantheism, Psychology, (Amherst NY: (ed.) (1991), 250-277. MILLER,R. (2001) 'Moderate modal University (ed.) Immortality 247-249. and the Individual, First Series, Supplementary Essay (New York NY: The Company). RUCKER,R. (1995) Infinity and theMind E. (2003) STEINHART, 'Supermachines (Princeton NJ: Princeton and superminds', Minds STUMP, F. and KRETZMANN, N. (1988) 'Being and goodness', TIPLER,F. (1994) The Physics of Immortality: (New York NY: Doubleday). Modern inMacDonald Cosmology, Press). University and Machines, God, and 13, 155-186. (ed.) (1991), 98-128. the Resurrection of the Dead