Atheism and Possibility

This is a guest post by Eric Steinhart, Professor of Philosophy at William Paterson University.

The concept of natural creative power (natura naturans) is found in both Wicca (where it is the ultimate deity) and in atheistic philosophers (who do not deify it).  Natural creative power is the ultimate immanent power of being; it is being-itself.

Unfortunately, being-itself, as the deepest and most abstract of all universals, also seems to have little or no meaning.  The concept of being-itself is so purely formal that it is like pure formal logic.  Pure formal logic does not assert the existence of any objects at all.  It is entirely devoid of ontological content.  Fortunately, being-itself manifests itself in many ways; it manifests itself in the various less abstract categories of being.

Within the scientific ontology outlined previously, being-itself divides into universals and particulars.  Particulars divide into the mathematical, the geometrical, and the material.  This division is equivalent to the division of being-itself into the abstract and the concrete.  The abstract includes universals and mathematical objects; the concrete includes geometrical and material things.  It really doesn’t matter how you slice it.

Categories gain ontological content only by being contrasted with other categories.  Thus the category of mathematical being has ontological content: in mathematics, to be is to be mathematically possible, and to be mathematically possible is to be consistently definable. Poincare writes that “in mathematics the word exist . . . means free from contradiction” (1913: 454).  And Hilbert wrote to Frege that “if the arbitrarily given axioms do not contradict one another with all their consequences, then they are true and the things defined by the axioms exist” (in Frege, 1980: 39-40).

So far, the best way to make this precise is via set theory.  While being-itself is purely logical, and so has no content, mathematical being is not purely logical: it is defined by the addition of one non-logical sign to the vocabulary of the predicate calculus.  This sign is the membership sign.  It is implicitly defined by the axioms of set theory.  Mathematical universals now supervene on various objects in the iterative hierarchy of sets.  The result is that the category of the abstract has been fully defined.

But what about the category of the concrete?  Here to exist is to be physically possible, and physical possibility must be made precise via some theory of possible universes.  Many atheists are scientific naturalists, and, as such, they are entirely free to affirm the existence of other worlds – that is, of other physical universes.  Current physics and cosmology contains many empirically justified (but not verified) theories that assert the existence of other physical universes.  Quantum mechanics, inflationary cosmology, and string theory all posit, in their own ways, other universes besides our own.   Max Tegmark is one of the foremost advocates of other universes (1998; 2003).  It is entirely reasonable to say that there is evidence for other universes.  Of course, to say that there is evidence for something does not guarantee that it exists – merely that positing its existence is reasonable.

Many philosophers have attributed the existence of other universes to the activity of natura naturans – to the activity of the natural creative power of being.  The American philosopher Charles Sanders Peirce developed an impressive evolutionary cosmology in which his version of natura naturans spawns an ever-branching tree of universes.   And Donald Crosby, the atheistic religious naturalist, affirms that the creative power of being also spawns an infinite plurality of universes.  He affirms that there is an “endless succession of radically different cosmic epochs spun off by nature in its fundamental role of natura naturans” (2002: 41; Crosby often talks about the multiverse in his 2002: ch.2).

The cosmologist Lee Smolin has developed a theory that advocates a branching tree of universes (1992; 1997).  His theory is based on the natural creative power of black holes.  One version of inflationary cosmology explicitly depicts physical reality as a branching tree of universes. Here the creative power of nature generates universe after universe.  This version of inflationary cosmology is the eternally self-producing universe theory (Linde, 1994).  It says that physical reality is a self-generating fractal:

Recent versions of inflationary theory assert that instead of being an expanding ball of fire, the universe is a huge growing fractal.  It consists of many inflating balls that produce new balls, which in turn produce more balls, ad infinitum. (p. 48) . . . one inflationary universe sprouts other inflationary bubbles, which in turn produce other inflationary bubbles.  This process, which I have called eternal inflation, keeps going as a chain reaction, producing a fractallike pattern of universes.  In this scenario the universe as a whole is immortal.  Each particular part of the universe may stem from a singularity somewhere in the past, and it may end up in a singularity somewhere in the future.  There is, however, no end for the evolution of the entire universe. (p. 54) . . . One can draw some optimism from knowing that even if our civilization dies, there will be other paces in the universe where life will emerge again and again, in all its possible forms. . . . Our cosmic home grows, fluctuates and eternally reproduces itself in all possible forms, as if adjusting itself for all possible types of life that it can support. (p. 55).  (Linde, 1994)

There is no guarantee that these other universes exist.  However, their existence is empirically justified.  Thus it is rational for scientific naturalists, and atheists inspired by scientific naturalism, to affirm that they do exist.  These other universes are not parts of our universe, and are not observable from within our universe.   But they are not supernatural; on the contrary, they are entirely natural things.  Nature is big.

References:

Crosby, D. (2002) A Religion of Nature.  Albany, NY: SUNY Press.

Frege, G. (1980) Philosophical and Mathematical Correspondence.  Chicago: University of Chicago Press.

Linde, A. D. (1994) The self-reproducing inflationary universe.  Scientific American 271 (5), 48-55.

Poincare, H. (1913) The Foundations of Science: Science and Hypothesis, The Value of Science Science and Methods.  Trans. G. Halstead.  Lancaster, PA: The Science Press.

Smolin, L. (1992) Did the universe evolve? Classical and Quantum Gravity 9, 173-191.

Smolin, L. (1997) The Life of the Cosmos. New York: Oxford University Press.

Tegmark, M. (1998) Is ‘the Theory of Everything’ merely the ultimate ensemble theory?  Annals of Physics 270, 1-51.

Tegmark, M. (2003) Parallel universes.  Scientific American 288 (5), 40-51.

Other posts in the series so far:

Atheism and Wicca

The Wiccan Deity

The Wiccan Deity: An Initial Philosophical Analysis

The Wiccan Deity: Related Concepts in Philosophy

On Atheistic Religion

Nine Theses on Wicca and Atheism

Atheistic Holidays

Criticizing Wicca: Energy

Do Atheists Worship Truth?

Some Naturalistic Ontology

Criticizing Wicca: Levels

Atheism and the Sacred: Natural Creative Power

Atheist Ceremonies: De-Baptism and the Cosmic Walk

The Impossible God of Paul Tillich

Atheism and the Sacred: Being-Itself

Pure Objective Reason

Criticizing Wicca: Rationality

The God and the Goddess

Wicca and the Problem of Evil

The Wiccan God and Goddess: Reality and Mythology

On Participation in Being-Itself

Criticizing Wicca: God and Goddess

The Increasing Prevalence of Woo

Wiccan Theology and Sexual Equality

Revelation versus Manifestation

  • colubridae

    *sigh*, I suppose philosophers must have their own string theory.

  • http://www.russellturpin.com/ rturpin

    So far, the best way to make this precise is via set theory.

    Set theory’s claim as “the logic of math” rests on its generality. As far as I know, every extant mathematical theory can be expressed within it. In particular, it is the formal system that encompasses all of classical analysis and topology.

    But. You don’t need set theory for the most garden-variety math. Euclidean geometry, as one example, has a far simpler logic. It’s even complete. There is an automated theorem-decider for Euclidean geometry.

    I’m curious to see someone still pushing the notion of “one ontology to rule them.” The thing about we modern nominalists isn’t that we’re opposed to ontologies. But that we see them merely as a definitional framework, useful to the extent to which the theory of which they’re part is useful.

  • Ariel

    Pure formal logic does not assert the existence of any objects at all. It is entirely devoid of ontological content.

    This is simply wrong, unless by “formal logic” you mean “free logic”. Some theorems of classical logic are quite plainly existential and they are true in nonempty domains only (e.g. “there is an x such that F(x) or not F(x)”).

    in mathematics, to be is to be mathematically possible, and to be mathematically possible is to be consistently definable. Poincare writes that “in mathematics the word exist . . . means free from contradiction” (1913: 454). And Hilbert wrote to Frege that “if the arbitrarily given axioms do not contradict one another with all their consequences, then they are true and the things defined by the axioms exist” (in Frege, 1980: 39-40).

    Both Poincare and Hilbert lived in good, old times, when mathematicians knew very little about the incompleteness phenomena. Consider two definitions. (1) x is the smallest natural number such that the continuum hypothesis is true. (2) y is the smallest natural number such that the continuum hypothesis is false. Both definitions can be consistently (although non-conservatively) added to ZFC. In this sense you can claim that both x and y are “mathematically possible”. However, you can’t claim that both x and y exist, because then you obtain a contradiction.

    I don’t know about physics – not my branch. But your math looks very messy.

    • SAWells

      His physics isn’t any better than his maths, but he’s not listening to anyone on the subject. See earlier posts in this ongoing trainwreck.

  • SAWells

    It’s amazing how far Eric is willing to go in singing the praises of something which is either imaginary (Natura Naturans the Immanent Power of Being, oh yeah) or trivial (Stuff exists.).

    And as for this:
    “There is no guarantee that these other universes exist. However, their existence is empirically justified. Thus it is rational for scientific naturalists, and atheists inspired by scientific naturalism, to affirm that they do exist.”

    I’m disgusted. It may be rational to affirm that other universes MIGHT exist; it is not rational to affirm that they DO, as they remain unevidenced, and your claim that their existence is “empirically justified” goes vastly beyond the truth. Eric, your sloppy thinking is appalling.

  • http://www.ericsteinhart.com Eric Steinhart

    @Ariel – Thanks for pointing out my sloppiness on this point. I should have said that formal logic entails no definite ontological commitments, since merely affirming (there exists x)(F(x) or not F(x)) is surely not definite.

    As for your claims about natural numbers and the continuum hypothesis, I don’t get it; how would there be a smallest natural number such that the continuum hypothesis is true (or false)? Are you thinking about something having to do with non-standard models of the natural numbers and the existence (or not) of certain large cardinals?

    I see nothing wrong with the Hilbert-Poincare view, which has recently been defended by Balaguer in detail. To be mathematically is to be consistently definable. This gets spelled out via set theory. Indeed, it’s fine to say that there are many set theories, each true at its own set theoretic world (on analogy with Lewisian modal realism). At one world, CH, at another world, -CH. At this world, Choice, at that world, Determinacy.

    • Ariel

      As for your claims about natural numbers and the continuum hypothesis, I don’t get it; how would there be a smallest natural number such that the continuum hypothesis is true (or false)?

      Ok, step by step.

      D 1. (introducing a new constant x)
      For every z, z = x iff (CH and for every s < z not CH)
      D 2. (introducing a new constant y)
      For every z, z = y iff (not CH and for every s < z CH)

      (In both cases the phrase starting with “for every s < z” guarantees uniqueness. Without such a clause each definition taken separately would produce a contradiction when added to ZFC. By the way, I know of course that both definitions are nonconservative. But you couldn't have meant "to be mathematically possible is to be conservatively definable" … could you?)

      Now I take your claim:

      to be is to be mathematically possible, and to be mathematically possible is to be consistently definable.

      The refutation goes as follows:
      1. It is mathematically possible that something satisfies D1, since ZFC+D1 is consistent.
      2. It is mathematically possible that something satisfies D2, since ZFC+D2 is consistent.
      3. Therefore (“to be is to be mathematically possible”), there is an object satisfying D1 and there is an object satisfying D2.
      4. Therefore CH and not CH. Contradiction. (This conclusion is just by logic)

      I hope the argument is clear now.

      Indeed, it’s fine to say that there are many set theories, each true at its own set theoretic world (on analogy with Lewisian modal realism). At one world, CH, at another world, -CH. At this world, Choice, at that world, Determinacy.

      Yes, insofar as it’s just a (reformulation of) completeness theorem. Consistent theories have models, yeah. If this is all you wanted, no quarrel. But I can see no transition from the completeness theorem to “in mathematics ‘exists’ means ‘free from contradiction’”. If you want to make such a move, answer please: does an object satisfying D1 exist? Does an object satisfying D2 exist? Yes or no? (Observe also that an answer of the sort “exists in a given model” is evasive. I ask about existence, and not about existence in some model. These are two different questions.)

      Ok, I’m done for today. My daughter is already impatient. See you tomorrow!

  • felicis

    I have asked about this before, but rather than explain yourself – you just repeat:

    “Particulars divide into the mathematical, the geometrical, and the material.”

    What is the difference between mathematical things and geometric things? From my point of view, all geometric things *are* mathematical things. Yet you persist in separating the two (as though vectors, to use one of your example geometric things, are not mathematical objects). What is the basis for your separation? Is it your next statement:

    “This division is equivalent to the division of being-itself into the abstract and the concrete. The abstract includes universals and mathematical objects; the concrete includes geometrical and material things.”

    Now you have two new categories not included in your ontology given a couple of posts ago. What is a ‘concrete object’? You have yet to explain your use of ‘abstract object’, which seems to change to suit your argument.

    But that still does not adequately separate ‘mathematical’ and ‘geometric’ things – to return to vectors; mathematically an n-tuple of real numbers can be considered to be a vector. Both real numbers and n-tuples can be constructed from the ground up using set theory. This makes them ‘mathematical objects’ by your ontology. So why are they ‘geometric objects’? Further – why do you feel the need to make this distinction, how will that fit into your argument later?

    I am also confused by your statement, “…mathematical being is not purely logical: it is defined by the addition of one non-logical sign to the vocabulary of the predicate calculus. This sign is the membership sign.”

    All A are B.
    a is an A. (a is a member of A.)

    Therefore, a is a B. (a is a member of B.)

    Perhaps this is more recognizable:

    All men are mortal.
    Socrates is a man.

    Therefore, Socrates is mortal.

    One of the oldest examples of logic implicitly uses the membership sign and you claim that it is not logical? You’ve got some ‘splainin’ to do!

  • http://www.ericsteinhart.com Eric Steinhart

    If you are a Pythagorean, you may indeed identify mathematical points with geometrical points; but that identification is tough to defend. Geometrical points literally are in space-time; mathematical points are not.

    You write that predication (in the syllogism example) implicitly assumes membership. Well, that means you’re just assuming that set theory provides the correct analysis of predication. Many philosophers would dispute that. And there’s a problem: what about the membership relation itself? There is no set of (x, y) such that x is a member of y. There is a proper class V such that (x, y) is in V iff set x is a member of set y. But the fact that (x, y) is a member of V cannot be expressed via membership in V.

  • felicis

    “Geometrical points literally are in space-time; mathematical points are not.”

    What does this even mean? What is a ‘geometrical point’? For that matter, what is ‘space-time’? From *my* point of view, both are mathematical constructs which happen to have some features that make them convenient for us to use in our description of ‘reality’, but that does not endow them with a special kind of existence apart from their mathematical definitions. (Indeed, if we allow *that*, why aren’t sets considered geometric objects in the same sense? Or mathematical points – what distinguishes a ‘mathematical point’ from a ‘geometric point’?

    “You write that predication (in the syllogism example) implicitly assumes membership. Well, that means you’re just assuming that set theory provides the correct analysis of predication. Many philosophers would dispute that.”

    Specifically, *you* are disputing that with an appeal to authority. If I’m wrong, please explain *why*. Certainly set theory seems to work in this example (and can be used in most mathematical logic) so find me an example where it *doesn’t*.

    “And there’s a problem: what about the membership relation itself? There is no set of (x, y) such that x is a member of y. There is a proper class V such that (x, y) is in V iff set x is a member of set y. But the fact that (x, y) is a member of V cannot be expressed via membership in V.”

    I’m going to try to make sense of this.

    There is no set of ordered pairs (x,y) such that x is a member of y.

    {({}, {{}})}

    False. Did you mean something else? If so, what?

    Why must we resort to proper classes for this? I do not see that is necessary for any but pathological examples. Take, for example, a finite collection C of (disjoint, nonempty, finite) sets X_i (indexed by a finite collection of natural numbers) and their power sets P(X_i) (which we can call C_P). The cartesian product C x C_P is likewise a set. The set of all (x,y) in C x C_P such that x is in y is a well-defined set. Do I need to invoke classes for this example? Even if I allow the number of X_i to be infinite (even uncountably so), even if I allow the X_i to be empty, not disjoint, and even for some X_i to contain (as members) others – though here I need to be careful about how that containment is set up – I can get by without using proper classes.

    And what does “But the fact that (x, y) is a member of V cannot be expressed via membership in V.” mean? The only way I can even assume this sentence makes sense is if you are using two different and inconsistent meanings for ‘member’ and ‘membership’ – could you be clearer?

    • http://www.ericsteinhart.com Eric Steinhart

      There is no set { (x, y) | x is a set & y is a set & x is a member of y }. If there were such a set, it would have a power set, and thus not contain all membership pairs. And if there were such a set, call it M, then for any sets x and y such that x is a member of y, (x, y) is a member of M; but (x, y) is a set and by hypothesis M is a set, so ((x, y), M) is a member of M; which introduces a loop into the membership relation, which contradicts Foundation.

    • Eric

      Ah – I see part of the problem, when you write, you tend to leave out universal quantifiers (‘for all’ is kind of important). I understand your objection now.

      You should rewrite this though:

      Instead of:
      “There is no set
      { (x,y) | x is a set & y is a set & x is a member of y }.”

      Say,
      “There is no set
      { (x,y) | x is any set & y is any set & x is a member of y }.”

      But that’s trivial, since you are just saying we cannot find a particular subset of UxU where ‘U’ is the set of all sets – which does not exist.

      So – M does not exist. So? The problem is not with membership, but with your desire to use the set of all sets in your (pardon me) setup. I think also that this is the time to ask just which version of set theory you plan on using for the remainder of the discussion – I’m partial to ZFC myself, but can find my way around others.

      It looks like you are trying to refute my position that ‘membership’ is a logical sign, whereas you claim it is not by using it within set builder notation in an illegal way and saying that the resulting set is not well-formed and thus the sign itself is not a logical sign. But

      N = { (x,y) | x is a set & y is a set }

      (to use your terminology) has exactly the same problems – do you claim that & is not a logical sign? If that’s not the problem with ‘membership’, then what is?

    • http://www.ericsteinhart.com Eric Steinhart

      I admit to having an annoying tendency, all too common among analytic philosophers, to assume that everything is universally quantified unless indicated otherwise.

      It’s interesting, the debate about whether set theory is part of logic or not, whether membership is a logical sign or not. Still, it’s probly not all that relevant here (and in the literature, the debate just goes back and forth…).

      I’m partial to Von Neumann – Godel – Bernays class theory plus axioms for all consistent large cardinals. This includes super-compacts, so that V is not L. But I also tend to be tolerant of the notion of multiple set theoretic worlds along the lines of Lewisian modal realism.

    • Eric

      Fair enough – so what about my question re: mathematical things vs. geometrical things. I really don’t understand the distinction you are giving ‘geometric things’ from ‘mathematical things’ – your statement “Geometrical points literally are in space-time; mathematical points are not.”, as I pointed out above, does not clarify your usage since for me ‘space-time’ is just as much a mathematical construct as a vector space.

      Further – to get back to the point of my disputation about membership being a logical sign:

      “While being-itself is purely logical, and so has no content, mathematical being is not purely logical: it is defined by the addition of one non-logical sign to the vocabulary of the predicate calculus. This sign is the membership sign. It is implicitly defined by the axioms of set theory.”

      I disagree (as noted), but am willing to stipulate for the sake of argument that this is true.

      “Mathematical universals now supervene on various objects in the iterative hierarchy of sets. The result is that the category of the abstract has been fully defined.”

      I sense a violation of the Incompleteness theorem lurking… Certainly this needs some expansion. If I understand this correctly, you are claiming that the entirety of the category of abstract things is characterizable by set theory – that cannot be what you mean, so you’ll need to explain this one.

  • http://www.russellturpin.com/ rturpin

    I should have said that formal logic entails no definite ontological commitments, since merely affirming (there exists x)(F(x) or not F(x)) is surely not definite.

    Which is fine, as long as “ontological commitment” means “of the formal system being discussed,” and not some kind of philosophical commitment that we are expected to make. We, as human mathematicians, logicians, and philosophers, are capable of using a variety of formal systems, studying their properties, and switching among them as suits our purposes. To reinforce my previous point, that nominalists have nothing against ontologies. The more the merrier!

    • http://www.ericsteinhart.com Eric Steinhart

      Perhaps nominalists these days have indeed gone over to a kind of fictionalism, so that any ontology is fine, as long as it’s preceded with an “in the fiction . . .” operator. Of course, that raises some delicate problems for atheists – is theism just a fiction in the same way? Is atheism merely theological anti-realism? It seems stronger than that; but maybe it’s not.

    • http://www.russellturpin.com/ Russell

      Eric Steinhart writes:

      …so that any ontology is fine, as long as it’s preceded with an “in the fiction …” operator.

      Ontologies aren’t fiction. They’re not fact, either. They are parts of theories or stories or narrative contexts. Some of those theories are good models of the world — the best we have. Some stories are entirely make-believe. Some theories are useful, even though we now know them wrong.

      Newtownian mechanics had its ontology: Euclidean space, velocity unbounded, particles and waves, distinct, etc. Relativity has its ontology. Star Trek has its ontology. Their ontologies overlap, which is part of how we can compare them.

      We now know where Newtonian mechanics fails, though it still is very useful. We don’t know where GR fails — it’s still one of our reigning champions. Star Trek is purposeful fiction. Yet, their ontologies overlap. Light waves appear in all three. Though behave quite differently between the first two. (I don’t know the third well enough to say where its make-believe physics deviates from GR.)

      Being comfortable with a variety of ontologies is like being comfortable with a variety of systems of units, or a variety of coordinate systems. It’s neither true nor false to make the speed of light dimensionless. It’s a mistake in classical mechanics, but allowable and convenient when working with relativity. Americans can argue with Europeans over kilometers or imperial miles. Meanwhile, navigators the world over use the nautical mile, because it is one minute of great circle arc.

  • SAWells

    Just to illustrate the depth of the problem here, let’s look at one of Eric’s paragraphs:

    “Many philosophers have attributed the existence of other universes to the activity of natura naturans – to the activity of the natural creative power of being. The American philosopher Charles Sanders Peirce developed an impressive evolutionary cosmology in which his version of natura naturans spawns an ever-branching tree of universes. And Donald Crosby, the atheistic religious naturalist, affirms that the creative power of being also spawns an infinite plurality of universes. He affirms that there is an “endless succession of radically different cosmic epochs spun off by nature in its fundamental role of natura naturans” (2002: 41; Crosby often talks about the multiverse in his 2002: ch.2).”

    Guy A said this and Guy B said that and Guy C has a really neat idea… none of this matters for reality, because no number of people writing fiction can make their fiction fact.

    • SAWells

      And before you make another passive-aggressive post about “some atheists being motivated by a hatred of abstract reasoning”, Eric, let me specify: I love abstract reasoning. I hate what you are doing, because it is not reasoning at all.

  • http://www.ericsteinhart.com Eric Steinhart

    @Eric – I’m not aware of too many people who think that space-time is mathematical; mosts folks, philosophers, physicists, and mathematicians, seem to think it’s physical, it’s concrete rather than abstract. Thus R^4 is a mathematical image of a 4D Euclidean etc. space-time. Now, there is this guy Max Tegmark who says that everything that exists mathematically also exists physically, and he might agree with you, but he’s a minority. (I really like Tegmark’s work, and I’ve been tempted by pythagoreanism myself; but I don’t think it ultimately works.)

    Yes, I think that once the iterative hierarchy of pure sets is defined as big and wide as possible, all universals supervene on set theoretic structures in it. All concrete structures have images in the hierarchy; so any universal that is concretely instantiated is also instantiated someplace in the hierarchy. And this gets even more reinforcement from the notion that all possible models of all consistent set theoretic axiom systems exist (as separate set-worlds). But you raise a good worry about incompleteness issues. And I’m not aware of anyone (least of all me) who’s thought through these issues.

  • http://www.russellturpin.com/ Russell

    Eric writes:

    I’m not aware of too many people who think that space-time is mathematical; mosts folks, philosophers, physicists, and mathematicians, seem to think it’s physical, it’s concrete rather than abstract. Thus R^4 is a mathematical image of a 4D Euclidean etc. space-time.

    There are two problems with this. The first is that in our best physical theories, space-time isn’t Euclidean: neither flat nor with positive signature.

    But that just hints at the second and larger problem. We don’t directly experience space and time as a mathematical manifold with Lorentzian signature. Yes, we have experience of time passing, and of up and down, left and right, front and back. But measuring those and mapping them in some precise way is a matter of considerable artifice. People have to learn how to measure distance and angles, and how local measurements carry over to more general contexts. Which means that every mathematical notion of space-time, whether Euclidean or Lorentzian, is part of some theoretical framework. The Lorentzian manifold of GR is neither more nor less physical than the theory’s tensors, field equations, etc. They all are part of a physical theory (model) that works very well. Just keep in mind the difference between the map and the ground.

    • felicis

      Exactly my point as well – the idea of ‘space-time’ is a mathematical construct that happens to model our observations fairly well, but a mathematical object, all the same.

      You (Eric) talk as though ‘geometric points’ have some separate kind of existence from their mathematical definition – that they exist in a ‘sapce-time’ that is itself not a mathematical construct. I have asked you several times for the distinction – how do you tell the difference between a geometric point and a mathematical point? In my view, you cannot, and that is not because I believe in some platonic ‘ideal point’ of which ‘real points’ are only a projection, but because the very concept of ‘point’ is a mathematical creation which may not have any physical (here I use ‘physical’ to mean ‘agreeing with physical theory’, not ‘material’) analog (to use some of our ‘best theories’ – the idea being that it is simply not possible to localize or measure anything shorter than the Plank length, but points both have zero size and absolute location).

    • http://www.russellturpin.com/ Russell

      Let me add that I partly agree. All of GR’s ontology is physical. It is, after all, a theory of physics. So it’s perfectly correct to say that “physical space and time are a four-dimensional, differentiable manifold with Lorentzian signature.” I suspect I could find a sentence like that somewhere in the introduction to Misner, Thorne, and Wheeler. If it weren’t also packed away.

      The one caveat is that that is correct to say, because it is part of our best, current physics. Perhaps at some point, experiments will show a more granular space-time, and our theories of it will change. Or maybe there will be a more radical theoretical change, and space-time will no longer look like a basic physical construct. If that last possibility seems dubious, it should only be so because we have great confidence in some aspects of theoretical physics.

  • grung0r

    Eric, you said:

    But what about the category of the concrete? Here to exist is to be physically possible, and physical possibility must be made precise via some theory of possible universes.

    And

    There is no guarantee that these other universes exist. However, their existence is empirically justified. Thus it is rational for scientific naturalists, and atheists inspired by scientific naturalism, to affirm that they do exist.

    If I read this correctly, you are saying that something exists if it is physically *possible*, and if it is, then it is rational and thus ok for athiests to affrim it’s existeince. Is that right?

    If so, what about(picking a non-creator god at random) Ginesh? Now, I’ll admit, a elephant headed, sixteen arm having, flying mouse riding demigod does seem somewhat unlikely, but physically impossible? I think not. Given an infinite amount of universes with an infinite amount of time, Ginesh would almost certainly appear. Does this mean that it is rational for scientific naturalists to affirm his existence? I went with a non-creator god, since I suppose it could be argued that the creator gods are physically impossible. But apart from maybe that, what have you eliminated other than square circles with this definition of “exists”?

    The other thing I’d like to point out I somewhat fear bringing up. While your philosophy is muddle-headed and silly, you are a philosophy professor, and thus almost certainly know more about the following topic than I. Still, I can’t help but notice this sentence:

    Many philosophers have attributed the existence of other universes to the activity of natura naturans – to the activity of the natural creative power of being

    Isn’t this a Use-mention mistake? You put “natura naturans” in italics, while “natural creative power of being” isn’t. Yet, when you say”natural creative power of being”, you are just repeating the previous statement about “natura naturans” for emphasis, so you can’t possibly be referring to both the use and the mention of these labels.

    I don’t point this out to pedantic or a grammar nazi. The sentence itself is of little import(it was just an obvious example). The point, I feel, is larger. I think you have been slipping between use and mention quite freely when referring to “natura naturans” or the UICPOB. I see no pattern in your italics other than to italicize “natura naturans” most of the time and never with the UICPOB. But how could you not sometimes be referring to a label or the words instead of the concept behind them when doing things like comparing the definitions and ontology of natura naturans and formal logic? It would have to be very carefully done, and yet from the above example alone, it would appear you are not being careful at all. Are you just ignoring the use-mention distinction so that you can hide your not-god in a confused muddle of definitions, labels and concepts? It seems that way to me, but like I said, you know more about this than I, and I’m sure you can shed some light on the situation.

  • felicis

    OH – by the way, I accidentally logged out and posted as ‘Eric’ in response to Eric a couple of times. That’s my name, but I’m trying to keep in as ‘felicis’ here to avoid confusion.