Sunday, July 15, 2007

Presuppositions and hypotheses

To understand the strong atheist position that it is provable and proven that God does not exist, we have to delve a little deeper into metaphysics to understand the foundation in metaphysical naturalism for this position.

Metaphysics and metaphysical presuppositions are a necessary feature of any logical philosophy, at least under our current conceptions of logic. Although they have some similar features, metaphysical presuppositions are very different from scientific hypotheses.

Both metaphysical presuppositions and hypotheses have the same logical function: They are axioms (a.k.a. premises) from which statements are derived using logical deduction. The difference is that if a statement contradicts a metaphysical presupposition, the statement is considered false. If a statement known to be true contradicts an hypothesis, the hypothesis is considered false. The italicized qualifier is critical: Hypotheses are offered to explain and account for statements known prior to logical deduction to be true.

Note that the definition of "hypothesis" offered above is a metaphysical presupposition. A statement that contradicts that definition is false by virtue of contradicting that definition. Implicit in this metaphysical presupposition is that we cannot know the the truth of any statement independently of deduction from the metaphysical presupposition.

One feature that distinguishes different metaphysical systems is whether the metaphysical system is open or closed. A closed metaphysical system enumerates all the statements that are considered true by definition; only those statements which can be rigorously derived from the metaphysical presuppositions are true. An open metaphysical system gives us some system for adding additional statements which are true by definition, not by derivation.

All empirical metaphysical systems are open by definition because they include the metaphysical presupposition: All statements of subjective experience are known directly to be true or false. (True statements about experience are properly basic).

Technically, from logic and mathematics, an axiom is simply a statement held true by definition; the set of axioms[1] defines a formal system. But because of the traditional use of logic in mathematics, axioms are usually chosen so that interesting statements can be formally derived from those axioms. This procedure works well in mathematics, but, as the Logical Positivists showed and as I discuss in more detail on my series on The Scientific Method, it fails miserably in trying to deal with statements of experience: Even when known directly to be true, statements of experience are too complex to draw any logical deductions from. We thus label statements about experience as evidence to distinguish them from mathematical axioms suitable as a basis for deduction.

Since we cannot straightforwardly draw deductions from experiential statements, we need a different meta-system to do more than simply enumerate such statements. We thus define "ontology": An ontological system is an axiomatic formal system in which true statements about experience are specific theorems of that formal system. In other words, an ontological system is a series of axioms—in the sense that they are suitable for derivation—which logically account for the evidence. Since these ontological axioms are not held by definition to be true in the same sense as metaphysical presuppositions or mathematical axioms, we label them as hypotheses.

There's one more problem: We can derive any finite set of theorems from an infinite number of axiomatic formal systems. At the very least, we can always add an irrelevant axiom—an axiom which does not entail any new theorems or nontheorems—to any axiom set. Therefore we add one additional metaphysical presupposition: If two ontological systems account for the same evidence, then the simpler system, the one with the fewer hypotheses, is better than the more complex system.

To recap, we have three metaphysical presuppositions:
  1. All statements of subjective experience are known directly to be true or false.
  2. An ontological system is an axiomatic formal system in which true statements about experience are specific theorems of that formal system.
  3. If two ontological systems account for the same evidence, then the simpler system, the one with the fewer hypotheses, is better than the more complex system.
This metaphysical system is Metaphysical Naturalism. Notice that Metaphysical Naturalism does not specifically talk about existence, reality, causality, nor does it even specify canonical logic (propositional calculus). All metaphysical naturalism presupposes is subjective experience, non-contradiction, weak countability (strict less-than ordering), and the preference for simplicity.

Given this definition, we are in a position to discuss the existence of God according to Metaphysical naturalism.

Before denying the existence of God, the metaphysical naturalist must assign meaning to the statement, "God exists". This task is rather difficult, since Metaphysical Naturalism does not directly assign any meaning at all to "God" or "exists". The statement, "God exists" is not by itself meaningful according to Metaphysical Naturalism. Because Metaphysical Naturalism only talks about axiomatic formal systems, not specific statements (other than statements of experience, and "God exists" is not a statement of experience), we must embed the statement in some hypothetical formal system, and evaluate the formal system according to Metaphysical Naturalism. This task is non-trivial: Every different sect of every religion defines a different formal system, and there is considerable individual variation even within the same sect. Even so, an examination of the most popular formal systems in which "God exists" is a valid theorem reveals three broad classes which can be evaluated in general:
  1. Trivial definitions (e.g. Einstein's God)
  2. Hypothetical systems
  3. Metaphysical definitions
We can dismiss the first class, which includes definitions of God like "'God' is everything that exists." "God exists" is true in this sense (everything that exists does indeed exist), but so what? We can—as Dawkins notes—"sex up" Metaphysical Naturalism as "pantheism", but we still end up with atheism in the sense implied by most practicing theists, especially as it seems silly to "worship" everything that exists.

Sometimes "God exists" is embedded in a prosaic formal system: "God exists" is an hypothesis in a collection of hypotheses, and the hypothetical system entails statements about experience. (I'll discuss truly metaphysical conceptions of God in a later essay.) What we invariably find, though, is that either the entailment is "degenerate" (the system entails statements like "the sun will rise tomorrow or the sun will not rise tomorrow"), false-to-fact (the system entails that if you pray for something it will be or become true), or are simply irrelevant elaborations of simpler ontological systems.

It is typically on the evaluation of hypothetical ontological formal systems which include "God exists" either as an hypothesis or a theorem which follows from other hypotheses that the atheist denies that "God exists" is true. Furthermore there are a sufficient number of hypothetical ontologies which are specifically false-to-fact that the active denial, "God does not exist," is meaningful and true.


[1] The derivation method also defines the formal system, but almost all formal systems use propositional calculus as a derivation method, so this criterion does not draw many distinctions in ordinary practice.

18 comments:

  1. Your entry really reminded me of my friend's post at http://artharaja.blogspot.com/ on metaethics. I really want to read this again, so I'll post a much more intelligent comment later. :)

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  2. I post more directly on metaethics in my series on Meta-Ethical Subjective Relativism.

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  3. """
    All statements of subjective experience are known directly to be true or false.""""


    Questionable, or at least depends on what is meant by "subjective experience." Only statements about one's own perceptions can be called true or false? That would make much inductive reasoning very difficult if not impossible. Living mammals have hearts: one doesn't have to inspect every living mammal to verify that. And what about contingent/probable events? There is no truth value for a bet that the Dodgers will win the pennant. What sorts of truth statements can one make about past events (history, really), given that sort of criterion? You never met or saw Napoleon, so what happens, logically-speaking, when you read a history about his life? Strict truth functionality (it's either true via verification , or not true) renders history impossible (and in some situations, that is really the case). Though we do not support theists, that criteria could be used as an argument in support of the likelihood of some Scriptural events as well : there are numerous reports of miracles, and you were not there, so can't say whether they happened or not. Who says the present laws of physics are immutable, or that Jee-sus couldn't have had some secret technique for changing H20 into chianti? Yeah highly unlikely, but not logically impossible.


    """"An ontological system is an axiomatic formal system in which true statements about experience are specific theorems of that formal system."""

    Given your own somewhat constructivist inclinations, "true" itself would a term requiring definition. Most of this sort of quasi-ontology begs the entire question of whether logic is itself empirically grounded: metaphysical tradition says no, but the positivists themselves--or more "nominalistic" ones like Quine, at least--- were willing to consider logic as a type of empirical endeavor. Logic as contructivist and nominalist presents all sorts of problems (which Quine was aware of): even defining "True" and defining many other "givens" is a problem, defining tautology and contradiction are problems. (how about this: either X loves Y, or X doesn't love Y. Supposedly a tautology, but look at it a bit: couldn't X love Y in the morning, and not in afternoon? Sure. Or she loves some things about Y, and not some others. And how is the predicate "love" even f-n defined? A great deal of language does not really work in predicate logic). Contradiction works fine with A or ~A; it's questionable whether it works at all when nouns or verbs (or empiricaly statements made from nouns and verbs) are introduced into logical form.


    """If two ontological systems account for the same evidence, then the simpler system, the one with the fewer hypotheses, is better than the more complex system"""

    Ockham reduced. Why is that true? Simpler is "truer" than complex? Hardly verifiable. Besides, any real scientist--who tend to be monists, not metaphysicians, or dualists, or mystics--- would question whether there are multiple ontological systems.

    Nice try.

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  4. Beauregard:

    Only statements about one's own perceptions can be called true or false?

    That's not quite accurate: Only statements about subjective experience are known directly to be true or false.

    Most of the rest of your critique seems to be based on the noted misreading of this premise.

    That would make much inductive reasoning very difficult if not impossible.

    Humean induction is, in my not-so-humble opinion, overrated. I replace Humean induction with hypothetical-evidentiary reasoning in premise 2.

    Given your own somewhat constructivist inclinations, "true" itself would a term requiring definition.

    "True" is defined by premise 1: It is what is directly known about statements of subjective experience.

    Ockham reduced. Why is that true? Simpler is "truer" than complex?

    Again, you don't seem to be reading accurately, even when you quote me. Premise 3 defines simpler to be better, not truer.

    Hardly verifiable.

    That's why it's its own metaphysical principle, and not imported under premise 1.

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  5. SO you mean then that any sort of accurate empiricism demands "direct" subjective experience? Then knowledge by "indirect" means (like, reading a book about Napoleon, or for that matter, reports on finches in the Galapagos) is not direct, and thus not allowable or possible. Even in "evidentiary" terms that would make establishing some types of empirical knowledge very difficult. In essence, you are upholding a strict scientific materialist and verificationist criteria not so different than Quine's "physicalist" epistemology. (So much for Truth, Beauty, Justice, etc.). Quine simply extends the "scope" of naive verificationism to the entire domain of science and scholarship: which might mean that in some cases no certain knowledge is, or has been attained (as is the case even with some medical or biological issues---or even global warming, since no real convincing evidence exists proving a causal relation between C02 emissions (and oher pollutants) and greenhouse effect). I don't exactly disagree with that viewpoint, but it does lead to some rather unsavory consequences (whether Darwinist, or a sort of radical behaviorism).

    Moreover, the logic issue has not really been dealt with: i.e. what is logic to a biologist? The argument and axiom system presupposes logical givens, whether truth, contradiction, tautology, "necessary," etc.: those are concepts that humans learn by observation and experience (regardless of what metaphysicans may assert). That doesn't necessarily make it wrong: but if logical truth is itself not necessarily true and "a priori" in some sense (as even Quine seems to suggest), then axiom systems based on those "truths" are not necessary either.

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  6. Beauregard:

    SO you mean then that any sort of accurate empiricism demands "direct" subjective experience? Then knowledge by "indirect" means (like, reading a book about Napoleon, or for that matter, reports on finches in the Galapagos) is not direct, and thus not allowable or possible.

    Again, it's helpful to read my actual words—perhaps you might start with a deep breath. At no point do I "disallow" anything.

    Reading a book is a direct perceptual experience: I know directly and properly basically what the book says; everything else—including conclusions about the veracity of the book's statements—gets subsumed under the principles establishing hypotheticals to account for that direct experience.

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  7. Beauregard: You might also want to read my series on The Scientific Method.

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  8. It's a type of naive verificationism, regardless. Read Quine's Two Dogmas a few times and see how an expert does it. Moreover, people do make use of indirect knowledge, and knowledge of probable/contingent events, and those sorts of indirect knowledge are often not trivial. Truth functionality works alright with circuitry or syllogisms: "real world" modeling entails a lot more uncertainty.

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  9. Beauregard: It's a type of naive verificationism, regardless.

    Regardless? Regardless of what? Regardless of what I actually say?

    Again, I exhort you to read what I actually say, not what you imagine I'm saying.

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  10. I'm reading what you say, and telling you that defining knowledge as direct, subjective perception of events (in order to term them T v F) is a type of naive verificationism: even Einstein, not to say Bohr and Co. took issue with that sort of verificationism. (another issue-- is Daisy Mae's observation of some state of affairs---a crime, whatever---equal to Dr. Finkleberg's? Not necessarily). Probability generally is an issue for ANY empirical knowledge--one makes inferences, estimations, gathers data, correlations, etc. You tend to oversimplify things. It's not "true" that simpler is better than complex. Newton's theories are simpler than Einstein's, and yet gen and spec. relativity have been proven to be "true" and it's quite more complex than newtonian mechanics. I'm not really sure what your purpose is anyways: read some Kuhn (along with the Quine)--. He describes how science works, how theories were established, how scientific "truth" (if such a thing "exists") comes about. He doesn't start with any a priori axiom system, and is quite opposed to metaphysical reflections. He may not be correct all the time, but rather good on the sorts of issues you are concerned with.

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  11. Beauregard: You apparently lack the wherewithal to even read Wikipedia: "A verificationist is someone who adheres to the verification principle, a criterion for meaningfulness that requires a non-analytic, meaningful sentence to be either verifiable or falsifiable."

    At what point do I talk about meaning in my post? (Hint: I don't: You are yet again responding to the prompting of your imagination, rather than the actual text of my argument.)

    You've demonstrated several times that you're not competent to accurately read simple declarative sentences in the English language, and now you're retreating into argument by pejorative label and appeal to authority.

    I've tried gently (well, relatively gently) to point out your mistakes, but now you're simply embarrassing yourself.

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  12. For my other readers: Beauregard is, I suspect, hallucinating the word "only" into principle 1 above. He's reading:

    "All statements of subjective experience are known directly to be true or false."

    as

    "Only statements of subjective experience can be known to be true or false."

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  13. You're a verificationist: take it from me. Requiring direct experience for all knowledge is verificationist, and indeed your idea was put forth by like Locke, if not earlier. You really don't know what you are talking about (again--ever heard of probability???), and your attempt at some all-encompassing a priori ontology which would account for all knowledge is not merely arrogance but like idiotic, and an insult to authentic science.

    Not only that, but as others have noted, any time anyone--left, right, secularist, religious, xtian, whoever--dares to challenge your theory du jour you become defensive, insulting, and start into the ad hominems. Maybe instead of Quine or Kuhn, jus' finish that Stats 101 class back at Bonehead JC or whatever, genius. Ciao

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  14. Ciao

    Don't let the door hit you in the ass on the way out.

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  15. Now, now! Calm down guys. Shades of Wittgenstein's poker....

    Having read this interesting thread, I haven't seen anything that persuades me it is reasonable to state dogmatically that God does not exist, as distinct from maintaining that his existence is more improbable than probable.

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  16. I don't think it's even possible to state dogmatically or metaphysically that God does or does not exist without creating a massively complex metaphysical system; and Metaphysical Naturalism is not at all complex.

    MN doesn't even define existence at the metaphysical level, much less "God"; the concept of existence itself is an ontological concept justified (or unjustified) according to its explanatory power (under premise 2).

    The Metaphysical Naturalist objects to the statement "God exists" not because it is metaphysically presupposed to be false, but because the ontological system surrounding such a statement either has no explanatory power whatsoever, or because theism merely adds gratuitous complexity without offering any more explanatory power than ordinary non-teleological physical law.

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  17. God is the same as dog.

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  18. Mike: I think you have it backwards.

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