Is Theism a Simple, and hence Probable, Explanation for the Universe?

Is Theism a Simple, and hence Probable,

Explanation for the Universe?

John Ostrowick

[email protected]

Abstract

Richard Swinburne, in his The Existence of God (2004), presents a cosmological argument in defence of

theism. (Swinburne, 1991, p119, p135). God, Swinburne argues, is more likely to bring about an ordered

universe than other states. (ibid., p144, p299). To defend this view, Swinburne presents the following arguments:

(1) That this ordered universe is a priori improbable (2004, p49, p150, 1991, p304 et seq.), given the stringent

requirements for life (cf. also Leslie, 2000, p12), and the Second Law of Thermodynamics (Giancoli, p396); (2)

That it seems as if this ordered universe can be explained by theism; (3) A theistic explanation for the universe

is more probable because it is a simple explanation. To this end, Swinburne makes use of Bayes’ Theorem.

Symbolically, this claim can be represented as (e) for the evidence of the existence of a complex universe, and

(h) for a hypothesis. Swinburne’s argument is that theism has a higher prior probability, P(htheism) >

P(hmaterialism), since theism is simpler than materialism. He concludes that P(e|htheism) > P(e|hmaterialism). In this

paper I will address only this argument (3) above, and defend the view that it is false: theism is not simpler than

materialism, nor it is more probably true. I conclude that theism is less probable than materialism, expressed

by P(htheism) < P(hmaterialism) : 2/N(2n+1) < 1/n, where N is the number of possible universes and n the number

of entities in existence.

John [email protected]

Introduction

Swinburne’s cosmological argument claims that our universe is more likely to have come about given the

existence of God, since:

(1) This ordered universe is a priori improbable given the stringent requirements for life, and the Second Law

of Thermodynamics;

(2) It seems as if this ordered universe can be explained by theism;

(3) The presence of such a universe supports the view that God exists;

(4) A theistic explanation for the universe is more probable because it is a simple explanation.

I will only be examining argument (4) in this presentation.


Whether Theism is a Simple Explanation

• Theism and materialism both fit the evidence.

• Theories also should have appropriate scope, fit and simplicity.

• Materialism can account for the facts of the universe; both theism and materialism fit the evidence.

• The scope of theism is the same as that of materialism

• But theism is a simpler explanation (for reasons we will explain shortly)

• Since theism is a simpler explanation, it is more probable as an explanation.

• Occam’s Razor: non sunt multiplicanda entia praeter necessitatem.

• The universe was designed intentionally by a person of the utmost simplicity

• This is simpler than materialism, because The Big Bang postulates more entities and processes than theism.

• S. is concerned about the lack of antecedent explanations prior to the Big Bang.

• Too many entities in a Big Bang scenario for it to count as a good final, complete or ultimate explanation.

• But what kind of ultimate simple Being are we talking about? What are his properties?


Why Theism is Simple

• Theism posits that there is a God who is omniscient, omnipresent, omnibenevolent, and omnipotent.

• All the omni- properties are the simplest possible, since lesser or other properties would require explanation

• God is one entity

• Davidson, in Actions, Reasons, and Causes, discusses whether personal explanations — e.g., about what a

person intends — can be reduced to materialist explanations; e.g., brain events.

• The simplest explanation for why something was done is a personal explanation

• Hence, if we are to explain the universe in the simplest possible way, and if a personal explanation is simpler

than a materialist explanation, we have to use a personal explanation for the universe.

• God is personal, acts as a person with intentions/plans

• If we know what God is like, we know what he is likely to do: create a universe (from omnipotence), because

some universe is better than none, and a good universe is better than a bad universe (from omnibenevolence).

• Where (e) is the evidence of the existence of a complex physical universe (PU), and (h) for any hypothesis:

• P(htheism) > P(hmaterialism), since theism is simpler than materialism.

• Thus, P(e|htheism) > P(e|hmaterialism).


Why theism is simple (2/3)

• So of these two hypotheses above, we would choose H1 rather than H2. Only if experimental data strongly

confirmed H2 and disconfirmed H1, would we abandon H1.

• Since God is more a priori probable because he’s simpler, and since the universe is improbably complex, it is

more likely the case that God created the universe — ex nihilo — as a basic action, an unmediated rational act

of a person of infinite properties.


Simple and Complex Hypotheses

Why theism is simple (3/3)

According to Bayes’ Theorem, the likelihood of any hypothesis is calculated by the product of its explanatory

power and its prior probability. (Swinburne, 2004, p56). P = probability, e = evidence, k = background

knowledge, h = hypothesis:

P(h|e&k) = P(e|h&k) P(h|k) / P(e|k)

If we simplify Bayes’ Theorem, replacing [P(e|h&k)/P(e|k)], the explanatory power, with EP, and P(h|k), the prior

probability, with PP, we get:

P(h|e&k) = EP x PP

• PP(PU) << PP(G) because of complexity

• EPtheism ≈ EPmaterialism

• Therefore P(htheism) > P(hmaterialism), or P(G) >> P(PU)

• It seems a priori improbable that a complex thing like the universe would have started complex. It is more

likely, a priori, that something simple, like God, would have been at the start of the universe.

• Therefore, it is much more likely that God would exist than the Physical Universe would exist.


Criticisms

1. Should we always prefer a simpler theory?

• Even if theism is simpler than materialism, should we prefer it purely on the grounds that it is simpler?

• Counter-examples: The number of elements (4 vs 118), Bohr’s atom vs Quantum Mechanics, Newton

(E=1/2mv2) vs Einstein (E=mc2), Phlogiston vs Oxygen, Spirit possession vs Pasteur’s Germ Theory.

• Occam’s Razor is a rough guide

• We only accept that a simpler theory if we have two theories that both equally well explain the facts

• What counts, is fit, or EP — is whether the explanation works.

• Swinburne recognises this, too (2001, p95).

• So does theism work? In what way is it a better explanation other than its simplicity?

• Does it predict this universe, or could it predict any universe, or perhaps even no universe?


Criticisms

2. Is God not perhaps superfluous?

• Two senses of “simplicity”: numerical (Swinburne, 2001, pp85-7) and intrinsic (ibid., 2001, p83) (Also in Lewis,

1973, p87). Let’s start with numerical simplicity: fewer entities = simpler.

• We could be talking about fewer entities, or, we could be talking about a simpler hypothesis (fewer terms).

• Assume S.’s target is materialism, rather than polytheism. If theists accept PU, then God is one extra entity.

• If God used the Big Bang to create the universe, but the Big Bang alone would suffice, God is superfluous.

Only need one sufficient cause. Otherwise it is overdetermined. If God alone could make the universe without

the Big Bang, and if the Big Bang alone could make the universe without God, and we’ve got evidence that the

Big Bang happened but only the barest evidence of God, theism is overdetermining.

• Materialists accept only PU (brute fact). We can grant that PU is not simple.

• Theists also accept PU, but they also accept God. Hence theism isn’t simpler than materialism; it has extras.

• So maybe theism is a trade-off (Brown, 2009); maybe theism has higher EP?

• Uranus has an irregular orbit. (Swinburne, 2001, p97). Explained by: extraneous entity: Pluto.

• Theism’s brute fact is simpler: God. (Swinburne, 2004, pp108-9). A modest extra entity. (ibid., p97).

• But is God a modest extra entity? Not obvious.


Criticisms

3. Is God not perhaps intrinsically complex?

• Is God a simple explanation, intrinsically? Consider Pluto again (Swinburne, 2001, p97).

• Positing Pluto was pink and shaped like a unicorn is complex and improbable.

• S. believes that God is the simplest possible hypothesis, because of his infinite properties (2004, p93 et seq.).

• But who says God not more like a pink unicorn?

• God is omnipresent in all universes and omniscient (Swinburne, 2004, p94 et seq.). No boundaries. No body.

• Thus every particle, object, person, etc., are in God’s mind as thoughts.

• Such a Being is necessarily more complex than its creation, just as a potter is more complex than a pot.

• God is more complex than PU and therefore less probable than PU (Dawkins, pp136-43).

• n = number of entities in PU. If God is a single entity, then theism claims that it posits n+1 entities.

• But theism must be at least as complex as (2n+1), since God is a mind only, his thoughts are his parts.

• We can grant that theism is only (2n+1) complex when a universe exists.

• But as soon as God contemplates making PU then his thoughts instantly become as complex as PU

• If creatio continuans is true (S., 2004, pp142-3), God’s even more complex because of causal sequences.

• God is the most complex possible being. Even if we accept EPtheism is greater, it is at too high a cost.

• God is a pink unicorn explanation.


Criticisms

4. Which model of materialist cosmology are we comparing theism to anyway?

• Theism may be less complex than MUTs like Wheeler universes (Pulsating Universe Theory), or Carter

universes (multiple parallel universes) since there may be infinite past or present alternative universes, i.e.

(hmaterialism ⊃ ∞n) but (htheism ⊃ 2n+1)

therefore P(hmaterialism) << P(htheism)

if simplicity is the determining characteristic of probably-true theories.

• But if we are relying on Hawking materialism (which has a definite starting time, t=0), however, then theism is

less simple, since Hawking materialism involves only a single universe. Hawking materialism also does not have

t<0, hence it does not have to explain what happened “before” creation, unlike theism, which should be able to

tell us what God was doing before he created, and why he was doing what he was doing, if it purports to be an

ultimate explanation.


Criticisms

5. Is God natural? Are persons simple anyway?

• Complex things come after simple things as a result of a process of growth or evolution.

• Unicellular animals first, single molecules before crystals, spears before Boeings, gas nebulae before life.

• Thus simpler things come before complex things.

• Since intelligence is complex, intelligence must come later. (Dawkins, p31).

• God is thus unnatural or an aberration or anomaly.

• There would have to be an explanation as to how an intelligent God came to exist before anything else.

• Persons are complex (cf. Mackie)

• S. responds: we can know someone’s intentions without knowing his brain states (2004, p34), hence personal

explanations are irreducible to complex materialist explanations. Response: misleading and irrelevant.

• Misleading: person’s brain states are immaterial to whether or not his intentions are his particular brain

states; this is a limit on our knowledge, not evidence of irreducibility. Digestion analogy. Not irreducible.

• Irrelevant: God is complex (not simple) qua person, regardless of how his mental states are instantiated.

• God is a different sort of person to the sort we’re used to, but if he has any mental states such as wants,

angers, reasons or intentions, he is complex.


Criticisms

6.a. Whether God has the highest prior probability

• S. says the prior probability, PP or [ P(h|k) ], is higher for theism. (1991, p15, p129, p102, p106, 2004, pp108-9).

• If PP is assessed on the complexity of an explanation, God may be the most complex possible explanation

• God has a mental state for each particle in the universe and each object in the universe and all events.

• Thus, God would have at most half the prior probability of a materialist explanation (from 2n+1).

• Hence God would not have the highest prior probability.

• Let’s recap S.’s argument from Bayes’ Theorem:

P(h|e&k) = EP x PP

• As we saw, S. argues that P(hmaterialism) ≈ P(htheism) in respect to EP, and assuming that theism is simpler

(PPtheism > PPmaterialism) — then the overall computation will yield P(htheism|e&k) > P(hmaterialism|e&k). This is even

more obviously true if EPmaterialism < EPtheism. So, if we suppose that theism explains the universe better than

materialism, and it is simpler, then theism is more likely the correct explanation for the universe.


Criticisms

6.b. Whether God has the highest prior probability

• But I’ve argued PPtheism ≲ 1/2PPmaterialism because God is more complex than PU, so S. must demonstrate that

EPtheism >> EPmaterialism such that it counteracts the negative effects of its lower PP.

• These probability estimates are subjective; Bayes’ is only as good as the data you give it. (Dawkins, pp105-7).

• Bayes’ tells you how to update probabilities, not what to start with (Brown, 2009); it doesn’t tell you what

the prior probability [P(h|k)], should be. So we’re likely to always guess it in a biased manner.

• I argue EPmaterialism >> EPtheism and EPmaterialism ≈ 1.0, since materialism is a sufficient explanation

(overdetermination counterargument earlier). Even if we don’t have the explanation, it lies in materialism.

• Now, if half of the possible universes would be evil, and if there could be N universes, EPtheism should be

approximately 1.0/(N/2), since God has the freedom to choose only reasonably good universes.

• PPtheism < 1/2 because God is not simple.

• For n = number of entities in the universe, htheism, posits (2n+1). But hmaterialism posits n.

• Materialism has thus a higher EP and PP than theism, and hence is more probable, since:

P(hmaterialism) = EP x PP = 1 x (1/n) = 1/n

P(htheism) = EP x PP = 1/(N/2) x (1/(2n+1)) = 1/(N(2n+1))/2 = 2/N(2n+1)


EP theism is 1.0/N/2 on theism since theists consider it a complete explanation, and thereare N/2 good universes

Criticisms

6.c. Whether God has the highest prior probability

• Since 2/N(2n+1) < 1/n, by the factor 2n/N(2n+1), materialism is more probable than theism.

• However, (2n)/((2n+1)) tends to 1.0 for large n, so (2n)/(N(2n+1)) tends to 1/N as n tends to infinity.

• So, the more possible universes there are, the more P(htheism) = P(hmaterialism) (Holder, p296).

Does PP matter?

• Brown (2009) and Resnick, p55, argue that if we keep performing an experiment and getting enough

evidence, eventually k will build up so that we get to the true probability. Over time, the PP will turn out to be

irrelevant, because the weight of evidence will come up to its correct level statistically.

• If we flip a coin and you guess that the probability of heads is 0.8, and I guess it’s 0.2, those are our prior

probabilities. But, over time, repeating the flip, the evidence and k will start to turn out closer and closer to

0.5, the true value. Our PPs in this case would become ever more irrelevant as more evidence comes in.

• But S. is relying on PP to make his case that P(htheism) > P(hmaterialism).


Criticisms

7. The Complexity Quotient

• P(h|k)/P(e|k) is “the complexity quotient” (Gwiazda). How complex h is, in comparison to e.

• A more complex h is less probable (Swinburne).

• Since probabilities must be <= 1.0, we can re-formulate as follows (omitting k) (Gwiazda, 2009, p4):

P(h|e) = P(e|h)P(h) / P(e)

1 >= (0.5)P(h) / P(e) (Swinburne, 2004, pp338-9: says P(e|h) = 0.5 and assuming P(htheism=1))

2 x 1 >= 2 x (0.5)P(h) / P(e)

2 >= P(h) / P(e)

• This means that theism is at most twice as simple as the universe, yet Swinburne claims that theism is the

most simple hypothesis ever. Therefore either S.’s claim that theism is the simplest hypothesis is false, or,

PP(e|htheism) ≠ 0.5.

• Hume argues (Dialogues of Natural Religion, Part 5) that the universe need not be, or is not, infinite, and if

so, there is no reason to suppose its cause is. Therefore God needn’t be omnifarious.


Criticisms

8. Sum of probabilities

• S. offers a range of possible explanations for the universe, so the probabilities of those other possible

explanations must add up to 1.0, due to PU existing. (Gwiazda, 2009, pp5-7).

• hp = polytheism, hm = materialism, hn = no explanation, & ht = monotheism:

P(ht) + P(hp) + P(hm) + P(hn) = 1.0

• S. admits that P(ht) may be very small (Swinburne, 2004, p112), say, 0.001.

• If so, then P(hp) + P(hm) + P(hn) = 0.999.

• But if P(hm) << P(ht), pace S., P(hn) + P(hp) must make up the bulk of that remaining 0.999.

• But S. argues that P(hp) << P(ht), therefore P(hn) is the most likely answer.

• Clearly that won’t do, so perhaps materialism is what really makes up the bulk of the certain existence of the

universe. Moreover, if one of these values — P(ht), P(hp), P(hm), P(hn) — is close to half, as Swinburne

estimates in other places for P(ht) — then at least one of the other values, say, P(hm), must also be close to

half, if the others are really small.

• Therefore materialism is likely as plausible as theism in S.’s own terms.


Conclusion

Theism is less probable than materialism since God’s mind is complex, at least n complex, where n is the

number of entities in the universe. Since God himself is an entity, theism is at least 2n+1 complex to

materialism’s n. Therefore if complexity is a measure of truth, theism is improbable. Theism is only more

probable if there are multiple universes in the materialist theory. However, if theism accepts materialists’

results, as S. does, then God would still exist and still know all those other multiple universes’s contents. Hence

theism would still be more complex.

We have also seen that on the sum of probabilities, that theism and materialism are roughly equivalently

probable, hence theism does not have a major lead in prior probability.

Finally, we have argued that many scientific theories which are more complex, have been preferred in the past,

therefore complexity of a theory is not the determinant of truth; its fit with the facts is.

Thank you!


Is Theism a Simple, and hence Probable, Explanation for the Universe?

Spiritual

john ostrowick

modest extra

highest prior

big bang

prior probability

bayes theorem

simpler theory

complexity