How could Occam's razor possibly be used metaphysically?

Question

Occam's razor, or the law of parsimony, states that the simplest explanation for any given data is most likely the correct one.

Some have attempted to use Occam's razor in a metaphysical sense, to say that, for example, God is unlikely because to assume that God exists introduces additional, and unlikely, complexity. However, I'm wondering how this can be applied. The Wikipedia article for Occam's razor gives a few justifications, but the only justifications that seem to work for metaphysics are the mathematical ones (correct me if I'm wrong), for all the others are either empirical, which is not related to metaphysics, or "aesthetic," which does not seem to be very rigorous.

The mathematical justification seems to state that because the probability of the assumptions needed, for example, to say God exists is less than 100%, each additional assumption decreases the probability of God. However, I have a few questions about this.

1. Why assume that the probability of any two given metaphysical ideas are the same? For example, how can you assign any probability to whether or not God exists? Why assume a uniform distribution any more than any other distribution?

2. Why assume that the assumptions to be made have a non-100% probability? Of course, you could then say that they are not really assumptions, but how could you justify that they really are assumptions at all?

3. Why is there a distinction between "positively defined" and "negatively defined" assumptions? For example, to say that God does not exist, you would have to assume that there is no being that exists that is all-powerful, no being that exists that is all-knowing, etc. It seems fairly easy to come up with additional assumptions that have to be made even in a "negatively defined" case, and how can you meaningfully assign probabilities to these assumptions?

I've also seen justifications based on minimum description length and Kolmogorov complexity, but I don't see how these computationally-based ideas have anything to do with metaphysics. How can one say that a metaphysical reality is in any way defined in a computational sense? Do simple statements that can be said to define metaphysical realities, such as x is true, y exists, etc., somehow link to computation?

While I don't really see any problems to these objections, I assume that there is at least some validity in using Occam's razor in a metaphysical way, given that so many well-known (and lesser-well known) atheists, such as Richard Dawkins, base their beliefs off of it. So what, if anything, is wrong with my objections?

Answer 1

Let me point out, first, that Occam's Razor is not a law; it's a rule-of-thumb that has more to do with pragmatics and aesthetics than necessity. It's a good rule of thumb, sure, but it is based on an a priori belief that the universe as a whole conforms to what human minds count as parsimony.

That being said, the main issue with applying Occam's Razor to metaphysics (or to anything, really) is that the concept of parsimony is sensitive to context. Parsimony is a conservation issue — by which I mean it tries to create a constant, minimal, necessary and sufficient ground for a field of knowledge — and so we need to consider what qualities we are trying to conserve before we can apply it fruitfully. In the atheist/theist divide pointed at above, atheists generally focus on the material/physical universe to the exclusion of everything else, and within that context it may very well be more parsimonious to assume there is no God. Theists, by contrast, are not overly concerned about the physical world. They focus on the social/moral world — the world of human experience and behavior — and within that context it may very well be more parsimonious to assume there is a God. God may be an unnecessary explanation for the Big Bang, but are Newton's Laws useful and relevant to an understanding of ethics?

The conflict between these groups is seemingly endless because both sides refuse to engage the context of the other: theists dismiss valid statements of science, while atheists reject theological moral, philosophical, and experiential arguments out of hand. There will not be a resolution to the issue until all those involved are willing to engage a larger context, and we cannot really talk about parsimony until that occurs.

Answer 2

I'm not sure this is exactly what you're asking, but it's very much possible to use Occam's razor with religion.

Of these two hypothesis:

• Humans made a mix of the beliefs and legends of their time about the world and its origin, based on their current knowledge, it stuck orally, and eventually got written in a book that was then described as the original word of God.

• God spoke to humans, and purposely gave an incomplete and incorrect depiction of the world (no mention of viruses or bacteria, plants created before the sun and moon[1]), and gave incoherent or plain arbitrary recommendations ("never cook a young goat in the milk of its own mother" [2]) instead of recommendations that could be actually useful ("wash your hands regularly and keep you waste far from your house").

which one seems more simple? And if you try to find reasons for God to give factually wrong information in the Bible, that would make your hypothesis even more complex and Occam razor would favor the first one even more.

This doesn't prove God doesn't exist of course, but here Occam's razor can be used for question related to religion (is the Bible man-made or the true word of God?) that can be used for a reasoning about the existence or God.

Though it's not a metaphysical question, and IMO I don't think Occam's razor can be used for something purely metaphysical in the sense that we have no data on any of the hypotheses we want to test.

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[1] : Genesis somewhere

[2] : Exodus 23:19

Answer 3

The same Occam who has a razor named after him also said:

Only faith gives us access to theological truths. The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic or rationality can uncover.

Furthermore

He believed that science was a matter of discovery and saw God as the only ontological necessity.

from Wikipedia

Emphases added in original showing Occam using his razor in the context of his calling...

Summary

1. Occam was a theologian
2. Occam's razor is named after said theologian

People wanting to affirm the second and ignore the first are suffering from acute tunnel-vision or mendacity.

Thought experiment

Here's a list of musicians who objected to Trump using their music.

If William of Occam – the theologian – were alive and found all the great anti-theists using his name to justify their godlessness would he say "It's ok! " or would he issue "cease&desist" orders?

Hint: Check what tough letters he sent the pope for not following the injunctions to poverty in holy-scripture.

Answer 4

An interesting point about your question is that Occam first applied the Razor - though the term is not his - to a metaphysical issue, the problem of universals.

Ockham was a nominalist - he denied the existence of "universals." What are they? Let us begin with what they are not. Universals contast with particulars. Particulars are the individual things that populate the universe - you, the hive of the bees in the park, the Eiffel Tower, Planet Earth. Universals are supposed to be the properties that multiple individual things have in common. For example, Socrates and Plato are particulars, and both philosophize. Does that mean that the statement "Socrates and Plato both philosophize" describes three things - the two men plus the universal to which the two individuals belong? Ockham's answer is no. According to Ockham, the two individuals exist and there is Socrztes's philosophizing and Plato's as well. Each of these properties is unique to the individual who has it. There is no universal here - there exists no property of philosophizing that is shared among the particulars. It is the human mind's invention of concepts (in this instance, the concept of philosophizing) that fosters the illusion that universals exist. (Elliott Sober, Ockham's Razors, ISBN 10: 1107692539 / ISBN 13: 9781107692534. Published by Cambridge University Press 2015-07-23, Cambridge, 2015: 9-10.)

This shows how the Razor can be used metaphysically whether considers it a correct use or not. Sober further refers to Ockham's use of the Razor in connexion with the problem of change, of explaining what happens when change occurs. I take change to be in broad terms another metaphysical issue, not least because universals can be invoked in handling it.

Answer 5

The short answer is that it is simply not justified. When it comes to metaphysics, it makes no sense to talk about the likelihood of God. What does it mean for God to have a 60 or 80 or 90% chance to exist? It seems meaningless and ill defined.

The real flaw with theories that you seem to be positing as complex is not parsimony. The real problem is that there is no direct evidence of them. There is no observation or explanation that shows us that God, complex or otherwise, is operating in the world. On the other hand, physical laws, whether blind or otherwise, atleast do exist. One cannot deny their existence and so we operate on the assumption of their existence and don’t postulate entities that we have no evidence of.

No observation that is possible under known physical laws can ever serve as evidence for a process that we cannot observe or detect.

Answer 6

If you are amenable to the musings of Immanuel Kant, I would offer his remarks on exactly this question:

We are not discussing the above-mentioned assertions regarding the immaterial unity of the soul and the existence of a Supreme Being as dogmata, which certain philosophers profess to demonstrate a priori, but purely as hypotheses. In the former case, the dogmatist must take care that his arguments possess the apodeictic certainty of a demonstration. For the assertion that the reality of such ideas is probable is as absurd as a proof of the probability of a proposition in geometry. Pure abstract reason, apart from all experience, can either cognize nothing at all; and hence the judgements it enounces are never mere opinions, they are either apodeictic certainties, or declarations that nothing can be known on the subject. Opinions and probable judgements on the nature of things can only be employed to explain given phenomena, or they may relate to the effect, in accordance with empirical laws, of an actually existing cause. In other words, we must restrict the sphere of opinion to the world of experience and nature. Beyond this region opinion is mere invention; unless we are groping about for the truth on a path not yet fully known, and have some hopes of stumbling upon it by chance.

As for simplicity proper, two things:

1. A particular consideration regarding the divine nature. Classically, the divine nature is supposed to be partless in some exceedingly important sense. For some, it is enough to say that God doesn't have spacetime parts. For others, it's not enough unless one goes on to say that God doesn't have nonspacetime parts either, where "nonspacetime" is a rough placeholder for the kinds of seemingly disparate terms that occur in analytic/scholastic theology. The argument is this: if there is no necessary being, then there must be an explanation for why there is no necessary being. But if a being actually were necessary, there would be a simple reason why it was as it was, and why it existed: automatically, by default, trivially. If a necessary being didn't exist, though, then also by default, the explanation for what could prevent a truly necessary being from existing would be a more complicated, and in the end absurd-seeming, explanation than the explanation for why a necessary being simply does exist.

2. In another, mathematically robust sense, abstract simplicity is too generically simple to be concretely simple. Or, the predicate "simple" is not absolute, but must be qualified; perhaps, as with God, there is a point in asking about absolute simplicity nevertheless, but if we mean to juggle whichever metaphysical poems and dialectical experiments there appear to be (and like Legion, they are many...), then perforce at some point, and then many points, we will run into the problem of a supposedly per se simpler explanation that is actually simpler modulo only one important factor, but another explanation is the simpler in terms of yet a different important factor. We see this, most clearly, in the impossibility of deciding whether logic or mathematics is truly more fundamental or all-encompassing (or both), and then whether specific kinds of logic or mathematics are the ultimate elements of our intellectual world (set theory? type theory? category theory? graph theory? algebra? geometry, after all? geometrical logic? first-order logic? zeroth-order logic? n-ordered logic? n-ordered arithmetic? philosophy itself, somehow, no less?).

Answer 7

Good question and I empathize with you. A few points that I feel are relevant:

1. Mathematically, probabilities are positive proper fractions. You might need to study properties of (proper) fractions if you want to make any headway into the problem.
2. A specific example from which you may abstract away ad lib. "I need at least 6 chairs, Jalal", said Julio.
3. A probabilistic interpretation of the novacula Occami is fine, but it's unlikely 🙂 that William of Occam knew anything about mathematical probability.

Answer 8

In fact, Occam (Ockham) himself acknowledged that there is a problem here. In reference to transubstantiation, Ockham disagrees with Aquinas, as described in by McCord Adams (page 164):

Aquinas to the contrary notwithstanding, neither reason, the Bible, nor the determinations of the saints force an endorsement of transubstantiation. It must be upheld only because Innocent III's council and other decretals pronounce in favor of it. Miracles should not be multiplied without necessity. But sometimes in the soteriological realm, it pleases God to violate Ockham's Razor! The nominal definition Ockham offers in his Sentence commentary merely conjoins the items theological consensus had settled upon.

[D11] transubstantiation is the succession of substance to substance (of S2 to S1) where S1 ceases to exist in itself and S2 comes to exist under S1's accidents.

(emphasis added).