Neither the Existence Nor the Nonexistence of God is Provable

A post of mine ends like this:

To theists, I say: go on being theists.  You are better off being a theist than not being one.  Your position is rationally defensible and the alternatives are rationally rejectable.  But don't fancy that you can prove the existence of God or the opposite.  In the end you must decide how you will live and what you will believe.

About "Don't fancy that you can prove the existence of God or the opposite," Owen Anderson asks:

How would we know if that claim is itself true?  Isn't it is possible that one or the other can indeed be proven?

To formulate my point in the declarative rather than the exhortative mood:  

 

    P. Neither the existence nor the nonexistence of God is provable.

 

How do I know (P) to be true?  By reflection on the nature of proof.  An argument is a proof if and only if it satisfies all of the following six requirements: it is deductive; valid in point of logical form; free of such informal fallacies as petitio principii; possesses a conclusion that is relevant to the premises; has premises each of which is true; has premises each of which is known to be true.

 

I say that an argument is a proof if and only it is rationally compelling, or rationally coercive.  But an argument needn't be rationally compelling to be a more or less 'good argument,' one that renders its conclusion more or less rationally acceptable.

 

Now if my definition above gives what we ought to mean by 'proof,' then it is clear that neither the existence nor the nonexistence of God can be proven. Suppose you present a theistic or anti-theistic argument that satisfies the first five requirements.  I will then ask how you know that the premises are true.  Suppose one of your premises is that change is the conversion of potency into act. That is a plausible thing to maintain, but how do you know that it is true?  How do you know that the general-ontological framework within which the proposition acquires its very sense, namely, Aristotelian metaphysics, is tenable?  After all, there are alternative ways of understanding change.  That there is change is a datum, a Moorean fact, but it would be an obvious mistake to confuse this datum with some theory about it, even if the theory is true.  Suppose the theory is true.  This still leaves us with the question of how we know it is.   Besides, the notions of potency and act, substance and accident, form and matter,  and all the rest of the Aristotelian conceptuality are murky and open to question.  (For example, the notion of prime matter is a necessary ingredient in an Aristotelian understanding of substantial change, but the notion of materia prima is either incoherent or else not provably coherent.)

 

To take a second example, suppose I give a cosmological argument the starting point of which is the seemingly innocuous proposition that there are are contingent beings, and go on to argument that this starting point together with some auxiliary premises, entails the existence of God.  How do I know that existnece can be predicated of concrete individuals?  Great philosophers have denied it.  Frege and Russell fanmously held that existence vannot be meaningfully predicated of individuals but only of cncepts and propositional functions.  I have rather less famoulsy argued that the 'GFressellina' view' is mstaken, but this is a point of controversy.  Furtrhertmore, if existence cannot be meaningfully predicated of individuals, how can individuals be said to exist contingently?

 

The Appeal to Further Arguments 

 

If you tell me that the premises of your favorite argument can be known to be true on the basis of further arguments that take those premises as their conclusions, then I simply iterate my critical procedure: I run the first five tests above and if your arguments pass those, then I ask how you know that their premises are true.  If you appeal to still further arguments, then you embark upon a vicious infinite regress.

 

The Appeal to Self-Evidence

 

If you tell me that the premises of your argument are self-evident, then I will point out that your and my subjective self-evidence is unavailing.  It is self-evident to me that capital punishment is precisely what justice demands in certain cases.  I'll die in the ditch for that one, and pronounce you morally obtuse to boot for not seeing it.  But there are some who are intelligent, well-meaning, and sophisticated to whom this is not self-evident.  They will charge with with moral obtuseness.  Examples are easily multiplied. What is needed is objective, discussion-stopping, self-evidence.  But then, how, in a given case, do you know that your evidence is indeed objective?  All you can go on is how things seem to you.  If it seems to you that it is is objectively the case that p, that boils down to: it seems to you that, etc., in which case your self-evidence is again merely subjective.

 

The Appeal to Authority

 

You may attempt to support the premises of your argument by an appeal to authority.  Now many such appeals  are justified. We rightly appeal to the authority of gunsmiths, orthopaedic surgeons, actuaries and other experts all the time, and quite sensibly. But such appeals are useless when it comes to PROOF.  How do you know that your putative authority really is one, and even if he is, how do you know that he is eight in the present case?  How do you know he is not lying to you well he tells you you need a new sere in your  semi-auto pistol?

 

The Appeal to Revelation

 

This is the ultimate appeal to authority.  Necessarily, if God reveals that p, then p!  Again, useless for purposes of proof.  See Josiah Royce and the Paradox of Revelation.

 

Move in a Circle?

 

If your argument falls afoul of petitio principii, that condemns it, and the diameter of the circle doesn't matter.  A circle is a circle no matter its diameter.

 

Am I Setting the Bar Too High?

 

It seems to me I am setting it exactly where it belongs.  After all we are talking about PROOF here and surely only arguments that generate knowledge count as proofs.  But if an argument is to generate a known proposition, then its premises must be known, and not merely believed, or believed on good evidence, or assumed, etc.  

 

"But aren't you assuming that knowledge entails certainty, or (if this is different) impossibility of mistake?"  Yes I am assuming that.  Argument here.  

 

 Can I Consistently Claim to Know that (P) is true?

 

Owen Anderson asked me how I know that (P) is true.   I said I know it by reflection on the concept of proof.  But that was too quick. Obviously I cannot consistently claim to know that (P) if knowledge entails certainty.  For how do I know that my definition captures the essence of proof?  How do I know that there is an essence of proof, or any essence of anything?   What I want to say, of course, is that it is very reasonable to define 'proof' as I define it -- absent some better definition -- and that if one does so define it then it is clear that there are very few proofs, and, in particular, that there are no proofs of God or of the opposite.

 

"But then isn't it is possible that one or the other can indeed be proven?"

 

Yes, if one operates with a different, less rigorous, definition of 'proof.'  But in philosophy we have and maintain high standards.  So I say proof is PROOF (a tautological form of words that expresses a non-tautological proposition) and that we shouldn't use the word to refer to arguments that merely render their conclusions rationally acceptable.  

 

Note also that if we retreat from the rationally compelling to the rationally acceptable, then both theism and atheism are rationally acceptable.  I suspect that what Owen wants is a knock-down argument for the existence of God.  But if that is what he wants, then he wants a proof in my sense of the world.  If I am right, that is something very unreasonable to expect.

 

There is no getting around the need for a decision.  In the end, after all the considerations pro et contra, you must decide what you will believe and how you will live.

 

Life is a venture and an adventure.  You cannot live without risk.  This is true not only in the material sphere, but also in the realm of ideas.

 

Related articles

The No True Scotsman or No True Muslim Fallacy

God, Proof, and Desire

The Problem of Dirty Hands

Quod Gratis Asseritur, Gratis Negatur and Petitio Principii

Does the Atheist Deny What the Theist Affirms?

An Insufficient Argument Against Sufficient Reason

Generic and Specific Problems of Evil: The Nature and Tractability of the Problem Depends on the Type of Theism Espoused

Josiah Royce and the Paradox of Revelation

Comments

[Andrew]

Your sixth requirement for an argument's being a proof is that its premises are "known to be true". I'm curious about your use of the passive voice here ("known by whom?", one wonders). It would appear to have this consequence: whether an argument is a proof or not is agent-relative. For the premises of an argument will be known to be true by some agents and not by others. If that's right, then, we shouldn't really talk about whether an argument is a proof or not -- as such. We should instead talk about whether an argument is a proof for you or a proof for me. Note too that those who fail to satisfy a requirement of knowing (by stubbornly refusing to believe, for example), may conveniently prevent an argument from reaching proof-hood (for them).

Somehow, though, I don't think you'll quite like those consequences.

Perhaps the sixth requirement is that the premises are known -- by someone, anyone -- to be true. But then, if there is an omniscient being, every sound argument will meet the sixth requirement; for someone -- namely, God -- will indeed know all truths and thus know all true premises. I'm tempted to conclude, then, that if classical theism is true, classical theism is provable.

[BV]

Thanks for the excellent comments, Andrew.

Known by whom? Known by us, or some suitably selected proper subset of us. We are the producers and consumers of arguments, and we produce them to convince ourselves of things, and sometimes others. To put it most 'existentially,' known BY ME. It is my intellectual and spiritual salvation that is of greatest interest to me.

>> if classical theism is true, classical theism is provable.<< No doubt. But God doesn't need a proof of his existence. His knowledge of his existence is immediate, not discursively mediated. WE need, or rather would like, one or more proofs of God's existence.

So the question is not whether the existence of God is provable by anyone, but whether it is provable by me and you and others like us. Discursive intellects, ectypal intellects.

I am comfortable with the notion that whether an argument is a proof or not is agent-relative. The ontological argument is not a proof for us -- Aquinas is right about this -- but it is a proof for God, though an unnecessary one for him.

[BV]

A rather more mundane example of agent-relativity:

Blacks are 12-14% of the population
Hispanics are 15-17% of the population
Ergo
There are more Hispanics than blacks.

I know that the first premise is true, but I don't know whether the second is true. So even if the argument is sound, this argument does not generate knowledge for me.

But if both premises are true, and you know that both are true, then this argument does generate knowledge for you.

So what is a proof for you is not a proof for me.

[Owen Anderson]

I don't think I was asking about what you call a knock down drag out argument. I think instead what stood out to me was your distinction about rationally compelling. Is this like persuasion? I don't think I would include that on the list. For instance, someone might believe that it is plausible to posit a universe from nothing. Others might find this compelling. I think this is different than your example about justice and capital punishment because it involves very basic terms like being and non-being. So perhaps what I should have asked first is what is meant by "God" in your statement about not having a proof? Once we have a definition perhaps we can begin thinking about how to give proof for the parts of the definition. Can we know that being doesn't come from non-being? Of course it doesn't show theism is true but it seems to be a necessary first step, and a relevant one since there are persons who say the entire universe can come into being from nothing (they don't mean creation ex nihilo).

[epimenides]

Sorry, I emailed without seeing the comments box was open.

Is it rational (a) to accept that your belief cannot be proved and at the same time (b) have a reason for believing?

I am not sure it is. A reason is what you would say if asked why you believe X. Is it rational to provide a reason for X that we accept does not prove or establish X?

Or is your point that we can believe X without having a reason? That seems equally strange to me.

[BV]

Owen,

You are not addressing the fundamental question: under what conditions is an argument a proof?

As for the definition of 'God,' I am assuming the standard definition.

[Owen Anderson]

What do you think about showing the opposite is impossible as an example of proof? We can apply this to the claim that the universe came from nothing.

[Owen Anderson]

I should have added that I agree with you if the claim you are arguing against is that there is a proof along the lines of: premise 1, premise 2, conclusion: this all men call God.

[Owen Anderson]

I doesn't seem that comments for your recent post are on so can I post here instead? A follow-up question: if the atheist is not irrational is there any sense in which one ought not to believe atheism? Or a sense in which one ought to believe theism?

[BV]

Well, prudential/pragmatic considerations might kick in.

[Johannes]

Proofs of the existence of God are based on the Principle of Sufficient Reason, which basically states that reality is ultimately rationally explainable. But why would someone assume that reality is ultimately rationally explainable whithout being theist or at least panentheist in the first place? I.e. without assuming that ultimate reality is Reason (Logos), of which our reason participates?

My argument for the existence of God starts from five facts:

F1. The universe is a contingent entity: it could have been different and it could not be at all. Moreover...

F2. The universe began to exist 13,800 million years ago, and there is no solid scientific theory that give a physical cause of that beginning, only unfalsifiable conjectures. (OTOH, a cyclic universe which bangs, expands to a maximum, then contracts to a minimum to bounce and bang again, is not plausible since it is well known since 1998 that the expansion is accelerating and will go on forever. And if "this" instance of the universe will expand forever, why would hypotethical "previous" instances have behaved differently?)

F3. The universe works causally according to mathematically expressible laws.

F4: Fundamental physical constants show a fine tuning that makes the universe adequate for the development of complex life forms.

F5: The human mind reasons based on causality and is capable of creating mathematical formal systems, including those that express the laws that describe the working of the universe.

Given those facts, each person can adopt one of two positions, the first explaining the facts rationally and the second simply accepting them as "brute facts".

Spiritual-Rational position:

There exists an ultimate, subsistent Being which is Spirit and Reason (Logos), Who created the universe (explains F1 & F2) according to reason (explains F3) with the purpose of hosting rational creatures (explains F4), whose rational capacity resides in a spiritual soul created in the image of Spiritual, Uncreated Reason (explains F5).

In this position, the universe has explanation and human life has meaning, subsisting after death.

Materialist-Evolutionist position

F1 ... F3: “brute fact”, “that’s just the way it is”.

F4: fine tuning is probably due to the fact that there are innumerable universes, in which case we have obviously appeared in one of them which is fit for life. Or maybe there are not many universes and F4 is just another brute fact.

F5: the monkey who thought the branch moved without reason was eaten by a predator and could not pass on his genes. On the other hand, the capacity for mathematics and abstract thinking is emergent from neural network complexity and does not require a spiritual soul, notwithstanding Thomists' TL;DR arguments on the contrary.

In this position, the universe does not have explanation and human life does not have meaning, ending in death. Nor does mankind as a whole have meaning, since it is well known that Earth will have been scorched by the sun in at most 2 billion years.

[Owen Anderson]

Do you think we can give a proof, given your definition, to show that something has existed from eternity?