An Anselmian Antilogism

Philosophy is its problems, and they are best represented as aporetic polyads.  One sort of aporetic polyad is the antilogism.  An antilogism is an inconsistent triad: a set of three propositions that cannot all be true.  The most interesting antilogisms are those in which the constitutent propositions are each of them plausible.  If they are more than  plausible, if they are self-evident or undeniable, then we are in the presence of an aporia in the strict sense.  (From the Greek a-poros, no way.)  Aporiai are intellectual impasses, or, to change the metaphor, intellectual knots that we cannot  untie.  Here is a candidate:

1.  God is a perfect being.

2.  A perfect being is one that exists necessarily if it exists at all.

3.   Whatever exists  exists contingently.

It is easy to see that the members of this trio are collectively inconsistent.  So the trio is an antilogism.  Now corresponding to every antilogism there are three valid syllogisms. (A syllogism is deductive argument having exactly two premises.)  Thus one can argue validly from any two of the propositions to the negation of the remaining one.  Thus there are three ways of  solving the antilogism:

A. Reject (1).  The price of rejection is high since (1)  merely unpacks the meaning of 'God'  if we think of God along Anselmian lines as "that than which no greater can be conceived," or as the greatest conceivable being.  It seems intuitively clearly that an imperfect being could not have divine status.  In particular, nothing imperfect could be an appropriate object of worship.  To worship an imperfect being would be idolatry.

B. Reject (2).  The price of rejection is steep here too since (2) seems merely to unpack the meaning of  'perfect being.'  Intuitively, contingent existence is an imperfection.

C.  Reject (3).  This is a more palatable option, and many will solve the antilogism in this way.  If ~(3), then there are noncontingent beings.  A noncontingent being is either necessary or impossible. So if God is noncontingent, it does not follow that God is necessary.  He could be impossible.

Unfortunately, the rejection of (3) is not without its problems.

According to David Hume, "Whatever we conceive as existent, we can also conceive as non-existent." (Dialogues Concerning Natural Religion)  I would put it this way, trading Latin for plain Anglo-Saxon:  no matter what we think of as existing, we can just as easily think of as not existing.  This includes God.  

Try it for yourself.  Think of God together with all his omni-attributes and then think of God as not existing.  Our atheist pals have no trouble on this score.  The nonexistence of God is thinkable without logical contradiction. 

The Humean reasoning in defense of (3) rests on the assumption that conceivability entails possibility.  To turn aside this reasoning one must reject this assumption.  One could then maintain that the conceivability by us of the nonexistence of God is consistent with the necessity of God's existence.

The price of rejecting (3) is that one must deny that conceivability entails possibility.

Is our antilogism an aporia in the strict sense?  I don't know. 

Related articles

Existence and Essence: An Aporetic Dyad

A Being-Knowledge Antilogism

Are All Genuine Problems Soluble? A Metaphilosophical Antilogism

A Tension in My Thinking: Hume Meets Parmenides

The Sense of Contingency and the Sense of Absurdity

Comments

[John]

Is rejecting the claim that conceivability entails possibility such a high price? It is interesting to note in this regard that by applying that principle, one seems to arrive at a contradiction. We may conceive of a necessarily existing being. (This is typically how the first premise of the modal ontological argument is defended.) It follows that such a being exists. We may also conceive of the nonexistence of a necessarily existing being. It follows that such a being does not exist. So, if conceivability entails possibility, then a necessarily existing being both exists and does not exist. Therefore, conceivability does not entail possibility.

Have I erred somewhere in this reasoning?

[Miloš]

Dear Sir,

I believe that (3) is inconsistent with theistic assumption that if God exist, He exist necessarily. I also think that we don't have strong independent reason to accept (3). We can reject (3) assuming that merely logical possibility does not entail metaphysical/broadly logical possibility. My way to avoid (3) is to make difference between logical (without contradiction in first order logic) and metaphysical possibility. I must admit that notion of broadly logical possibility is, for me, very hard to grasp.

As I notice in some contemporary literature on philosophy of religion some authors like Richard Swinburne and Michael J. Almeida (in Freedom, God, and Worlds) don't think if God exist that He exist necessarily but contingently so they reject second member of this trio.

[BV]

John,

Your reasoning is impeccable. If a man can be an argument, then you are an argument for an open ComBox.

Rejecting conceivability-implies-possibility, however, does seem to come at the price of making it impossible for us to gain rational insight into the possibility of a necessary being.

[BV]

Milos,

Thank you for your comment. I assume that broadly logical possibility alone is at issue. It is not clear to me how the NL/BL distinction allows us to avoid (3).

God is the Absolute Reality, and many of us find it hard to understand how such a Reality could just happen to exist.

[Elliott]

Does the Humean point confuse epistemic with metaphysical possibility?

(3) concerns metaphysical possibility. Hume’s statement addresses epistemic possibility. Hume's point seems true about what is thinkable or imaginable. But, ontologically, a perfect being is either necessary or impossible regardless of my thinking/imagining.

The confusion is roughly like the mix-up between moral ontology and moral epistemology. One argues “God must exist for objective morality to exist” and another replies “I can be good without believing in God.” The argument concerns moral ontology but the reply concerns moral epistemology.

[BV]

Hi Elliot,

True, a perfect being is either necessary or impossible independently of what we think, but only if there are noncontingent beings. (3), however, states in effect that there are no noncontingent beings.

Moreover, there is an argument for (3), the Humean one. To turn it aside one must reject conceivability-entails-possibility. That is not a confusion of the epistemic with the metaphysical but a principle whereby we determine what is possible.

[Elliott]

Thanks, Bill. I see the importance of the c-e-p principle. I guess I’m wondering how to apply it to (3).

In an epistemic sense, I can conceive things to exist or not. This helps me to understand the world. Here, if conceivable then for all I know, possible.

In a metaphysical sense, things seem different (assuming one has separate reasons to think noncontingent beings exist). For example, the modal ontological argument holds that the greatest conceivable being is possible because not contradictory. Here, absence of contradiction entails possibility; mere conceivability does not.

Apparently the epistemic sense is acceptable if the possibility is mental, but not if the possibility is metaphysical. And the metaphysical sense is acceptable if understood as “absence-of-contradiction-entails-possibility”, but not if “conceivability-entails-possibility.”

Is this a mistaken distinction?

[Elliott]

Regarding ~(3), consider:

Every contingent fact or thing has an explanation (PSR). Suppose everything exists contingently. Then “everything exists contingently” (EEC) is a contingent fact having an explanation. But nothing contingent explains EEC and nothing contingent explains itself. It seems EEC has and does not have an explanation. So, not everything exists contingently.

[BV]

I think you reasoning is incorrect.

The following are consistent: (a) Each thing exists contingently; (b) It is necessary that something or other exist.

[Elliott]

I suppose (b) means “Necessarily (something exists)”, not “Something (necessarily exists)”.

So in every possible world something exists. The thing could be different, contingent, in each world. Still, one thing seems necessary: the proposition “Necessarily (something exists)” -- or the case that something is. But (a) seems right if c-e-p is true. A tough challenge!

An Anselmian might deny the c-e-p principle but affirm the “strict logical possibility" principle. Another tough challenge!