- Anselm claims that the non-existence of God is self-contradictory, so that anyone who says “God does not exist” is contradicting himself just as, though not as blatantly as, someone who says a rectangle has 6 sides.
- If correct, Anselm’s argument answers the question why there should be anything at all (which is Van Inwagen’s interest in this article), though this isn’t the same question as why there should be a physical universe.
- Claims of “Scandalous invalidity” from Gaunilo to Schopenhauer, via Aquinas.
- Descartes’ argument – a variant of Anselm’s. Descartes takes the most perfect being to be God, and claims that existence is a perfection. Just as we can’t conceive of a triangle without 3-sidedness1, so we can’t conceive of God without existence.
- Existence as a “good thing” might be denied by suicides, but Kant2 allegedly had the answer, namely that existence is not a property. A concept is a list of properties. Analogy of “egmounts” – existing mountains of pure gold.
- Van Inwagen thinks Kant has only found a peripheral fault with Descartes argument, which can be re-stated without treating existence as a property.
- Something has necessary existence if its non-existence would have been impossible – by which Van Inwagen means “absolutely impossible” – ie. involving a logical contradiction.
- So, necessary existence is a property, and a more impressive property than mere existence (if it is a property) even if (maybe) necessary existence is not a possible one (it is hard to think of an uncontroversial example of something with necessary existence).
- Van Inwagen restates Descartes’ argument as:-
- A perfect being has all perfections
- Necessary existence is a perfection
Hence, A perfect being has necessary existence
- Whatever has necessary existence has existence
Hence, A perfect being has existence
- Whatever has existence exists
Hence, A perfect being exists
- But this argument is obviously invalid, and Van Inwagen runs the argument through with a “negmount” – which is just an “egmount” with necessary existence; it has all “negmontanic” properties, of which necessary existence is one → So, while this argument “proves” that “negmounts” exist, it can’t possibly be sound as its conclusion is false – and necessarily so as physical objects are contingent, And, even if we cavil at this – the argument can be run through with “nousquares” – a necessarily existent round square.
- So, given that the argument’s invalid3, what’s wrong with it? Van Inwagen points out an ambiguity in “a negmount has all negmontanic properties” between:-
This is due to the ambiguity in the indefinite article, which may or may not imply existence.
- Anything that is a negmount has all negmontanic properties
- There is a negmount that has all negmontanic properties.
- Hence we have two arguments bundled together, neither of which is convincing that negmounts exist.
- One says that anything that is a negmount exists; the argument is sound but unexciting, as anything that is an X exists, whatever X.
- The other proceeds from the premise that there is a negmount to the conclusion that there is a negmount that exists. This just begs the question.
- Any plausibility in Descartes’ argument arises from running the two arguments together with the premise of the first argument leading to the conclusion of the second.
- Van Inwagen spells out all this for Descartes (revised) argument, and states his conviction that “the earlier argument4 of Anselm” is also a failure.
- But, Van Inwagen thinks that the modal5 argument has more going for it. This should be spelled out in terms of possible worlds. Van Inwagen gives a useful definition: “a possible world is a complete specification of the way the World might have been, one so precise that it settles every detail, no matter how minor6”. If everything there is or could be is subject to the flow of time (not7 a wise assumption, Van Inwagen says) then a possible world is detailed history-and-future. Van Inwagen gives an “impressionistic account” of the meaning of “truth in” and “existence in” a possible world.
- Then Van Inwagen moves on to defining modal8 operators – a proposition is possibly true if it is true in at least one possible world and necessarily true if true in all possible worlds. The actual world is the way that the world really is. He usefully notes that the actual world is just a specification9, so it is not the World itself. He (later) notes that actuality is an indexical notion, true “in” every possible world – so if we are in a possible world, that is the actual world. This is the only thing residents of different possible worlds disagree on about the set of possible worlds. He compares the reality of (even) the actual world to that of a computer program. The World is not a description, but the things themselves10. Possible-world semantics are not necessary for formulating modal11 ontological arguments, but are useful in avoiding logically invalid arguments that look valid.
- We now need two notions:-
- A necessary being is one that exists in every possible world, and
- An essential property is one without which a being could not exist. So, x has a property essentially if it has it in every possible world in which x exists.
- The converse terms are contingent and accidental. There are few examples of essential properties – for instance people disagree over whether we have the property human being essentially, because they disagree about what we are.
- Descartes tells us that the subject of the Ontological Argument – a perfect being – is one that possesses all perfections. But does this being possess the perfections essentially or contingently. Van Inwagen says it doesn’t matter12 (with one exception – that of necessary existence) what these perfections are – but takes wisdom as an example. He thinks that possessing wisdom essentially rather than accidentally would provide a better candidate for a perfect being, so takes the properties of the perfect being to be had essentially from now on.
- So, the Modal13 Ontological Argument is:-
So, we have two tasks: to determine whether the argument is valid, and whether the two premises should be granted.
- A perfect being – one that possesses all perfections essentially – is not impossible.
- Necessary existence is a perfection.
Hence, A perfect being exists.
- Van Inwagen describes world-diagrams. A world-diagram is “correct in” a given possible world if all its assertions are true in that world – including its assertions about other possible worlds. He then uses world diagrams, rather laboriously, to prove that the Modal14 Ontological Argument is valid.
- He rejects an objection based on the supposition that possibility is not fixed and necessary (ie. that some possible worlds – in particular that in which God is actual – do not exist from the perspective of all possible worlds). So, if God exists in all possible worlds but the actual world, but the other possible worlds cannot “see” the actual world, then they will think that God necessarily exists, as he exists in all the worlds they can see.
- Van Inwagen distinguishes “conditional” impossibilities that are dependent on other contingencies from “intrinsic” impossibilities, that aren’t. His claim is that while conditional possibilities may vary from world to world, intrinsic possibilities don’t. This “principle of modal15 inference” is effectively a third premise in the argument.
- The only outstanding obstacle – given that the argument is valid, and we’ve accepted the principle of inference and the second premise (that necessary existence is a perfection) – is the possibility of a perfect16 being. We cannot give the benefit of the doubt, as in common law, because pairs of alleged possibilities can be mutually incompatible.
- What are the options?
- Instances: The most reliable way of proving possibility is to appeal to actuality, but there is no agreement that we have common knowledge that perfect beings exist.
- Abstract Metaphysical Argument: Leibniz realised the importance of possibility, and argued as follows:-
→ A perfect being is perfect if it has all perfections.
→ It is possible if these perfections are consistent with one another.
→ Every perfection is a simple positive17 property, where “positive” simply means “not negative” (a negative property is eg. “being not round”).
→ Simple positive properties cannot conflict as this only arises where one is “X” and the other “not X”, or one a complex that includes the negative of a property in or included in the other.
So, simple positive properties cannot conflict. But we need these properties to be had essentially. So, we need:-
→ if property X is a perfection, then the property “having property X essentially” is a perfection.
- There are many problems with Leibniz’s argument. Van Inwagen only discusses one – that of the analysis of properties, and the category “non-negative” in particular. Properties are not negative or positive in themselves as the same property can be named “simple” and “not having parts”.
- So, if we can’t prove that a perfect being is possible, can we prove that it is impossible? Findlay at one time thought he could prove that a necessary being was impossible. His reason was that necessarily true existential propositions are impossible, because all necessary truths are analytic – true merely because of our use of words, and we can’t define anything into existence. This ends in the modal18 ontological argument being deemed unsound, as it has a false premise (that a perfect being is possible).
- The problem with Findlay’s argument is with his theory of necessary truth which, while almost universally accepted in his day (194819), is no longer in fashion20. Van Inwagen gives the example “The atomic number of iron is 26”. Many philosophers take this to be a necessary truth, because the atomic number of an element is its essence, but not one due to the meaning of words as the meaning and reference of “iron” was set before anyone knew of the atomic theory, and something can be part of the meaning of a word only if a person who knows the meaning of the word knows it is.
- Even so, this doesn’t prove there are any necessary existential propositions, as “The atomic number of iron is 26” does not claim that any iron exists. But it does show that Findlay’s account of necessary truth is mistaken.
- Also, there are some propositions that some philosophers would claim to be “necessary existential”. Van Inwagen gives a mathematical example, and admits that this only implies the necessary existence of universals21. But, he claims that Findlay’s theory of necessity is independent of its subject-matter, and so is refuted by mathematics.
- Even so, we’ve not given an example of a necessarily existent individual thing, only a universal22. Van Inwagen claims that a perfect being would have to be an individual thing23. Van Inwagen knows of no non-Findlay-style arguments that purport to show that there could not be a necessarily-existent individual thing. They would have to show that “being necessarily existent” and “individual thing” are inconsistent, and Van Inwagen can’t see how this could be done, given that Findlay’s argument “proves too much” in denying the existence of universals24.
- So, we now have the minimal modal25 ontological argument:-
- If a necessarily-existent individual is possible, then there is a necessarily-existent individual in some possible world.
- Therefore, it is true in that possible world that that necessarily-existent individual exists in all possible worlds.
- Since the only thing that changes from one possible world to another is which possible world is actual, it is true in every possible world that that necessarily-existent individual exists in all possible worlds.
- The property being an individual thing is an essential property.
- So, this thing is an individual thing in every possible world.
- So, there is a necessarily-existent individual thing in every possible world, including the actual world.
- So, there is a necessarily-existent individual thing.
- This argument has nothing to do with a perfect being, because it works for a necessarily-existent being with any set of essential properties whatever. Van Inwagen only needs the minimal argument for his purposes, which is to answer the question why there is something rather than nothing.
- So, is the contentious premise of the minimal modal26 ontological argument is true – that is, whether a necessarily-existent individual thing is possible, ie. whether existent necessarily and individual thing are compatible. He doesn’t think we can deduce a formal contradiction, yet they may be incompatible for all that.
- There are only two fool-proof ways of showing whether two properties are compatible:-
If Van Inwagen had a positive example, he’d have no need of the argument; and yet he knows of no way of deducing a contradiction.
- Positively: If we know of something that has both.
- Negatively: If we can deduce a formal contradiction.
- If we can’t show that a necessarily-existent individual thing is possible, we certainly can’t show that a perfect being is possible, as this has further properties that might or might not be incompatible.
- Van Inwagen claims that all the extant attempted disproofs27 of the possibility of a perfect being all focus on the impossibility of necessary existence.
- In summary, all versions of the Ontological Argument are either invalid or have a premise of a truth-value we cannot evaluate. But if we could show that there was a necessarily-existent individual thing, then we’d know that it was impossible for there to be nothing, which would explain why there is something.
- Van Inwagen seems to think there’s a way forward, as many have suggested28 that without a necessary being, there could be no beings at all, and since there obviously are beings, there must be a necessarily-existent one.
- Further reading: Van Inwagen recommends:-
→ Plantinga, Alvin (Ed.) The Ontological Argument
→ "Plantinga (Alvin) - God, Freedom and Evil",
→ "Kripke (Saul) - Naming and Necessity",
→ "Hume (David), Tweyman (Stanley), Ed. - Dialogues Concerning Natural Religion", Part IX,
→ "Putnam (Hilary) - The Meaning of 'Meaning'", and
→ "Schwartz (Stephen P.), Ed. - Naming, Necessity and Natural Kinds", including
→ "Kripke (Saul) - Identity and Necessity".
Footnote 1: Presumably the quotation is from the Third Meditation, as the Fifth refers to Pythagoras’ Theorem.
Footnote 2: The passage Van Inwagen quotes isn’t "Kant (Immanuel) - The Impossibility of an Ontological Proof of the Existence of God"; maybe it’s Van Inwagen’s exegesis.
- I had thought that Van Inwagen was using “invalid” when he meant “unsound”.
- I’d thought that the problem was not with the argument form, but with one of the premises.
- But it turns out that it is the form that contains the problem.
Footnote 6: This would seem to make possible worlds impossible to specify.
- So, not recognising that there are (according to Normal Malcolm and others) two arguments in Anselm.
- Since Van Inwagen takes up the modal argument, he does agree with Anselm in a manner of speaking.
Footnote 7: Presumably if God is timeless rather than eternal.
Footnote 9: Presumably a realist about possible worlds would disagree.
Footnote 10: So introducing, but not mentioning, the de re / de dicto distinction.
Footnote 12: So, we need to watch out that this perfect being is in fact the theistic God.
Footnote 16: Which, as no other perfections have been mentioned, is simple a necessarily existent being.
Footnote 17: Godel picks up on this idea.
Footnote 19: Van Inwagen doesn’t quote which paper, but I assume it’s "Findlay (J.N.) - Can God's Existence Be Disproved?".
Footnote 23: This sounds controversial, as God isn’t a thing.
- Van Inwagen doesn’t quote or refer to Kripke until the “further reading” section, but this change of perspective is down to him.
- His example is of gold, atomic number 79, in "Kripke (Saul) - Naming and Necessity: Lecture III", section 4.8 of my précis.
Footnote 27: This is strange, as there are obvious tensions between (say) God’s omniscience and his granting of human free-will, or between God’s justice and his mercy, or of the concept of omnipotence itself.
- But a nominalist would not be worried, as he denies that there are any such things as universals.
- Do unicorns exist (as universals)?
Footnote 28: Van Inwagen doesn’t spell this out, but presumably it’s the Cosmological Argument he has in mind?
Text Colour Conventions (see disclaimer)
- Blue: Text by me; © Theo Todman, 2019