Maverick Philosopher

The requisites of an office are the properties that must be possessed by anything that occupies the office, if anything does occupy it. Thus, among the requisites of the office of U. S. president, there is the property of being at least 35 years of age. Among the requisites of the divine office we find the familiar omni-attributes or 'perfections,' omniscience, etc. Both the presidential and the divine offices are individual offices in the sense that, if they are occupied, then they are occupied by an individual. Note that the requisites of an individual office are first-level properties of the office-holders, if there are any.

Tichý finds two fallacies in the above Cartesian argument.

The first is that it assumes that existence is a first-level property, a property of individuals. For if existence is one of the requisites of the divine office, as it must be if existence is a perfection, then existence is a property that can be meaningfully attributed to individuals. But we have seen that for Tichý, existence is not a property of individuals but of offices. It is the second-level property of being-occupied.

The second mistake in the Cartesian argument is that it relies on the following fallacious argument-pattern:

P is a requisite of office O
Therefore
The occupant of O instantiates P.

The argument-form is indeed invalid. Let O be the office of King of France. Let P be being human. P is a requisite of O. But it doesn't follow that the occupant of the office of King of France is human. For there is no occupant. Similarly, even if existence were a requisite of the divine office, it would not follow that the occupant of the divine office exists. For the office may be unoccupied. All we can safely infer from the fact, if it is a fact, that existence is a requisite of the divine office is that, if the office is occupied, then the occupant exists.

This is a very old objection, and it strikes me as sound. The concept of God is the concept of a being possessing all perfections. Now let it be granted that existence is a perfection, a "great-making property" in Alvin Plantinga's phrase. From these premises we may validly infer that the concept of God is the concept of a being that exists, indeed, the concept of a being that is as inseparable from its existence as the idea of a mountain from the idea of a valley, to revert to a Cartesian analogy. Still, how does this get us to the conclusion that God exists? For all that this argument shows, the concept of God might fail of instantiation: there might not be anything that falls under it. If something instantiates the God-concept, then that thing has an essence which includes or entails existence. But from this one cannot validly infer that something does instantiate the God-concept, or occupy the divine office.

Of course, Tichy does not grant that existence is a perfection, a great-making property of God. For his whole point is that existence cannot be attributed to individuals. This yields a much more radical objection to the Cartesian ontological argument, an objection one finds already in Frege, but not before Frege: Kant does not anticipate Frege's exact point about existence, contrary to what many, including Tichy, think. (To establish this would require a separate post.) In The Foundations of Arithmetic, we read, "Because existence is a property of concepts, the ontological argument for the existence of God breaks down." (p. 65) This amounts to a very radical criticism since it implies that 'God exists,' interpreted as the attribution of existence to an individual is meaningless.

Now I reject this more radical Fregean objection to the ontological argument. First, it implies a theory of existence open to powerful objections, a couple of which are sketched here. Second, the argument for it is not compelling, as explained here.

Simplified version: if God is possible, then God is actual. God is possible, therefore God is actual.

The problem, of course, is to give a good reason for thinking that God is possible. The fact that one can conceive of God without contradiction does not establish that God is possible. Conceivability (thinkability) without contradiction is no sure guide to real, extramental, possibility. The following modal ontological argument, then, though valid, and perhaps sound, is not probative unless we can give a good reason for supposing that a maximally perfect being is possible:

1. If a maximally perfect being is possible, then it is actual.
2. A maximally perfect being is possible.
Therefore
3. A maximally perfect being is actual.

What we need is an argument for (2). Here is one:

4. A maximally perfect being ought to exist.
5. Whatever ought to exist, is possible.
Therefore
2. A maximally perfect being is possible.

This is a valid argument, and the premises are very plausible. A maximally perfect being is deontically perfect and so ought to exist. If you deny that, then you are saying that a being can be both perfect in every respect but also either such that it ought not exist (which would be absurd) or such that it neither ought to exist, nor ought not exist. Either way, a greater can be conceived, namely a being that ought to exist.

(5) is also exceedingly plausible. If you were to deny it you would be saying that there are things or states of affairs that both ought to exist and are impossible.

Now putting the deontic subargument and the ontological subargument together we get a deontic ontological argument that is not only valid but appears probative. So a maximally perfect being exists, "and this all men call God." So far, I have presented something similar to the argument Carl R. Kordig gives in "A Deontic Argument for God's Existence," Nous, vol. 15, no. 2(May 1981), pp. 207-208)

But wait a minute! Is premise (4) really self-evident? Could one not argue, with an equal show of plausibility, that God (the maximally perfect being) ought not exist? And that as a result God does not exist? As follows:

6. Everything is such that it ought not exist.
Therefore
7. God is such that he ought not exist. (From 6)
Therefore
8. It ought to be the case that God does not exist. (From 7)
9. If it ought to be the case that p, then it is possible that p.
Therefore
10. It is possible that God does not exist. (From 8, 9)
11. If it is possible that God does not exist, then God does not exist. (A corrolary of Anselm's Insight)
Therefore
12. God does not exist. (From 10, 11)

The (6)-(12) argument is a deontic ontological disproof. It is valid. The crucial premise is (6). You will tell me that we have no reason to accept the nihilist premise, (6), and I will be inclined to agree with you. But do we have reason to accept the presupposition on which the deontic ontological proof rests, namely, that to exist is good? The proof assumes that necessary existence is better than contingent existence. But if so, then existence is good. As a scholastic might put it, ens et bonum convertuntur. Would Schopenhauer and Sartre find that self-evident?

The conclusion I am steering toward is that the proof and the disproof cancel each other, and that therefore neither is conclusive. Each is valid, and both make use of the apparently unexceptionable principles that God is a necessary being and that whatever ought to be the case is possibly such that it is the case. They differ in that the proof rests on the fundamental assumption that to exist is good, while the disproof rejects this assumption.

Unless we can somehow justify the assumption that to exist is good, or its negation, we are left with neither a genuine proof nor a genuine disproof. We end aporetically.

Invalid as it stands, this argument can be made valid by adding a premise. (Any invalid argument can be made valid by adding a premise.) Add 'All men die' and the argument comes out valid. Peirce writes:

The leading principle of this is nota notae est nota rei ipsius. Stating this as a premiss, we have the argument,

Nota notae est nota rei ipsius
Mortality is a mark of humanity, which is a mark of Enoch
-----
Mortality is a mark of Enoch.

But is it true that the mark of a mark is a mark of the thing itself? There is no doubt that mortality is a mark of humanity in the following sense: The concept humanity includes within its conceptual content the superordinate concept mortal, which implies that, necessarily, if anything is human, then it is mortal. But mortality is not a mark, but a property, of Enoch. I am alluding to Frege's distinction between a Merkmal and an Eigenschaft. Frege explains this distinction in various places, one being The Foundations of Arithmetic, sec. 53. But rather than quote Frege, I'll explain the distinction in my own way using a totally original example.

Consider the concept bachelor. This a first-order or first-level concept in that the items that fall under it are not concepts but objects. The marks of a first-order concept are properties of the objects that fall under the concept. Now the marks of bachelor are unmarried, male, adult, and not a member of a religious order. These marks are themselves concepts, concepts one can extract from bachelor by analysis. Given that Tom falls under bachelor, he has these marks as properties. Thus unmarried, etc. are not marks of Tom, but properties of Tom, while unmarried, etc. are not properties of bachelor but marks of bachelor.

To appreciate the Merkmal/Eigenschaft distinction, note that the relation between a concept and its marks is entirely different from the relation between a concept and its instances. A first-order concept includes its marks without instantiating them, while an object instantiates its properties without including them.

This is a very plausible line to take. It makes no sense to say of a concept that it is married or unmarried, so unmarried cannot be a property of the concept bachelor. Concepts don't get married or remain single. But it does make sense to say that a concept includes certain other concepts, its marks. On the other hand, it makes no sense to say of Tom that he includes certain concepts since he could do such a thing only if he were a concept, which he isn't. But it does make sense to say of Tom that he has such properties as being a bachelor, being unmarried, being an adult, etc.

Reverting to Peirce's example, mortality is a mark of humanity, but not a mark of Enoch. It is a property of Enoch. For this reason the scholastic formula is false. Nota notae NON est nota rei ipsius. The mark of a mark is not a mark of the thing itself but a property of the thing itself.

No doubt commenter Ockham will want to wrangle with me over this slight to his scholastic lore, and I hope he does, since his objections will aid and abet our descent into the labyrinth of this fascinating cluster of problems. But for now, two quick applications.

One is to the ontological argument, or rather to the ontological argument aus lauter Begriffen as Kant describes it, the ontological argument "from mere concepts." So we start with the concept of God and analyze it. God is omniscient, etc. But 'surely' existence is also contained in the concept of God. For a God who did not exist would lack a perfection, a great-making property; such a God would not be id quo maius cogitari non posse. He would not be that than which no greater can be conceived. To conceive God, then, is to conceive an existing God, whence it follows that God exists! For if you are conceiving a nonexistent God, then you are not conceiving God.

Frege refutes this version of the OA — not the only or best version I hasten to add — in one sentence: Weil Existenz Eigenschaft des Begriffes ist, erreicht der ontologische Beweis von der Existenz Gottes sein Ziel nicht. (Grundlagen der Arithmetik, sec. 53) "Because existence is a property of concepts, the ontological argument for the existence of God fails to attain its goal." What Frege is saying is that the OA "from mere concepts" rests on the mistake of thinking of existence as a mark of concepts as opposed to a property of concepts. No concept for Frege is such that existence is included within it. Existence is rather a property of concepts, the property of having an instance.

The other application of my rejection of the scholastic formula above is to the logical question of the correct interpretation of singular propositions. The scholastics treat singulars as if they are generals as I explained fully in previous posts. But if Frege is right, this is a grave logical error since it rides roughshod over the mark/property distinction. To drag this all into the full light of day will take many more posts.

1. Ontological Disproofs of Nondivine Items. Some people think that conceptual analysis is irrelevant to questions of real existence: what exists and what does not must be determined empirically. But this is not the case. By sheer analysis of the concept round square I can know, and know a priori, that there cannot exist a round square. Round squares and the like can be ruled out on conceptual grounds alone. Even if nothing can be ruled in by conceptual analysis, surely some things can be ruled out. By sheer thinking one can know something, albeit something negative, about reality.

2. Ontological Disproofs of God. Nothing could count as God that did not have the property of aseity, or in plain Anglo-Saxon, from-iself-ness. The concept of God is the concept of something that by its very nature cannot be dependent on anything else for its nature or existence, and this holds whether or not anything in reality instantiates the concept. This is equivalent to the assertion that God exists necessarily if he exists at all. But if everything that exists exists contingently, as philosophers of an empiricist bent are likely to maintain, then we have the makings of an ontological disproof of God. In a 1948 Mind article, J. N. Findlay gave essentially the following argument:

a. God cannot be thought of as existing contingently.
b. Everything that exists can only be thought of as existing contingently.
Therefore
c. God does not exist.

This ontological disproof of God turns Anselm on his head while retaining the Anselmian insight that God is “that than which no greater can be conceived.” Precisely because God is maximally great, supremely perfect, id quo maius cogitari non posse, he cannot exist. For if everything that exists exists contingently, then nothing exists necessarily. Necessary existence, however, is a divine perfection. Ergo, God does not exist.

The trouble with Findlay’s 1948 argument, an argument that the older and wiser Findlay renounced, is that premise (b) is by no means obviously true, even if we replace ‘everything’ with ‘every concrete thing.’ Indeed, I believe that (b) is demonstrably false. But the argument for this belongs elsewhere. Here my task is a mere typology of ontological arguments.

3. Ontological Proofs of God. Here is an example. God, by definition is ens perfectissimum, a maximally perfect being. Now a maximally perfect being cannot be modally contingent, but must be modally noncontingent: it must be either impossible (existent in no possible world) or necessary (existent in every possible world). But surely it is possible that there be a maximally perfect being. (There is at least one possible world in which God exists.) Therefore, God exists in every possible world, whence it follows that he exists in the actual world.

Simplified version: if God is possible, then God is actual. God is possible, therefore God is actual.

The problem, of course, is to give good reason for thinking that God is possible. The fact that one can conceive of God without contradiction does not establish that God is possible. Conceivability (thinkability) without contradiction is no sure guide to real, extramental, possiblility.

4. Ontological Proofs of Nondivine Items. Can one establish, by conceptual analysis alone, that something exists even if one cannot establish, by this means, that God exists?

Consider the concept true proposition. This concept is either instantiated, or it is not. If it is not instantiated, then it is true that it is not instantiated, which implies that the concept true proposition IS instantiated. If, on the other hand, the concept in question is instantiated, then of course it is instantiated. Therefore, necessarily, the concept true proposition is instantiated, and there necessarily exists at least one truth, namely, the truth that the concept true proposition is instantiated.

This is a valid ontological argument for the existence of at least one truth using only the concept true proposition, the law of excluded middle, and the unproblematic principle that, for any proposition p, p entails that p is true. By 'proposition' here I simply mean whatever can be appropriately characterized as either true or false. That there are propositions in this innocuous sense cannot be reasonably denied.