Maverick Philosopher

Is the Modal Ontological Argument Rationally Compelling?

I argue that it isn't.

Four Kinds of Ontological Argument

A Substack typology.

Nota Notae Est Nota Rei Ipsius, Kant, and the Ontological Argument

This is a re-post, redacted and re-thought, from 22 July 2011. I dust it off because something caught my eye the other morning in the Translator's Introduction to Kant's Logic. Robert S. Hartman and Wolfgang Schwarz tell us that for Kant the principle of all inference or mediate judgment is the rule Nota notae est rei ipsius nota. (p. xlii). I'm guessing that C. S. Peirce got wind of the principle from Kant. As for Hartman, I remember hearing good things about him and his work in axiology from Hector-Neri Castañeda. I also recall Hector saying that Hartman died young. Details of Hartman's eventful life here. He died at age 63, which is young for a philosopher.  Hector died at 66.

.........................................................................

"The mark of a mark is a mark of the thing itself." I found this piece of scholasticism in C. S. Peirce. (Justus Buchler, ed., Philosophical Writings of Peirce, p. 133) It is an example of what Peirce calls a   'leading principle.'

Let's say you have an enthymeme:

   Enoch was a man
   -----
   Enoch died.

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 invoking Gottlob 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 is 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 (mark)-Eigenschaft (property) 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 Edward the Nominalist 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 Immanuel Kant describes it, the ontological argument "from mere concepts." So we start with the concept God and analyze it. The concept God includes omniscience, etc. But 'surely' existence is also contained in the concept 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 ontological argument -- 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 ontological argument "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.  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 would take many more posts.

Given Anselm's Insight, How is Empirical Evidence Relevant to the Existence/Nonexistence of God?

ANSELM'S INSIGHT

I take what I call Anselm's Insight to be non-negotiable.  St. Anselm appreciated, presumably for the first time in the history of thought, that a divine being, one worthy of worship, must be non-contingent.  If your god is contingent, then your god is not God. For if your god is contingent, and he exists, then his nonexistence is possible, and nothing like that could count as God. God, by definition, is that than which no greater can be conceived, to use use Anselm's signature phrase, and necessity is a greater or higher modal status than contingency. Contingency in an existing thing is an ontological defect. God is an absolute, and no absolute worth its salt is contingent.  If, on the other hand, your god is contingent and he doesn't exist, then it is worse still: your god is impossible. 

Anselm's point, expressed with the help of Leibniz, is that the concept of God is the concept of a being that either exists in every metaphysically possible world, or in no metaphysically possible world.  This formulation has the advantage of not presupposing the existence of God by the use of 'God.' For it may be that the concept is not instantiated, as it would not be if God is impossible.

Anselm's Insight rests on the assumption that the necessarily existent is 'better' than the contingently existent, which in turn rests on the Platonic sense that the immutable is higher in value than the mutable. This assumption can be reasonably questioned but also reasonably defended. But I won't go into that now. For present purposes I endorse both the Insight and the Assumption upon which it rests.

ANSELM'S ARGUMENT

But it does not follow from Anselm's Insight that Anselm's Argument is probative. I am referring to the modal ontological argument found in Proslogion III. One cannot validly infer from God's non-contingent status alone that he exists.  For it is epistemically possible -- possible for all we know -- that God is modally impossible. 'Non-contingent' does not mean 'necessary.' It means 'either necessary or impossible.'  To arrive at God's existence, one needs a possibility premise to the effect that God  is possible.  But how would you know that the premise is true? Conceivability is no sure guide to real possibility. 

For more on the Argument see here. Today's topic is different.

IS EMPIRICAL EVIDENCE RELEVANT TO THE EXISTENCE/NON-EXISTENCE OF A NON-CONTINGENT GOD?

A question posed to me by a reader requires only Anselm's Insight although he thinks it requires the probativity of Anselm's Argument. I take him to be asking how empirical evidence could be relevant to the existence of a non-contingent God.  

Suppose God does not exist.  Then, by the Insight, he is impossible.  But no amount of empirical evidence could show that what is impossible is actual.  So no miraculous event could show that God exists. If God is impossible, any putative empirical evidence to the contrary could be legitimately dismissed a priori.  Compare round squares and colored sounds. They are impossible. The claims of anyone who said he had empirical evidence to the contrary would be legitimately dismissed a priori.  We know that there  cannot be any round squares or colored sounds. We do not know that God is impossible. But we do know (given Anselm's Insight) that either God necessarily exists or God is impossible.  

If, on the other hand, God does exist, then he cannot fail to exist and no empirical evidence is needed or could be relevant.  Suppose that someone demanded empirical evidence of the truth of 7 is prime or the existence of 7 or the existence of the proposition, 7 is prime.   You would show that person the door.

Now either God exists or he does not. Either way, empirical evidence is irrelevant to the existence of God.

What then of natural and moral evil? Are they evidence of the nonexistence of Anselm's God?  No, and to think otherwise is to assume that God is a contingent being.

The above is my interpretation of my reader's reasoning.  I am inclined to accept it as I interpret it.

A Weird 'Fregean' Ontological Argument

London Ed asks:

Which step of the argument below do you disagree with?

a) If a sentence containing a proper name is meaningful, then the proper name is meaningful, i.e. it designates.

This is a standard assumption about compositionality.

BV: I have a  problem right here. I accept the compositionality of meaning. But a proper name can have meaning without designating anything.  As I see it, meaning splits into sense (Sinn) and reference (Bedeutung).  And I don't see any need to distinguish between reference and designation. So there can be a proper name that has meaning (sense) without designating anything. 'Vulcan' (the planet) is an example.   Here is another:

'Kepler died in misery.'  The sentence is meaningful; hence, by compositionality, 'Kepler' is meaningful.  Now assume that presentism is true and that only present items exist. Then Kepler does not exist.  (Of course he does not exist now; the presentist implication is that he does not exist at all.)  If Kepler does not exist at all, then he cannot now be referred to or designated.  But when I now assertively utter 'Kepler died in misery,' I assert a proposition that is true now and is therefore meaningful now. It follows that the meaning of 'Kepler' is not exhausted by its designatum.  'Kepler' is not a mere Millian tag.  There may be Millian tags, but ordinary proper names are not such. 

Now London Ed is, I think, a presentist. If so, he ought to be open to the above argument.

b) If the proper name does not designate, the sentence containing it is not meaningful (contraposition).

BV: That is the case only if the meaning of a name = its referent, the thing designated.  That cannot be. Consider 'Vulcan does not exist.' It's true, hence meaningful. So 'Vulcan' has a meaning, by compositionality. If so, and if meaning = referent, then 'Vulcan' does not have meaning. Contradiction. Ergo, a proper name can have meaning without designating anything.  Negative existentials are a real problem for Millian theories of names.

c) If ‘God does not exist’ is true, then ‘God’ does not designate.

BV: No doubt.

d) If ‘God does not exist’ is true, then ‘God does not exist’ is meaningless.

BV: That is the case only on the assumption that the meaning of a name is exhausted by its reference, i.e., that the meaning of a name just is its designatum.  The assumption is false.

e) ‘God does not exist’ is not meaningless. (it is something debated over many centuries, no firm conclusion so far)

BV: That's right!

f) ‘God does not exist’ is meaningful, but not true (d and e above)

BV: That follows, but (d) is false.

g) ‘God does exist’ is true (excluded middle)

 BV: Valid move, but again (d) is false. So argument unsound.

h) Therefore God exists (disquotation)

BV: Valid inference, but again unsound.

From the Mailbag: The Ontological Argument

P. M. writes,

Thank you for your work on the Ontological Argument for the Existence of God.  I would really appreciate if you could answer some of my questions that are bulleted below:

 

You discuss the following Ontological Argument in your paper: "Has the ontological argument been refuted?." Religious studies 29.1 (1993): 97-110. 

1. If the concept of an x is internally coherent, then an x exists in some possible world.
2. The concept of the GCB is internally coherent.
3. Therefore, the GCB exists in some possible world. (1, 2)
4. Either the GCB is impossible (exists in no world) or the GCB is necessary (exists in all worlds).
5. Therefore, the GCB is necessary. (3, 4)
6. Therefore, the GCB actually exists. (5) 

(Where GCB is of course the "Greatest Conceivable Being").

• Is the above ontological argument a good one? If not, what are its flaws?
  
• In your opinion what is the strongest version or case for the Ontological Argument today?

Is the above argument good? Well, it's valid.  All that means is that the conclusion follows from the premises: necessarily, if the premises are all true, then the conclusion is true. A further condition on argumentative goodness is soundness: an argument is sound just in case it is valid and all of its premises are true.  But if an argument is sound, it doesn't follow that it is probative, i.e., that it proves its conclusion.

For an argument to be probative, it must not only be sound, but must also satisfy a relevance constraint: the conclusion must be relevant to the premise(s). The following argument is valid in the sense that it is impossible for the premise to be true and the conclusion false, and its premise is true. Yet it surely does not amount to a proof of its conclusion:

Trump is president
ergo
7 + 5 = 12.

The following argument is valid, sound, and satisfies the relevance requirement, but is not proof of anything:

7 + 5 = 12
ergo
7 + 5 = 12.

This is because the argument is circular. Every circular argument is valid and satisfies relevance, and some circular arguments are sound; but none are probative.  So we add freedom from informal fallacy to our list of conditions on probativeness.

But this is still not enough to have a probative argument.  We add: the premises must not only be true; they must be known to be true.

So I deny that the modal ontological argument above is probative. It does not constitute a proof of the existence of a GCB because we do not know whether (1), the possibility premise, is true.  I explain why in Is the Modal Ontological Argument Compelling?

Of course, one could argue for the possibility premise. I've done it myself. Just last month the following paper of mine appeared:

Vallicella, William F. (2018). "Does God Exist Because He Ought To Exist?" In Mirosław Szatkowski (ed.), Ontology of Theistic Beliefs. De Gruyter. pp. 205-212.

In this paper I essay a deontically supercharged modal ontological argument.  Very briefly, I argue that since a greatest conceivable, or maximally perfect, being ought to exist, and since whatever ought to exist is possible, a greatest conceivable, or maximally perfect, being is possible.  I conclude, however, that not even a deontically supercharged modal OA gets the length of a proof.

In fact, I hold that none of the so-called theistic 'proofs' are proofs strictly speaking. The existence of God cannot be proven or disproven. (Thus no argument from evil disproves the existence of God.) One cannot rationally compel belief in God, though I think one can render theistic belief rationally acceptable. My friend Ed Feser disagrees strenuously.

I refer you to his Five Proofs of the Existence of God (Ignatius Press, 2017) which is available via Amazon for less than fifteen semolians.   Ironically, the onto-cosmological argument I deploy in A Paradigm Theory of Existence (Kluwer 2002) a book that  is also available via Amazon for a paltry 170 semolians, ends up as one of Ed's proofs in Chapter Two, "The Neo-Platonic Proof." Ed's discussion of my argument, which I do not consider a proof, commences on p. 75.  He doesn't present my argument in its full subtlety and richness, but then his book is more of a high-level survey than a technical treatise. I thank Ed for the citation. A version of my onto-cosmological argument is presented here:

Vallicella, William F. (2000). From facts to God: An onto-cosmological argument. International Journal for Philosophy of Religion 48 (3):157-181.

Finally, I should say that I am not fully versed in all forms of the Ontological Argument. So I won't offer an opinion on the reader's second question. For further instruction I recommend the work of Graham Oppy and Alexander Pruss.

Gödel: The Third Degree

An article by Graham Oppy on Kurt Gödel's ontological argument.

Is the Modal Ontological Argument Compelling?

In a comment, Patrick Toner writes,

. . . there is no substantive philosophical position for which there is *better* philosophical support than theism. I'm open to the possibility that at least one other philosophical position--namely, dualism--is at least as well supported by philosophical argument as theism. But nothing's got better support.

[. . .]

That said, I find St. Thomas's second way indubitable. I also find the modal ontological argument compelling. The kalam cosmological argument seems pretty much irrefutable.

In another comment in the same thread, Toner writes,

But we still do (or can) know God and the soul with certainty through the use of natural human reason. (emphasis added)

What interests me in this entry is Toner's explicit claim that the modal ontological argument is (rationally) compelling, and his implicit claim that this argument delivers (objectively) certain knowledge of the existence of God.  While I consider the argument in question to be a good argument, I don't find it to be compelling.  Nor do I think that it renders its conclusion certain. My view is that no argument for or against theism is rationally compelling.  No such argument resolves the issue.  I think it would be wonderful if there were a compelling argument for the existence of God.  The metaphysical knowledge generated by such an argument would be the most precious knowledge that one could possess.  So I would be much beholden to Toner if he could show me the error of my ways.  

Perhaps there is a theistic argument that is rationally compelling. If there is I should like to know what it is.  I am quite sure, however, that the following argument does not fill the bill.

A Modal Ontological Argument

'GCB' will abbreviate 'greatest conceivable being,' which is a rendering of Anselm of Canterbury's "that than which no greater can be conceived."  'World' abbreviates 'broadly logically possible world.' 'OA' abbreviate 'ontological argument.'

1. Either the concept of the GCB is instantiated in every  world or it is instantiated in no world.

2. The concept of the GCB is instantiated in some world.  Therefore:

3. The concept of the GCB is instantiated in every world.  (1, 2 by Disjunctive Syllogism) 

4. The actual world is one of the worlds. Therefore:

5. The concept of the GCB is instantiated in the actual world. (3, 4 ) Therefore:

6. The GCB exists. (5)

This is a valid argument: it is correct in point of logical form.  Nor does it commit any informal fallacy such as petitio principii, as I argue in Religious Studies 29 (1993), pp. 97-110.  Note also that this version of the OA does not require the controversial assumption that existence is a first-level property, an assumption that Frege famously rejects and that many read back (with some justification) into Kant.  (Frege held that the OA falls with that assumption, cf. Die Grundlagen der Arithmetik, sec. 53; he was wrong: the above version is immune to the Kant-Frege objection.)

(1) expresses what I call Anselm's Insight.  He appreciated, presumably for the first time in the history of thought, that a divine being, one worthy of worship, must be noncontingent, i.e., either necessary or impossible.  I consider (1) nonnegotiable.  If your god is contingent, then your god is not God. There is no god but God.  God is an absolute, and no absolute worth its salt is contingent.  End of discussion.  (If, however, (1) is reasonably disputable, then this only strengthens my case against compellingness.)

It is premise (2) -- the key premise -- that ought to raise eyebrows.  What it says -- translating out of the patois of possible worlds -- is that it it possible that the GCB exists.

Whereas conceptual analysis of 'greatest conceivable being' suffices in support of (1), how do we support (2)?  Why should we accept it?  How do we know that (2) is true?  Some will say that the conceivability of the GCB entails its possibility.  But I deny that conceivability entails possibility.  

Conceivability Does not Entail Possibility

The question is whether conceivability by finite minds like ours entails real possibility.  A real possibility is one that has a mind-independent status.  Real possibilities are not parasitic upon ignorance or on our (measly) powers of conception.  Thus they contrast with epistemic/doxastic possibilities.  Since what is epistemically possible for a person might be really impossible (whether broadly-logically or nomologically), we should note that 'epistemic' in 'epistemically possible' is an alienans adjective: it functions like 'decoy' in 'decoy duck.'  Ducks don't come in two kinds, real and decoy.  Similarly, there are not two kinds of possibility, epistemic and real.  To say that a state of affairs is epistemically/doxastically possible for a subject S is to say that the obtaining of the state of affairs is logically compatible with what S knows/believes.  For example, is it possible that my State Farm insurance agent Tim be working his office during normal business hours today ?  Yes, epistemically: it is not ruled out by anything I know.  But if Tim unbeknownst to me 'bought the farm' last night, then it is not really possible that Tim be working in his office today.

By 'conceivability' I mean thinkability by us without apparent logical contradiction.  

First Argument

Why should the fact that a human being can conceive something without apparent logical contradiction show that the thing in question can exist in reality? Consider the FBI: the floating bar of iron. If my thought about the FBI is sufficiently abstract and indeterminate, then it will seem that there is no 'bar' to its possibility in reality. (Pun intended.) If I think the FBI as an object that has the phenomenal properties of iron but also floats, then those properties are combinable in my thought without contradiction. But if I know more about iron, including its specific gravity, and I import this information into my concept of iron, then the concept of the FBI will harbor a contradiction. The specific gravity of iron is 7850 kg/cu.m, which implies that it is 7.85 times more dense than water, which in turn means that it will sink in water.

The upshot is that conceivability without contradiction is no sure guide to (real) possibility. Conceivability does not entail possibility.

Second Argument

Both the existence and the nonexistence of God are conceivable, i.e., thinkable by us without apparent logical contradiction.  So if conceivability entails possibility, then both the existence and the nonexistence of God are possible.  If so, God is a contingent being.  But this contradicts the Anselmian Insight according to which God is noncontingent.  So if the Anselmian Insight is true, then conceivability-entails-possibility is false and cannot be used to support premise (2) of the modal OA.  The argument can be put in the form of a reductio:

a. Conceivability entails possibility.  (assumption for reductio)

b. It is conceivable that God not exist. (factual premise)

c. It is conceivable that God exist.  (factual premise)

d. God is a noncontingent being. (true by Anselmian definition)

Ergo

e. It is possible that God not exist and it is possible that God exist.  (a, b, c)

Ergo

f. God is a contingent being. (e, by definition of 'contingent being')

Ergo

g. God is a noncontingent being and God is a contingent being. (d, f, contradiction)

Ergo

~a. It is not the case that conceivability entails possibility. (a-g, by reductio ad absurdum) 

Or, if you insist that conceivability entails possibility, then you must give up the Anselmian Insight.  But the modal OA stands and falls with Anselmian insight.  

 

Is Conceivability Nondemonstrative Evidence of Possibility?

 

We don't need to discuss this in any depth.  Suppose it is.  This won't help Toner's case.  For if it is not certain, but only probable that (2) is true, then this lack of certainty will be transmitted to the conclusion, which will be, at most, probable but not certain. In that case, the argument will not be compelling.  I take it that an argument is compelling if and only if it renders its conclusion objectively certain.

Are There Other Ways to Support the Possibility Premise?

I can think of one other way.  It has been suggested that the possibility premise can be supported deontically:

A. A maximally perfect being ought to exist.
B. Whatever ought to exist, is possible.
Therefore
C. A maximally perfect being is possible.

I discuss this intriguing suggestion in a separate post  wherein I come to the conclusion that the deontically supercharged modal OA is also not compelling.

What is it for an Argument to be Compelling? 

My claim on the present occasion is that the modal OA provides no demonstrative knowledge of the truth of theism. Demonstrative knowledge is knowledge produced by a demonstration.  A demonstration in this context is an argument that satisfies all of the following conditions:

1. It is deductive
2. It is valid in point of logical form
3. It is free of such informal fallacies as petitio principii
4. It is such that all its premises are true
5. It is such that all its premises are known to be true
6. It is such that its conclusion is relevant to its premises.

To illustrate (6).  The following argument satisfies all of the conditions except the last and is therefore probatively worthless:

Snow is white
ergo
Either Obama is president or he is not.

On my use of terms, a demonstrative argument = a probative argument = a proof = a rationally compelling argument.  Now clearly there are good arguments (of different sorts) that are not demonstrative, probative, rationally compelling.  One type is the strong inductive argument. By definition, no such argument satisfies (1) or (2).  A second type is the argument that satisfies all the conditions except (5). 

And that is the problem with the modal OA. Condition (5) remains unsatisfied.  While the possibility premise may be true for all we know, we do not know it to be true.  So while the modal OA is a good argument in that it helps render theism rational, it is not a compelling argument. 

Related articles

Soloveitchik on Proving the Existence of God

Modality, Possible Worlds, and the Accidental-Essential Distinction

Does the Atheist Deny What the Theist Affirms?

An Ontological Disproof of God

Nothing could count as God that did not have the property of aseity, or in plain Anglo-Saxon, from-itself-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 nequit, 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 which 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.

Again on the Ontological Argument for Truth

I gave the following argument:

We have 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.

A reader asks: Does not your argument presuppose that "to be instantiated" means "to exist extra-mentally"? What if someone believed that esse est percipi? If your argument was based on the aforementioned  assumption, then would not it beg the question because it presupposes what needs to be demonstrated?

Let us first note that it cannot be coherently maintained that to be is to be perceived without qualification.  To be perceived is to be perceived by someone or something.  For Bishop Berkeley, the someone in question is God whose being is precisely not identical to his being perceived.  The slogan therefore does not apply to God.  If absolutely everything were such that its being were its being perceived, then a vicious infinite regress would arise.  To put it figuratively, the world cannot be mere percepts 'all the way down.'  You have to come eventually to something whose being is in excess of its being perceived.

Perhaps what the reader is getting at is that any true proposition that instantiates the concept true proposition is  true only for a mind, and not true absolutely.  But this too leads to an infinite regress which appears to be vicious.  For consider the proposition *Every truth is true-for some mind or other; no truth is true absolutely.*  Call this proposition 'P.'  Is P true?  No, it is true-for some mind or other.  Call that proposition P*.  Is it true? No, it is true-for some mind or other.  An infinite regress arises, and it appears to be vicious.

An Ontological Argument for Truth and the Correspondence Theory

A Pakistani correspondent e-mails:

Regarding your recent post An Ontological Argument for Objective Reality, do you think your argument demonstrates that the correspondence theory of truth is inherent to our notion of objective reality, because we cannot meaningfully, without contradiction, even talk about truth in the absence of objective reality? If so, your argument also settles the case in favor of correspondence theory of truth.

Excellent question.  I define 'ontological argument' in the earlier post, and note that 'ontological argument' and 'ontological argument for the existence of God' are not to be confused.  Here is an ontological argument for the existence of at least one truth:

We have  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 sound 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.

Does it follow that the correspondence theory of truth is true?  I don't think so.  What the above argument shows is that there are truths.  A truth is a true proposition, or, more generally, a true truth-bearer.  But a truth-bearer is not the same as a truth-maker.  A correspondence theory of truth, however, requires truth-makers.  And so there is a logical gap between

1. There are truths

and

2. There are truth-makers of these truths.

My ontological argument establishes (1).  It establishes the existence, indeed the necessity, of at least one truth 'outside the mind.'  But truths outside the mind might just be true Fregean propositions.  Such items are truth-bearers but not truth-makers.  So (2) does not straightaway follow from (1).

To get to (2), we need to introduce a truth-maker principle as supplementary premise. Discussions of truth-maker principles can be found in the Truth category.

An Ontological Argument for Objective Reality

The proprietor of Beyond Necessity has a post on objective reality which is directed against some New Age mumbo-jumbo.  One of the commenters remarks, "Your argument for the existence of objective reality sounds very much like the ontological argument for God, and about as plausible."  Ed, the proprietor, responds, ". . . the argument in no way resembles the logical form of the ontological argument."

What I will now do is present a sound ontological argument for objective reality.  In so doing I will show that both proprietor and commenter are wrong. The latter because the argument is plausible; the former because it is ontological in form.

Definition.  An ontological argument from mere concepts (aus lauter Begriffen, in Kant's famous phrase) is a ratiocinative procedure whereby the being instantiated  of a concept is proven by sheer analysis of the concept.  It is thus an argument in which one attempts to infer the existence of X from the concept X.  For example, the existence of God from the concept God; the existence of a golden mountain from the concept golden mountain; the existence of objective reality from the concept objective reality. Concepts are mental items by definition.  So a sound ontological argument will take us from thought to (extramental) being, in a manner to please Parmenides.

To mention a concept I use italics.  Thus a word in italics refers to a concept. 

1. We have and understand the concept the (total) way things are. It doesn't matter how we acquired this concept.  We have it and we understand it.  The way things are includes every fact, every obtaining state of affairs.  So the way things are is equivalent to the world in Wittgenstein's sense: "Die Welt ist die Gesamtheit der Tatsachen, nicht der Dinge."  (Tractatus 1.1) It is also equivalent to objective reality.

2. Now let us entertain the possibility that nothing answers to the concept the way things are, that the concept is not instantiated.  We are thus to entertain the possibility that there is the concept in our minds but nothing to which it applies.  We can formulate this possibility using the proposition *There is no objective reality.*  Call this proposition P.

3. Could P be true?  If P is true, then P is true in objective reality: that is just what 'true' means.  So if P is true, then it is true in objective reality that there is no objective reality.  This is a contradiction.  So we must conclude that If P is true, then P is false.  And if P is false, then of course P is false.  So, necessarily, P is false, which implies that its negation is not only true but necessarily true: it is necessarily true that there is objective reality. So by sheer analysis of the concept objective reality one can validly infer that there is objective reality.  Here then is a case in which an ontological argument from mere concepts is sound.

4.  Have I pulled a fast one?  Not as far as I can see.  I have merely analyzed the concept objective reality, teasing out an implication of the claim that the concept is not instantiated. 

5. Response to the commenter.  The commenter is right to appreciate that the above sort of reasoning is ontological and thus similar to the God proof found in Descartes' Meditation V and criticized famously by Kant.  He is wrong, however, to think that the former reasoning is cogent if and only if the latter is.

6. Response to the proprietor.  The proprietor is right, as against the commenter, when it comes to the cogency of the above sort of reasoning.  But the commenter is wrong to fail to see that it is ontological reasoning in a clear sense of that term.  It is a priori reasoning from thought to being, from concept to existence.

Companion post: Four Kinds of Ontological Argument 

Nota Notae Est Nota Rei Ipsius and the Ontological Argument

(By popular demand, I repost the following old Powerblogs entry.)

"The mark of a mark is a mark of the thing itself." I found this piece of scholasticism in C. S. Peirce. (Justus Buchler, ed., Philosophical Writings of Peirce, p. 133) It is an example of what Peirce calls a   'leading principle.'

Let's say you have an enthymeme:

   Enoch was a man
   -----
   Enoch died.

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 is 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 (mark)-Eigenschaft (property) 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 Edward the Nominalist 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.

Does God Exist Because He Ought to Exist?

Steven, Peter, et al.:  This paper has been languishing  on my hard drive for some time.  Comments appreciated. 

Abstract.  Modal ontological arguments for the existence of God require a possibility premise to the effect that a maximally perfect being is possible. Admitting the possibility of such a being may appear to be a minimal concession, but it is not given that the admission, together with the uncontroversial premise that a necessary being is one whose possibility entails its actuality, straightaway entails the actual existence of a maximally perfect being. The suspicion thus arises that the modal ontological argument begs the question at its possibility premise. So various philosophers, including J. N. Findlay, A.C. Ewing, John Leslie and Carl Kordig have attempted to support the possibility premise by broadly deontic considerations concerning what ought-to-be, where this ought-to-be subsists independently of the powers of any agent. The basic idea is that God, conceived as a maximally perfect being, is possible because (i) he ought to exist, and (ii) whatever ought to exist is possible. The basic idea is that the non-agential oughtness or axiological requiredness of the divine existence certifies the possibility and in turn the actuality of the divine existence. The overall argument could be described as a broadly deontic God proof along modal ontological lines. This article sets forth and defends the argument before explaining why it is not ultimately compelling.

God: Necessary or Noncontingent?

Many theists in the tradition of Anselm and Aquinas define God as a necessary being.  But if God is a necessary being, then he cannot not exist: he exists in all broadly-logically possible worlds.  The actual world is of course one of these worlds.  So it would seem to follow from the very definition of God favored by Anselmians that God exists.  But surely the existence of God cannot be fallout from a mere definition!

I have hammered the Objectivists (Randians) for their terminological mischief as when they rig up 'existence' in such a way that the nonexistence of the supernatural is achieved by terminological fiat.  So doesn't fairness demand that I hammer the Anselmians equally?  (This is one way of attaching sense to Nietzsche's notion of philosophizing with a hammer, although it is not what he had in mind.)

The trouble with defining God as a necessary being is that 'necessary being' conflates modal status and existence.  For any item we ought to distinguish its modal status (whether necessary, impossible, or contingent) from its existence or nonexistence.

The concept of God as "that than which no greater can be conceived" is the concept of a being that exists in every possible world if it exists in any world.  But from this one cannot validly infer that God exists.  For it might be (it is epistemically possible that) God exists in no world, in which  case he would be impossible.  God is either necessary or impossible: that was Anselm's great insight.  He cannot be a contingent being.

If we want one word to express this disjunctive property of being either necessary or impossible, that word is 'noncontingent.'  So we should not say that God is a necessary being.  We should say that he is a noncontingent being.

Companion post:  Necessary, Contingent, Impossible: A Note on Nicolai Hartmann

Pavel Tichý on Descartes' Meditation Five Ontological Argument

This post is the fourth in a series on Pavel Tichý's "Existence and God" (J. Phil., August 1979, 403-420). In section II we find a critique of Descartes' Meditation Five ontological argument. Tichý claims to spot two fallacies in the argument. I will argue that only one of them is a genuine fallacy. One could present the Cartesian argument in Tichý's jargon as follows:

1. The requisites of the divine office include all perfections.
2. Existence is a perfection.
Therefore
3. The divine office is occupied.

Four Kinds of Ontological Argument

The essence of ontological argumentation is the inferential move from the concept/essence of F to the existence/nonexistence of F. We are all familiar with ontological arguments for the existence of God. They have been a staple of philosophy of religion discussions from Anselm to Plantinga. But there is nothing in the nature of ontological argumentation to require that God be the subject matter, or that the argument conclude to the existence of something. There are nontheistic ontological arguments as well as ontological disproofs. Thus there are four possible combinations.