Modal Matters – Page 6 – Maverick Philosopher

Necessary Being: A Note on a Post by James Barham

In the context of a reply to a "nasty attack on [Alvin] Plantinga by Jerry Coyne that cannot go unanswered," James Barham explains why he is an atheist:

The other reason I balk [at accepting a theism like that of Plantinga's] is that I can’t help suspecting there is a category mistake involved in talking about the “necessity” of the existence of any real thing, even a ground of being. When we speak of the ground of being’s existing “necessarily,” perhaps we are conflating the nomological sense of “necessity”—in the earth’s gravitational field an unsupported object necessarily accelerates at 32 feet per second squared—with the logical sense of the word—if all men are mortal and Socrates is a man, then necessarily Socrates is mortal.

Many experience intellectual discomfort at the thought of a being that is, as Barham says, real (as opposed, presumably, to ideal or abstract) but yet exists of broadly logical (metaphysical) necessity. To discuss this with clarity I suggest we drop 'real' and use 'concrete' instead. So our question is whether it is coherent to suppose that there exists a concrete being that necessarily exists, where the necessity in question is broadly logical. The question is not whether it is true, but whether it is thinkable without broadly logical contradiction, and without 'category mistake.' But what does 'concrete' mean? It does not mean 'material' or 'physical.' Obviously, no material being could be a necessary being. (Exercise for the reader: prove it!) Here are a couple of definitions:

D1. X is concrete =_df X is causally active or passive.
D2. X is abstract =_df X is causally inert, i.e., not concrete.

The terms of the concrete-abstract distinction are mutually exclusive and jointly exhaustive: everything is one or the other, and nothing is both. And the same goes for the physical-nonphysical distinction. The distinctions are not equivalent, however: they 'cut perpendicular' to each other. There are (or at least it is coherent to suppose that there could be) nonphysical concreta. Whether there are physical abstracta is a nice question I will set aside for now.

Plantinga's God, if he exists, is concrete, wholly immaterial, and necessarily existent. Obviously, one cannot imagine such a being. (A point of difference with Russell's celestial teapot, by the way.) But I find Plantinga's God to be conceivable without contradiction or confusion or conflation or category mistake. Barham thinks otherwise, suggesting that the notion of a necessarily existent concretum trades on a confusion of nomological necessity with logical necessity. I find no such confusion, but I do find a confusion in Barham's thinking.

First of all, there is a genuine distinction between nomological necessity and logical necessity. Barham's sentence about an unsupported object in Earth's gravitational field is nomologically necessary, but logically contingent. It is the latter because there is no logical contradiction in the supposition that a body in Earth's gravitational field accelerate at a rate other than 32 ft/sec^2.The laws of nature could have been other than what they are. But what does this have to do with the possibility of the coherence of the notion of a concrete individual that exists in all broadly logically possible worlds if it exists in one such world? Nothing that I can see. Barham points, in effect, to a legitimate difference between:

1. Necessarily, an unsupported object in Earth's gravitation falls at the rate of 32ft/sec²and
2. Necessarily, if all men are mortal, and Socrates is a man, then Socrates is mortal.

The difference is in type of modality. In (1) the modality is nomological while in (2) it is logical. Both cases are cases of de dicto modality: the modal operator operates upon a dictum or proposition. But when we speak of God as a necessary being, we are not speaking of the necessary truth of a proposition, whether the necessity be nomological or logical. We are speaking of the necessary existence of a 'thing,' a res. Accordingly, the modality is de re. So I am wondering whether Barham is succumbing to de dicto-de re confusion. Of course, there is the proposition

3. Necessarily, God exists

where the necessity in question is broadly logical. The truth-maker of this proposition, however, is God himself, a necessarily existent concrete individual.

My point, then , is that there is no logical mistake involved in the concept of God as necessary being, no confusion, no category mistake. Even if the concept fails of instantiation, the concept itself is epistemically in the clear.

Barham will no doubt continue to be an atheist. But he ought to drop the above accusation of category mistake. He can do better. He could argue that all modality is de dicto. Or that all necessity is linguistic/conventional in origin. Or he could give J. N. Findlay's 1948 ontological disproof, which I will feature in my next post.

I should add that Barham's post, What Happened to Jerry Coyne's Sensus Divinitatis, only a small part of which I examined above, is extremely good and should be carefully read.

Material Composition and Modal Discernibility

(For David Brightly, whom I hope either to convince or argue to a standoff.)

Suppose God creates ex nihilo a bunch of Tinker Toy pieces at time t suitable for assembly into various (toy) artifacts such as a house and a fort. A unique classical mereological sum — call it 'TTS' — comes into existence 'automatically' at the instant of the creation ex nihilo of the TT pieces. (God doesn't have to do anything in addition to creating the TT pieces to bring TTS into existence.) Suppose further that God at t assembles the TT pieces (adding nothing and subtracting nothing) into a house. Call this object 'TTH.' So far we have: the pieces, their sum, and the house. Now suppose that at t* (later than t) God annihilates all of the TT pieces. This of course annihilates TTS and TTH. During the interval from t to t* God maintains TTH in existence.

I set up the problem this way so as to exclude 'historical' and nonmodal considerations and thus to make the challenge tougher for my side. Note that TTH and TTS are spatially coincident, temporally coincident, and such that every nonmodal property of the one is also a nonmodal property of the other. Thus they have the same size, the same shape, the same weight, etc. Surely the pressure is on to say that TTH = TTS? Surely my opponents will come at me with their battle-cry, 'No difference without a difference-maker!' There is no constituent of TTH that is not also a constituent of TTS. So what could distinguish them?

Here is an argument that TTH and TTS are not identical:

1. NecId: If x = y, then necessarily, x = y.

2. If it is possible that ~(x = y), then ~(x = y). (From 1 by Contraposition)

3. If it is possible that TTS is not TTH, then TTS is not TTH. (From 2, by Universal Instantiation)

4. It is possible that TTS is not TTH. (God might have assembled the parts into a fort instead of a house or might have left them unassembled.)

5. TTS is not TTH. (From 3, 4 by Modus Ponens)

If you are inclined to reject the argument, you must tell me which premise you reject. Will it be (1)? Or will it be (4)?

Your move, David.

Absolute Truth and Necessary Truth

Absolute truth and necessary truth are not the same.

Let our example be the proposition p expressed by 'Julius Caesar crossed the Rubicon in 44 B.C.' Given that p is true, it is true in all actual circumstances. That is, its truth-value does not vary from time to time, place to place, person to person, or relative to any other parameter in the actual world. P is true now, was true yesterday, and will be true tomorrow. P is true in Los Angeles, in Bangkok, and on Alpha Centauri. It is true whether Joe Blow affirms it, denies it, or has never even thought about it. And what goes for Blow goes for Jane Schmoe.

In this sense, p is absolutely or nonrelatively true. But that is not to say that p is necessarily true. A proposition q is necessarily true if and only if q is true in all possible worlds, to use a Leibnizian expression. To avoid 'world' I can say: in all possible circumstances. (A world could be thought of as a maximal circumstance.) A proposition q is contingently true iff (i) q is true in the actual circumstances, but (ii) not true in all possible circumstances. Now our proposition p concerning Caesar is obviously only contingently true: there is no broadly logical or metaphysical necessity that he cross the Rubicon in 44 BC. He might have crossed it earlier or later, or not at all. Or said river might never have existed for him to cross.

Note that contingent is not the same as contingently true. If a proposition is contingently true, then it is actually true. But if a proposition is contingent it may or may not be actually true. I was born by Caesarean section but I might not have been. So the proposition *BV was not born by Caesarean section* though false is contingent: it is true in some but not all possible worlds and false in the actual world.

Here are some theses I am fairly sure of:

1. There are no relative truths: every truth is absolute.
2. An absolute truth need not be a necessary truth: some absolute truths are contingent.
3. Every truth, whether necessary or contingent, is true in all actual circumstances.
4. The ontological property of absoluteness is not to be confused with any epistemological property such as that of being known with certainty.

How Does One Know that There Are Contingent Beings?

When I was writing my book on existence I was troubled by the question as to how one knows that there are contingent beings. For I took it as given that there are, just as I took it as given that things exist. But one philosopher's datum is another's theory, and I was hoping to begin my metaphysical ascent from indubitable starting points. So it bugged me: how do I know that this coffee cup is a contingent being? Given that it exists, how do I know that it exists contingently? I satisfied my scruples by telling myself that I was writing about the metaphysics of existence and that concerns with its epistemology could be reserved for a later effort. What exactly is the problem? Let's begin with a couple of definitions:

D1. X is contingent =_df possibly (x exists) & possibly (x does not exist).

The possibility at issue is non-epistemic and broadly logical. And note that the definiens of (D1) is not to be confused with 'possibly (x exists & x does not exist)' which is necessarily false.

D2. X contingently exists =_df x exists & possibly (x does not exist).

Note that to say that x exists contingently is not to say that x depends for its existence on something else; it is merely to say that x exists and that there is no broadly logical (metaphysical) necessity that x exist. Suppose exactly one thing exists, an iron sphere. Intuitively, the sphere is contingent despite there being nothing on which it depends for its existence. For though it exists, it might not have.

Note also that to say that x exists contingently is not to say that x is actual at some times and not actual at other times. (Even if everything that contingently exists exists at some times but not at all times, the contingency of what contingently exists does not consist in its existing at some but not all times.) If one said that contingency is existence at some but not all times, then one would have to say that x exists necessarily just in case x exists at all times. Something that exists at all times, however, could well be contingent in a clear sense of this term, namely, possibly nonexistent. For example, suppose the physical universe always existed and always will exist. It doesn't follow that it necessarily exists (is impossibly nonexistent). It would remain a contingent fact that it exists at all in the D2 sense. And then there that are items that are not in time at all: numbers, Fregean propositions, and other 'abstracta.' They exist necessarily without being temporally qualified. Their necessity is not their existence at all times.

For example, my coffee cup exists now — how I know this is a separate epistemological question that I here ignore — but is possibly such that it does not exist now, where 'now' picks out the same time. But how do I know that the cup is now possibly nonexistent? That's my problem.

This is a variant of the problem of modal knowledge. (See Notes on Van Inwagen on Modal Epistemology.) The cup is full, but it might not have been. It is full of coffee, but it might have been full of whisky. It is two inches from the ashtray, but it might have been three inches from it. It exists now but it might not have existed now. It has existed for 20 years; it might never have existed at all. And so on. I can see that the cup is full, and I can taste that it contains coffee and not whisky. But I cannot see or taste what doesn't exist (assuming that 'see' is being used as a verb of success), and the cup's being empty or the cup's containing whisky are non-obtaining states of affairs. Thus there seems to be nothing for my modal knowledge to 'grab onto.'

If I know that the cup exists contingently, then I know that it is possibly nonexistent. But how do I know the latter?

"You know it from your ability to conceive, without contradiction, of the cup's nonexistence." This is not a good answer. First of all, conceivability (without contradiction) does not entail possibility. Example here. Does the conceivability of p raise the probability of p's being possible? This is a strange notion. Discussion here.

If conceivability neither entails nor probabilifies possibility, then my question returns in full force: how does one know, of any being, that it is a contingent being?

"Well, you know from experience that things like coffee cups come into existence and pass out of existence. If you know that, then you know that such things do not exist of metaphysical necessity. For what exists of metaphysical necessity exists at all times, if it exists in time at all, and your coffee cup, which exists in time, does not exist at all times. Now what does not exist of metaphysical necessity is metaphysically contingent. Therefore, you know that coffee cups and such are contingent existents."

This argument may do the trick. To test it, I will set it forth as rigorously as possible. To save keystrokes I omit universal quantifiers.

1. If x is a material thing, and x does not exist at all times, then x is not a necessary being (one whose nonexistence is broadly-logically impossible).
2. If x is not a necessary being, then x is either a contingent being or an impossible being.
Therefore
3. If x is a material thing, and x does not exist at all times, then x is either a contingent being or an impossible being.
4. My coffee cup is a material thing and it does not exist at all times.
Therefore
5. My cup is either a contingent being or an impossible being.
6. If x exists, then x is not impossible.
7. My cup exists.
Therefore
8. My cup is a contingent being.
9. I know that (8) because I know each of the premises, and (8) follows from the premises.

The inferences are all valid, and the only premise that might be questioned is (1). To refute (1) one needs an example of a material being that does not exist at all times that is a necessary being. But I can't think of an example.

The argument just given seems to be a rigorous proof that there is at least one contingent (possibly nonexistent) existent. But does it show that this existent is possibly nonexistent at each time at which it exists? (The latter is the question I posed above.)

Would it make sense to say that my cup, though not a necessary being, is necessarily existent at each time at which it exists? If that makes sense, then my cup is contingent in that it might not have existed at all, but not contingent in the sense that at each time at which it exists it is possibly nonexistent. Are these two propositions consistent:

a. x is contingent in that it might not have existed at all

and

b. x is not contingent in the sense of being possibly nonexistent at each time at which it exists?

If (a) and (b) are consistent, then it appears that I have not proven that my cup is contingent in the sense of being possibly nonexistent at each time at which it exists. For then the above argument shows merely that the cup is contingent in that it might not have existed at all.

The Rabbit of Real Existence and the Empty Hat of Mere Logic

Consider again this curious piece of reasoning:

1. For any x, x = x. Ergo:
2. a = a. Ergo:
3. (Ex)(x = a). Ergo:
4. a exists.

This reasoning is curious because it seems to show that one can deduce the real existence of an individual a from a purely formal principle of logic, the Law of Identity. And yet we know that this cannot be done. We know that the rabbit of real existence cannot be pulled from the empty hat of mere logic. Since the argument cannot be sound, it must be possible to say where it goes wrong. (It is a strange fact of philosophical experience that arguments that almost all philosophers reject nevertheless inspire the wildest controversy when it comes to the proper diagnosis of the error. Think of the arguments of Zeno, Anselm, and McTaggart.)

The move from (1) to (2) appears to be by Universal Instantiation. One will be forgiven for thinking that if everything is self-identical, then a is self-identical. But I say that right here is a (or the) mistake. To move from (1) to (2), the variable 'x' must be replaced by the substituend 'a' which is a constant. Now there are exactly three possibilities:

Either 'a' refers to something that exists, or 'a' refers to something that does not exist or 'a' does not refer at all. On the third possibility it would be impossible validly to move from (2) to (3) by Existential Generalization. The same goes for the second possibility: if 'a' refers to a Meinongian nonexistent object, then one could apply existentially-neutral Particular Generalization to (2), but not Existential Generalization. This leaves the first alternative. But if 'a' refers to something that exists, then right at this point real existence has been smuggled into the argument.

I hope the point is painfully obvious. One cannot move from (1) to (2) by logic alone: one needs an extralogical assumption, namely, that 'a' designates something that exists. To put it another way, one must assume that the domain of quantification is not only nonempty but inhabited by existing individuals. After all, (1) is true for every domain, empty or not. (1) lacks Existential Import. The truth of (1) is consistent with there being no individuals at all.

Let's now consider Peter's supposed counterexample to the principle that if p entails q and p is necessary, then q is also necessary. He thinks that the above argument shows that there are cases in which necessary propositions entail contingent ones. Thus he thinks that the conjunction of (1) and (2) entails (3), but that (3) is contingent.

Well, I agree that if we are quantifying over a domain the members of which are contingent individuals, then (3) is contingent. But surely the conjunction of (1) and (2) is also contingent. For the conjunction of a necessary and a contingent proposition is a contingent proposition. Now of course (1) is necessary. But (2), despite appearances, is contingent. For if 'a' designates a contingent individual, then it designates an individual that exists in some but not all worlds, and in those worlds in which a does not not exist it is not true that a = a.

In the worlds in which a exists, a is essentially a. But a is not necessarily a because there are worlds in which a does not exist.

What accounts for the illusion that if (1) is necessary, then (2) must also be necessary? Could it be the tendency to forget that while 'x' is a variable, 'a' is an arbitrary constant?

Does Any Noncontingent Proposition Entail a Contingent Proposition?

This post continues the discussion in the comment thread of an earlier post.

Propositions divide into the contingent and the noncontingent. The noncontingent divide into the necessary and the impossible. A proposition is contingent iff it is true in some, but not all, broadly logical possible worlds, 'worlds' for short. A proposition is necessary iff it is true in all worlds, and impossible iff it true in none. A proposition p entails a proposition q iff there is no world in which p is true and q false.

The title question divides into two: Does any impossible proposition entail a contingent proposition? Does any necessary proposition entail a contingent proposition?

As regards the first question, yes. A proposition A of the form p & ~p is impossible. If B is a contingent proposition, then there is no possible world in which A is true and B false. So every impossible proposition entails every contingent proposition. This may strike the reader as paradoxical, but only if he fails to realize that 'entails' has all and only the meaning imputed to it in the above definition.

As for the second question, I say 'No' while Peter Lupu says 'Yes.' His argument is this:
1. *Bill = Bill* is necessary.
2. *Bill = Bill* entails *(Ex)(x = Bill)*
3. *(Ex)(x = Bill)* is contingent.
Ergo
4. There are necessary propositions that entail contingent propositions.

Note first that for (2) to be true, 'Bill' must have a referent and indeed an existing referent. 'Bill' cannot be a vacuous (empty) name, nor can it have a nonexisting 'Meinongian' referent. Now (3) is surely true given that 'Bill' is being used to name a particular human being, and given the obvious fact that human beings are contingent beings. So the soundness of the argument rides on whether (1) is true.

I grant that Bill is essentially self-identical: self-identical in every world in which he exists. But this is not to say that Bill is necessarily self-identical: self-identical in every world. And this for the simple reason that Bill does not exist in every world. So I deny (1). It is not the case that Bill = Bill in every world. He has properties, including the 'property' of self-identity, only in those worlds in which he exists.

My next post will go into these matters in more detail.

Addendum 28 May 2011. Seldom Seen Slim weighs in on Peter's argument as follows:

I believe your reply to Peter is correct. It follows from how we should define constants in 1st order predicate logic. A domain or possible world is constituted by the objects it contains. Constants name those objects. If a domain has three objects, D = {a,b,c}, then the familiar expansion for identity holds in that domain, i.e., (x) (x = x) is equivalent to a = a and b = b and c = c. But notice that this is conditional and the antecedent asserts the existence in D of (the objects named by) a, b, and c. Thus premise 2 of Peter's argument is actually a conditional: IF a exists in some domain D, then a = a in D. The conclusion (3) must also be a conditional: if a exists in D , then something in D is self-indentical. That of course does not assert the existential Peter wants from (x)(x = x). Put simply, a = a presumes [presupposes] rather than entails that a exists.

God, Probability, and Noncontingent Propositions

Matt Hart comments:

. . . most of what we conceive is possible. So if we say that

1) In 80% of the cases, if 'Conceivably, p' then 'Possibly, p'
2) Conceivably, God exists
Ergo,
3) Pr(Possibly, God exists) = 80%
4) If 'Possibly, God exists' then 'necessarily, God exists'
Ergo,
5) Pr(Necessarily, God exists) = 80%,

we seem to get by.

I had made the point that conceivability does not entail possibility. Hart agrees with that, but seems to think that conceivability is nondemonstrative evidence of possibility. Accordingly, our ability to conceive (without contradiction) that p gives us good reason to believe that p is possible.

What is puzzling to me is how a noncontingent proposition can be assigned a probability less than 1. A noncontingent proposition is one that is either necessary or impossible. Now all of the following are noncontingent:

God exists
Necessarily, God exists
Possibly, God exists
God does not exist
Necessarily, God does not exist
Possibly, God does not exist.

I am making the Anselmian assumption that God (the ens perfectissimum, that than which no greater can be conceived, etc.) is a noncontingent being. I am also assuming that our modal logic is S5. The characteristic S5 axiom states that Poss p –> Nec Poss p. S5 includes S4, the characteristic axiom of which is Nec p –> Nec Nec p. What these axioms say, taken together, is that what's possible and necessary does not vary from possible world to possible world.

Now Possibly, God exists, if true, is necessarily true, and if false, necessarily false. (By the characteristic S5 axiom.) So what could it mean that the probability of Possibly, God exists is .8? I would have thought that the probability is either 1 or 0. the same goes for Necessarily, God exists. How can this proposition have a probability of .8? Must it not be either 1 or 0?

Now I am a fair and balanced guy, as everyone knows. So I will deploy the same reasoning against the atheist who cites the evils of our world as nondemonstrative evidence of the nonexistence of God. I don't know what it means to say that it is unlikely that God exists given the kinds and quantities of evil in our world. Either God exists necessarily or he is impossible (necessarily nonexistent). How can you raise the probability of a necessary truth? Suppose some hitherto unknown genocide comes to light, thereby adding to the catalog of known evils. Would that strengthen the case against the existence of God? How could it?

To see my point consider the noncontingent propositions of mathematics. They are all of them necessarily true if true. So *7 + 5 = 12* is necessarily true and *7 + 5 = 11* is necessarily false. Empirical evidence is irrelevant here. I cannot raise the probability of the first proposition by adding 7 knives and 5 forks to come up with 12 utensils. I do not come to know the truth of the first proposition by induction from empirical cases of adding. It would also be folly to attempt to disconfirm the second proposition by empirical means.

If I can't know that 7 + 5 = 12 by induction from empirical cases, how can I know that possibly, God exists by induction from empirical cases of conceiving? The problem concerns not only induction, but how one can know by induction a necessary proposition. Similarly, how can I know that God does not exist by induction from empirical cases of evil?

Of course, *God exists* is not a mathematical proposition. But it is a noncontingent proposition, which is all I need for my argument.

Finally, consider this. I can conceive the existence of God but I can also conceive the nonexistence of God. So plug 'God does not exist' into Matt's argument above. The result is that probability of the necessary nonexistence of God is .8!

My conclusion: (a) Conceivability does not entail possibility; (b) in the case of noncontingent propositions, conceivability does not count as nondemonstrative evidence of possibility.

De Dicto/De Re

In the course of thinking about the de dicto/de re distinction, I pulled the Oxford Companion to Philosophy from the shelf and read the eponymous entry. After being told that the distinction "seems to have first surfaced explicitly in Abelard," I was then informed that the distinction occurs:

     . . . in two main forms: picking out the difference between a
     sentential operator and a predicate operator, between 'necessarily
     (Fa)' and 'a is (necessarily-F)' on the one hand, and on the other
     as a way of highlighting the scope fallacy in treating necessarily
     (if p then q) as if it were (if p then necessarily-q).

It seems to me that this explanation leaves something to be desired. I have no beef with the notion that the first distinction is an example of a de dicto/de re distinction. To say of a dictum that it is necessarily true if true is different from saying of a thing (res) that it has a property necessarily. Suppose a exists in some, but not all, possible worlds, and that a is F in every possible world in which it exists. Then a is necessarily F, F in every possible world in which it exists. But since there are possible worlds in which a does not exist, then it will be false that 'a is F' is necessarily true, true
in all possible worlds. So the de dicto 'Necessarily, a is F' is distinct from the de re 'a is necessarily F.'

So far, so good. But the distinction between

1. Nec (if p then q)

and

2. If p, then Nec q

is situated entirely on the de dicto plane, the plane of dicta or propositions. The distinction between (1) and (2) is the well-known distinction between necessitas consequentiae and necessitas consequentiis. To confuse (1) and (2) is to confuse the necessity of the consequence with the necessity of the consequent. Or you could think of the mistake as a scope fallacy: the necessity operator in (1) has wide scope whereas the operator in (2) has narrow scope. But what makes (2) de re? What is the res in question? Consider an example:

3. Necessarily, if a person takes Enalapril, then he takes an ACE inhibitor

does not entail

4. If a person takes Enalapril, then necessarily he takes an ACE inhibitor.

A second example:

5. Necessarily, if something happens, then something happens

does not entail

6. If something happens, then necessarily something happens.

It can't be that easy to prove fatalism. The point, however, is that the distinction between (5) and (6) does not trade on the distinction between dicta and rei, between propositions and non-propositions: the distinction is one of the scope of a propositional operator. Our author thus seems wrongly to assimilate the above scope fallacy to a de dicto/de re confusion.

I conclude that the de dicto/de re distinction is a bit of a terminological mess. And note that it is a mess even when confined to the modal context as demonstrated above. If we try to apply the distinction univocally across modal, doxastic, temporal, and other contexts we can expect an even bigger mess. A fit topic for a future post.

Terminological fluidity is a problem in philosophy. It always has been and always will be. For attempts at regimentation and standardization harbor philosophical assumptions and biases — which are themselves fit fodder for philosophical scrutiny.

Cf. Notes on Philosophical Terminology and its Fluidity

More on Modes of Being with Two Applications

Clarity will be served if we distinguish the following four questions:

Q1. What is meant by 'mode of being'?
Q2. Is the corresponding idea intelligible?
Q3. Are there (two or more) modes of being?
Q4. What are the modes of being?

So far in this series of posts I have been concerned only with the first two questions. Clearly, the first two questions are logically prior to the second two. It is possible to understand what is meant by 'mode of being' and grant that the notion is intelligible while denying that there are (two or more) modes of being. And if two philosophers agree that there are (two or more) modes of being they might yet disagree about what these modes are.

I assume that if talk of modes of being is intelligible, then there is no mistake such as Peter van Inwagen alleges, or fallacy such as Reinhardt Grossmann alleges, that is committed by partisans of any modes-of-being doctrine. Van Inwagen's claim, you will recall, is that such partisans illictly transfer what properly belongs to the nature of an F to the existence of the F. And Grossmann's claim, you will also recall, is that one cannot validly infer from a dramatic difference in properties as between two kinds of thing (concreta and abstracta, for exsample) that the two kinds of thing differ in their mode of being.

An Application to Philosophical Theology

Suppose you have two philosophers. They agree that God exists and they agree as to the nature of God. But one claims that God exists necessarily while the other claims that he exists contingently. What are they disagreeing about? That there is a being having such-and-such divine properties is not in dispute. Nor is the nature of God in dispute. It is at least arguable that the disagreement centers on God's Seinsweise, or modus essendi, or way of being, or mode of being or however you care to phrase it. The one philosopher says that God exists-necessarily while the other says that God exists-contingently. This is not a difference in nature or in properties but in mode of being.

This suggests that with respect to anything, we can ask: (i) What is it? (ii) Does it exist? (iii) How (in what way or mode) does it exist? This yields a tripartite distinction among quiddity (in a broad sense to include essential and accidental, relational and nonrelational properties), existence, and mode of existence (mode of being).

My claim, at a bare minimum, is that, contra van Inwagen, Grossmann, Dallas Willard, and a host of others, the notion that there are modes of being is intelligible and defensible, and needn't involve the making of a mistake or the commission of a fallacy. Of course I want to go beyond that and claim that a sound metaphysics cannot get by without a modes-of-being doctrine. But for now I am concerned merely to defend the minimal claim. Minimal though it is, it puts me at loggerheads with the analytic establishment. (But what did you expect for a maverick?)

A contemporary analytic philosopher who adheres to the thin conception of being according to which there are no modes of being will accommodate the difference between necessary and contingent beings by saying that a necessary being like God exists in all possible worlds whereas a contingent being like Socrates exists in some but not all possible worlds. So instead of saying that God exists in a different way than Socrates, he will say that God and Socrates exist in the same way, which is the way that everything exists, but that God exists in all worlds whereas Socrates exists only in some. But this involves quantification over possible worlds and raises difficult questions as to what possible worlds are.

(It is worth noting that a modes-of-being theorist can reap the benefits of possible worlds talk as a useful and graphic façon de parler without incurring the ontological costs. You can talk the talk without walking the walk.)

Presumably no one here will embrace the mad-dog modal realism of David Lewis, according to which all worlds are on an ontological par. So one has to take some sort of abstractist line and construe worlds as maximal abstracta of one sort or another, say, as maximal (Fregean not Russellian) propositions. But then difficult questions arise about what it is for an individual to exist in a world. What is it for Socrates to exist in a possible world if worlds are maximal (Fregean) propositions? It is to be represented as existing by that world. So Socrates exists in the actual world in that Socrates is represented as existing by the actual world which, on the abstractist aspproach, is the one true maximal proposition. (A proposition is maximal iff it entails every proposition with which it is consistent.) And God exists in all possible worlds in that all maximal propositions represent him as exsiting: no matter which one of the maximal propositions is true, that proposition represents him as existing.

But veritas sequitur esse, truth follows being, so I am inclined to say that the abstractist approach has it precisely backwards: the necessity of God's existence is the ground of each maximal proposition's representing him as existing; the necessity of God's existence cannot be grounded in the logically posterior fact that every maximal proposition represents him as existing.

The ground of the divine necessity, I say, is God's unique mode of being which is not garden-variety metaphysical necessity but aseity. God alone exists from himself and has his necessity from himself
unlike lesser necessary beings (numbers, etc) which have their necessity from God. The divine aseity is in turn grounded in the divine simplicity which latter I try to explain in my SEP article.

Summing up this difficult line of thought that I have just barely sketched: if we dig deep into the 'possible worlds' treatment of metaphysical necessity and contingency, we will be led back to an ontology that invokes modes of being.

Application to the Idealism/Realism Controversy

Consider this thing on the desk in front of me. What is it? A coffee cup with such-and-such properties both essential and accidental. For example, it is warm and full of coffee. These are accidental properties, properties the thing has now but might not have had now, properties the possession of which is not necessary for its existence. No doubt the coffee cup exists. But it is not so clear in what mode it exists. One philosopher, an idealist, says that its mode of being is purely intentional: it exists only as an intentional object, which means: it exists only relative to (transcendental) consciousness. The other philosopher, a realist, does not deny that the cup is (sometimes) an intentional object, but denies that its being is exhausted by its being an intentional object. He maintains that it exists mind-independently.

What I have just done in effect is introduce two further modes of being. We can call them esse intentionale and esse reale, purely intentional being and real being. It seems that without this distinction between modes of being we will not be able to formulate the issue that divides the idealist and the realist. No one in his right mind denies the existence of coffee cups, rocks, trees, and 'external' items generally. Thus Berkeley and Husserl and other idealists do not deny that there exist trees and such; they are making a claim about their mode of existence.

Suppose you hold to a thin conception of being, one that rules out modes of existence. On the thin conception, an item either exists or it does not and one cannot distinguish among different ways, modes, kinds, or degrees of existence. How would an adherent of the thin conception formulate the idealism/realism controversy? The idealist, again, does not deny the existence of rocks and trees. And he doesn't differe with the realist as totheir nature. Without talk of modes of being, then, no sense can be made of the idealism/realism controversy.

A Modal Ontological Argument and an Argument from Evil Compared

After leaving the polling place this morning, I headed out on a sunrise hike over the local hills whereupon the muse of philosophy bestowed upon me some good thoughts. Suppose we compare a modal ontological argument with an argument from evil in respect of the question of evidential support for the key premise in each. This post continues our ruminations on the topic of contingent support for noncontingent propositions.

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.'

1. The concept of the GCB is either 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.

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; he was wrong: the above version is immune to the Kant-Frege objection.)

(1) expresses what I will 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. End of discussion. 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? Some will say that the conceivability of the GCB entails its possibility. But I deny that conceivability entails possibility. I won't argue that now, though I do say something about conceivability here. Suppose you grant me that conceivability does not entail BL-possibility. You might retreat to this claim: It may not entail it, but it is evidence for it: the fact that we can conceive of a state of affairs S is defeasible evidence of S's possibility.

Please note that Possibly the GCB exists — which is logically equivalent to (2) — is necessarily true if true. This is a consequence of the characteristic S5 axiom of modal propositional logic: Poss p –> Nec Poss p. ('Characteristic' in the sense that it is what distinguishes S5 from S4 which is included in S5.) So if the only support for (2) is probabilistic or evidential, then we have the puzzle we encountered earlier: how can there be probabilistic support for a noncontingent proposition? But now the same problem arises on the atheist side.

An Argument From Evil

4. If the concept of the GCB is instantiated, then there are no gratuitous evils.

5. There are some gratuitous evils. Therefore:

6. The concept of the GCB is not instantiated.

This too is a deductive argument, and it is valid. It falls afoul of no informal fallacy. (4), like (1), is nonnegotiable. Deny it, and I show you the door. The key premise, then, the one on which the soundness of the argument rides, is (5). (5) is not obviously true. Even if it is obviously true that there are evils, it is not obviously true that there are gratuitous evils.

In fact, one might argue that the argument begs the question against the theist at line (5). For if there are any gratuitous evils, then by definition of 'gratuitous' God cannot exist. But I won't push this in light of the fact that in print I have resisted the claim that the modal OA begs the question at its key premise, (2) above.

So how do we know that (5) is true? Not by conceptual analysis. If we assume, uncontroversially, that there are some evils, then the following logical equivalence holds:

7. Necessarily, there are some gratuitous evils iff the GCB does not exist.

Left-to-right is obvious: if there are gratuitous evils, ones for which there is no justification, then a being having the standard omni-attributes cannot exist. Right-to-left: if there is no GCB and there are some evils, then there are some gratuitous evils. (On second thought, R-to-L may not hold, but I don't need it anyway.)

Now the RHS, if true, is necessarily true, which implies that the LHS — There are some gratuitious evils — is necessarily true if true.

Can we argue for the LHS =(5)? Perhaps one could argue like this (as one commenter suggested in an earlier thread): If the evils are nongratuitous, then probably we would have conceived of justifying reasons for them. But we cannot conceive of justifying reasons. Therefore, probably there are gratuitous evils.

But now we face our old puzzle: How can the probability of there being gratuitous evils show that there are gratuitous evils given that There are gratuitous evils, if true, is necessarily true?

Conclusion

We face the same problem with both arguments, the modal OA for the existence of the GCB, and the argument from evil for the nonexistence of the GCB. The key premises in both arguments — (2) and (5) — are necessarily true if true. The only support for them is evidential from contingent facts. But then we are back with our old puzzle: How can contingent evidence support noncontingent propositions?

Neither argument is probative and they appear to cancel each other out. Sextus Empiricus would be proud of me.

God, Possibility, and Evidential Support for Non-Contingent Propositions

Mike Valle gave a presentation yesterday before the ASU philosophy club on the skeptical theist response to the evidential argument from evil. A good discussion ensued among Guleserian, Nemes, Lupu, Reppert, Valle, Vallicella, et al. Peter Lupu made a comment that stuck in my mind and that I thought about some more this morning. For what puzzles him puzzles me as well. It may be that we are both just confused.

1. Let us assume that our concept of God is the concept of a being that has a certain modal property, the property of being such that, if existent, then necessarily existent, and if nonexistent, then necessarily nonexistent. Call this the Anselmian conception of deity. It follows that God exists, if true, is necessarily true, and if false, necessarily false. Simply put, the proposition in question is either necessary or impossible, and thus necessarily noncontingent.

2. Peter's question, I take it, was: how can such a noncontingent proposition have its probability either raised or lowered by any empirical consideration? In particular, how can considerations about the kinds and amounts of natural and moral evil in the world lower the probability of God exists? If true,then necessarily true; if false, then necessarily false. Peter's sense — and I share it — is that evidential considerations are simply irrelevant to the probability of noncontingent propositions.

3. The problem — if it is one — arises in other contexts as well. I once argued that conceivability does not entail (broadly logical) possibility. I got the response that, though this is true, conceivability of p raises the probability of p's being possible. That is not clear to me. Assuming the modal system S5, if p is possible then necessarily p is possible, and if p is necessary, then necessarily p is necessary. (The possible and the necessary do not vary from world to world.)

I happen to think that S5 caters quite well to our modal intuitions. Assume it does. Then It is possible that there be a talking donkey is necessarily true, if true. If so, how can the fact that I (or anyone or all of us) can conceive of a talking donkey raise the probability of the proposition in question?

4. Reppert made a comment in response to Lupu about the probability being epistemic in nature. I didn't follow it. If p is noncontingent, and we are concerned with the probability of p's being true, and if truth is not an epistemic property (i.e., a property reducible to some such epistemic property as rational acceptability), then I don't see how evidential considerations are relevant.

The ComBox is open if Victor or Peter want to add to their remarks.

Can a Bundle Theory Accommodate Change?

0. Peter L. has been peppering me with objections to bundle theories. This post considers the objection from change.

1. Distinguish existential change (coming into being and passing out of being) from alterational change, or alteration. Let us think about ordinary meso-particulars such as avocados and coffee cups. If an avocado is unripe on Monday but ripe on Friday, it has undergone alterational change: it has changed in respect of the property of being ripe. One and the same thing has become different in respect of one or more properties. (An avocado cannot ripen without becoming softer, tastier, etc.) Can a bundle theory make sense of an obvious instance of change such as this? It depends on what the bundle theory (BT) amounts to.

2. At a first approximation, a bundle theorist maintains that a thing is nothing more than a complex of properties contingently related by a bundling relation, Russellian compresence say. 'Nothing more' signals that on BT there is nothing in the thing that exemplifies the properties: there is no substratum (bare particular, thin particular) that supports and unifies them. This is not to say that on BT a thing is just its properties: it is obviously more, namely, these properties contingently bundled. A bundle is not a mathematical set, a mereological sum, or a conjunction of its properties. These entities exist 'automatically' given the existence of the properties. A bundle does not.

3. Properties are either universals or property-instance (tropes). For present purposes, BT is a bundle-of-universals theory. Accordingly, my avocado is a bundle of universals. Although a bundle is not a whole in the strict sense of classical mereology, it is a whole in an analogous sense, a sense sufficiently robust to be governed by a principle of extensionality: two bundles are the same iff they have all the same property-constituents. It follows that the unripe avocado on Monday cannot be numerically the same as the ripe avocado on Friday. And therein lies the rub. For they must be the same if it is the case that an alteration in the avocado has occurred.

So far, then, it appears that the bundle theory cannot accommodate alterational change. Such change, however, is a plain fact of experience. Ergo, the bundle theory in its first approximation is untenable.

4. This, objection, however, can be easily met by sophisticating the bundle theory and adopting a bundle-bundle theory. Call this BBT. Accordingly, a thing that persists over time such as an avocado is a diachronic bundle of synchronic or momentary bundles. The theory then has two stages. First, there is the construction of momentary bundles from universals. Then there is the construction of a diachronic bundle from these bundles. The momentary bundles have properties as constituents while the diachronic bundles do not have properties as constituents, but individuals. At both stages the bundling is contingent: the properties are contingently bundled to form momentary bundles and these resulting bundles are contingently bundled to form the persisting thing.

Accordingly, the unripe avocado is numerically the same as the ripe avocado in virtue of the fact that the earlier momentary bundles which have unripeness as a constituent are ontological parts of the same diachronic whole as the later momentary bundles which have ripeness as a constituent.

5. A sophisticated bundle theory does not, therefore, claim that a persisting thing is a bundle of properties; the claim is that a persisting thing is a bundle of individuals which are themselves bundles of properties. This disposes of the objection from change at least as formulated in #3 above.

6. BBT also allows us to accommodate the intuition that things have accidental properties. On the proto-theory BT according to which a persisting thing is a bundle of properties, it would seem that all properties must be essential, where an essential property is one a thing has in every possible world in which it exists. For if wholes have their parts essentially, and if bundles are wholes in this sense, and things are bundles of properties, then things have their properties essentially. But surely our avocado is not essentially ripe or unripe but accidentally one or the other. On BBT, however, it is a contingent fact that a momentary bundle MB1 having ripeness as a constituent is bundled with other momentary bundles. This implies that the diachronic bundle of bundles could have existed without MB1 and without other momentary bundles having ripeness as a constituent. It therefore seems to follow that BBT can accommodate accidental properties.

7. That is, BBT can accommodate the modal intuition that our avocado might never have been ripe. But what about the modal intuition that, given that the avocado is ripe at t, it might not have been ripe at t? This is a thornier question and the basis of a different objection that is is not defused by what I have said above. And so we reserve this objection for a separate post.

Metaphysics at Cindy’s: The Ontological Stucture of Contingent Conreta

Over Sunday breakfast at Cindy's, a hardscrabble Mesa, Arizona eatery not unwelcoming to metaphysicians and motorcyclists alike, Peter Lupu fired a double-barreled objection at my solution to Deck's Paradox. The target, however, was not hit. My solution requires that (a) concrete particulars can be coherently 'assayed' (to use a favorite word of Gustav Bergmann), or given an ontological analysis in terms of constituents some or all of which are universals, and (b) modally contingent concrete particulars can be coherently assayed as composed of necessary beings.

Peter denies both of (a) and (b), without good reason as it seems to me. Let's begin with some definitions pithily presented.

Definitions

Abstract =df causally inert.

Concrete =df not abstract.

Universal =df repeatable (multiply exemplifiable).

Particular =df unrepeatable.

Modally contingent=df existent in some but not all broadly-logically possible worlds.

Modally necessary =df not modally contingent and not modally impossible.

Ad (a). One form of the question is: Could a concrete particular be coherently construed as a bundle universals? Peter thinks not: "But the unification of two universals U and V is another universal W, not a particular." (From a two page handout he brought to breakfast. How many people that you know bring handouts to breakfast?!) Now bundle-of-universals theories of particulars face various standard objections, but as far as I know no one in the literature has made Peter's objection. Presumably for good reason: it is a bad objection that confuses conjunction with the bundling relation.

We understand conjunction as a propositional connective. Given the propositions a is red and b is round we understand that the conjunction a is red & b is round is true iff both conjuncts are true. It is clear that a conjunction of propositions is itself a proposition. By a slight extension we can speak meaningfully of a conjunction of propositional functions, and from there we can move to talk of conjunctions of properties. Assuming that properties are universals, we can speak of conjunctions of universals. It is clear that a conjunction of universals is itself a universal. Thus the conjunction of Redness and Roundness is itself a universal, a multiply exemplifiable entity. I will use 'Konjunction' to single out conjunction of universals.

Now it should be obvious that a bundle of universals is not a conjunction of universals. Let K be the Konjunction operator: it operates upon universals to form universals. Let B be the bundling operator: it operates upon universals to form particulars. Bundling is not Konjunction. So far, then, Peter seems to have failed to make an elementary distinction.

Now suppose Peter objects that nothing could operate upon universals to form a particular. Universals in, universals out. Then I say that he is just wrong: the set-theoretical braces — { } — denote an operator that operates upon items of any category to form sets of those items. Now it should be obvious that a set of universals is not itself a universal, but a particular. A Konjunction of universals is a universal, but a set of universals is not a universal, but a particular. The Konjunction of Redness and Roundness is exemplifiable; but no set is exemplifiable.

Am I saying that a bundle of universals is a set of universals? No. I am saying that it is false to assume that any operation upon universals will result in a universal. What I have said so far suffices to refute Peter's first objection, which was that the unification of two universals yields a third universal. You can see that to be false by noting that the unification into a set of two or more universals does not yield a universal but a particular.

Ad (b). Our second question is whether a contingent particular could have as ontological constituents necessary beings. Peter thinks not. He thinks that anything composed of necessary beings will itself be a necessary being. And so, given that universals are necessary beings, and that concrete particulars are composed of universals, no concrete particular can be modally contingent.

This objection fares no better than the first. Suppose Redness and Roundness are compresent. (You will recall that Russell took the bundling relation to be the compresence relation. See An Inquiry into Meaning and Truth, 1940, Chapter 6.) Each of these universals, we are assuming, is a necessary being. But it doesn't follow that their compresence is necessary; it could easily be contingent. Here and now I see a complete complex of compresence two of whose constituent universals are Redness and Roundness. But surely there is no necessity that these two universals co-occur or be com-present. After all, Redness is often encountered compresent with shapes that are logically incompatible with Roundness. Compresence, then, is a contingent relation. It follows that complexes of compresence are contingent. Necessarily, Rednessexists. Necessarily, Roundness exists. But it does not follow that, necessarily, Redness and Roundness are compresent: surely there are possible worlds in which they are not.

Peter's argument for his conclusion commits the fallacy of composition:

1. Every universal necessarily exists.

2. Every concrete particular is composed of universals. Therefore,

3. Every concrete particular is composed of things that necessarily exist. Therefore,

4. Every concrete particular necessarily exists.

The move from (3) to(4) is the fallacy of composition. One cannot assume that if the parts of a whole have a certain property, then the whole has those properties.