Category: Modal Matters

God, Simplicity, Freedom, and Two Senses of ‘Contingency’

Fr. Aidan Kimel wants me to comment on his recent series of posts about divine simplicity, freedom, and the contingency of creation. In the third of his entries, he provides the following quotation:

As Matthew Levering puts it: “God could be God without creatures, and so his willing of creatures cannot have the absolute necessity that his willing of himself has” (Engaging the Doctrine of Creation, p. 103). That is the fact of the case, as it were. Granted the making of the world by a simple, immutable, and eternal Deity, we have no choice but to accept the apparent aporia:

Indeed, there is no ‘moment’ in God’s eternity in which he does not will all that he wills; there is no God ‘prior’ to God’s will to create. In this sense, God can be said to will necessarily everything that he wills. The potency or possibility stems not from God’s will, but from the contingent nature of the finite things willed; they do not and cannot determine the divine will. (Levering, p. 103)

The problem is to understand how the following  propositions can all be true:

1) There is no absolute necessity that God create: "God could be God without creatures."

2) God created (better: ongoingly creates and sustains) the universe we inhabit.

3) God, being simple or metaphysically incomposite, is devoid of potency-act composition and unexercised powers: God is pure act.

4) The universe we inhabit, and indeed any universe God creates, is modally contingent: it does not exist of metaphysical necessity.

The problem, in brief, is to understand how a universe that is the product of a divine act of willing that is necessary (given God's simplicity) can yet be contingent. Levering's answer does not help at all. In fact, he seems to be confusing two senses of contingency when he says that "the contingent nature of the finite things willed" does not determine the divine will.  That's right, it doesn't and for the simple reason that the finite things willed depend entirely on the divine will and are in this sense contingent upon the divine will; but this is not the relevant sense of 'contingency.' Let me explain.

In the modal sense, a contingent item is one that is possible to be and possible not to be, as Aquinas says somewhere. In 'possible worlds' jargon, x is modally contingent =df x exists in some but not all metaphysically (broadly logically) possible worlds.  

In the dependency sense, x is dependently contingent =df there is  some y such that (i) x is not identical to y; (ii) necessarily, if x exists, then y exists; (iii) y is in some sense the ground or source of x's existence. 

It is important to see that an item can be (a) modally contingent without being dependently contingent, and (b) dependently contingent without being modally contingent.

Russell v. CoplestonAd (a). If the universe is a brute fact, as Russell (in effect) stated in his famous BBC debate with Copleston, then the universe exists, exists modally contingently, but has no cause or explanation of its existence.  If the universe is a brute fact, then of course it does not depend on God for its existence.  Its existence is a factum brutum without cause or explanation. It is contingent, but not contingent upon anything. It is modally but not dependently contingent.

Ad (b). Not all necessary beings are "created equal."  That is because one of them, God, is not created at all. The others are creatures, at least for Aquinas. (A creature is anything that is created by God.) The number 7 serves as an example, as does the proposition that 7 is prime.  That proposition is a necessary being. (If it weren't it could not be necessarily true.)  But it has its necessity "from another," namely, from God, whereas God has his necessity "from himself."  The doctor angelicus himself makes this distinction.

These so-called 'abstract objects' — not the best terminology but the going terminology — are creatures, and, insofar forth, dependent on God, and therefore contingent upon God, and therefore (by my above definition), dependently contingent. They are dependently contingent but modally necessary. 

Now let's apply the distinction to our problem. The problem, again, is this: How can the product of a necessary creating be contingent? One might think to solve the problem as follows.  God necessarily creates, but what he creates is nonetheless contingent because  what he creates is wholly dependent on God for its existence at every moment. But this is no solution because it involves an equivocation on 'contingent.'

The problem is: How can the product of a modally necessary creating be modally contingent? 

Think of it this way. (I assume that the reader is en rapport with 'possible worlds' talk.) If God is simple, and he creates U in one world, then he creates U in all worlds. But then U exists in every world, in which case U is necessary. But U is contingent, hence not necessary. Therefore, either God does not exist or God is not simple, or U is not a divine creation.  

Fr. Kimel wanted me to comment on his posts. One comment is that they are top-heavy with quotations.  Quote less, argue and analyze more.

Now I would like the good padre to tell me whether he agrees with me.  I think he just might inasmuch as he speaks of an aporia.  We have good reasons to believe that God is simple, and we have good reasons to believe that the created universe is modally contingent. Suppose both propositions are true. Then they must be logically consistent.  But we cannot understand how they could both be true. So what do we do?

One way out is to jettison the divine simplicity. (But then we end having to say that God is a being among beings and neither I nor Kimel will countenance that, and for good reasons.) A second way is by denying that the created universe is contingent, either by maintaining that it is necessary or by denying that there is any real modality, that all (non-deontic) modality is epistemic.  The second way leads to a load of difficulties.

A third way is by arguing that there is no inconsistency. But I have argued that there is both above and in other recent posts dealing with the dreaded 'modal collapse.'  And it seems to me that my argumentation is cogent.

Well suppose it is. And suppose that the relevant propositions are all true. There is yet another way out. We can go mysterian.  The problem is a genuine aporia. It is insoluble by us. God is simple; he freely created our universe; it is modally contingent.  How is this possible? The answer is beyond our ken. It is a mystery.

Now if Fr. Kimel is maintaining something like this, then we agree.

Corrigendum (9/25). A reader points out, correctly, that in the above graphic the gentleman on the left is not Fr. Copleston, but A. J. Ayer.

Is Talk of ‘Possible Worlds’ Wholly Dispensable?

I made a bold claim earlier:

If I am right, the patois of possible worlds is a dispensable manner of speaking: we can make every [modal] point we want to make without engaging in possible worlds talk.  What I just said is not perfectly obvious and there may be counterexamples. 

Here is a candidate counterexample that I borrow from Barbara Vetter, 'Can' Without Possible Worlds, 22:

(CC) Someone can see us.

This is an alethically or as Vetter would say "dynamically" modal statement. It is modal but not expressive of either epistemic or deontic modality. Interestingly, (CC) is susceptible of being read either de re or de dicto:

(DR) There is a person who can see us.

(DD) It is possible that someone see us.

(DR) commits us to an actual person who is able to see us.  (DD) does not. The first entails the second, but the second does not entail the first. So the two readings are non-equivalent.  Suppose that no actual person can see us. Suppose, that is, that no actual person has both the ability to see us and is positioned in such a way that he can exercise his ability. Even so, it is  'surely' possible that there be such a person. There could have been a person, distinct from every actual person, who sees us. 

So (DD) is a true alethically modal statement whose truth is not grounded in, or made true by, a power or ability of any actual item.

(DD) would thus appear to be a counterexample to Vetter's "potentiality semantics" according to which "all dynamic modality is de re . . . ." (22)  It seems that (DD) expresses a 'free-floating' possibility, one not grounded in any actual concrete thing's power or potentiality. If so, then 'possible worlds' talk might not be wholly dispensable.  

One response to the putative counterexample is rejectionist: Vetter toys with  simply rejecting (DD) as a statement of dynamic modality by suggesting that it is really an example of epistemic possibility (23).

I fail to see, however, how (DD) could be construed as epistemic.  The idea is not that, for all we know, someone can see us, but that it is really possible, apart from our knowledge and ignorance, that there be someone who can see us.  In the actual world, no one can see us now. But 'surely' there is a possible world, very much like the actual world, in which someone can see us now.  If there is this possibility, it is real, not epistemic. 

But there is another line of rejection that Vetter does not clearly distinguish from the first.  And that is simply to say that her topic is dynamic modality, the sort of real modality that we encounter in actual changing things, and not real modality in general.   'Dynamic' is from the Greek dynamis which in Latin is potentia, whence our 'potency' and 'potentiality.' The second way of rejection, then, is to dismiss (DD) as simply off-topic.

But then her thesis is less interesting: it is not the thesis that all alethic modality is de re, but that only the modality of actual concrete things subject to change is de re.  If this is her thesis, then it seems we need possible worlds to accommodate such de dicto possibilities as (DD). 

Divine Simplicity, Modal Collapse, and a Powers Theory of Modality

This is the third in a series on whether the doctrine of divine simplicity (DDS) entails modal collapse (MC). #1 is here and #2 here. Most of us hold that not everything possible is actual, and that not everything actual is necessary. I will assume that most of us are right. A doctrine entails modal collapse if it entails that, for every x, x is possible iff x is actual iff x is necessary.  

In God's Powers and Modality: A Response to Mullins on Modal Collapse (no bibliographical information provided, date, or author's name, but presumably by someone named 'Lenow') we read:

Our problem is not with the notion that God has created the world; it is with the fear that we will be forced by divine simplicity to say that God has created the world necessarily. 

[. . .]

I believe that the recent work of Barbara Vetter offers an account of potentiality and modal grounding capable not only of resisting modal collapse, but of doing so along the traditional Thomist lines Mullins rejects as incoherent. Vetter presents us with the theoretical resources needed to affirm divine simplicity without forcing a breakdown in our modal language, and thus allows us to avoid being cornered into asserting that God creates necessarily or that all creaturely events occur necessarily.

We shall see.

What Vetter calls the “standard conception” of a dispositionalist account of modality runs roughly as follows. Objects possess dispositional properties: a vase, for example, possesses the property of fragility; an electron possesses the property of repelling other particles with a negative charge; I have the ability to learn how to play the violin. (3)

I am well-disposed (pun intended) toward this sort of view. 

I am seated now, but I might not have been. I might have been standing now or in some other bodily posture. What makes this true? What is the ontological ground of the (real, non-epistemic) possibility of my not being seated now?  As useful as possible worlds talk is for rendering modal concepts and relations graphic, it is of no use for the answering of this question if we take an abstractist line on possible worlds as sanity requires that we do. On the other hand, David Lewis' concretist approach is, if I may be blunt, just crazy. 

The best answer invokes my presently unexercised ability to adopt a physical posture other than that of the seated posture, to stand up for example.  Ultimately, the ground of real modality is in the powers, abilities, capacities, dispositions, potencies, tendencies, and the like of the things the modal statements are about.

The typical wine glass is fragile: it is disposed to shatter if struck with moderate force. Fragility is a stock example of a dispositional property.  But fragility comes in degrees.  Think of a spectrum of breakability from the most easily breakable items all the way up to items that are breakable only with great difficulty such as rocks and metal bolts and steel beams. We do not apply 'fragile' to things like steel beams, but they too are breakable. 

Yet Vetter is most interested in the property that characterizes all the objects on
this spectrum: the possibility of being broken, the manifestation that she takes to
individuate this property. This modal property that extends from one end of this spectrum
to the other she calls a potentiality—in this case, the potentiality of a thing’s being
breakable.(4)

Now let's see if Vetter's power theory of modality solves our problem.  The problem can be put as follows without possible worlds jargon. There is a tension between divine simplicity and divine freedom.  

1) If God is simple, then he is pure act (actus purus) and thus devoid of unexercised powers and unrealized potentials. He is, from all eternity, all that he can be.  Given that God is simple, there can be no real distinction in him between potency and act. This is necessarily true  because God exists of metaphysical necessity and is essentially pure act.

2) As it is, God freely created our universe from nothing; but he might have created a  different universe, or no universe at all. Had he created no universe, then his power to create would have gone unexercised.  In that case he would not be pure act: he would harbor an unactualized potential.

The dyad is logically inconsistent. What I called a tension looks to be a contradiction. If (1) is true, then it is impossible that God have unexercised powers such as the never-exercised power to create.  But if (2) is true, it is possible that God have unexercised powers. So if God is both simple and (libertarianly) free, then we get a logical contradiction.

If we hold to (1), then we must reject (2). The upshot is modal collapse. For given that God willed our universe with a will that is automatically efficacious, both the willing and the willed are necessary. And so the existence of Socrates is necessary and the same goes for his being  married to Xanthippe and his being the teacher of Plato, etc.

To what work can we put Vetter’s theory in forestalling the threat of modal collapse? Consider God’s will, using Vetter’s language, as an intrinsic maximal first-order potentiality to will God’s own infinite goodness as the ultimate and perfect end of the divine nature. Let me take each descriptor in turn. First, this potentiality is intrinsic, because it does not depend upon any external circumstances for its manifestation and is not possessed jointly. Second, it is maximal, because God cannot fail to manifest this potentiality. As Vetter argued, something is maximally breakable if it is not possible for it not to break—it will break under any circumstances. Similarly, the willing of God’s goodness as end is a potentiality that can be possessed in degrees: rocks do not seem to possess it at all, demons possess it only to the extent that their wills remain a corrupted version of their original unvitiated creation, humans possess it to a greater extent in that the possibility of redemption remains open to them, angels possess it in the highest created degree as a gift from God; yet God “possesses” this potentiality in qualitatively different fashion, possessing it maximally because it is identical with God’s nature—God cannot fail to will God’s goodness. Third, this is a potentiality simpliciter—that is, a first order iterated potentiality, rather than as a potentiality to acquire some other potentiality; the doctrine of divine simplicity removes the possibility of any such composition. Finally, to avoid the threat of modal collapse, this must be a multi-track potentiality, multiply realizable (as are most potentialities); in effect, this means that God is capable of willing God’s goodness in multiple ways, but that no one instance of such willing is any more or any fuller a manifestation of this potentiality than any other such willing. Defenders of divine simplicity typically hold that God’s life is itself full and infinite goodness, lacking nothing.[ . . .] Consequently, had God willed to exist without creation, God would not have willed a lesser goodness than God has willed in creating the world; similarly, had God willed the creation of a different world, God would not have willed a lesser (or greater) goodness than God has willed in creating this one. Each of these acts of willing would have produced different effects, to be sure—but in each case, the potentiality manifested is the same, the potentiality to will God’s infinite goodness as ultimate end.

What is the argument here? It is none too clear.  But one key notion is that of a maximal potentiality. A maximal potentiality is one that cannot fail to be manifested.  An example of a non-maximal potentiality is that of a wine glass to break into discrete pieces when dropped onto a hard surface or struck. That disposition need never be manifested. (Imagine that the glass ceases to exist by being melted down, or maybe God simply annihilates it.) Or think of all the abilities that people have but never develop.

Breakability looks to be a candidate for the office of maximal potentiality. It cannot fail to be manifested. "As Vetter argued, something is maximally breakable if it is not possible for it not to break—it will break under any circumstances." This is a strange formulation. It is true that some things are such that they must eventually break down. But this is not to say that they will break under any circumstances. But let that pass.

Consider now God's power to will his own goodness. We may grant that this is a power that cannot fail to be exercised or manifested. Since it is not possible for God not to exercise this power, it is no threat at all to the divine simplicity. There is no real distinction between God and his willing his own goodness. God's willing his own goodness just is his power to will his own goodness.  This power is plainly compatible with God's being pure act.

But how does this avoid modal collapse?  

Finally, to avoid the threat of modal collapse, this must be a multi-track potentiality, multiply realizable (as are most potentialities); in effect, this means that God is capable of willing God’s goodness in multiple ways, but that no one instance of such willing is any more or any fuller a manifestation of this potentiality than any other such willing.

The second key idea, then, is that of the multiple realizability of liabilities and potentialities and such. I am not now actually sick, but I am liable to get sick, or I have the potential to get sick, in many different ways.  I can get sick from bad food, or polluted water, or a virus can attack me, etc.  My liability to get sick is multiply realizable. The same goes for active powers and abilities.  My power to express myself is realizable in different ways, in writing, in speech, in different languages, using sign language etc. 

God's power to will his own goodness is realizable by creating our universe, some other universe, or no universe at all. So it too is multiply realizable. Fine, but how does this solve the problem? 

Suppose I will to buy whisky. I go to the liquor story and say, "I want whisky!"  The proprietor says, "Very well, sir, would you like bourbon or scotch or rye or Irish?"  If I insist that I just want whisky, I will learn that whisky is not to be had. One cannot buy or drink whisky without buying or drinking either bourbon or scotch or rye or Irish or . . . .

It is the same with God. He cannot will his own goodness 'in general'; he must will it in some specific way, by willing to create this universe or that universe or no universe.

But then we are back to our problem. For whatever he does, whether he creates or not, is necessary and we have modal collapse.  The modal collapse that we all agree is in the simple God spreads to everything else.

As far as I can see, Lenow's response to Mullins fails.

UPDATE (9/4). Joe Lenow writes,

Hi Bill—I am Spartacus. Thanks for engaging the paper. 
 
This is a version of the argument from a conference presentation a couple of years ago; hadn't realized that the conference papers were public view. I've got a much more carefully worked-out version of the argument presently under review; please find it attached. I'd appreciate any thoughts you have on it!
 
Best wishes,
 
Resident Assistant Professor of Theology
Creighton University
I will have to study Professor Lenow's latest version. It cannot be reproduced or discussed here, of course, since it is under review.

From the Mailbag: Modality and Perfection

Daniel C. writes,

A quick remark on your recent possible worlds post. 

You only mention it in  passing but one thing possible worlds talk surely does throw into sharp relief is the issue of the modality of modal statements i.e. if a certain proposition is possibly true is it necessarily possibly true or merely possibly possibly true? To the best of my knowledge most pre-modern metaphysicians simply presumed the truth of the Brouwer axiom (Leibniz and Scotus) or of S5. Far be it from me to challenge these venerable principles but as far as I know very few thought of disputing them before the question could be phrased in terms of accessibility relations between worlds.
Your general point is important and correct: possible worlds talk allows for the rigorous formulation of questions about the modal status of modal statements, which in turn hinges on accessibility relations between worlds.  But I hope you are not suggesting that the Brouwer axiom is the same as the characteristic S5 axiom. I am not a logician, but my understanding is that they are not.
 
Brouwer Axiom: p –> Nec Poss p. That is to say, if a proposition is true, then it is necessarily possibly true.
 
Characteristic S5 axiom: Poss p –> Nec Poss p. That is, if a proposition is possibly true, then it is necessarily possibly true.
Also: On the contrary, I say that God's status as a necessary being follows from His perfection rather than simplicity (although the former may entail the latter as Anselm certainly thought).

I take it that a perfect being is one that possesses all perfections. The Plantingian gloss on 'perfection' seems good enough: a perfection is a great-making property. So a perfect being is one that possesses all great-making properties and the maximal degree of those great-making properties that admit of degrees. 

Now A. Plantinga famously denies the divine simplicity while upholding the divine perfection. I take it we all agree that God is a necessary being.  That than which no greater can be conceived cannot be a mere contingent being. But what makes a necessary being greater than a contingent being? On a possible worlds approach, it will presumably be the fact that a being that exists in all worlds is greater than one that exists in some but not all worlds. It is a matter of quantity of worlds.

But then I will press the question: what makes it the case that God exists in all possible worlds?  What grounds this fact? My answer: the divine simplicity, which implies the identity in God of essence and existence.  Divine perfection is not enough. For God could be perfect in Plantinga's sense while harboring a real internal difference between essence and existence. But this leaves open the question as to why God is necessary.

If you say that God is necessary because he exists in all worlds, then you give a bad answer. It is true that God exists necessarily iff all world-propositions say he exists. But it doesn't follow that God is necessary because all world-propositions say he exists. It is the other way around: he exists according to every world-proposition because he is necessary!

Mundane example. Am I seated because the proposition BV is seated is true? No. The proposition is true because I am seated. The truth-maker is what makes the truth true; it is 'bass ackwards' to say that truths make states of affairs exist.  

Same with God. It is the divine necessity that makes it true that God exists in (i.e., according to) every possible world, and not the other way around. But to be necessary in the unique way that God is necessary, a way he does not share with garden-variety necessary beings such as the number 9 and the set of prime numbers, God must be metaphysically simple.

Why Talk of ‘Possible Worlds’?

 This from a commenter:

I have a question about a tangential matter, in case you care to respond to it. You say [in your discussion of divine simplicity and modal collapse] that you don't need talk of possible worlds. I don't think I find such talk puzzling, but I've never understood the vogue for it. Since many absolutely first-rate philosophers seem to insist on using it, I assume there must be some great advantage to doing so, and not seeing what that is I assume that there is something important I don't understand. If you care to explain I'd be interested.

The notion of possible worlds dates back at least to G. W. Leibniz (1646-1716) but the current vogue began roughly in the middle of the 20th century when philosophers and logicians applied themselves to the formal semantics of the different systems of (alethic) modal logic. Now this is a highly technical topic but the technicalities can be avoided for present purposes.  I will assume the S5 axiom set. 

Assumption: reality has a modal structure

I will also assume that reality has a modal structure, that modality is somehow ingredient in extramental reality. Thus modality is not a merely epistemic/doxastic matter.  For example, Hillary could have won in 2016. It was really possible for her to have won. Had she worked harder and smarter, kept her trap shut about the 'deplorables,' etc., then she probably would have won.  Things really could have gone otherwise, and this possibility is not parasitic upon our ignorance of all the factors involved in her losing. 

The utility of talking the talk

As I see it, the utility of 'possible worlds' talk is that it allows for an especially  perspicuous representation of modal relationships in extensional terms.  And it seems to me that one can talk the talk without walking the walk. That is, one can  make use of 'possible worlds' (PW) jargon without taking on too many heavy-duty ontological commitments. What do I mean? One thing I mean is that one can employ PW jargon without buying into David Lewis' extreme modal realism. For Lewis, possible worlds are maximal mereological sums of concreta. One can surely talk the talk without walking that walk. How?

Sketch of an abstractist approach to possible worlds

A much saner way of thinking about possible worlds is as follows. If the Lewisian way is concretist, the following way is abstractist: possible worlds are abstract objects, maximal Fregean propositions on one abstractist approach.

14) If worlds are maximal Fregean propositions, then no concretum such as Socrates can exist in any world in the manner of a constitutent. This is because concreta are not among the constituents of Fregean propositions. Therefore, to say that there is a possible world in which Socrates exists but dies in battle, is to say that there is a maximal proposition according to which Socrates dies in battle. 

Restriction to alethic modalities

The concern here is with alethic modality, not deontic or epistemic modality. By alethic modalities I understand the modalities of truth, of existence, and of property-possession.

Truth

It is necessary that 2 is a prime number, impossible that 2 is an an odd number, and contingent that 2 is the number of my cats. In PW jargon: 

Every metaphysically possible world w is such that *2 is prime* is true in w.
No metaphysically possible world w is such that *2 is odd* is true in w.
Some (but not all) metaphysically possible worlds are such that *2 is the number of my cats* is true in w.

If we quantify over possible worlds, we can understand the modal terms 'necessary,' 'impossible,' and 'contingent' by analogy with the quantifiers of standard, first-order predicate logic: 'every,' 'no,' 'some.'  And we can then set up a modal square of opposition in analogy to the standard square of opposition.

  Modal square of opp

Isn't that neat? The modal relationships fairly jump out at you. Necessarily p entails possibly p. Of course. What is true is true in every world is true in some world, but not conversely.

When I say that the PW representation of modal propositions and inferences is extensional, all I mean is that the representation involves quantifying over possible worlds assumed as given.

Existence and Property-Possession

A necessary being is one that exists in all worlds; an impossible being one that exists in no worlds; a contingent being is one that exists in some but not all worlds. If x has a property essentially, then x has the property in every world in which x exists; if x has a property accidentally, then x has it in some but not all of the worlds in which x exists. If a necessary being has a property essentially, we can say that it has the property necessarily in that there is no world in which it does not have the property. Thus the number 7 is necessarily prime and God is necessarily omniscient.  Socrates, by contrast, is essentially human but not necessarily human.

An important Euthyphro-type question

Now let's dig a little deeper.

God is a necessary being. He exists in every world. But does he exist in every world because he is necessary, or is he necessary because he exists in every world?  I say the former.  His metaphysical necessity grounds and thus explains his existence in every world.  He exists according to every maximal proposition because he is metaphysically necessary.  But what grounds the divine necessity? The divine simplicity: existence and essence are one in God.

Now take Socrates. He is a contingent being: he exists in some but not all possible worlds.  But does he exist in some but not all worlds because he is contingent, or is he contingent because he exists in some but not all worlds? I say the former. Only some world-propositions say he exists because he is contingent.  But what makes him contingent? One answer is that he is contingent because there is in him and in all contingent beings that actually exist a real distinction between essence and existence.

Answering the reader's question

The reader asked about the advantage of PW talk.  My answer is that such talk allows for an especially perspicuous representation of modal propositions and relationships.   

If I am right, the patois of PW is a dispensable manner of speaking: we can make every point we want to make without engaging in PW talk.  What I just said is not perfectly obvious and there may be counterexamples. I have one in mind right now. Stay tuned. 

More on Divine Simplicity and Modal Collapse

This entry continues my ruminations on whether the doctrine of divine simplicity (DDS) entails modal collapse (MC). The commenters in the earlier thread gave me no reason to think that DDS does not entail MC. But one of them sent me to Christopher Tomaszewski's paper which is worth reading and deserves a response.

Tomaszewski presents one of R. T. Mullins' arguments as follows:

1) Necessarily, God exists.
2) God is identical to God’s act of creation.
Therefore
3) Necessarily, God’s act of creation exists.

Tomaszewski claims that above argument is invalid and for the same reason that the following argument is invalid:

7) Necessarily, God exists.
8) God is identical to the Creator.
Therefore
9) Necessarily, the Creator exists.

Now the second argument is clearly invalid. It takes us from true premises to a false conclusion. God exists in every possible world. But in only some worlds does he instantiate the role of Creator. So it is not the case that the Creator exists in every possible world.

Some find the Leibnizian patois of 'possible worlds' puzzling. I don't need it. The point can be made without it, as follows. God exists of metaphysical necessity. But he does not create of metaphysical necessity: creation is a contingent act. Therefore, it is not the case that, necessarily, God is the Creator. Had he created nothing, he would exist without being Creator.

So the second of the two arguments is invalid. Now if the first argument has the same logical form as the second, then it too will be invalid.  But the first argument does not have the same logical form as the second.

The form of the first is:

Necessarily, for some x, x = a.
a = b.
ergo
Necessarily, for some x, x = b.

Clearly, this argument-form is valid, whence it follows that any argument having this form is valid. I am assuming that the individual constants 'a' and 'b' are Kripkean rigid designators: they denote the same object in every possible world in which the object exists.  I am also assuming Kripke's Necessity of Identity principle: For any x, y if x = y, then necessarily, x = y.  By instantiation, if a = b, then necessarily a = b. Now if necessarily a exists, and a cannot exist without being identical to b, then necessarily b exists.

Contra Tomaszewski, the arguments have different forms. The first instantiates a valid form and is therefore valid while the second instantiates an invalid form and is therefore invalid.

I expect someone to object that (2) above – God is identical to God’s act of creation — is not an instance of the logical form a = b, where the terms flanking the identity sign are Kripkean rigid designators. But I say they are; indeed they are strongly rigid designators.  A rigid designator is a term that picks out the same item in every possible world in which the item exists. A strongly rigid designator is a term that picks out the same item in every possible world, period.  Thus the designatum of a strongly rigid designator is a necessary being.

My claim, then, is that (2) is a statement of identity and that  'God' and 'God's act of creation' in (2) are both strongly rigid designators. My claim is entailed by DDS which says, among other things, that there is no real distinction in God between agent and action.  So if God is identical to his act of creating our universe, and God exists in every possible world, then the creation of our universe occurs in every possible world, which in turn entails modal collapse.

Tomaszevski has an interesting response (pp. 7-8):

While God’s act is indeed intrinsic (and therefore identical) to Him, “God’s act of creation” designates that act, not how it is in itself, but by way of its contingent effects. That is, whether “God’s act of creation” designates God’s act depends on the existence of a creation which is contingent, and so the designation is not rigid. And since the designation is not rigid, the identity statement is not necessary, as it must be in order to validate the argument from modal collapse. 

This response begs the question. For it assumes that the effect of the divine act of creation is contingent. But that is precisely the question!  If you just assume — as we all want to assume –  that creation is contingent, then of course there is no modal collapse. The issue, however, is whether one can adhere to that assumption while holding fast to DDS.  Besides, the second sentence in the above quotation makes little or no sense. The act of creation is individuated by the object of creation (our universe, say, in all its detail); an act of divine creation is nothing without its object.  

Am I assuming what I need to prove (and thus begging the question) when I insist that (2) above is necessarily true and thus that the first argument is valid?  No, I am merely unpacking what DDS implies.  

My conclusion is that Tomszevski has clarified the problem for us, but he has not refuted the above argument from DDS to MC. 

Divine Simplicity and Modal Collapse

Fr. Aidan Kimel would like me to discuss  the question whether the doctrine of divine simplicity entails the collapse of modal distinctions.  I am happy to take a crack at it.  I take my cue from a passage in a paper Fr. Kimel kindly sent me.  In "Simply Impossible: A Case Against Divine Simplicity" (Journal of Reformed Theology 7, 2013, 181-203), R. T. Mullins asks (footnote omitted):

Could God have refrained from creating the universe? If God is free then it seems that the answer is obviously ‘yes.’ He could have existed alone. Yet, God did create the universe. If there is a possible world in which God exists alone, God is not simple. He eternally has unactualized potential for He cannot undo His act of creation. He could cease to sustain the universe in existence, but that would not undo His act of creating. One could avoid this problem by allowing for a modal collapse. One could say that everything is absolutely necessary. Necessarily, there is only one possible world—this world. Necessarily, God must exist with creation. There is no other possibility. God must create the universe that we inhabit, and everything must occur exactly as it in fact does. There is no such thing as contingency when one allows a modal collapse. (195-196)

The foregoing suggests to me one version of the problem.  There is a tension between divine simplicity and divine freedom.

1) If God is simple, then he is purely actual (actus purus) and thus devoid of unexercised powers and unrealized potentials. He is, from all eternity, all that he can be. This is true in every possible world because God exists in every possible world and is pure act in every possible world.

2) As it is, God freely created our universe from nothing; but he might have created a different universe, or no universe at all. Had he created no universe, then his power to create would have gone unexercised. In those possible worlds in which God freely refrains from creating, God has unexercised powers. 

The dyad seems logically inconsistent. If (1) is true, then there is no possible world in which God has  unexercised powers. But if (2) is true, there is at least one possible world in which God has unexercised powers. So if God is both simple and (libertarianly) free, then we get a logical contradiction.

There are two main ways to solve an aporetic polyad. One is to show that the inconsistency alleged is at best apparent, but not real.  The other way is by rejection of one of the limbs. I take the dyad to be inconsistent.

Many if not most theists, and almost all Protestants, will simply (pun intended) deny the divine simplicity.  I myself think there are good reasons for embracing the latter.  To put it in a cavalier, bloggity-blog way: God is the Absolute, and no decent absolute worth its salt can be a being among beings. We have it on good authority that God is Being itself self-subsisting.  Deus est ipsum esse subsistens. Platonic, Plotinian, Augustinian, Aquinian, Athenian. It can be shown that simplicity is logical fallout if God is Being itself.  So it seems I must deny (2) and deny that God could have refrained from creating.  But this seems to lead to modal collapse. How so?

Modal Collapse

We have modal collapse just when the following proposition is true: For any x, x is possible iff x is actual iff x is necessary.  This implies that nothing is merely possible; nothing is contingent; nothing is impossible.  If nothing is merely possible, then there are no merely possible worlds, which implies that there is exactly one possible world, the actual world, which cannot fail to be actual, and is therefore necessary.

(The collapse is on the extensional, not the intensional or notional plane: the modal words retain their distinctive senses.)

Suppose divine simplicity entails modal collapse (modal Spinozism). So what? What is so bad about the latter?  Well, it comports none too well with God's sovereignty. If God is absolutely sovereign, then he cannot be under a metaphysical necessity to create. Connected with this is the fact that if God must create, then his aseity would seem to be compromised. He cannot be wholly from himself, a se, if his existence necessarily requires a realm of creatures.  Finally, creaturely (libertarian) freedom would go by the boards if reality is one big block of Spinozistic necessity.

An Aporia?

It seems that the proponent of divine simplicity faces a nasty problem.  At the moment, I see no solution.

The aporetician in me is open to the thought that what we have here is a genuine aporia, a conceptual impasse, a puzzle  that we cannot solve. God must be simple to be God; the modal distinctions are based in reality; we cannot see how both limbs of the dyad can be true and so must see them as contradictory.   

It could be like this: the limbs are both true, but our cognitive limitations make it impossible for us to understand how they could both be true.  Mysterianism may be the way to go.  This shouldn't trouble a theologian too much. After all, Trinity, Incarnation, etc. are mysteries in the end, are they not?  Of course, I am not suggesting the doctrine of divine simplicity can be found in the Bible. 

Later I will evaluate an attempt to solve the problem via an approach to real modality via potentialities and dispositions.  

References to relevant literature appreciated. By the end of the year I have to update my Stanford Encyclopedia of Philosophy Divine Simplicity entry.  

Is the Wholly Past Now Impossible?

Boston's Scollay Square is an example of a wholly past item. It existed, but it does not now exist. Boston's Copley Square, by contrast, existed and still exists: it has a past but it is not wholly past.

In an earlier exercise I gave an anti-presentist argument one of the premises of which is:

d) It is not the case that Scollay Square is [now] either merely possible or impossible: what passes away does not become merely possible or impossible.

The Ostrich objected:

I didn’t follow the assumption (d) above. Scollay Square  is impossible, having perished. 

The question is this:  When a thing that actually existed passes away and becomes wholly past, does it cease to be actual and become impossible?  Can the passage of time affect an object's  modal status?

I say No; the Ostrich says Yes.  My No, however, will be nuanced by a distinction I shall introduce shortly.

A Concession

Scollay Square novelI concede to the Ostrich that there is a sense in which Scollay Square, that very item, is now impossible: it cannot be restored to existence. (If you made a copy of it, the copy would not be it.) After the demolition was complete, there was nothing anyone could do to bring back that very item.  In this respect the demolition of the famous square is like a person's loss of virginity. If you lose your virginity at time t, then there is nothing anyone can do after t to undo the loss. (Repairing a girl's hymen would not do the trick. Hymenoplasty is possible but it is not the same as restoration of virginity.) 

Now there is no need to drag the Deity into this debate, but I will do it anyway just to throw the issue into relief. Not even God can restore a virgin or bring back Scollay Square (where many a sailor lost his virginity).  This is because it is the very natures of time and existence that prevent the restoration.  (Now please forget that I even mentioned God, and do not ask me any questions about divine omnipotence.)

Let's consider another example. Our patron Socrates was executed by the Athenian state. That event might not have occurred. That is, his execution was not metaphysically necessary. In the patois of 'possible worlds,'  there are possible worlds in which Socrates is executed and possible worlds in which he is not.  Therefore, his execution was metaphysically contingent and remains sub specie aeternitatis metaphysically contingent despite the fact that the execution cannot be undone.  But if the execution cannot be undone and was impossibly undone from the moment of the event onward, then how can the execution be contingent?  Is it not necessary?  Obviously, we need to make a distinction.

Metaphysical versus Time-Bound Modalities

We have to make a distinction between metaphysical modalities and time-bound modalities.  We can say that Socrates' execution, while metaphysically contingent, nevertheless enjoys necessitas per accidens and its undoing impossibilitas per accidens.  Nothing hinges on this particular terminology, but there is a distinction to be made here.

Someone could say, and the Ostrich perhaps will say, that before Socrates came to be, he was merely possible, that when he came to be he became actual, and that after he passed away he became impossible. If this makes sense, then our man's modal status is time-dependent.

I think the following are logically consistent:

1. It is impossible that an actual being that no longer exists be restored to existence.

2. A metaphysically contingent being that exists in the sense that it existed, exists, or will exist retains its modal status when it passes away. Socrates exists in this disjunctive sense. When Socrates ceased to exist (assuming no immortal soul) he retained his modal status: actual but not necessary.

(1) is a concession to the Ostrich. But (2) is also true. I am inclined to accept  a Growing Block theory of time: as time passes the 'block of reality' gets bigger and bigger. Everything that IS is actual, and everything that WAS is also actual.  The past is not nothing: it is real.  

Socrates is (in the disjunctive sense) an actual being.  This may be the same as saying that he is tenselessly actual. His passing away does not affect his metaphysical modal status. He is no longer temporally present but he is nonetheless metaphysically actual. 

Furthermore, he remains a contingent being after his passing.  He does not become an impossible being.

So I think we can achieve a sort of irenic if not quite Hegelian  synthesis. The Ostrich is speaking from the perspective of the present. (I suspect he is a presentist and I should like him come clean on this.) From the point of view of the present, the wholly past is now impossible in the sense that nothing ANYONE can do can restore the past or bring it back.  I believe I have accommodated, with all due charity, the insight of the Ostrich.

But we also have the power to view things 'from above,' We are time-bound to be sure, but we are also "spectators of all time and existence" as Plato once taught us.  Looking down upon this scene of flux and folly we can 'see' with the eye of the mind the tenseless modal relationships that obtain here below. These are not affected by the passage of time.

For example, no contingent being  is impossible.  Socrates is a contingent being.  Ergo, Socrates is not impossible.  He was not impossible before he became present; he was not impossible when he was present; and he is not impossible now when he is past. He is tenselessly contingent.

The stable view sub specie aeternitatis is just as valid as the view from one's shifting temporal location.

Taking Stock

The question is this: When a thing that actually existed, or an event that actually occurred, passes away and becomes wholly past, does it cease to be actual and become impossible? 

The Ostrich answers in the affirmative.  I think this answer is sustainable only if presentism is true.  Presentism, however, is hard even to formulate (nontrivially), let alone evaluate.  

I must now demand of the Ostrich that he come clean and tell us whether he is indeed a presentist.  If I am not mistaken most if not all of the medieval philosophers he studies are presentists; if so, he may be unaware that there are alternatives to ptesentism.  It may just seem obvious to him when it ought not seem obvious to him. 

God, Necessity, and Truth

Jacques e-mails:

You think that if God exists, He exists necessarily, and if He does not exist, He does not exist necessarily.  But suppose that God does not exist.  We agree, I think, that we can't rationally rule out the possibility?  For instance, you've often argued that our evidence doesn't settle the question of theism versus atheism.  But then, supposing that God doesn't exist, and supposing that He might not exist in the actual world (for all we know), isn't it evident that regardless there are lots of truths?  For instance, even if God does not exist, it would still be true that He does not exist, or that He does not exist necessarily.  I'm not sure that you'd agree with this, but if you would, shouldn't you also agree that if God does not exist, there are some truths?

That is not quite what I said. I accept what I call Anselm's Insight: if God exists, then he exists necessarily; if he does not exist, then necessarily he does not exist.  What does not exist necessarily might be contingent; what necessarily does not exist is impossible. I know you understand the idea; it is just that your formulation suffers from scope ambiguity. Anselm's Insight, then, is that God is either necessary or impossible. He is necessarily non-contingent. (The non-contingent embraces both the necessary and the impossible.) In the patois of possible worlds, either he exists in every, or in no, world. If you wonder why I don't capitalize 'he,' it is because I hold that while piety belongs in religion, it does not belong in philosophy of religion.

Agreed, we cannot rationally rule out the possibility of God's nonexistence. I would say we cannot rationally rule it out or rule it in. "But then, supposing that God doesn't exist, and supposing that He might not exist in the actual world (for all we know), isn't it evident that regardless there are lots of truths? "

I would rewrite your sentence as follows:

It is epistemically possible that God not exist. Nevertheless, it is evident that there are truths.

I agree with the rewrite.  It is evident that there are truths, but for all we can claim to know, God does not exist. But this leaves open how God and truth are related.  Here are five different views:

1) There is truth, but there is no God.

2) There is truth, and there is God, but God is not the ontological ground of truth.

3) There is truth, there is God, and truth ultimately depends on the existence of God. There is truth because there is God.

4) There is no truth, because there is no God.

5) There is God, but no truth.

Ad (1). This I would guess is the view of  many. There are truths, and among these truths is the truth that God does not exist.  This, I take it, would be the standard atheist view.

Ad (2). This, I take it, would be the standard theist view among analytic philosophers.  Consider a philosopher who holds that God is a necessary being and also holds that it is necessarily the case that there are some truths, but would deny the truth of the subjunctive conditional, If, per impossibile, God were not to exist, then truths would not exist either. 

Ad (3). This is the view that I am inclined to accept.  Thus I would affirm the subjunctive conditional lately mentioned. The difference between (2) and (3) is subtle. On both sides it is held that both God and truths are necessary, but the Augustinian — to give him a name — holds that God is the ultimate  'source' of all truth and thus all intelligibility, or, if you prefer, the ultimate 'ground' of all truth and intelligibility.

Ad (4). This is Nietzsche's view.  

Ad (5). I have the impression that certain post-Nietzschean POMO-heads hold this. It is view not worth discussing.

I should think only the first three views have any merit.  

Each of the three has difficulties and none of the three can be proven.

I will mention quickly a problem for the admittedly plausible first view.  

Among the truths there are necessary truths such as the laws of logic. Now a truth is a true truth-bearer, a true proposition, say. Nothing can have a property unless it exists. (Call this principle Anti-Meinong). So no proposition can have the property of being true unless the proposition exists. A necessary truth is true in every metaphysically possible world. It follows that a necessarily true proposition exists in every possible world including worlds in which there are no finite minds.  But a proposition is a thought-accusative that cannot exists except for a mind.  If there is no God, every mind is contingent. A contradiction ensues: there is a world W such that, in W, there exists a thought-accusative that is not the thought-accusative of any mind.

Here are some ways an atheist might 'solve' the problem:

a) Deny that there are necessary truths.

b) Deny that truth is any sense a property of propositions.

c) Deny Anti-Meinong.

d) Deny that propositions are thought-accusatives; accept some sort of Platonism about propositions.

But each of these denials involves problems of its own which I would have no trouble unpacking.

 What say you, Jacques?

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Maverick Philosopher: God, Truth, Reality Denial: A Response to Some Questions
Maverick Philosopher: Lukáš Novák on Use and Mention

Four Types of Ontological Egalitarianism

There are egalitarians in ontology as there are in political theory.

Herewith, four types of ontological egalitarianism: egological, spatial, temporal, and modal.

Egological egalitarianism is the view  there is a plurality of equally real selves.  I take it we are all egological egalitarians in sane moments. I'll assume that no one reading this thinks, solipsistically, that he alone is real and that others, if they exist at all, exist only as merely intentional objects for him. The problem of Other Minds may concern us, but that is an epistemological problem, one that presupposes that there are other minds/selves. On ontological egalitarianism, then, no self enjoys ontological privilege.

Spatial egalitarianism is the that there is a plurality of equally real places.  Places other than here are just as real as the place picked out by a speaker's use of 'here.'  I take it we are all spatial egalitarians.  No one, not even a Manhattanite, thinks that the place where he is is the only real place.  Here is real but so is yonder.  No place enjoys ontological privilege. All places are equal. 

Temporal egalitarianism is the view that there is a plurality of equally real times.  Times other than the present time are just as real as the present time. No time enjoys ontological privilege, which implies that there is nothing ontologically special about the present time. All times are equal. No time is present, period.  This is called the B-theory of time. Here is a fuller explanation.

Modal egalitarianism is the view that there is a plurality of equally real possibilities.  Possibilities other than those that are actual are just as real as those that are actual. It is plausible to think of possibilities as coming in maximal or 'world-sized' packages.  Call them possible worlds.  On modal egalitarianism, then, all possible worlds are equally real.  No world enjoys ontological privilege.  Our world, the world we take to be actual, is not absolutely actual; it is merely actual for us, or rather, actual at itself.  But that is true of every world: each is actual at itself. No world is actual, period.  In respect of actuality, all possible worlds are equal. 

What is curious about these four types of ontological egalitarianism is that, while the first two are about as close to common sense as one is likely to get, the second two are not.  Indeed, the fourth will strike most people as crazy. Was David Lewis crazy?  I don't know, but I hear he was a bad driver. 

Related: Philosophers as Bad Drivers?

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What is Potentiality? An Exploration

On Possibility

 David Brightly comments:

The view I've arrived at is that sentences involving 'possibility' can be re-written into sentences involving just 'possibly', and that our modal notions arise from our encounter with inference. I'm happy to say, There is the possibility that the bulb will shatter — we say things like that all the time — provided it's understood to mean, Possibly, the bulb will shatter. I certainly don't want to commit myself to things called possibilities, unless they can be seen as constructions out of sentences, roughly, Possibly, S ≡ The truth value of sentence S cannot be determined from what we currently know together with deduction from known principles.

Can you persuade me otherwise? A 'big topic' I would imagine!

LightbulbLet B be an ordinary light bulb. Light bulbs are typically fragile: they are disposed to shatter if suitably struck or dropped from a sufficient height onto a hard surface. I take Brightly to be saying two things.  He is maintaining, first, that there is no more to the possibility of B's shattering in circumstances C than the truth of the sentence, 'Possibly, B will shatter in C.' Second, he is offering an analysis of 'possibly' in such sentences.

First Claim

I take Brightly to be saying that there is nothing in B, and thus nothing in reality, that could be called B's disposition to shatter. In general, unrealized possibilities have no ontological status. But then what makes the sentence 'Possibly, B shatters in C' true? Presumably, Brightly will say that nothing makes it true: it is just true.  He would not, I take it, say the same about 'B exists.'  He would not say that nothing makes 'B exists' true, that the sentence is just true.  I would guess that he would say that it is B itself, or perhaps the existence of B, that makes 'B exists' true.  So there is something in reality that 'B' names, and this item is, or is part of, the truth-maker of 'B exists.'  

But if he says this, should he not also admit that there is something in reality that make 'B is disposed to shatter in C' true? 

To appreciate the point one must see that a disposition and its manifestation are different.  B is disposed to shatter at every time at which it exists.  But it needn't ever shatter.  It might remain intact throughout its career.  Therefore, the reality of a disposition cannot be identified with its actual manifestation.  The same goes for powers and potentialities.  If a man has a power he never exercises, it does not follow that he does not have the power.  The potentiality of a seed to sprout in the right conditions is something real even if the seed remains on a shelf and its potentiality is never actualized.  

There is an epistemological question that I want to set aside lest it muddy the waters. The question is: How does one know de re, of a particular light bulb, that it is disposed to shatter if it never does?  I am not concerned here with the epistemology of modal knowledge, but with the ontology of the merely possible, which includes the ontology of unmanifested dispositions.

A disposition, then, is real whether or not it is ever manifested. But doesn't this just beg the question against Brightly? I maintain that unmanifested dispositions are real.  Brightly denies this. If I understand him, he is eliminating unmanifested dispositions in favor of the truth of possibility sentences.

My objection to this invokes the Truth-Maker Principle: truths need truth-makers.  Or at least many classes of truths need truth-makers, one of these being the class of truths about the powers, potentialities, dispositions, and the like of concrete individuals. (I am not a truth-maker maximalist.) My point against Brightly is that the sentence, 'Possibly, B shatters in C,' if true, is true in virtue of or because of something external to this sentence, namely, the unmanifested disposition in B to shatter.

My view is consistent with the view that unmanifested dispositions reduce to the so-called 'categorical' features of things like light bulbs. Unmanifested dispositions can be real without being irreducibly real. What I have said above does not commit me to irreducibly real dispositions.  It commits me only to the reality of unmanifested dispositions, whether reducible or not.

Second Claim

" Possibly, S ≡ The truth value of sentence S cannot be determined from what we currently know together with deduction from known principles."

S in Brightly's example is 'The bulb will shatter.' True or false? I grant that the truth value cannot be known from what we currently know together with what we can deduce from known principles.  But this cannot be what the possibility that the glass will shatter consists in. Brightly is making the very real possibility that the glass shatter, the bomb explode, the round fire, the cat scratch, Hillary throw a lamp at Bill, etc., depend on our ignorance.  But then real possibility is eliminated in favor of epistemic possibility.

Suppose Sally knows that Tom is in Boston now and believes falsely that Scollay Square still exists.  I ask Sally: is it possible that Tom is in Scollay Square now?  She replies, "Yes, it is possible." But of course this is a mere epistemic possibility sired by Sally's ignorance. It is possible for all Sally knows. It is not really possible that Tom is in Scollay Square now given that the place no longer exists.

I don't think we should say that the possibility of the bulb's shattering consists in our igntrance as to whether or not 'The bulb will shatter' is true or false. Consider also that long before minded organisms arose in our evolutionary history, and thus long before there was knowledge or ignorance,  there we seeds and such with real potencies some of which were actualized and some of which were not.  

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Bertrand Russell: Empiricism is Self-Refuting. Is He Right?
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The Necessity of Identity: A Puzzle and a Challenge

The Opponent comments in black; my responses are in blue:

Here is the puzzle: how can we establish the necessity of identity without appealing to principles which are either insufficient, or which are not universally valid? The principle of identity (necessarily, a = a) is not sufficient. We agree that necessarily, Hesperus is identical with Hesperus. That planet could not be numerically different from itself in any circumstance. But the question is whether necessarily, Hesperus is identical with Phosphorus. You will object that if H = P, then necessarily, H = P, because necessarily, H = H. is H. I reply: this begs the question. Under what law of logic or reasoning does nec (H = H) imply nec (H = P)? The principle of identity is insufficient on its own to establish necessity of identity.

BV:  This seems correct.  There is no immediate valid inference from the principle of identity to the necessity of identity.  The inference would seem to be  valid only in the presence of auxiliary 'mediating' premises.

But let me play the role of advocatus diaboli.  We know empirically that H = P. And we know a priori about the identity relation. We know that it is an equivalence relation (reflexive, symmetric, transitive). We also know that it is governed by the Indiscernibility of Identicals  (InId) which states that for any x, y, if x = y, then whatever is true of x is true of y and vice versa.  InId is not a principle external to the notion of (numerical) identity, but part of what we mean by 'identity.'  Obviously, if two putatively distinct items are one item, i.e., are identical, then whatever is true of the one is true of the other, and vice versa.  We would never apply the concept of identity to any thing or thing that violated InId.

So if we know that H = P, then we know that in reality (i.e., extralinguistically, and extramentally) there is just one thing where H and P are.  Call this one thing 'V.'   We know from the principle of identity that necessarily, V = V.  Now suppose, for reductio, that it is not the case that necessarily, H = P.  Suppose, in other words that possibly, ~(H = P).  One would then be supposing that the identity of H and P is contingent.  But that is to suppose that the identity of V with itself is contingent, which is absurd. Therefore, the necessity of identity holds.

So it appears that I have validated the inference from the the principle of identity to the necessity of identity by adducing premises that are well-nigh self-evident.  One of my supplementary premises is that we know some such truths as that H = P.  I also assumed that if x = y, then there are not two things denoted by 'x' and 'y,' but one thing.  I also assumed that when we use terms like 'H' and 'P' we are referring to things in reality with all their properties and relations and not to items like sense data or Husserlian noemata or Castanedan guises or any sort of incomplete object or epistemic deputy.  I am assuming that our thought and talk about planets and such reaches right up to the thing itself and does not stop short at some epistemic/doxastic intermediary.

And now back to the Opponent:

What if ‘Hesperus’ means exactly the same thing as ‘Phosphorus’? This is the principle of Semantic Identity. Then it certainly follows that nec (H = H) implies nec(H = P), because both statements mean exactly the same thing. But does ‘Hesperus’ mean exactly the same thing as ‘Phosphorus’? Surely not. When the names were given, when those planets were dubbed, people understood the meaning of both names perfectly. But while they understood that H=H, they did not understand that H=P. The names cannot have meant the same. So the assumption of semantic identity does not hold.

BV:  That's right.  The names do not have the same Fregean sense (Sinn). This is why 'H = H' and 'H = P' do not have the same Fregean cognitive value (Erkenntniswert).  To know one is to know an instance of the principle of identity.  It is to know a logical truth.  To know the other is to know a non-logical truth, one that is synthetic a posteriori in Kant's sense.

Finally, let’s try the principle of substitutivity, which states that Fa and a = b implies that Fb. Then let F be ‘nec (a = –)’. The principle of identity says that nec(a = a), i.e. Fa. Then if a = b, the principle of substitutivity says that Fb, i.e. nec(a = b). This is valid, but is the principle of substitutivity valid? There are many counterexamples to this, so we cannot assume it is valid. You will object that the principle of substitutivity may be invalid for a type of necessity known as ‘epistemic necessity’, but valid for a type of necessity known as ‘metaphysical necessity’. I reply: under what assumption or principle can you justify that substitutivity is valid for metaphysical necessity, when it is clearly not valid for other types of necessity. You object: we shall define metaphysical necessity as that type of necessity for which substitutivity is valid. I reply: how do you know that anything whatsoever fits that definition? You need to establish that the principle of substitutivity holds for some kind of necessity, without assuming the principle of substitutivity itself. But of course you can’t. If this were possible, Marcus and Quine would have been able to prove the necessity of identity without having to assume substitutivity. But they couldn’t.

BV:  it is true that there are counterexamples to the principle of substitutivity in the 'wide open' formulation that the Opponent provides. Sam can believe that Hesperus is a planet, not a star, without believing that Phosphorus is a planet, not a star, despite the fact that Hesperus = Phosphorus.  So the following is a non sequitur:

Hesperus has the property of being believed by Sam to be a planet.
Hesperus = Phosphorus.
Ergo
Phosphorus has the property of being believed by Sam to be a planet.

This example is also a counterexample to the Indiscernibility of Identicals which is presumably equivalent to the substitutivity principle.  I think that should worry us a bit.

To appreciate the dialectical lay of the land it may help to set forth the problem as an aporetic tetrad:

A. InId:  For any x, y, if x = y, then whatever is true of x is true of y and conversely.
B. Hesperus = Phosphorus.
C. It is true of Hesperus that it is believed by Sam to be a planet.
D. It is not true of Phosphorus that it is believed by Sam to be a planet.

The tetrad is inconsistent: any three limbs entail the negation of the fourth.  One could solve the problem by rejecting InId in its wide-open or unrestricted formulation.  What speaks against this solution is that InId in its unrestricted formulation is part and parcel of what we mean by '=.'  If you were trying to explain to a student what relation '=' stands for, you couldn't just say that it stands for an equivalence relation since not every such relation is picked out by '=.'  You would have to bring in InId.

A second way to solve the tetrad is by denying (B).  It can be true that H is the same as P without it being the case that H = P.  Note that '=' is not a bit of ordinary language; it is a terminus technicus.  One can't just assume that the only type of sameness is the sameness denoted by '=.'  Suppose we distinguish between formal identity statements of the form a = a and material identity statements of the form a =* b.  While both are equivalence relations, the former are necessary while the latter are contingent.  We can then say that H and P are materially identical and thus contingently the same.  Because they are contingently the same, they are not one and the same.  H and P are together in reality but are nonetheless distinct items.  If so, (C) and (D) can both be true in the presence of InId/Substitutivity.

At this point I ask the Opponent whether his denial of the necessity of identity amounts to an affirmation of the contingency of the relation picked out by '=,' or whether it amounts to a rejection of the relation picked out by '=.'  It seems to me that if you admit that there is a relation picked out by '=,' then you must also admit that it holds noncontingently in every case in which it holds.

One could hold the following view.  There is a relation picked out by '=.' Call it formal identity.  It holds of everything.  But no synthetic identity statement is noncontingently true if true.  No such statement is reducible to the form a = a. All are contingently true if true.  So 'Hesperus is Phosphorus' is contingently true, and what the names refer to are distinct items.  They refer directly to these items.  But these items are something like Castaneda's ontological guises or Butchvarov's objects.   

My problem is therefore that we cannot establish the identity of necessity without appealing to principles which are either insufficient (the principle of identity) or which are not universally valid (the principles of semantic identity and substitutivity). We could of course assume it as a sort of bedrock, a truth which is obviously true in its own right, a per se nota principle which requires no further demonstration. But I am not sure it is such a truth. It’s not obvious to me, for a start.

So my challenge to Bill and others is to demonstrate necessity of identity by appeal to principles of reasoning which are stronger than the ones given above, or by demonstrating its self-evidence. Neither will work, in my view.

BV:  It seems to me I gave a reductio-type demonstration in my first comment. The paradigm cases of the relation picked out by '=' are the cases of the form a = a.  Now if 'H' and 'P' designate one and the same entity, then what appears to be of the form a = b, reduces to the form a = a.  Clearly, if a = a, then necessarily a = a.  The assumption that the identity of H and P is contingent entails the absurdity that a thing is distinct from itself. Therefore the relation denoted by '=' holds necessarily in every case in which it holds. Q. E. D.

Note that I didn't use Substitutivity/Inid or Semantic Identity in this reductio.   But I did assume that there is a relation picked out by '=' — which is not obvious! — and that it is this relation that the 'is' expresses in the synthetic truth 'H is P.'  Which is also not obvious!

Identity and Quasi-Epistemic Contingency

The Opponent sends the following puzzle to vex us:

Story: there was someone called 'a', and there was someone called 'b'.

This is all we have of the story. Let the predicate F be 'The story is consistent with a
not being identical with ___'. Then clearly Fa is false, and Fb is true. 

This is the case even if a, in fact, is identical with b.

Is there a puzzle here?  It may be only a malformed attempt at a puzzle. We are presented with a very short story consisting of exactly two claims.  We are given no information as to whether the person called 'a' is the same as or different from the person called 'b.'  So the story allows for the possibility that the person called 'a' is not the same as the person called 'b.'  This is the case even if, in fact, outside the story, it is not the case that a = b.

It is not clear that there is a puzzle here since the following propositions are logically consistent:

A. Within the story, it is possible that the person called 'a' is not the same as the person called 'b.' 
B.  It is the case that a = b.
C. For any x, y, if x = y, then necessarily, x = y.  (Kripke's Necessity of Identity thesis)

It is the presence of the story operator in (A) that saves the triad from inconsistency.

Suppose 'Axwell' and 'Buswell' are the two names in the story and that both refer to an existing man, the same man.  That a = b is no part of the story.  Given only what we know from the story it is possible that a not be identical to b.  But this possibility is something like an epistemic possibility which, as such, cannot be used to show the real (non-epistemic) possibility that a not be identical to b in reality.

So on this New Year's Day I tax the Noble Opponent with a metabasis eis allo genos (μετάβασις εἰς ἄλλο γένος), which is something like a Rylean category mistake: he shifts illicitly from a story-immanent perspective to a story-transcendent perspective. Within the story there is a story-immanent contingency as to both the identity and the difference of the referents of the names.  But this is a sort of epistemic contingency consequent upon the fact that literary fiction leaves much indeterminate: the literary characters have all and only the properties assigned to them in the story.  

So it looks as if the Opponent may be conflating a sort of epistemic contingency with real contingency.  He does not have the makings of a sound argument for the claim  that real-world identities are contingent, contra Kripke.

By contrast, the following triad is plainly inconsistent.  This is the case whether we take names to be Kripkean rigid designators or Russellian definite descriptions in disguise. 

A*. Possibly, it is not the case that a = b.
B. It is the case that a = b.
C. For any x, y, if x = y, then necessarily, x = y.   

Related articles
Theism Meets Metaphysical Naturalism
Modal Axioms
Maverick Philosopher: Contingent and Necessary
Tropes as Truth-Makers? Or Do We Need Facts?
Nothing is Written in Stone
Bertrand Russell: Empiricism is Self-Refuting. Is He Right?
The Decline of the Culture of Free Discussion and Debate

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?

Of Birth and Barcan

The Opponent writes,

"Death is not an end to existence, but the process of becoming non-concrete. Birth is the making concrete of something that has existed since the beginning of time and will exist until the end of time." (Reina Hayaki)

This is one way of interpreting the Barcan formula (possibly for some x Fx implies for some x possibly Fx).  If the formula is true, there are no ‘contingent objects’, i.e. no objects that exist in some worlds but not others.

My position is that there are contingent entities (as well as contingent identities). I imagine you will be less sympathetic to this, however. Interested in your thoughts.

The Opponent is misrepresenting Professor Hayaki's view.  On a careful reading of her article, the quotation above is not her view but expresses a temporal analog of the modal view of Linsky and Zalta that she is opposing.

Barcan Contrapositive T-ShirtBe that as it may.  Let's consider the Barcan formula by itself.

The formula is that Possibly, something is F implies Something is possibly F.  The modality in question is 'broadly logical' in Plantinga's sense.  Some call it 'metaphysical.'   

By my modal intuitions, the formula is false.  A trio of  'possible' counterexamples.

A. Sally wants a baby.  But there is no actual baby such that Sally wants it.  Sally wants to have a baby, i.e, give birth to a baby, her own baby, one that does not yet exist.  What Sally wants is possible. So, possibly, some baby is such that Sally wants it.  But it doesn't follow that some actual baby is possibly such that Sally wants it. For every actual baby is such that Sally does not want it.

B. It is possible that there be a sinless man.  But it does not follow that one of the men who exist is possibly sinless.  

 

C. Possibly, some sloop satisfies Ortcutt's exacting specifications.  (It is possible that there be such a sloop.)  But it doesn't follow that some existing sloop (without modifications) is possibly such as to satisfy Ortcutt's exacting specifications.  For it could be that every sloop that exists fails to satisfy our man.

I am assuming actualism: there are no merely possible objects.  The truth of Possibly, something is F does not commit us to the existence of a merely possible individual that is F. 'Possibly, something is a matter transmitter,' for example, does not commit us to the existence of a merely possible matter transmitter.  I should think it commits us only to the existence of a conjunctive property that is possibly instantiated.

The Barcan formula may hold for necessary beings such as the number 7.  But it fails for contingent beings.

Of course I hold that there are contingent beings.  Whether there are contingent identities is another topic entirely.  One topic at a time.