Maverick Philosopher

Is the Modal Ontological Argument Rationally Compelling?

I argue that it isn't.

Intentionality, Singularity, and Individual Concepts

Herewith, some notes on R. M. Sainsbury, Intentionality without Exotica.  (Exotica are those items  that are "nonexistent, nonconcrete, or nonactual." (303) Examples include Superman and Arcadia.)

'Jack wants a sloop' could mean three different things. (a) There is a particular sloop Jack wants.  In this case, Jack's desire is externally singular.  Desire is an object-directed mental state, and in this case the object exists and is singular.

(b) There is no particular sloop Jack wants; what he wants is "relief from slooplessness" in Quine's phrase. In this case the desire, being "wholly non-specific," is not externally singular.  In fact, it is not singular at all.  Jack wants some sloop or other, but no particular sloop whether one that exists at present or one that is to be built.

(c) Jack wants a sloop of a certain description, one that, at the time of the initial desire, no external object satisfies. He contracts with a ship builder to build a sloop to his exact specifications, a sloop he dubs The Mary Jane. It turns out, however, that the sloop is never built.  In this case, Sainsbury tells us, the desire is not externally singular as in case (a), but internally singular:

The concept The Mary Jane that features in the content of the desire is the kind of concept appropriate to external singularity, though that kind of singularity is absent, so the desire counts as internally singular. The kind of concept that makes for singularity in thought is one produced by a concept-producing mechanism whose functional role is to generate concepts fit for using to think about individual things. I call such a concept an ‘‘individual concept’’ (Sainsbury 2005: 217ff). Individual concepts are individuated by the event in which they are introduced. In typical cases, and when all goes well, an act of attention to an object accompanies, or perhaps is a constituent of, the introduction of an individual concept, which then has that object as its bearer. In cases in which all does not go well, for example in hallucination, an individual concept is used by the subject as if it had an object even though it does not; an act internally indistinguishable from an act of attending to an object occurs, and in that act an individual concept without a bearer comes into being. A concept so introduced can be used in thought; for example an individual concept C  can be a component in wondering whether C is real or merely hallucinated. In less typical cases, it is known to the subject that the concept has no bearer. An example would be a case in which I know I am hallucinating.     

    External singularity is relational: a subject is related to an object. Internal singularity is not relational in this way. (301, bolding added.)

 

What interests me here is the notion of an individual concept (IC). We are told above that an IC is distinct from its bearer and can exist without a bearer.  So the existence and identity of an IC does not depend on its having a bearer. We are also told that one and the same IC can figure in both a veridical and a non-veridical  (hallucinatory) experience, the seeing of a dagger, say.  So it is not the bearer that individuates the IC. What individuates it is the mental event by which it is introduced.

 

To these two points I add a third: it is built into the sense of 'individual concept' that if an individual concept C has a bearer, then it has exactly one bearer in the actual world, and the same bearer in every  possible world in which it has a bearer.  So if there is an individual concept SOCRATES, and it has a bearer, then it has exactly one bearer, Socrates, and not possibly anything distinct from Socrates.  This implies that individual concepts of externally singular items are as singular in content as the items of which they are the concepts. This in turn implies that no individual concept of an externally singular item is general:  no such concept is multiply instantiable or multiply 'bearable.'

 

I now add a fourth point: concepts are mental entities in the sense that they cannot exist apart from minds. Concepts are representations and therefore mental entities in the sense indicated.  A fifth point is that our minds are finite and our powers of conceptualization correspondingly limited. One obvious limit on our power to conceptualize is that no concept of ours can capture or grasp the haecceity (thisness) of any externally singular item.  We ectypal intellects cannot conceptually eff the ineffable, where what is ineffable is the individual in its individuality or singularity or haecceity, i.e.,  in that which makes it be this individual and no other actual or possible individual.  God, the archetypal intellect, may be able to grasp the haecceity of an individual, but this is clearly beyond our 'pay grade.' If God can do it, this is presumably because he creates the individual ex nihilo.

 

It follows from the fourth and fifth points that all of our concepts are general.  Suppose that the concept FASTEST MARATHONER (FM) applies to Jones. That concept is general despite the fact that at any given time t only one person can instantiate or bear it.   For at times earlier and later than t, some other runners were and will be the FM.  Therefore, FM does not capture Jones' haecceity. But even if Jones is the FM at every time in the actual world, there are possible worlds in which some other person is the FM at every time. What's more, at any time at which Jones is the FM, he might not have been the FM at that time.

 

Sainsbury's theory of individual concepts strikes me as incoherent.  The following cannot all be true:

 

1) There are individual concepts.

2) Concepts are representations in finite minds, and our minds are finite.

3) Individual concepts of externally singular items must be as singular in content as the items of which they are the concepts.

4) Every externally singular item exists. (There are no 'exotica.')

5) Every externally singular item is wholly determinate or complete where x is complete =_df x  satisfies the property version of the Law of Excluded Middle (tertium non datur).

6) No concept in a finite mind of an externally singular item is singular in content in the sense of encoding every property of the wholly determinate or complete thing of which it is the concept.

7) One and the same individual concept can figure in both a veridical and a non-veridical  (hallucinatory) experience.

 

Sainsbury is committed to each of these seven propositions, and yet they cannot all be true. The first five propositions, taken in conjunction, entails the negation of (6).   Or if (6) is true, then (1) is false.  (6) and (7) cannot both be true.

 

I conclude that there are no individual concepts, and that the distinction between externally singular and internally singular object-directed mental states cannot be upheld.  

Why I Reject Individual Concepts

This entry was first posted on 24 July 2011. Time for a repost with minor modifications. I find that I still reject individual concepts. Surprise!

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Consider the sentences 'Caissa is a cat' and 'Every cat is an animal.'  Edward the Nominalist made two  claims in an earlier comment thread that stuck in my Fregean craw:

1) The relation between 'Caissa' and 'cat' is the same as the relation between 'cat' and 'animal'.

2) The relation between *Caissa* and *cat* is the same as the relation between *cat* and *animal.*

Single quotes are being used in the usual way to draw attention to the expression enclosed within them.  Asterisks are being used to draw attention to the concept expressed by the linguistic item enclosed within them.  I take it that we agree that concepts are mental in nature in the sense that, were there no minds, there would be no concepts. 

Affirming (2), Edward commits himself to individual or singular concepts.  I deny that there are individual concepts and so I reject (2).  Rejecting (2), I take the side of the Fregeans against the traditional formal logicians (TFL-ers) who think that singular propositions can be analyzed as general.  Thus 'Caissa is a cat' gets analyzed by the TFL-ers  as 'Every Caissa is a cat.'

To discuss this profitably we need to agree on the following definition of 'individual concept':

D1. C is an individual concept of x =_df x is an instance of C, and it is not possible that there be a y distinct from x such that y is an instance of C.

So if there is an individual concept of my cat Caissa, then Caissa instantiates this concept and nothing distinct from Caissa does or could instantiate it. We can therefore say that individual concepts, if there are any, 'capture' or  'grasp' or 'make present to the mind' the very haecceity (non-qualitative thisness) of the individuals of which they are the individual concepts.

We can also speak of individual concepts as singular concepts and contrast them with general concepts.  *Cat* is a general concept.  What makes it general is not that it has many instances, although it dos have many instances, but that it can have many (two or more) instances.  General concepts are thus multiply instantiable. 

The concept C1 expressed by 'the fattest cat that ever lived and ever will live' is also general.  For, supposing that Oscar instantiates this concept, it is possible that some other feline instantiate it.  Thus C1 does not capture the haecceity of Oscar or of any cat.   C1 is general, not singular.  C1 is multiply instantiable in the sense that it can have two or more instances, though not in the same possible world or at the same time. 

And so from the fact that a concept applies to exactly one thing if it applies to anything, one cannot validly infer that it is an individual or singular concept.  Such a concept must capture the very identity or non-qualitative thisness of the thing of which it is a concept.  This is an important point.  To push further I introduce a definition and a lemma.

D2. C is a pure concept =_df C involves no specific individual and can be grasped without reference to any specific individual.

Thus 'green,' 'green door,' 'bigger than a barn,' 'self-identical,'  and 'married to someone' all express pure concepts.  'Taller than the Washington Monument,' 'married to Heidegger,' and 'identical to Heidegger' express impure concepts, if they express concepts at all. 

Lemma 1: No individual concept is a pure concept.

Proof.  By (D1), if C is an individual concept of x, then it is not possible that there be a y distinct from x such that y instantiates C.  But every pure concept, no matter how specific, even unto maximal specificity, is possibly such as to have two or more instances.  Therefore, no individual concept is a pure concept.  

Consider the famous Max Black example of two iron spheres alike in all monadic and relational respects.  A pure concept of either, no matter how specific, would also be a pure concept of the other.  And so the non-qualitative haecceity of neither would be captured by that pure concept.

Lemma 2.  No individual concept is an impure concept.

Proof.  An individual  concept is either pure or impure.  If C is impure, then by (D2) it must involve an individual.  And if C is an individual concept it must involve the very individual of which it is the individual concept. But individuum ineffabile est: no individual can be grasped precisely as an individual.  But that is precisely what one would have to be able to do to have an impure concept of an individual.  Therefore, no individual concept is an impure concept.

Putting the lemmata together, it follows that an individual concept cannot be either pure or impure.  But it must be one or the other.  So there are no individual concepts. Q. E. D.!

On God's Not Falling Under Concepts

Fr. Deinhammer tells us,  ". . . Gott fällt nicht unter Begriffe, er ist absolut unbegreiflich. . . ." "God does not fall under concepts; he is absolutely inconceivable or unconceptualizable. . . ."

Edward the Logician sent me an e-mail in which he forwards a stock objection:

Who is it who is absolutely inconceivable or unconceptualizable? Either ‘he’ tells us, or not. If so, the proposition is false. If not, the proposition is incoherent.

I appreciate that you are quoting the person who wrote to you, but my aporia stands.

Ed's aporetic point can be summed up as follows. Talk of God as inconceivable is either false or meaningless. If the person who claims that God is inconceivable is operating with some concept of God, then the claim is meaningful but false. If, on the other hand, the person is operating with no concept of God, then saying that God is inconceivable is no better than saying that X is inconceivable, which says nothing and is therefore meaningless. (X is inconceivable is at best a propositional function, not a proposition, hence neither true nor false. To make a proposition out of it you must either bind the free variable 'x' with a quantifier or else substitute a proper name for 'x.')

A Response to the Objection

Suppose we make a distinction between those concepts that can capture the essences or natures of the things of which they are the concepts, and those concepts that cannot. Call the first type ordinary concepts and the second limit concepts (Grenzbegriffe). Thus the concept cube captures the essence of every cube, which is to be a three-dimensional solid bounded by six square faces or sides with three meeting at each vertex, and it captures this essence fully.   The concept heliotropic plant captures, partially,  the essence of those plants which exhibit diurnal or seasonal motion of plant parts in response to the direction of the sun.

Now the concept God cannot be ordinary since this concept cannot capture the essence of God. For in God essence and existence are one, and there is no ordinary concept of existence.  (The existence of a thing, as other than its essence, cannot be conceptualized.) Again, in God there is no real distinction between God and his nature, whereas no ordinary concept captures the individuality of the thing of which it is the concept. Since God is (identically) his nature, there can be no ordinary concept of God.

There is, then, a tolerably clear sense in which God is unconceptualizable or unbegreiflich: he cannot be grasped by the use of any ordinary concept. But it doesn't follow that we have no concept of God.  The concept God is a limit concept: it is the concept of something that cannot be grasped using ordinary concepts. It is the concept of something that lies at the outer limits of discursive intelligibility, and indeed just beyond that limit. We can argue up to this Infinite Object/Subject, but then discursive operations must cease. We can however point to God, in a manner of speaking, using limit concepts. The concept God is the concept of an infinite, absolute and wholly transcendent reality whose realitas formalis so exceeds our powers of understanding that it cannot be taken up into the realitas objectiva of any of our ordinary concepts.

If this is right, then there is a way between the horns of the above dilemma. But of course it needs further elaboration and explanation.

On Conceiving that God does not Exist

In a recent post you write:

The Humean reasoning in defense of (3) rests on the assumption that conceivability entails possibility.  To turn aside this reasoning one must reject this assumption.  One could then maintain that the conceivability by us of the nonexistence of God is consistent with the necessity of God's existence.

I’m not convinced this is right. Conceivability has a close analogue with perception. If it seems to S that p, then S is prima facie justified in believing that (actually) p. So consider cases of perceptual seemings. Care must be taken to distinguish two forms of negative seemings:

1. It does not seem that p.
2. It seems that ~p.

Clearly, (1) is not properly a seeming at all; it is denying an episode of seeming altogether. If I assert (1), me and a rock are on epistemic par with respect to it seeming to us that p. (2) also faces an obvious problem: how could ~p, a lack or the absence or negation of something, appear to me at all? Photons do not bounce off of lacks. There are ways around this, but for now I just want to register the distinction between (1) and (2) and the prima facie difficulties with them that do not attend to positive seemings.

 

BV:  Excellent so far, but I have one quibble.  Suppose I walk into a coffee house expecting to encounter Pierre.  But Pierre is not there; he is 'conspicuous by his absence' as we say.  There is a sense in which I perceive his absence, literally and visually, despite the fact that absences are not known to deflect photons.  I see the coffee house and the people in it and I see that not one of them is identical to Pierre. So it is at least arguable that I literally see, not Pierre, but Pierre's absence.

 

Be this as it may.  You are quite right to highlight the operator shift as between (1) and (2).

So now consider conceivability. The analogue: If it is conceivable to S that p, then S is prima facie justified in believing that possibly p. Now for our two negative conceivablility claims:

1’. It is not conceivable that p.
2’. It is conceivable that ~p.

Again, (1’) is trivial; it is (2’) we’re interested in. Does (2’) provide prima facie evidence for possibly ~p? It depends. What we do when we try to conceive of something is imagine "in our mind’s eye" a scenario—i.e., a possible world—in which p is the case.  So really (2’) translates:

2’’. I can conceive of a possible world in which ~p.

 

BV:  Permit me a second quibble.  Although 'conceive' and 'imagine' are often used, even by philosophers, interchangeably, I suggest we not conflate them.  I can conceive a chliagon, but I cannot imagine one, i.e., I cannot form a mental image of a thousand-sided figure.  We can conceive the unimaginable.  But I think we also can imagine the inconceivable. If you have a really good imagination, you can form the mental image of an Escher drawing even though what you are imagining is inconceivable, i.e., not thinkable without contradiction.

 

More importantly,  we should avoid bringing possible worlds into the discussion.  For one thing, how do you know that possibilities come in world-sized packages?  Possible worlds are maximal objects.  How do you know there are any?  It also seems question-begging to read (2') as (2'') inasmuch as the latter smuggles in the notion of possibility.

 

Given that the whole question is whether conceivability either entails or supplies nondemonstrative evidence for possibility, one cannot help oneself to the notion of possibility in explication of (2').  For example, I am now seated, but it is conceivable that I am not now seated: I can think this state of affairs witout contradiction.  The question, however, is how I move from conceivability to possibility.  How do I know that it is possible that I not be seated now?

 

It is obvious, I hope, that one cannot just stipulate that 'possible' means 'conceivable.'

 

(2'') seems innocent enough, but whether it gives us prima facie evidence for possibly ~p will depend on what p is; in particular, whether p is contingent or necessary. Consider:

3. There is a possible world in which there are no chipmunks.
4. There is a possible world in which there are no numbers.

(3) seems totally innocent. I can conceive of worlds in which chipmunks exist and others in which they don’t.

 

BV:  It seems you are just begging the question.  You are assuming that it is possible that there be no chipmunks.  The question is how you know that.  By conceiving that there are no chipmunks?

 

(4), on the other hand, is suspect. This is because numbers, unlike chipmunks, if they exist at all exist necessarily; that is, if numbers do not exist in one world they do not exist in any. Thus, what (4) really says is

(4*) There is no possible world in which there are numbers.

 

BV:  (4) and (4*) don't say the same thing; I grant you, however, that the first entails the second.

With its conceivability counterpart being

(4’) I cannot conceive of a possible world in which there are numbers.

which looks a lot like the above illicit negative seemings: negations or absences of an object of conceivability. But my not conceiving of something doesn't entail anything! But suppose we waive that problem, and instead interpret (4’) as a positive conceiving:

(4’’) It is conceivable to me that numbers are impossible

The problem now is that (4’’) is no longer a modest claim that warrants prima facie justification. In fact, (4*) has a degree of boldness that invites further inquiry: presumably there is some obvious reason—a contradiction, category mistake, indelible opacity—etc. apparent to me that has led me to think numbers are impossible. But if that’s so, then surely my critic will want to know what exactly I’m privy to that he isn’t.

Mutatis mutandis in the case of God qua necessary being.

Thoughts?

 

BV:  You lost me during that last stretch of argumentation.  I am not sure you appreciate the difficulty.  It can be expressed as the following reductio ad absurdum:

 

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 necessary 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)

Ergo

g. God is a necessary being & God is a contingent being. (d, f, contradiction)

Ergo

~a. It is not the case that conceivability entails possibility. 

 

Is short, as John the Commenter has already pointed out, it seems that the Anselmian theist ought to reject conceivability-implies-possibility.

Related articles

An Anselmian Antilogism

 

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.

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.

Does Inconceivability Entail Impossibility?

In an earlier thread James Anderson makes some observations that cast doubt on the standard entailment from inconceivability to impossibility.  (I had objected that his  theological mysterianism seems to break the inferential link connecting inconceivability and impossibility.) He writes,

But even though we have no direct epistemic access to any other inconceivability than our own, and despite the formidable historical pedigree of the idea, it still strikes me as implausible to maintain that inconceivability to us entails impossibility.  [. . .] For the principle in question is logically equivalent to the principle that possibility entails conceivability. But is it plausible to think that absolutely whatsoever happens to be possible in this mysterious universe and beyond must be conceivable to the human mind, at least in principle? Can this really be right?

I want to emphasize that I'm not advocating some form of modal skepticism, i.e., the view that our intuitions as to what is possible or impossible are generally unreliable. On the contrary, I think they're reliable. I just deny that they're infallible.

This does indeed give me pause.  Anderson is certainly right that if inconceivability entails impossibility, then, by contraposition, possibility entails conceivability.  These entailments stand or fall together.  But is it plausible to maintain that whatever is possible is conceivable?  Why couldn't there be possible states of affairs that are inconceivable to us?

But there may be an ambiguity here.  I grant that there are, or rather could be, possible states of affairs that we cannot bring before our minds.  These would be states of affairs that we cannot entertain due to our cognitive limitations.  But that is not to say that a state of affairs that I can bring before my mind and in which I find a logical contradiction is a possible state of affairs.  Thus we should distinguish two senses of inconceivable, where S is a state of affairs and A is any well-functioning finite cognitive agent:

S is inconceivable₁ to A =df A entertains S and finds a contradiction in S.

S is inconceivable₂ to A =df A is unable to entertain (bring before his mind) S.

Now it seems clear that inconceivability₂ does not entail impossibility.  But I should think that inconceivability₁ does entail impossibility.  For if S is contradictory, then that very state of affairs as the precise accusative of my thought that it is, cannot obtain.  Its possibility in reality is ruled out by the fact that it cannot be entertained without contradiction.

Now does possibility entail conceivability?  No, in that the possible need not be thinkable by us: there could be possibilities that lie beyond our mental horizon.  But possibility does entail conceivability if what we mean is that possible states of affairs that we can bring before our minds must be free of contradiction.

So, in apparent contradiction to what Anderson is claiming, I urge that we can be infallibly sure that a state of  affairs in which we detect a logical contradiction cannot obtain in reality.  There is more to reality, including the reality of the merely possible,  than what we can think of; but what we can think of must be free of contradiction if it is to be possible.

Conceivability without contradiction is no infallible guide to possibility.  But inconceivability₁ is an infallible guide to impossibility.  Where Anderson apparently sees symmetry, I uphold the traditional asymmetry.

Conceivability and Epistemic Possibility

My disembodied existence is conceivable (thinkable without apparent logical contradiction by me and beings like me). But does it follow that my disembodied existence is possible? Sydney Shoemaker floats the suggestion that this inference is invalid, resting as he thinks on a confusion of epistemic with metaphysical possibility. (Identity, Cause, and Mind, p. 155, n. 13.)  Shoemaker writes, "In the sense in which I can conceive of myself existing in disembodied form, this comes to the fact that it is compatible with what I know about my essential nature . . . that I should exist in disembodied form.  From this it does not follow that my essential nature is in fact such as to permit me to exist indisembodied form."

We need to think about the relation between conceivability and epistemic possibility if we are to get clear about the inferential link, if any, between conceivability and metaphysical possibility.   Pace Shoemaker, I will suggest that the inference from conceivability to metaphysical possibility need not rest on a confusion of epistemic with metaphysical possibility.  But it all depends on how we define these terms.