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Monday, January 18, 2010


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HEP, interpreted as applying to everything, got to be false. Consider (Ex)(x = 2+2). One sure can conceive of such an x; right. But, could one conceive the nonexistent of such an x while conceiving the existence of 2 and understanding the relevant terms ('+', '=') involved in the equation? I do not see how?

I suppose you could argue conceivability provides good prima facie though defeasible grounds for real possibility, like Moreland said in your post on the Prosblogion, and if problems arise, we would have to think it over some more and see what seems more plausible--that it is really possible, or that it really isn't.

When we ask whether some state of affairs is logically possible, we simply think about it and see if there are any contradictions we can discern. So, if I wonder if it is logically possible that I be the strongest man on the planet, I simply think about some way the world could have been which would make that true--like, say, if I were the only man on the planet--and determine that yes, it is possible.

If we stop and think about its being possible that I survive the destruction of my body, and I discern no real contradictions, then I should conclude for the time being that yes, indeed, it is possible.

You bring up the issue of the conceivability of the nonexistence of a necessary being. Well, in that sort of case when we run into modal troubles, we simply have to back up our intuitions with other sorts of evidence and see which is more plausible: that it really is possible that such a being exist, or that it really is possible that such a being not exist.

But if there are no such problems in the case of the conceivability of my existing without my body, then I don't see why we shouldn't just take the conceivability of such a state of affairs as being reason sufficient--for the time being--of its being possible, and why the materialist shouldn't have to then accept the argument. We don't normally require extra evidence in discerning whether or not it is possible that I be the strongest man on the face of the planet; why not also in other cases where we don't right away run into any modal problems?

Dr. Vallicella:

"Clearly, much depends on what we mean by 'conceivable.' Trading Latin for Anglo-Saxon, to be conceivable is to be thinkable. But since there is a sense in which logical contradictions are thinkable . . ."

I found this interesting. Could I trouble you to expound the "sense in which" to which you refer?


I wonder if your suggestion would only pose a difficulty for a realist about numbers, or, for that matter, a realist about all abstracta. (Suppose the realist considers the proposition HEP to be an abstract object A, such that the existence of A serves as the truthmaker for HEP. By conceiving of the nonexistence of A, the realist removes from her ontology HEP's truthmaker.) Even then, however, I suspect that the realist might insist that conceiving of the nonexistence of x must be accompanied by the conceiving of the nonexistence of 2. For as you note, it appears impossible to conceive of x's nonexistence while conceiving of 2's existence (along with the relevant understanding of the terms).


-- Marc

This argument appears to be lifted from Plantinga's 'Against Materialism'.
This is part one of the paper that presents what he refers to as the 'replacement argument'. He briefly describes it like this:
"The general strategy of this first argument is as follows. It seems possible that I continue
to exist when B, my body, does not. I therefore have the property possibly exists when B does
not. B, however, clearly lacks that property. By Leibniz' Law, therefore (more specifically, the
Diversity of Discernibles), I am not identical with B. But why think it possible that I exist when
my body does not? Strictly speaking, the replacement argument is an argument for this premise.
Again, I conduct the argument in the first person, but naturally enough the same goes for you
(although of course you will have to speak for yourself)." Plantinga,Alvin, 'Against Materialism', p.3


So far as I recall Hume endorsed a version of HEP only regarding what he called "matters of fact". Hume himself did not extend the principle to existents obtained based on reason. Matters of fact here is equivalent to contingent existents. So my comment above merely points out the problematic nature of an unrestricted version of HEP.

However, even in the realm of the contingent HEP may face some difficulties. Consider an example such as this: my fall broke the vase. Then the breaking of the vase is an effect of my fall. Can we conceive of the breaking of the vase as an *effect* while at the same time conceiving of no cause that caused the vase to break: i.e., that no cause exists that broke the vase? I don't think that we can conceive such a thing. If one conceives of the breaking of the vase as an effect, then one must conceive of some event that caused its breaking, although perhaps one need not conceive of any particular event as that cause. On the other hand, if one just considers the breaking of the vases as merely an *event*, then this is compatible with not conceiving of a cause; perhaps, nothing caused the vase to break. So if we think about the breaking of the vase as an effect, then we must conceive of some cause; if on the other hand we think about it as an event, then we are not compelled to conceive of a cause. This issue quickly leads to a connection between HEP, on the one hand, and the distinction between causal-relations vs. causal-explanations, on the other.

Regarding the mathematical example; of course, one could argue as you propose that one can conceive the nonexistence of x by conceiving the nonexistence of 2; but, then, the question immediately arises whether one can conceive of the nonexistence of 2, given that one conceives that 2 is greater than 1? And so on. So such a move will lead to a wholesale denial that mathematical objects exist and to familiar issues about Platonism in mathematics.

The conclusion, I think, is that HEP is not as innocent as one might initially suppose.

i agree with HEP, "Everything is such that its nonexistence is conceivable."

Online Doctor says:

"i agree with HEP, "Everything is such that its nonexistence is conceivable.""

Well, then, according to you, you could conceive the following: "I conceive that I do not exist."

As I recall, Leibniz thought that the success of the ontological argument hinged on showing that God, a necessary being, was logically possible. The success of such a project would minimally entail demonstrating that there are no inconsistencies or contradictions in the concept.

Is it possible to do that? Imaginable, yes. Conceivable? I don't know. Even if such a project could successfully be undertaken, someone could retort, as Bill implied, "Have you considered that a contradiction might exist here?"

Besides that, pragmatically speaking, the materialist, particularly the eliminative kind, would probably be suspicious of any kind of argument not grounded in a sense datum.

By the way, thanks for posting my cat's picture again. His Highness will be pleased.


Thank you for your nice crisp objection. It is unusual for you to be so pithy. To put your objection more simply, you are asking me whether I can conceive of the nonexistence of the number 4, an abstract entity which, if it exists at all, exists necessarily.

Actually, my formulation of HEP was sloppy. I meant to say that everything concrete is such that its nonexistence is conceivable.

That would accommodate your objection. I am inclined to agree with you that it is inconceivable that there be nothing at all, not even any abstract objects. But nominalists seem to have no trouble conceiving the nonexistence of abstract objects.


Thanks for your question. Contradictions are thinkable in the sense that one can entertain them, i.e., bring them before one's mind for consideration. It is thinkable that snow is white and it is thinkable that snow is not white. And we know how to form conjunctive propositions from any two propositions. So we form the proposition *snow is white and snow is not white* and we think about it. In that sense contradictions are thinkable, able to be thought of. If we weren't able to do this we wouldn't be able to perform reductio ad absurdum reasoning.


The argument is one found (in different forms) in Plantinga, Moreland, Kripke and a number of other contemporaries. Plantinga in the paper you cite points back to Descartes and Augustine. Plantinga's replacement argument deserves a separate discussion in conjunction with van Inwagen's critique of it. http://philosophy.nd.edu/people/all/profiles/van-inwagen-peter/documents/PlantRplArg4.doc


Two distinctions that cut perpendicular to each other and so should not be conflated: contingent/noncontingent and concrete/abstract. God is noncontingent but concrete (where 'concrete' is defined in terms of causal efficacy).

You are right that HEP should not be given the unrestricted formulation that I originally gave it (out of sloppiness). It should be restricted to the concrete. But that is not the same as restricting it to the contingent. God is concrete but not contingent.

Necessarily, no effect without a cause. (Humean relation of ideas, Kantian analytic judgment.) But that an event is an effect is a contingent matter. Surely every event is such that its nonexistence (nonoccurrence) is conceivable. Do you deny that? I of course grant that if an event is an effect, then there must be a cause. But it is contingent that the event be an effect.


The Online Doctor could respond by saying that he can conceive his nonexistence. Using 'OD' as a rigid designator, he thinks to himself: OD might not have existed.

There are very tricky issues here as you well know!


I think that in a suitably restricted form, HEP may be true. In that case, you are correct that either CEP must be false or perhaps both HEP and CEP are false. i.e., conceivability does not entail possibility and everything (suitably restricted) can be conceived as nonexistent. One such restriction must be the Cartesian cogito. Of course, the fact that conceivability does not entail possibility does not mean that we cannot use thought experiments to envision counterfactual circumstances etc.


Please forgive me for posting the cat picture without attribution, but I didn't know your real name and your blog is offline. Tell His Highness that he is well on his way to international fame.

The Leibnizian move from conceivability to possibility is precisely what I am questioning here. Leibniz moved too fast on this one. If I fail to detect a contradiction within my concept of God, there might still be one there that a more penetrating intellect would uncover.


I certainly agree that it is a contingent matter that an event is an effect. What is not contingent (I suppose analytical) is the following: If an event is an effect, there there exists a cause. So if we conceive of an event as an effect, we must conceive that it has a cause. So how do we formulate this:

(a) Nec( if e is an effect, then there exists an e* such that e* causes e.


(b) If e is an effect, then Nec(there exists an e* such that e* causede).

What do you think, which one is the correct formulation?


Re: Online Doctor.
My example was this: "I conceive that I do not exist."

This proposition he cannot conceive, unless he denies the referential status of the pronoun 'I'. Of course, if we replace the pronoun with some other referential expression, then everything changes depending upon the character of the replacing expression. I have made the objection in connection with his claim that everything (unrestricted) can be conceived as nonexistent. When 'everything' is unrestricted, the claim is incoherent (like so many other universal claims).

Is 'I' rigid? I think Kaplan's treatment here is better than Kripke's pure rigidity.


>>I suppose you could argue conceivability provides good prima facie though defeasible grounds for real possibility,<<

Did you read the comment thread over at Prosblogion? The guy Christian had an interesting objection to the notion that conceivability is defeasible evidence of possibility. I'm not sure I understood it, though. That deserves a special post.

Here is the problem in a nutshell. (1) The existence of God and the nonexistence of God cannot both be possible. (This is because God is noncontingent.) But (2) both the existence of God and the nonexistence of God are conceivable, whence it follows (by CEP) that both the existence of God and the nonexistence of God are possible, which contradicts (1). Therefore, conceivability cannot be relied upon as a guide to what is really possible.


The Online Doctor is a spammer, and you took the bait! But the underlying issue re: the cogito is a deep and fascinating one which we will come back to. Your man Katz managed to squeeze a lot out of it.

Right. I suppose all that follows from that problem is that we need to take determining possibility by conceivability on a case-by-case basis; I see no reason to throw out conceivability because of one sticky case dealing with a necessary being. To jump from "our conceiving something to be possible was not reliable in one instance" to "conceivability cannot be relied upon as a guide to what is really possible" is sort of a leap, if you ask me.

Like I said above, unless we run into some modal problems, why not just trust our intuitions and conceivings as sufficient reason for the time being to think that X is possible?

If we did throw conceivability out, how do we determine if anything at all is logically possible? Like Moreland, I can't see any other way.

As for Christian's objection, I'll wait around until you can explicate it (if you ever do); I don't think I understand it completely either.


"Can we conceive of the breaking of the vase as an *effect* while at the same time conceiving of no cause that caused the vase to break: i.e., that no cause exists that broke the vase? I don't think that we can conceive such a thing."

I agree that it doesn't seem conceivable to have an effect in the absence of a cause. (That appears to be necessary in (what Lowe would call) the narrowly logical sense.) I think Hume would concur as well, given the terms involved. But since he wasn't sanguine about causal realism, the problem you raise may not have troubled his HEP. I suspect he might suggest that the causal relations essential to your example don't obtain.

Dr. Vallicella:

Thanks for your response. Your clarification was helpful.

Concerning Christian's objection which you distilled, suppose one claimed that (2) was false and proceeded to support the claim as follows. (I'm not terribly confident, however, in this rejoinder.) Cohering with (1), take the proposition "God exists," which expresses a metaphysically necessary truth. Call this proposition P1. Take another metaphysically necessary proposition, such as "No physical object can be purple all over and orange all over," and call this P2. Christian's objection appears to imply that P1's being false is conceivable. But what about P2? Is it conceivable that a physical object be purple all over and orange all over? This seems inconceivable. Consequently, there may be inductive justification to suppose that metaphysically necessary propositions can't be conceived of as false, appearances notwithstanding. Of course, a problem could arise because P1 refers to a concrete, necessary being, whereas P2 doesn't enjoy this distinction.


-- Marc


The last paragraph of my response to Steven is what I'm saying -- has nothing to do with Christian's point.

But the appearances of noncontraduictoriness are all we have to go on. Conceivability and possibility coincide for God or for the IRS (the ideally rational subject). But none of us are God or the IRS. I grant you that nothing is purple all over and orange all over at the same time, that this is a necessary truth, that its negation is impossible and also inconceivable. I want to go further and say that it is inconceivable to any subject including God. So I admit that there are case in which it seems that conceivability entails possibilty and inconceivability entails impossibility.

But how do we know that any given case it like this case? It might be like the following case. It is conceivable both that 77777 occurs in the decimal expansion of pi and that it doesn't. So both are possible by CEP. But this can't be since math props are necessary.

I agree with Bill over Marc here. This would seem to be the position of Aquinas when he argued that the existence of God is not self-evident to us, though evident in itself, because we do not know the essence of God.

I might also add to my earlier comments that with something like the experience of colors, we see enough of a color's essence through simple perception to know that nothing can simultaneously be orange and purple all over. With other propositions, such as the existence and nature of God or of the self, neither our intellect nor our senses give us enough insight into their natures to enable us to judge accurately whether they are free of contradiction.

Steven comments, " I suppose all that follows from that problem is that we need to take determining possibility by conceivability on a case-by-case basis; I see no reason to throw out conceivability because of one sticky case dealing with a necessary being. To jump from "our conceiving something to be possible was not reliable in one instance" to "conceivability cannot be relied upon as a guide to what is really possible" is sort of a leap . . . ."

First of all, there is more than one case where the C-P inference is invalid. I gave another in my main post, and yet another in my last response to Marc. I can generate as many cases as you like. More importantly, if an inference is invalid in one case, then it is invalid in all cases that have the same form: this is because validity is a matter of the form of an argument. The following argument form is invalidated by one counterexample:
Conceivably p
Possibly p.

You can't say it is valid in some cases but not in others.
Furthermore, you need the validity of that inference pattern to sanction the inference from (1) to (2) in the original argument. Given that that inference pattern is not valid, the original argument is not sound. (Sound = valid + true premises.)

(1) Why not readjust our principle of conceivability to include only conceivable states of affairs dealing with logically or metaphysically contingent entities? I don't see problems arising from that.
(2) Why not make the argument inductive, as opposed to deductive, and argue that the premises give good reasons to believe the conclusion, though they are not conclusive?
(3) If we don't use conceivability as a guide to judging if states of affairs are possible, I don't know what else to use--if you've got an idea, I would like to hear it. Then we can ask whether or not Plantinga's procedure is possible, and if so, the argument goes through.
(4) We can also adjust the argument to drop talk of some states of affairs being actually possible, and simply argue that, given our epistemic practices involving judging states of affairs to be possible, we should believe Plantinga's procedure is possible (we use conceivability as a guide to judging some simple state of affairs like my being the only human alive as possible--why not in this case also?), and therefore we ought to believe I have a property P that my body B does not, and therefore...
(5) I'm not sure how all this is relevant to our original discussion, that of whether or not Lycan is rational.

Excellent suggestions. For now I have time to comment only on (1).

CEP* For all contingent p, conceivably p entails possibly p.

This formulation would block such counterexamples as the noncontingent *God does not exist.*

Can anyone think of a CE to CEP*? If not, this principle may validate the inference from (1) to (2) in the original argument.

I do not have a counterexample to CEP*, but I have a conceivable argument that it may be vacuously true. I hope someone finds something wrong with it.

CEP* is logically equivalent to its contra-positive:

~CEP*: For all contingent p, not-possible p entails not-conceivable p.

Suppose we define ‘contingent p’ as: possible p and possible ~p.

Then ~CEP* has the form:

~CEP(*): For all p, if (possible p & possible ~p & not-possible p) then not-conceivable p.

But the antecedent of ~CEP(*) is a contradiction and therefore always false. Hence ~CEP(*) is vacuously true. But since ~CEP(*) is logically equivalent to CEP*, the later is also vacuously true. So something is wrong here, although I admit I cannot put my finger exactly what. Perhaps, my argument is faulty.


Your argument is certainly not logically faulty. One can arrive at your conclusion directly from CEP*. Basically, p contingent implies possibly p. Thus, "conceivably p entails possibly p" is trivially true for p contingent.

I have to think some more whether we equivocate the term 'possibly' here.

After I wrote my last comment, I went for a 2 hour run during which I realized that CEP* (For all contingent p, conceivably p entails possibly p) won't help us validate the inference from (1) It is conceivable that I exist without my present body (or any part of it) to (2) it is possible that I exist without my present body (or any part of it).

The reason is that to instantiate CEP*, I must know that *I exist without my present body, etc* is contingent. But a proposition p is contingent just in case p and its negation ~p are both possibly true. So I need to know that *I exist without my present body* is possibly true. But that is precisely what is at issue. CEP* thus proves to be worthless: I cannot apply it unless I alread y know what it is supposed to teach me.

So this throws us back onto CEP, whihc I have proven is invalid.

Peter and Jan,

I concur with Jan that your reasoning is correct, though your spelling leaves something to be desired. (When you make a mistake it is spelling, when I make a mistake it is mere typography.) It is a very clever argument. What you have shown is that CEP* is a logical truth. CEP* is equivalent to

For any p, if p is contingent and conceivable, then p is possible.

But then conceivability drops out and we do not forge any link between it and possibility.

So I think the three of us are in agreement that CEP* is useless for the purposes of validating the move from (1) to (2) in the original argument.

I think I was suggesting something a bit different from CEP*.

First, I am outlandishly suggesting that we can do such a thing as conceive of state of affairs occuring--by which I mean something imagining them happening, like a movie in our head. It would need more development than that, if I plan on writing a paper on this, surely, but for our present purposes I think this is fine.

Let me say some state of affairs contains an entity (a concrete object, let's say) just in case if the state of affairs obtains, then that entity exists.

I'm suggesting that for any state of affairs that contains only contingent entities, if it is conceivable in the above sense, then it is logically possible.

I think with a principle like this, we can save Plantinga's argument.

I don't know how to accurately translate that into symbols. I'll let someone else do the dirty work for me.

I don't know yet if my principle is open to the same sort of objection, or if it is even substantially different from CEP*. I trust you or Peter can point it out if it is.


I am neither dr. Vallicella nor Peter Lupu, but perhaps the analysis will prove useful. You say:

(*) If a state of affairs contains only contingent beings and is conceivable, then it is possible.

This does not however account for the relationship between those objects. When you write about conceiving as imagining, you probably mean imagining the spatial relationships between objects. Thus, conceiving various objects in this sense means simply making sure that they do not occupy this same points of space. When we imagine a spatial configuration of apples, we only make sure that they do not overlap, and we conclude that such a configuration is possible. We do so, because we implicitly assume the relationship between apples to be spacial only. Thus, apples being physical objects, the only principle that can be violated is the non-overlapping principle. Things are rarely so simple, and there are usually much more principles that can be violated. To assume the relationship between self and body to be spatial only is to beg the question against the materialist. The following example illustrates this.

I can conceive of Superman being put into a sufficiently large box made from cryptonite. Both Superman and the box are contingent beings. But does it make it possible? Certainly not, it may be that the cavity in the cryptonite is impassable to Superman. We can similarly conceive of a man being put in a wooden box, and we conclude it is possible. Why is that so? Because we understand the relationship between a man's body and wood, whilst we do not understand the relationship between Superman's body and cryptonite.

Similarly, I can conceive of an apple traveling with a speed of 300,001 kilometers per second. It is so because I do not understand the relationship between a physical object and the space-time, which are both contingent.

One can propose criteria of conceivability further than the spatial. But to conclude that a state of affairs is possible, one needs to show that the proposed criteria are exhaustive. That is, that we took into account all the principles that obtain in our case. This needs to be done on a case by case basis. We are thus thrown back to fundamental arguments trying to establish the relationship between self, body and soul.

Under my current understanding of the word 'conceive', the step from 1. to 2. is a step from 'I cannot see why it is impossible' to 'it is possible'. This cannot succeed unless 'conceive' is given a much stronger meaning. I also do not think conceivability can be treated as inductive evidence for possibility. To me, conceivability is rather an enabling condition for the existence of inductive evidence.

1) Conceivable and possible overlap: some things that are conceivable are also possible; however, there are things conceivable that are not possible and some things possible that are inconceivable (at least by us). Therefore, we are not going to get any valid inference from conceivable to possible.

2) I agree with Jan when he says "I also do not think conceivability can be treated as inductive evidence for possibility." For how would such inductive evidence work? Surely we do not mean to say that if P is conceived a sufficient number of times by many people, then it is possible. They all could be wrong. And conversely, even if P is conceived only once in the whole history of the human race, it still could be possible. But surely no good induction is forthcoming based upon just one instance. I think that any *evidential* account between conceivability and possibility must be of a different character than the typical induction based upon instances. What sort of evidential relation is involved?

3) Jan says: "To me, conceivability is rather an enabling condition for the existence of inductive evidence." We need to examine this proposal carefully.

3.1) What sort of property is *conceivability* and to what kind of entities does it apply? Is *conceivability* a disposition, ability, capacity, competence? If so, of what or whom? We have been speaking thus far as if conceivability is a property of *propositions* or *state of affairs*. (i.e., if p is conceivable, then ...etc) We had to speak thus because possibility is a property of propositions or state of affairs and conceivability and possibility had to apply to the same sort of thing in order to even consider whether the argument is valid.

3.2) But we got here two nasty problems.

First, if conceivability is a property of propositions and we think of conceivability as a sort of disposition or capacity, then we got to make sense of the following question: do propositions have dispositions, capacities, abilities, etc,? Perhaps, state of affairs do: I guess, there is a sense in which state of affairs have *causal* dispositions and capacities. But we are not talking here about causal efficacy, do we?

Second, even if it makes sense to attribute *conceivability* to propositions or state of affairs, it also applies, and applies primarily, to the one who does the conceiving. But possibility does not. Possibility applies to a proposition or state of affairs. So we need to forge a conceptual link between the conceiver and the thing conceived: i.e., propositions and state of affairs in order to somehow have a conceptual bridge between conceivability and possibility. And here we once again face the familiar and nasty problem of the gap between the mind and the world.

3.3. So before we can make sense of Jan proposal to view conceivability as "enabling conditions" for the existence of inductive evidence, we must clear up some of the above issues. I myself think that the connection is conceptual rather than evidential. We have a relatively clear model of the modal possibility: i.e., possible world semantics. We need a corresponding model for conceivablity: i.e., conceivable world semantics.

3.4) Some of the questions that this raises are: What are the constraints upon such a semantics? What is the underlying logic for such conceivable models? It might turn out that paraconsistent logic rather than classical logic is more suitable unless the 'able' is interpreted as including consistency? But since consistency may require the concept of possibility, we will end up characterizing conceivability in terms of possibility.


Distinguished philosophers consider conceivability to be defeasible evidence of possibility, so, although what you say above in #2 is plausible, we need to tread carefully here.

If a proposition is conceivable, it is conceivable to someone. We can leave God and the IRS (ideally rational subject) out of this since what we want to know is whether finite schmucks like us can get genuine metaphysical knowledge by the exercise of reason. So we can say that conceivability is a relational property of propositions/state of affairs. These abstract objects lack powers, but we have the power to think (conceive). So one of your nasty problems may be a psuedoproblem.

You are right though: the overall problem is that of the gap between mind and world. How do I know that what I conceive is possible? Analogy: How do I know that what I PERCEIVE is ACTUAL?

You mention possible worlds semantics of modal discourse. But you may be ignoring the fundamental questions: Do we have any modal knowledge in the first place? And how do we acquire it? How do you know that there are any unrealized possiblities? By conceiving them? But that is just the problem. Possible worlds semantics won't help because it presupposes that we have answers to the fundamental questions.

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