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Mereological Ontological Arguments and Pantheism (19??) [1]

Graham Oppy

 

Mereological ontological arguments are--as the name suggests--ontological arguments which draw on the resources of mereology, i.e. the theory of the part-whole relation.[2]

An instance of arguments of this kind is the following:

1. I exist. (Premise, contingent a priori)
2. (Hence) Some--i.e. least one--thing exists. (From 1)
3. Whenever some things exist, there is some thing of which they are all parts. (Premise, from mereology)
4. (Hence) There is exactly one thing of which every thing is a part. (From 2, 3)
5. The unique thing of which every thing is a part is God. (Definition, pantheism)
6. (Hence) God exists. (From 4, 5)

The status of premise 1 is controversial: friends of two-dimensional modal logic (and others) will be reluctant to grant that the proposition that I exist is both contingent and knowable a priori (even by me). Instead, they will insist that all that I know a priori is that the sentence "I exist" expresses some true proposition or other when I token it. But, of course, even that will suffice for the purposes of the argument. Provided that I know a priori that the sentence "I exist" expresses some true singular proposition or other--i.e. some proposition or other which contains an individual--then I have an a priori guarantee that there are some individuals, and so I am entitled to assert 2. Of course, it will remain true that there are some people who refuse to accept 2: consider, for example, those ontological nihilists who think that the proper logical form of every sentence can be given in a feature-placing language.[3] However, many people will be prepared to grant that we can know a priori that there are at least some individuals--and that it enough to sustain interest in our argument to this point.[4]

The status of premise 3 is also controversial: there are various reasons why one might be inclined to reject it. However, it is important to be clear about exactly what the premise says. Note, in particular, that it does not say that, whenever some things exist, there is some thing which is the mereological sum of those things. Rather, what it says is that, whenever some things exist, there is some thing of which all of those things are parts--i.e. the thing completely overlaps each of the parts, but the parts together need not completely overlap the thing. Of course, given the mereological claim about sums, the weaker claim follows: so friends of unrestricted mereological composition will certainly be happy with 3. But one could subscribe to 3 on independent grounds: one might think, for example, that it is just impossible for there to be two things which are not both parts of a single, more-inclusive, thing. Again, there will be people who are not prepared to accept 3. But, for now, it seems reasonable to suppose that there will be lots of people who are quite happy with it. (We shall have more to say about 3 later.)

The inference of 4 from 3 looks distinctly suspicious. Indeed, it seems to have the form of the quantifier-exchange fallacy which moves from [universal][existential] to [existential][universal]. However, we can patch this. What we need to suppose is that we can talk unrestrictedly about every thing. Now, consider all things. If premise 3 is correct, then it does indeed follow that there is some thing of which every thing is a part. (By `part', I mean `proper or improper part' of course.) Moreover, it is then extremely plausible to suggest that there can only be one such thing: in order to deny this, one would need to deny the uniqueness of composition (a course which is possible, but, at least prima facie, quite unattractive). Of course, some people will not be happy with the claim that we can talk unrestrictedly about every thing. Among the reasons which might be given for this unhappiness, perhaps the most important is the suggestion that unrestricted quantification leads to paradox. However, it is important to bear in mind that we are talking about quantification over individuals here. Whether one supposes that there are finitely many, or countably many, or continuum many, or Beth-2 many, or even proper class many, individuals, it is hard to see how any contradiction can arise from this assumption. Of course, there are other objections which one might make to the totality assumption. However, it again seems reasonable to suppose that there will be lots of people who are quite happy with it. (Once more, we shall return to this assumption later.)

On the basis of the above considerations, it seems reasonable to suggest that there will be lots of people--including lots of people who do not count themselves as having any kinds of religious beliefs--who will be happy with the argument to 4. Or, perhaps better, there will be lots of people--including lots of people who do not count themselves as having any kinds of religious beliefs--who will be prepared to accept the following argument at least as far as 5:

1. I exist. (Premise, contingent a priori)
2. Some things--i.e. at least one--exist. (From 1)
3. If some things exist, then there are some things which are all of the things that exist. (Premise, from the meaning of `all'.)
4. Whenever some things exist, there is some thing of which they are all parts. (Premise, from mereology)
5. There is exactly one thing of which every thing is a part. (From[5] 3, 4)
6. The unique thing of which every thing is a part is God. (Definition, pantheism)
7. Hence God exists. (From 5, 6)

In other words, there will be lots of people who are happy to allow--on more or less a priori grounds--that there is exactly one thing of which every thing is a part. So, for these people, the important question will be whether the thing of which every thing is a part deserves to be called `God'. If this thing does deserve the name, then pantheism is vindicated; if this thing does not deserve the name, then--presumably--pantheism (or, at least, this kind of pantheism) is simply a mistake.[6]

I

Before we can decide whether the thing of which every thing is a part deserves to be called `God', we need to know more about the attributes of this thing. Even if our mereological ontological argument is successful, it doesn't give us much information about the thing of which every thing is a part (nor about its parts). Morevoer, it is clear that opinion here will divide widely according to prior metaphysical conviction.

Consider physicalists--i.e. those who suppose that there is exactly one physical universe, which has none but physical parts. These people will suppose that the thing of which every thing is a part is the physical universe. (I assume, of course, that these physicalists suppose that there are no non-physical individuals.)

Consider modal realists--i.e. those who suppose that there are many possible worlds.[7] These people will suppose that the thing of which every thing is a part is the mereological sum of the possible worlds. (I assume, of course, that these modal realists suppose that there are no individuals which are not overlapped completely by the sum of possible worlds.)

Consider Platonists--i.e. those who suppose that, amongst the things which there are, there are non-spatio-temporal individuals laid up in Plato's Heaven. These people will suppose that all of these individuals number among the parts of the thing of which every thing is a part.

And so on.[8] Some of these views seem to lead to better candidates for the name `God' than others. However, in order to make progress on this question, we need to think some more about what a decent deserver of that name should be like.

In some respects, the result is bound to be heterodox. However we proceed, we are not going to arrive at a personal creator. But that's as it should be: pantheists--of the kind under consideration here--typically do not suppose that there is a personal creator. Moreover, there are ways of recovering many other parts of religious orthodoxy. Consider the modal realist view mentioned above. Everything that can be done is done by some part of the thing of which every thing is a part--so there is a sense in which this being is omnipotent. Everything that can be known is known by some part of the thing of which every thing is a part--so there is a sense in which this being is omniscient. Every possible virtue is possessed by some part of the thing of which every thing is a part--so there is a sense in which this being is omnibenevolent. (Not quite the traditional sense, of course. After all, every possible vice is also possessed by some part of the thing of which everything is a part--so, in the same kind of sense, this being is omnimalevolent. Moreover, this remains true even if lots of apparently possible evil worlds are deemed impossible.) Every thing is located in the thing of which every thing is a part--so there is a sense in which this being is omnipresent. Provided that one is prepared to allow temporal parts into one's ontology, one can also get a sense in which the thing of which every thing is a part is omnitemporal. And so on. (Perhaps you could even make a case for the claim that the sum of possible worlds is a being than which no greater can be conceived: after all, on this view, there is no greater being to have conceptions of!)

Perhaps it is worth noting that similar points can be made about the physicalist view mentioned above. Everything that is done is done by some part of the thing of which every thing is a part--so there is a sense in which this being is omnipotent. Everything is known is known by some part of the thing of which every thing is a part--so there is a sense in which this being is omniscient. Every virtue that is possesses is possessed by some part of the thing of which every thing is a part--so there is a sense in which this being is omnibenevolent. (Not quite the traditional sense, of course. After all, every vice that is possessed is also possessed by some part of the thing of which everything is a part--so, in the same kind of sense, this being is omnimalevolent..) Every thing is located in the thing of which every thing is a part--so there is a sense in which this being is omnipresent. And so on. (Perhaps you could even make a case for the claim that the physical world is a being than which no greater can be conceived: after all, on this view, there is no greater being to have conceptions of!)[9]

These kinds of considerations about the attributes of the thing of which every thing is a part do not speak to the most important issue. Somehow or other, the appropriateness of the application of the name `God' to an object depends upon (i) whether or not it is appropriate to take up typical religious attitudes towards that object; and perhaps also on (ii) whether or not that object could properly be seen as the focus of one of the well-known organised religions. Of course, it isn't easy to say what the typical religious attitudes are: but, amongst them, there should surely be some kind of awe and also some kind of dependence and gratitude. Awe is easy: it is natural to think that our physicalists would be in awe of the physical thing of which all other things are parts. (Such awe may not be mandatory; however, it would surely be widespread.) But if that's all we are talking about--something on the order of an aesthetic response to a spectacular landscape--then it just seems wrong to say that there is anything of religious significance here. In order to deserve the appellation `religious' there must be more: feelings of dependence and gratitude (or other responses on which the machinations of organised religion can get a grip). But there is no reason to think that these responses will be appropriate for the kinds of things of which all other things are parts mentioned above. Indeed, it would just be a mistake to respond to the physical universe--or the sum of possible worlds--with responses that are only appropriately directed towards persons. (There are, of course, senses in which one might have feelings of dependence upon, and gratitude towards, the thing of which every thing is a part, First, dependence: clearly, your continued existence depends upon its continued existence--if it goes out of existence, then so do you. Second, gratitude: given the first point, there is clearly some sense in which you should be grateful that the thing of which every thing is a part has not gone out of existence. Of course, the important point to make is that these are not the `religious' responses to which reference was made above. Even though it is hard to articulate precisely, there is clearly a good sense in which the kinds of dependence and gratitude which it would be appropriate to have are not religious.)

No doubt, the conclusion of this discussion was obvious from the beginning. Even if we are as concessive as we can be about the claim that there is one thing of which every thing is a part, our merological ontological argument is bound to lack probative force. You can call my physicalists `pantheists' if you like--after all, the word can be yours to do with as you please--but it won't follow that these people have religious beliefs (in any ordinary sense of the word `religious belief'). Likewise for our modal realists and Platonists. Of course, it remains at least a doxastic possibility that the thing of which every thing is a part is a being with religious significance--that all depends on what the thing of which every thing is a part turns out to be. But we aren't going to learn anything about this from our ontological argument (or from any other ontological argument either). If our physicalists and modal realists and Platonists are wrong about the nature of the thing of which every thing is a part, then it could turn out that their beliefs about this thing ought to be religious--but, as things stand, there is no reason to think that it is in fact the case that beliefs about the thing of which every thing is a part ought to be religious (in the sense gestured at above).

II

The objection of the previous section might be thought of as a minimal objection to our mereological ontological argument. As we noted, it is certainly possible to contest some of the metaphysical assumptions which the argument requires. However, the argument can be firmly resisted even if all of these assumptions are allowed to stand. Consequently, the sensible thing to do is to adopt this line of resistance, since it costs so little in terms of theoretical commitments.

This approach is consistent with the general approach to ontological arguments which I advocated in my Ontological Arguments and Belief in God.[10] In that book, I developed a taxonomy of six different kinds of ontological arguments, and then suggested that each kind of ontological argument is vulnerable to the same kind of minimal criticism, viz. that the arguments have one reading on which they are invalid, and another reading on which they are question-begging (i.e. require assumptions which non-theists can reasonably reject, at least for all that the ontological arguments in question show).

However, the identification of mereological ontological arguments--given only the briefest of treatments in my book[11]--suggests that this general criticism is not quite right. For, in many cases, ontological arguments will also have a third reading on which they are neither question-begging, nor invalid, but on which the entity whose existence they establish is a being of no religious significance. Consider, for example, the following argument:

1. I conceive of a being than which no greater can be conceived. (Premise)
2. (Hence) A being than which no greater can be conceived exists. (From 1, by a familiar argument which I shan't reproduce here.)
3. (Hence) God exists.

The question to ask about this argument is how to construe expressions of the form "I conceive of X". Clearly, there is a "relational" sense in which a sentence of this form can only be true if X exists; and there is another "non-relational" sense in which a sentence of this form can be true whether or not X exists. If "I conceive of X" is meant to be construed in the latter "non-relational" way, then an opponent of the above ontological argument should insist that the argument is invalid. (I omit further details, since they are not relevant to the point I wish to make here.) On the other hand, if "I conceive of X" is meant to be construed in the former, "relational" way, then the opponent of the argument has a choice: either deny that X exists--which is tantamount to claiming that the argument is question-begging--or else accept that X exists, but deny that X is a being which has any religious significance. (As noted above, in the case in question, our modal realist could claim that the being than which no greater can be conceived is just the mereological sum of all possible worlds, a being which is in no sense a good deserver of the name `God'.)[12]

III

One way of restating the conclusion of our minimal criticism of mereological ontological arguments in section I is that they do not provide an interesting or informative mode of presentation of the being whose existence they purport to establish. There are many metaphysical perspectives from which one can accept the claim that there is a thing which has every thing as a part--but many of these seem to have nothing at all to do with religious belief.

A similar point can be made concerning a debate about the interpretation of St. Anselm's Proslogion. Some people hold that the existence of God is established by the end of Part II; others hold that the existence of God is not established until the end of Part III; and yet others hold that the existence of God is not established until the end of the entire work, or at any rate the end of Part XXIII. However, all agree that the existence of a being than which no greater can be conceived is established by the end of Part II--and they also all agree that the being than which no greater can be conceived is God. So the point of disagreement is just about whether a mode of presentation has been found which makes it clear that the being whose existence has been established is God.

Our discussion of pantheism suggests that there may be some point to this debate--c.f. the dismissive remarks in my book[13]. For--to use the same example again--it might be that our modal realists can agree that there is a unique being than which no greater can be conceived: and, if that is right, then there is reason to think that the existence of God has not been established by the end of Part II. (Of course, theists should agree that the being whose existence is established by the end of Part II is God; but they should not think that the argument will persuade non-theists of the truth of the claim that the sentence `God exists' expresses a truth.) Naturally, there are reasons why one might be sceptical about the claim which I have just made: one might doubt that `greater than' should be cashed out in mereological terms; one might doubt that our modal realists are really entitled to analyse conceivability in terms of possibility; and so on. However, the point I want to make is just this: there will be some people who will (apparently) reasonably think that the argument of Proslogion II is sound, but that the being whose existence it establishes is not a being of any religious significance.

(It is also worth thinking a little more about the expression `being than which no greater can be conceived'. It is at least possible to take this expression to exhibit the same `relational' / `non-relational' ambiguity which was discussed above in connection with the expression `I conceive of X'. In one sense, the greatest being--if there is such--is the being than which no greater can be conceived. For our modal realists, and under plausible assumptions about the mereological nature of greatness, this being is just the sum of possible worlds. So, on the `relational' reading, the being than which no greater can be conceived just is the sum of possible worlds. Since some traditional theistic conceptions talk about `the sum of all possibilities', it is not obvious that we should think that these considerations are entirely irrelevant to traditional theistic argumentation.)

IV

Many people will feel that the minimal criticism of mereological ontological arguments for which I have argued can be supplemented with much stronger criticisms. In particular, there will be many people who will think that premises 3 and 4 of the revised version of the argument will not stand up to scrutiny. So perhaps it will be a good idea to close with a slightly closer look at these premises.

Premise 3 says that if some things exist, then there are some things which are all of the things that exist. Why might one be disposed to reject this claim? Apart from the worries about `total' entities mentioned in the introduction, the most likely suggestion is that considerations from ordinary language suggest that quantification is always restricted quantification: there is no sense to be made of the suggestion that there can be unrestricted quantification. In my view, one only has to state this claim in order to see how implausible it is. Consider the claim that everything is self-identical. Surely the most natural way to understand the quantifier here is to take it to be unrestricted: absolutely every single thing without exception is identical to itself. But, when we quantify unrestrictedly, we quantify over absolutely all the things there are: and, if we can quantify over all the things there are, then there are some things such that they are all the things there are. (Perhaps my counterargument is question-begging. Too bad. The claim that, if there are some things, then there are some things which are all the things there are strikes me as a very good candidate for a claim which is both analytic and a priori. It is often hard to find good arguments for primitive claims of this sort.)

I suppose that some people will hold that `exists' is ambiguous: it has different senses in different discourses. On this view, to say that chairs and numbers exist will be, strictly speaking, nonsensical. For while according to number discourse, it is analytic that there are numbers, and according to chair discourse, it is analytic that there are chairs, there is no discourse in which one can say that there are both chairs and numbers (and hence in which one can ask whether there are chairs, and whether there are numbers).[14] However, against this kind of Carnapian position, I want to side with Quine: `exists' is univocal, and there is a single language in which all claims about existence can be assessed.[15] Of course, I'm not offering an argument here; rather, I have identified one class of people who will not be disposed to accept Premise 3. As I have already hinted, I think that this view is extreme; moreover, I expect that only something equally extreme will suffice for the rejection of Premise 3.

Premise 4 is--at least prima facie--much more problematic. Premise 4 says that whenever some things exist, there is some thing of which they are all parts. But there seem to be lots of views on which this claim is mistaken. Suppose, for example, that you think that there are non-spatio-temporal individuals (such as numbers). Suppose further that you are not a friend of unrestricted mereological composition. Then it might well seem natural to you to claim that there are lots of pairs of things which are not both parts of some more inclusive thing: e.g. my heart and the number 2. Of course, if you are a friend of unrestricted mereological composition, then you get Premise 4 for free: but, otherwise, it seems that the acceptability of Premise 4 will depend upon prior metaphysical conviction about what there is.[16]

Curiously, the kind of thought which typically motivates opposition to unrestricted mereological composition--namely, that deservers of the appellation `thing' must have some kind of `inner unity' which is not bequeathed by mere mereological composition--is an intuition which is shared by many theists and pantheists. One of the key religious intuitions is that there is--or, indeeed, that there must be--some kind of `inner unity' to things. Consequently, there is some reason to think that Premise 4 of our mereological ontological argument cannot properly be motivated by an appeal to unrestricted mereological composition: the principle of unrestricted mereological composition doesn't capture--and, indeed, is plausibly at odds with--one of the principle intuitions of many theists and pantheists.

Even amongst those who are prepared to accept unrestricted mereological composition, there may be some who are prepared to deny (the standard mereological axiom of) uniqueness of composition. For instance, there are those who think that there is a relation of constitution which is not mereological in nature: the statue and the lump of clay from which the statue is constituted are distinct, even though they have the same clay-ey parts. However, this example isn't enough to motivate rejection of uniqueness of composition: for, in this example, the relation of constitution is not symmetrical--the clay constitutes the statue, but the statue does not constitute the clay. Consequently, the statue has parts--e.g. the left hand part of the statue and the right hand part of the statue--which the clay does not (remember that we are supposing that the statue is distinct from the clay from which it is constituted). In order to deny uniqueness of composition on these kinds of grounds, one needs to find a case in which the relation of constitution is symmetrical: for then one could hold that there are two distinct entities which have exactly the same parts. It is not easy to think of a plausible example of this, however.

In sum, then: there are various views which will lead one to reject the mereological ontological argument for the existence of the thing of which all things are parts. I doubt that there are arguments which will persuade people who hold these views to change their minds. However, there are also many people who will accept the argument for the existence of the thing of which all things are parts. Some of these people will be pantheists--but if they are, it will be for reasons which the mereological ontological argument does not make apparent.

Appendix: Dessert

Many formulations of mereology include the null part--i.e. the thing which is part of every thing. (The inclusion of the null part bestows a nice symmetry on the resulting theory.) This fact provides the means to include a discussion of `the devil' in our theory--provided, of course, that we are prepared to identify `the devil' with the null part. Of couse, this suggestion doesn't make much sense from the standpoint of orthodox theism--the devil is not merely the contrary or opposite of God--but it is important to remember that pantheism already stands at a considerable remove from orthodoxy.[17] Moreover, we can see that `the devil' will have lots of interesting properties once the identification with the null part is made. (For instance, since `the devil' is part of every thing, there is a good sense in which `the devil' is omnipresent. Moreover--as noted above--`the devil' turns out to be the exact opposite--the dual--of the thing of which every thing is a part. Given the attitudes which the pantheist supposes are appropriate for the thing of which every thing is a part, it seems natural to think that the pantheist will suppose that contrary attitudes are appropriate for `the devil'. And so on.)

As I mentioned above, not all mereologists accept the existence of the null part. Those who do not, and who provide reasons for rejecting the null part, can be taken to be providing reasons for rejecting `the devil' (under the proposed identification). However, I shan't bother to labour this point here.[18]


[1] "Whenever two or three of you are gathered together in my name, there I am also" Matthew 18:20.

[2] For more information about mereology, see, for example, Simons, P (1987) Parts: A Study in Ontology New York: Oxford University Press.

[3] See, for example, O'Leary-Hawthorne, J. and Cortens, A. (1995) "Towards Ontological Nihilism" Philosphical Studies 79,2, pp.143-165

[4] Also, it might be possible to develop a related argument within the framework of ontological nihilism. For, presumably, the sentence `I exist' will translate into a sentence which is contingent a priori, and which entails the translation of the sentence `Some things exist'. Of course, mereological pantheism would also need to be reconceived--as indeed would mereology. I leave all of this as an exercise for ontological nihilists (if such there be).

[5] Strictly speaking, the axiom of uniqueness of composition is also required to get to 5 from 3 and 4. Cf. the discussion in Section IV below.

[6] One should distinguish between distributive pantheism--the view that each thing is divine--and collective pantheism--the view that the thing of which all things are parts is divine. Moreover, when considering collective pantheism, one should distinguish between mereological collective pantheism--the view that the thing of which all things are parts is just the mereological sum of all its proper parts--and non-mereological collective pantheism--the view that the thing of which all things are parts is something over and above the mereological sum of all its proper parts. Throughout this paper, the topic of discussion is collective pantheism--and, in particular, mereological collective pantheism.

[7] For more about modal realism, see Lewis, D. (1986) On The Plurality of Worlds Oxford: Blackwell.

[8] Another view which deserves mention in this connection is that kind of physicalism which is committed to the many-worlds interpretation of quantum mechanics. On this view, the thing of which all things are parts is (of course) the mereological sum of all of the many worlds.

[9] It will be natural to object that omniscience, omnipotence, etc. should not be given the radically extensional understanding which our physicalists provide. This is a fair point; however, it is also worth noting that omniscience, omnipotence, and so on, are sometimes understood in the non-modal way which we have indicated: most powerful (or, at least, than which there is none more powerful), most knowing (or, at least, than which there is none more knowing), and so on.

[10] Graham Oppy (1996) Ontological Arguments and Belief in God New York: Cambridge University Press.

[11] See p.262.

[12] If I were revising my book, I would certainly add mereological ontological arguments to my taxonomy, and devote a chapter to their discussion. However, this addition would not make any substantive difference to the criticisms of ontological arguments which I develop there.

[13] See pp.208-9.

[14] The locus classicus for this view is Carnap's "Empiricism, Semantics, and Ontology" in Meaning and Necessity: A Study in Semantics and Modal Logic (second edition, enlarged) Chicago, Ill: Chicago University Press, 1956. See also Huw Price (1992) "Metaphysical Pluralism" Journal of Philosophy 89, 8, pp.387-409.

[15] For Quine's arguments, see "On What There Is" in From a Logical Point of View Cambridge MA: Harvard University Press, pp.1-19.

[16] For some other arguments which might plausibly be taken as objections to the idea that there is one thing of which all other things are parts, see van Fraassen, B. (1995) "World ` Is Not A Count Noun" Nous 29, 2, pp.139-157. I hope to discuss these arguments elsewhere.

[17] Similar points can be made about discussions of the being than which no lesser can be conceived, the being than which no worse can be conceived, etc. Even if these beings have nothing to do with the devil--as traditionally conceived--they are of interest in their own right in the discussion of parodies of ontological arguments. (C.f. Oppy (1996), p.182.)

[18] I am indebted to Daniel Nolan for discussion of the material presented in this paper. In particular, the idea that one might identify the null part with `the devil' is his. (Perhaps he will produce a more elaborate discussion of this idea elsewhere).


"Mereological Ontological Arguments and Pantheism" is copyright © 19?? by Graham Oppy. All rights reserved.
The electronic version is copyright © 1998 by Internet Infidels with the written permission of Graham Oppy. All rights reserved.

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