Pantheism, Quantification and Mereology

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. 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. 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. 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 ∀∃ to ∃∀. 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 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

Philosophical Studies, 2015

David Lewis (1991, 84) famously argued that mereology is ontologically innocent. Many who have considered this claim believe he was mistaken. Mereology is not innocent, because its acceptance entails the acceptance of sums, new objects that were not previously part of one’s ontology. This argument, the argument from ontological parsimony, has two versions: a qualitative and a quantitative one. I argue that the defender of mereology can neutralize both arguments by holding that, given mereology, a commitment to the parts of an object is not an extra ontological commitment, made in addition to the commitment to the object; and that if the parts of an object are ‘ontologically innocent’, then sums cannot fail to be innocent either.

2009

Ontological arguments are deductive arguments for the existence of God from general metaphysical principles and other assumptions about the nature or essence of God. There have been three very signifi cant developments in the history of ontological arguments. The fi rst is the ontological argument developed by St Anselm of Canterbury in the eleventh century. The second is the argument sketched by Descartes in the late seventeenth century and completed by Leibniz in the early eighteenth century. And the third development consists of the numerous ontological arguments of the twentieth century that explicitly utilize modal logic, particularly those of Malcolm, Hartshorne, Plantinga, and Godel. My chief aim in this chapter is to logically evaluate logical reconstructions of each of these six arguments. I shall also present and logically discuss two of my own explicitly modal ontological arguments. The logical evaluation of a logical reconstruction of an argument often requires that we e...

2020

1991

Saint Anselm of Canterbury offered several arguments for the existence of God. We examine the famous ontological argument in Proslogium II. Many recent authors have interpreted this argument as a modal one.'But we believe that Jonathan Barnes has argued persuasively that Anselm's argument is not modal.

2007

Our 1991 paper on the logic of the ontological argument contained an analysis of the structure of Anselm's argument for the existence of God. We showed that there is a valid argument for God's existence in Proslogion II. However, in that paper, we deliberately decided not to include a discussion and analysis of the soundness of the argument. In these afterthoughts, we shall take up this question. We plan to argue for the following:

The Review of Symbolic Logic, 2009

In Parts of Classes (1991) and Mathematics Is Megethology (1993) David Lewis defends both the innocence of plural quantification and of mereology. However, he himself claims that the innocence of mereology is different from that of plural reference, where reference to some objects does not require the existence of a single entity picking them out as a whole. In the case of plural quantification “we have many things, in no way do we mention one thing that is the many taken together”. Instead, in the mereological case: “we have many things, we do mention one thing that is the many taken together, but this one thing is nothing different from the many” (Lewis, 1991, p. 87). The aim of the paper is to argue that—for a certain use of mereology, weaker than Lewis’ one—an innocence thesis similar to that of plural reference is defensible. To give a precise account of plural reference, we use the idea of plural choice. We then propose a virtual theory of mereology in which the role of indivi...

Croatian journal of philosophy, 2004

Academia Letters, 2021