Lewis as the philosophically insane.

I’ve been reading van Iwagen lately and I now realize why he is so revered. A topic which has come up several times in his articles is the role propositions play in ones ontology. He critiques Lewis’ possible world assay almost entirely on the fact that his Lewis’ reductionism does violence to what we thought we mean when we express modal propositions. Consider the following:

(1) It’s possible that that JFK died of natural causes.

On Lewis’ account, the proposition expressed in (1) really means this:

(1)’ There is a world spatiotemporally unrelated to ours where JFK died of natural causes.

The ramifications of such a reduction are manifest, for it implies there really is world, full of atoms and space and even has JFK as one of its members that really exists (in the sense that it’s a concrete world), but we are spatiotemporally not related to that world. Other queer entailments include the following: The word ‘actual’ functions as an indexical: When we express the proposition ‘It’s actually the case that JFK was assassinated’ the word ‘actually’ is referring to the world we are spatiotemporally related to. When the people in W2 say ‘it’s actually the case JFK died of natural causes’, by ‘actually’ they are pointing out the world (W2) where they are spatiotemporally related. Does this mean that proposition ‘JFK died of natural causes’ (as well as its contrary) is both true and false? No, because the referent of that proposition is ambiguous- for it does not designate a specific world. HA!
The craziest implication of Lewis’ view, I think, is that there is not just one unique JFK, but possibly millions. Consider the following propositions:

(2) JFK never married.
(3) JFK lived until 1989.
(4) JFK was a Soviet spy.

(2)-(4) are all true in some really existing world and the singular term ‘JFK’ in each proposition picks out the JFK in that world where the proposition is true. What’s worse, every possible proposition that includes the singular term ‘JFK’ picks out a really existing JFK. Ergo, there is an uncountable (if not an infinite) number of JFKs currently in existence.

Are you kidding? What’s the fruit of a reductive analysis if it comes at such a cost? And back to van Inwagen’s point (and Plantinga, and Kripke, et al.), the proposition expressed in the sentence ‘It’s possible JFK died of natural causes’ I am predicating a modal term on a proposition, and to say what I really mean by this is the nonmodal proposition ‘there is world spatiotemporally unrelated to us where JFK died of natural causes’ is to change subjects.

the argument from universals.

An argument for platonic realism regarding universals (that abstract entities exist and can do so without dependence on their instances) takes the following form:

(1) There is a possible world where there are no particular things colored red.

(2) Despite the fact of (1), the following propositions are true, and necessarily so; that ‘necessarily, red is a color (there is no possible world where red is not a color)’, and ‘necessarily, red resembles orange more than it does blue, (there is no possible world where red doesn’t resemble orange more than it does blue’, and also that ‘necessarily, no single indivisible entity can be both red and green at the same time (there is no possible world where a single thing can be both red and green).

(3) Since the propositions expressed in (2) are necessary truths, they are also true in the possible world expressed in premise (1). But (1) stipulated that that there is a world where no particular thing is colored red. So the question is, if propositions are true or false in virtue of the content they express, how can it be the case in the possible world where there are no instances of red that propositions expressed in premise (2) are true? The way it out is to assert (4).

(4) In a possible world where nothing in particular is colored red the necessary propositions expressed in (2) are true because they refer to the form of red, which is an uninstantiated universal. Therefore,

(5) Platonism in true.

The only way out of this consequence, it seems, is the denial of the last part of (3); namely, that propositions can only be true or false in virtue of the content they express and refer too. To say it another way, one must deny that propositions need not have intention to be true or false. But this seems crazy, and I cannot even begin to conceive of what this might look like, so pending further enlightenment by some sneaky Aristotelians, I must declare (5).

Well, assuming everything I’ve articulated adds up, consider the following proposition:

(6) Necessarily, to be a person is to have rational faculties (either dormant or otherwise).

If (6) is true, then so is

(7) There is a possible world where there are no instances of persons, but since (6) is necessarily true, it’s also true in such a world. But if (6) is true (and necessarily so),

(8) (6) is (necessarily) true in virtue of the fact that it expresses, namely, that a person necessarily has rational faculties (dormant or otherwise). If this is a fact, then there is at least one person, and He must necessarily exist, since (6) could only be true in virtue of this fact. And if there is a person that exists necessarily, then he can be nothing other than what men call God.

... No, I presume I may say that we
more certainly know that there is a
God than that there is anything else without
us. When I say we know I mean there
is such knowledge within our reach which
we cannot miss, if we will but apply our
minds to that, as we do to several other
inquiries.

John Locke,
Chapter X of Essay Concerning Human Understanding

what the heavens are abstract objects?

A week or so ago James Gibson let me borrow Peter van Inwagen’s essays on philosophical theology, and the first article is a critique of all (known) ontological arguments, with special attention given to Alvin Plantinga’s formulation.

I’ve yet to fully comprehend the meat of van Inwagen’s argument against all known ontological arguments, but I definitely have beef with something van Inwagen says in the preliminary stages of his argument. I’ll quote the beginning of the section III at length:

Let us now turn to ontological arguments. We said that there were ontic
arguments that could be regarded as arguments for the existence of a
Deity. But this is vague, since it is not clear in the case of every set
of properties whether it could be instantiated only by a Deity. For
example, could something that is not a Deity instantiate the set {N, being the
maker of the world}(1)? It seems (epistemically) possible that, if
there were a necessary being who was the maker of the world, this being
might also be rather limited in power and knowledge, indifferent to the
sufferings of its creatures, and perhaps even made the world out of some
inchoate stuff that existed independently of its will. Should we be
willing to apply the term ‘Deity’ to such a being? Perhaps some would and
some wouldn’t, and this indicates the concept of a Deity (and hence our concept
of an ontological argument) is vague.
Let us therefore replace this vague idea of an ontological argument with a more precise one. It is clear that, whatever ‘Deity’ might reasonably be supposed to
mean, and Deity must be a nonabstract object. (I shall call nonabstract
objects concrete without regard for the etymology or philosophical history of
this word.)
I am not sure how to go about analyzing the notion of an abstract object, but I
think it is an important and intelligible notion. There are things that we
can see, hear, be cut or burned by, love, hate, worship, make, mend, trust in,
fear, and covet. These are the sorts of thing I mean by “concrete
object.” And there are things we could not possibly stand in anyone of
these relations to, for example, properties, propositions, sentence-types, sets,
and systems of natural deduction- and these I call “abstract objects.”
Let us suppose that the distinction between abstract and concrete objects is
clear enough to go on… (pg. 28)

My point of contention is this ostensive distinction between abstract and concrete objects doesn’t at all make clear the salient differences between the two. What exactly is the criterion for a certain object to be either abstract of concrete?

I’ve never actually done any studying on the distinction between abstract and concrete objects; they’ve only come up as peripheral points in the metaphysics literature I’ve been exposed to. To my knowledge I don’t think there is even a book whose primary content is the exposition of the distinction. In the little research I’ve done Frege’s On the Foundation of Mathematics and David Lewis’ The Way of Negation seems to be the primary places to which our current assay has been inherited. At this point I’m going to give my current and extremely tentative view of the nature of the distinction and what objects I think fall into which category.

In my experience thus far I’ve come to think of the word ‘abstract’ as having two different senses: the first is adjectival and referring to a type or class of object and the second sense verbal and epistemological.

When ‘abstract’ is used in the former sense it’s about an entity which has no spatial or temporal location. An entity that I almost always read about being in such a category is numbers. The number 1 for instance is an object which has no spatial location and no duration within the universe. It’s also been argued that properties such as “redness” and “being snub-nosed” are things are also abstract entities; but if the criterion for being abstract is that an entity must necessarily not be extended in space and have a specifiable duration then I don’t know what to make of the idea of that properties are abstract. Surely it’s the case the whiteness and being snub-nosed has been extended in space and time, for my door is white and Socrates was said to be snub-nosed, and those things are (and were) extended in space and time.

I suppose this is where the verbal and epistemological sense of ‘abstract’ usually comes into the discussion. Philosophers have maintained that properties are extended in space and time, but the mind has the capacity to abstract from its experience certain properties like whiteness and snub-nosedness from the spatial/temporal things which have such qualities and to think of such properties “in abstraction,” that is, as things in themselves and apart from the object which ‘actually’ have them.

Indeed, some philosophers have maintained that all abstract entities are reducible to the set of things which humans have abstracted from the things which actually have them, and numbers too, are no different. This view says numbers are only true of the world when there is a number of objects, and when the mind observes these objects they abstract from the number of things to think of just number themselves, and only at this point do numbers take on a mode of existence that lacks spatial and temporal dimensions.

For such philosophers then, there presumably is only one genuine sense of ‘abstract,’ and this sense is the epistemological sense which describes the ability of the human mind to artificially remove a property of a thing spatially and temporally extended and to be thought of without being such. Such a construal is often what allows philosophers to make sense of mathematics while still being materialists.


Along with the non-spatiality criterion, Frege thought that the second requisite to be an abstract object was to be causally inefficacious. But I think this account flies in the face of some serious tradition. Plato would deny such a construal. Abstract objects, though neither spatial or temporal entities are surely causally efficacious. What accounts for the possibility of predication in sensible objects (like the white pages in my book) is that such instances stand in certain causal relations to abstract entities, like the form whiteness. If Plato’s account is correct, then abstract entities are not only causally efficacious but causes par excellence.

From what I can tell so far the only unanimous criteria for an entity to abstract is the non-spatial/temporal criteria.

So what of concrete objects? The most obvious contrast that concrete objects have to abstract ones is that concrete objects are spatially and temporally located. May we say then to be concrete is exist temporally and spatially? I think this is uncontroversial, and so it has my tentative alliance.

Well maybe not. If dualism is true or if humans have genuine conscious states that escapes physical description (and reduction), then there is the possibility of existing without being spatially located, for consciousness has no spatial location (if so, where?). But maybe this is too quick. Even if it is the case that consciousness itself is not located anywhere spatially speaking, the perspective had by a conscious state it seems must necessarily be a conscious state of some spatial location or another. I can’t imagine myself being conscious without having a point of view, a vantage point of some space in the universe. Does necessarily having a spatial perspective allow consciousness to join the class of concrete objects? I have no idea.

But let’s pretend the consciousness cannot be admitted to class of concrete objects, does this mean that consciousness is an abstract thing? No. To be abstract an entity cannot be temporally situated, and it seems to be the case that all conscious states are temporally situated.

So this seems to imply that conscious entities are neither abstract nor concrete, and I have no idea how to make sense of this.

Notice, however, that just because something is not concrete it does not mean that it doesn’t exist. Abstract entities, whatever they are, must exist in at least some fashion, or else we wouldn’t be able to intelligibly discuss them.

So let’s go back to van Inwagen’s construal. He seems to think that if God exists, then he’s a concrete object. But what of the fact that to be concrete one must be spatially and temporally located, and if God did exist, and assuming it’s possible he can have a temporal mode of existence, he most certainly would not be spatially located anywhere. So it’s not all clear how van Inwagen thinks that if God does exist he must be a concrete object. Assuming I’m right here, that van Inwagen has misconstrued the mode of God’s existence, I don’t know what kind of implications this might have on his argument.

Any thoughts?






____________________________________

Notes
1. N = the property of necessarily existing.


Works Cited___________________________

SEP on abstract objects.
SEP on God and other necessary beings.


Further Reading________________________

Edward Zalta's webpage.
Edward Zalta's online papers on extremely sexy topics.