Contemporary metaphysics by Micheal Jubien chapter 3 Platonism 45-62
3.2 Alternatives to Platonism We begin by considering accounts that accept the existence of properties (etc.) but deny that they have one or another of the essential features that the Platonist claims they have. What about the physicalist idea that properties (etc.) are somehow concrete? It may seem plausible to think that at least some properties, like redness or being a table, are actual physical parts of the things that have them, and hence are concrete because they're located in spacetime. But a closer examination shows this particular in re theory cannot really be right. The property of being a table cannot literally be a physical part of a table. For suppose we have two tables in front of us. If being a table were a physical part of one of them, then the other wouldn't be a table since it doesn't share any parts with the first. (What is critical, of course, is that it doesn't share the part that happens to be the property of being a table.) But of course it is a table. One of the crucial features of the property of being a table — however it is ultimately understood ontologically — is that distinct, nonoverlapping things are capable of instantiating it simulta-neously. Of course, most properties have this feature of possible multiple instantiation (and for this reason they are sometimes called "universals"). So the idea that such properties are literal parts of their instances is untenable. 45 Platonism But there may be another way to locate these properties in spacetime, where" their instances are located. Is California located where San Fran-cisco is? Well, not all of it. But when you're in San Francisco, you're in California. Some of California is located there. So, in a not-quite-literal sense, California is. Suppose you have a pain in your hand, say in the palm near the top knuckle of your index finger. If you say "My hand hurts," you are not saying something that is false, even though other parts of your hand don't hurt. In a not-quite-literal sense, your hand is where the hurting is occurring. Following these leads, we might modify the physicalist view by making a similar departure from the literal. To do this, we identify the property of being a table with the "scattered totality" of all tables existing anywhere in spacetime. Now, this totality is simply a disconnected array of specific physical stuff, of which every actual table happens to be a (literal) part. Let's call this array of stuff "T." According to the revised theory, then, to instantiate the property of being a table is to be an appropriate part of T. (Notice that lots of parts of T aren't tables; for example, the parts that are the tables' legs aren't tables.) Now, on this account, the property of being a table, that is, T, is located where any given table is located in the same not-quite-literal sense in which California is located where San Francisco is located (and your hand is located where the pain is located). This revised theory is therefore not literally an in re theory like the original, but it is certainly in re in spirit. But the theory has a tragic flaw: It cannot accommodate various ways in which things could have been different from how they actually are. For example, the world might not have contained the physical stuff T at all, and yet it might have included tables. These tables would then have been made entirely of stuff not included in T. So, in that circumstance, there would be things instantiating the property being a table, but none of these things would be parts of T. Since the theory says that to be a table is to be an appropriate part of T, it must be wrong. [Exercise: Explain why it would be circular to hold that the tables existing in the imagined circumstance would collectively constitute T.] Now let's turn to the case of propositions. It is tempting to think that at least some propositions are concrete — that they are actual physical parts of the physical world. For instance, the proposition that the dog is in the yard (where the context fixes a specific dog and yard) might be thought to be that part of the world that contains the yard, along with the dog. But there are two major problems with this idea. First of all, if there really are propositions, then some of them are true and some of them are false. If the 46 Platonism dog really is in the yard, then what part of the world would he the proposition that the dog isn't in the yard? Obviously it can't be any part oldie world that includes both the yard and the dog. But nor can it be a part of the world including all of the yard except for the part where the dog is. In short, there is no part of the world that can plausibly serve as the negation of a true proposition. The second problem is this. Suppose the dog is lying down in the yard, and again suppose the proposition that the dog is in the yard is some physical part of the world including the yard and the dog. Then what part of the world is the proposition that the dog is lying down in the yard? The only remotely reasonable answer is that it's the part containing the yard and the recumbent dog. But this is precisely the same part as the part containing the yard and the dog! This means that the theory forces the proposition that the dog is in the yard to be the same as the proposition that the dog is lying down in the yard. But these are obviously different propositions, since the former could be true while the latter was false. So the theory should be rejected. Now let's return to properties. We have seen two overtly concrete approaches fail for fairly simple reasons. but there is a more sophisticated in re theory that may not he so easy to dismiss. The central idea of any in re theory is that properties are somehow "in" their instances. The two we considered above got into trouble as soon as they got specific about how this was supposed to work. Maybe the best in re theory would avoid the trouble by not getting specific! The theory would claim that one and the same property can be "in" various disparate things that occupy various disparate locations (and that the existence of any property depends on its having instances), but it would refuse to say what "in" means or how this "multiple instantiation" works. The "in" relation holding be-tween property and instance would be taken as a "primitive notion" of the theory. Logically speaking, this is irreproachable. Every theory has to leave some of its central notions unanalyzed or else it will be involved in an infinite regress of analysis (or a vicious circle). For example, set theory takes the relation of set-theoretic "membership" as a primitive notion. The axioms and theorems of the theory tell us many things about membership, but they don't analyze it and they don't tell us how membership "works." Any understanding we might have of the inner nature of membership could only take place at an intuitive level. Now, on the face of it, the idea that the world could contain an entity 47 Platonism with the capacity of being located "in" different physical things (in differ-ent places) seems very mysterious. The mystery seems as deep as the more or less opposite religious mystery of the Trinity. Just as it is hard to make sense of the idea that three Gods can be "in" one God, it is hard to make sense of the idea that one "property" can be "in" more than one thing at once. A sophisticated in re theorist will not deny that there is an air of mystery here, but will claim that it is much more acceptable than the "myth" of a Platonic "heaven" outside of spacetime. It appears, however, that there are two serious problems for the sophis-ticated in re view (which we will call S). The first problem takes the form of a double dilemma. S does not tell us about the nature of the "in" relation. That's fair enough, as we saw above. Still, the relation must have some essential nature, and there just aren't too many possibilities. If each possibility leads to trouble, then it looks like the sophisticated strategy of leaving the relation unexplained serves only to obscure the trouble. Here is the major dilemma: Either "in" means physically in (that is, part of) or it doesn't. If it means physically in, then the property itself will have to be physical, and it looks like we're back to one of the two "concrete" theories that were rejected above. [It's hard to think of an even remotely plausible theory other than these that makes the property be physi-cal and "in" its instance. Exercise: Give it a try.) On the other hand, if "in" doesn't mean physically in, then the properties won't themselves be physical entities and the "in" won't be literal, but just a figure of speech. That might be fine, but now we face a second dilemma: Do these nonphysi-cal properties occupy spacetime or not? If they don't, then S evidently has "degenerated" into a covert version of Platonism. (After all, a Platonist is free to adopt a special, nonliteral sense of "in" according to which the claim that redness is "in" the rose merely means that the rose instantiates redness. Plato's heaven (and the Great Line of Being) are just vivid figures of speech anyway.) (Another question worth thinking about is this: If the prop-erties aren't in spacetime, then why are they dependent on their instances for their existence?) So suppose instead that S's properties do occupy spacetime. Then, to say that redness is "in" the rose would mean that redness — now a nonphysical entity — occupies the same spatiotemporal location that (part of) the rose occupies. So (assuming the above options are unsatisfactory, as suggested), we now have something that S was originally unwilling to provide, namely, an explanation of the nature of the "in" relation. The veil of 48 Platonism sophistication has been lifted. But the result is that what appeared through the veil merely to be mysterious now seems downright absurd. S's proper-ties, though nonphysical, are nevertheless spatiotemporal entities (and hence "concrete" as we are using that term). Certainly if a spatiotemporal entity occupies a specific region, R, at a certain time, then it does not occupy any region entirely separate from R at that same time. Of course, this does not deny the possibility that a spatiotemporal entity might have different parts occupying entirely separate regions, unconnected by other parts of the entity. But the present understanding