Why Platonism?

Why make so much of fragmentary blue
In here and there a bird, or butterfly,
Or flower, or wearing-stone, or open eye,
When heaven presents in sheets the solid hue?

Since earth is earth, perhaps, not heaven (as yet)--
Though some savants make earth include the sky;
And blue so far above us comes so high,
It only gives our wish for blue a whet.

          — Robert Frost

One natural view about truth is to think that for some claim to be true, there must be something in the world that makes it true. For example, it seems true that ‘Rowan likes coffee’ because I do, in fact, like coffee. ‘Grass is green’ is true because grass is, in fact, green. Of course, the case of colour (like everything else) becomes complicated: what exactly do we mean by ‘green’ and what is it for something, like grass, to be green? 

Of those that attempt to explain this seeming fact, different stories could be told. But however this is done, there will be some reality that makes the fact true. For example, one view might say that ‘green’ refers to the surface properties of physical bodies that reflect light within a certain range of wavelengths. This view says that ‘grass is green’ is true because the properties of grass mean light is reflected in just this way. Another view says that green is a specific qualitative character of experience, one that is not part of the physical world. Such a view can nonetheless say that our statement ‘grass is green’ is still true because we perceive grass and in perceiving it, our experience is of this specific character. Finally, another view thinks that grass is green because grass has the power to produce green sensations in us. This power that grass has to make us have a certain kind of sensation is what makes ‘grass is green’ is true. In each case, once we settle the interpretation of ‘green’ we find that there is some reality it refers to that makes claims like ‘grass is green’ true. This general view of truth is called the ‘truthmaker’ view, which basically says that every truth has a truthmaker. I think the view is basically right (and it explains why I don’t believe in truths). And even if it is not exactly right, I think it at least constitutes the right kind of attitude we should take towards doing metaphysics – an attitude that thinks truth does not come reality-free.

Once we start thinking in the truthmaker register, questions of fundamental reality start coming in thick and fast. For example, it seems like the claim that ‘Rowan had a coffee with breakfast yesterday’ is true. But what is the truthmaker for this claim? The most natural answer is the past event, that is, my having a coffee for breakfast yesterday. But this means that if the truthmaker view is right and it is true that I had coffee with breakfast yesterday, then it follows that the past exists. This conclusion is nothing to sneeze at, it is a substantive metaphysical thesis. Indeed, if you are a presentist (someone who thinks the only thing that exists is the present) and take the truthmaker view, it seems that you must either say that all statements about the past are false (which is a difficult view to maintain) or say that truths about the past are somehow made true by features of the present (which is less difficult but somewhat strange).

A somewhat underrated seeming truth that needs explanation is the following. Imagine two apples. Suppose one is a little beat up and bruised, and the other is not, but both are a bright red colour. These apples are obviously different from one another, but they are also the same, at least in some respect. Namely, they are the same with respect to their redness. Of course, one apple’s redness is not the same as the other’s in the sense that they are identical rednesses. It is obviously not the case that the redness of one apple is the redness of the other apple—each apple’s redness is its own redness. Nevertheless, both apples can truly said to be red. (Consider the alternative that it is false that they are both red – this really seems wrong.) Call this phenomenon, the seeming fact that two different things can nonetheless be the same in some respect, sameness-in-difference.

What could the truthmaker be for claims about sameness-in-difference? Let’s continue with the two apples. As I just noted, it cannot be the surface properties or powers of each apple, nor the experiential character of our experience of each of them, because in each of these cases, the apples are not exactly the same. Their individual redness is different from each other. That is to say, listing the properties of each individual apple cannot, by itself, explain the fact that the claim: “both apples are red” appears to be true, because whatever counts as ‘redness’ for each apple is different in each case. For example, if you think ‘red’ refers to a particular character of conscious experience, each apple’s redness will differ in some small way, otherwise they would look identical, which they do not. What we need an explanation for is that despite these differences, we can truly say that the apples are both red, and that they are the same in precisely that respect. We need this to make seemingly true claims like: “both apples are red”, true.

One way of explaining this is as follows: what makes it true that both apples are red, is that there is some further reality that exists independently of any particular thing that is red, namely, red itself, or redness that makes our grasp of sameness-in-difference, the true recognition of something. However, we must be careful to distinguish this reality, redness itself, both from the individual apples that are red and each individual apple’s redness, which, as I said above, cannot account for sameness-in-difference. Redness itself is an entity in its own right, over and above individuals and their properties. Call such realities forms and call the call the relationship between the form and the thing that instantiates it, participation. For something to participate in a form is just for it to (truly) count as an instance of that form (hat-tip to Badiou).

If we take forms to be the truthmaker for sameness-in-difference, there will be forms for every category that allow us to truly predicate of two different things that they are the same, in some respect. Hence, there will be forms for every conceivable property or category. For example, there will be a form of justice, courage, equality, humanity, horse, tree, mud, chair, and car, to which every instance of these things, will be related. These forms explain our repeated recognition of these qualities in the world, across situations, and across domains. They make our conviction that different things can truly said to be the same, in some respect, true.

Now, what I have said so far may suggest that only if there is an actual case of sameness-in-difference is there a form corresponding to the identifiable quality. For, it seems that a truthmaker is only required if there are two individuals which we identify as being a real case of sameness-in-difference. For example, suppose that there were no red things. Then it seems we no longer need the form of red to account for the truth of statements like ‘these apples are both red’ because, in fact, there are no such apples. (This is sometimes called the Aristotelian view that there exist no uninstantiated universals. However, it is not clear to me that Aristotle held such a view, as forms are something different to universals.) On this view, forms are simply common ways things actually happen to be or common ways things actually happen to stand in relation to one another.

However, this view, that forms merely describe the actual structure of the world, cannot be right if we follow roughly the same approach we’ve already been taking. Suppose again that there are no individuals that are red. Even if this were the case, we still have claims like ‘something could be red’ or ‘apples could be red, even though they are all green.’ Taken in their purely logical sense, these statements are plausibly true, just like it could have been true that there were no squirrels. (Though this will depend on your views about modality. Necessitarians and actualists have plausible ways of denying this.) But what is to account for possible truths like these? Once again, the form of red. And this is so for every other form. Forms are also the truthmakers for the possibility that things could be any way whatsoever. This means that, while sameness-in-difference is the thing that gets us to recognise that there are discrete ways that things could be, there are forms regardless of whether there are instances of sameness-in-difference or even the unique instantiation of some form. Even if there are no actual unicorns, if it is true that it is possible there could be unicorns, then there is a form of unicorns.

This entails three things: that forms are necessary, eternal, and ontologically prior to their participants. (1) They exist necessarily because it is not contingent upon the actual structure of the world for it to be true that something could be red. All that is required is that red is one way things metaphysically could have been. We can see this because ‘something could be red’ would still be true in the logical sense, even if the actual universe was such that scientific laws excluded the physical (or phenomenological) possibility of redness. (2) They are eternal because ‘something could be red’ is true at any given time, not just at this or that particular time. Just as something could be red 50,000 years ago, something can be red now. The truth of such possibilities is not sensitive to time. (3) Finally, it also means forms exist ontologically prior to, and even explain, their instances. I said before that the form of red is the truthmaker for the claim ‘things could be red.’ This means that if the form did not exist, then the statement would be false, and things could not, in fact, be red. But if things cannot be red without the form of redness, then an individual’s redness depend on the existence of the form, and not vice versa. Therefore, forms exist ontologically (and not merely temporally) prior to their participants. And because their instances could not exist without their prior existence, forms also explain their existence.

(It is also worth noting at this point that, since individuals are what they are because of the qualities they have, as their persistence conditions are certainly constituted by their peculiar combination of qualities, individuals themselves must be ontologically dependent, in a non-trivial way, on the forms their qualities are participants of. Hence without forms, there would be no distinct individuals at all, because there would be no distinct and intelligible ways they could possibly be.)

Of course, this has some potentially odd consequences. It implies there being a (perhaps infinite) number of necessary existents that are never instantiated in our world corresponding to all the ways things could possibly be. It also means there is likely a (perhaps infinite) number of forms that are instantiated but that are beyond our in-principle ability to grasp. But so what? Once you admit forms at all, admitting more should not make us feel any worse, metaphysically speaking. It is not a stronger offence to admit further entities of a kind which we have already accepted. Nor should the fact that we are ignorant of some offend us either. Who doesn’t think that some existents elude us? Further, once we remember that a form is simply a way some thing could be, like the way a blueberry is sweet, or a knife is sharp, these are not such odd consequences (no matter whether you take the ‘subjective’ or ‘objective’ interpretation of those terms). It is surely logically possible, and therefore metaphysically innocuous (again, at least on non-actualist or necessitarian interpretations of modality), that things could be any number of an infinite of different ways, some of which we will never see, or think of. The forms are just what ground this possibility and thus explain not only the way things actually are, but the possibility of anything being any way whatsoever.

Most entities we engage with and think about have a spatiotemporal location. That glass is over there, and that concert was back then. It is therefore natural to ask whether forms are spatiotemporally located, as well. The individuals which participate in them certainly are. Apples are grown, harvested, and then eaten by us. But what about the apple’s redness? The powers view and the surface properties view would surely both have the apples redness be spatiotemporally located. In both cases, the redness of the apple is a physical, hence spatiotemporal, property of the apple itself. If we think that red is a characteristic of consciousness experience, then, depending on one’s view, we might think that the apple’s redness is not in space, because it is essentially mental, but is in time, because there is only a finite duration in which we perceive the phenomenal apple’s redness. But is redness itself, the form of redness, in space or time? We neither, grow, harvest, or eat the form.

One reason to think that forms are spatiotemporally located is that the individuals that instantiate them are. However, what I’ve said already rules out this out, because there is a necessary distinction between somethings-being-red, and redness itself. That is, between an individual that participates in a form, and the form itself. This is the essential transcendence of the forms from their participants. If they did not transcend their instances, they could not antecedently ground the possibility of their instantiation. Thus, the mere fact that individuals are spatiotemporally located and participate in forms is no reason to think that the forms themselves are so located. One reason to think they are not so located is because we cannot, even conceivably, come into causal contact with the form of something. Given that we tend to think that something spatiotemporally located could, in principle, be something to which we could see or touch, or in some way cause or be caused by, this would rule out forms. True, we come into contact with the things that participate in them, but what conceivable step could be made from coming into contact with, for example, an instance of goodness, to goodness itself? We merely grasp the form, which is made intelligible to us through it’s instances. Therefore, we should think forms are abstract, which just means non-spatiotemporal.

It may be tempting to reply at this point: if we cannot conceivably come into causal contact with forms, then we shouldn’t think they exist, given they could make ‘no difference’ in the world. What kind of silly theoretical postulate makes no difference in the world? However, this objection is all wrong. Apart from presupposing a much too vulgar empiricism, having a too narrow conception of difference-making (constrained only to causal difference-making), and failing to appreciate the explanatory role forms play, and hence the difference they actually do make, on this account, it also rules out the possibility that other abstract entities we might plausibly think exist, in fact do. For example, numbers or laws of logic. They are both abstract (non-spatiotemporal) yet often thought to be metaphysically innocent (certainly more so than forms). Their relative metaphysical innocence will hopefully show the forms have an innocence similar in kind.

Numbers, we might think, certainly exist, but are not here or then – they are abstract. They just exist. There can be one or two of something, and this fact can be directly intelligible to us. Yet we cannot conceivably come into causal contact with one-itself or two-itself. In other words, we can truly say of our apples that, taken together, there are two, but to truly say this, there is such a thing as one and two, and they are of a different ontological nature to the apples which participate in them. They don’t make a strictly causal difference to the apples, but they make it the case that certain relations hold between them. Logical truths too, might exist, but are not here or then – they are also abstract. They just exist. Take the principle of non-contradiction, that □~(p&~p). This principle is often taken to be necessarily true, but it is certainly not something we could see or touch, in-itself. This principle is particularly interesting because people often go further. They think not only that it is necessarily true, but also that it strictly governs the space of metaphysical possibility – possible existence. That is, they think that it is impossible that some contradictory state of affairs could come to exist, because the principle is necessarily true (though whether this governing role is supposed to be constitutive or descriptive is another question). If this is not making a difference, I do not know what is. Such is the case with forms, as I’ve presently theorised them. They are necessary, abstract, existents, and, as I said above, they govern the space of all possible existence as they constitute the infinite ways things in which things could possibly be.

Let’s take stock. We have eternal, necessary, transcendent, and abstract beings called forms that explain the possibility of sameness-in-difference and the possibility of there being any way anything could be, whatsoever. This is Platonism in a nutshell. And while I have so far considered no alternatives, nor have I discussed the relationship of participation, I think the case for its truth is strong.

The most common way of denying Platonism is to reject the existence of forms and to try tell a different story about the truthmakers of general statements and sameness-in-difference like “both of these apples are red.” Any such view obviously begins by asserting at the outset that there are no forms, entities over and above individuals and their properties. Call this view nominalism.

A nominalist story about the truthmakers of statements like “both apples are red” will go something like the following. Rather than saying that two red apples participate in the form of redness, which is the thing by virtue of which they are both red, it instead says that there are just two apples, each with their specific properties. The specific properties of these apples happen to be such that they are similar enough that they fall within the boundary of what we have conventionally called, as a society, ‘red.’ On this view, it is the convention to call this or that range of subjective experiences, wavelengths, surface properties, or powers, ‘red’, that makes the claim true, not the fact that they are actually both this identical thing, red, that both of them participate in. There is no such thing.

A good way to think about this is to consider the intuitive difference between a name and a category. A name picks out an individual, like Rowan Anderson or Henri Bergson. Neither name is meant to pick out multiple different things, they are meant to pick out exactly one thing, namely, Rowan and Bergson. It does not make sense to say that a name could pick out different things that are nonetheless the same, as a name is ordinarily thought to refer to a single individual that is always the same (in spite of any differences over time). A category, on the other hand, is supposed to pick out multiple different individuals that, in spite of their ultimate difference, nonetheless fall under the same category because they are the same in some respect. For example, a flock of sheep is made up of individual sheep that are all different individuals but nonetheless fall under the same category.

With this in mind, Platonism can be understood to be saying that categories are something real, over and above the individuals that fall under them, and which even depend in no way on there being anything that falls under them. Rather, they explain how things could come to be such that they fall under these categories in the first place. Whereas nominalism can be understood to be saying that there are no such categories: they literally do not exist, never have, and never will. All that exists are the individuals that we put in categories by convention. Thus, a more metaphysically accurate way of getting at the real structure of the world for a nominalist would be to give everything a name, and categorise nothing, letting each thing shine forth in its ultimate, primitive, individuality. Of course, we have neither the patience, reason, nor the time, to engage in such a task – a task that Locke, the arch-nominalist, postulated (and condemned). So instead, we come up with categories to speak of groups of individuals, the categories themselves arising entirely out of convention and need, having no reality in themselves.

The most obvious problem with this is that leaves completely unexplained what we are doing when we are categorising things, given that all categories are supposed to be unreal. However, what nominalists can say is that there is a relationship between individuals which explains why we categorise them in some ways rather than others. They say that there is a real, primitive, metaphysical relation between them that we grasp when we categorise individuals. That relation is resemblance, and it is no more suspect, the nominalist will say, than is distance or size. This explains, for example, why we call a specific cluster of similar seeming sensations ‘red’ and not just any sensation whatsoever: because there is a relation of resemblance between the individual surface properties or experiences that we grasp in perception. On this view, it is just individual things and resemblances between them, all the way down. Categories are just what conventionally point to those resemblances.

Now, if you had never thought about this problem before, this is more than likely how you assumed things worked anyway. This is because modern assumptions about metaphysics are overwhelming nominalist in flavour, and this can be traced directly back to the early modern philosophers, who almost unanimously rejected most versions of Platonism in favour of nominalism, and the scientific revolutions, who unanimously rejected their explanatory necessity. This rejection has largely remained to this day, except in some odd ways. However, if you take a look at what I’ve said so far, nothing about how science or philosophy has developed thus far has refuted the metaphysical or explanatory necessity of forms. The argument in no way relies on ‘outdated’ beliefs about the world and science could be developed on a platonistic or nominalistic basis. Further, while nominalism may seem convincing to the modern sensibility, it has a problem, which, according to the Platonist, is fatal to the project and shows that, in fact, our ordinary conception of science could not proceed on a nominalistic basis.

Simply put, the Platonist thinks that the very notion of an individual, on which nominalism must be founded, presupposes a kind of Platonism. To see why, consider again something I discussed only briefly: numbers. Each number is a form that our universe often participates in. A flock of eight sheep can be truly said to be made up of eight sheep, and hence participates in the form of eight. Now imagine the sheep are taken away, one by one. You now have a flock that participates in seven, six, five and so on. Eventually, you get to an individual sheep. Just as many sheep participated in the corresponding number, one single sheep participates in the form of one. And so it is for any other individual which there is one of. It is what makes nominalist seeming statements like: “there is only one Rowan Anderson” or “Henri Bergson is an individual”, true. Oneness, the form, is what makes the identification of single unique individuals intelligible to us, not as a conglomerate of many things, but as one individual, a unified being. If there is no form of the individual, then there are no individuals. 

But if this is right, then the intelligibility of individuality, as a way things are, presupposes the form of oneness. And if the notion of individual presupposes a form, then the very intelligibility of nominalism as a philosophical position presupposes the truth of Platonism. Further, the lesson of the sheep story above tells us that oneness, or individuality, is not special in the order of being. Its just one way things could be among many. No matter how unique something is, it is just as conceivable there could be two or three of something, and hence that once one form is let through, all others must be too. Hence, we either accept Platonism, or reject individuality, the only form to which our thought seems to take place at all.