Monday, January 24, 2011

Plato and the Metaphysical Problem of Rationality

Plato, like Kant, was reacting to contemporary currents of thought that he regarded as dangerous. He took seriously an epistemological problem that he thought was posed by Heraclitus’ doctrine of universal flux (Plato disregards Heraclitus’ view that “all things happen in accord with the divine Logos” and sets Heraclitus up as the materialist foil to Parmenides). In a world where nothing was eternal, unchanging and universal, knowledge with those qualities was also not possible: it had no object. To try to compose a description of an ever-fluxing world was like “shooting after flying game” (as Socrates says in the Theatetus). That sort of knowledge was a snapshot of a mere moment, quickly passed. Plato’s strategy for addressing this epistemological problem was metaphysical: identify the eternal, unchanging and universal object.

Plato also opposed the reductive materialism of Anaxagoras and the other Melisians, early natural scientists (Aristotle, who shared Plato’s opposition to reductive materialism, addresses Democritus’ atomism). The word “reductive” in the phrase “reductive materialism” is also epistemological in its import: the idea is that macro-level phenomena (such as the minds of persons) will ultimately be explained in terms of micro-level phenomena (such as the parts of bodies). Materialism understood this way is committed to the view that properties are caused by matter. The materialist answer to the question “Why is this property what it is?” is “Because the underlying matter is what it is.” Both Plato and Aristotle argued that causation (and thus explanation) ran the other way.

Plato and Aristotle hold respective versions of the form-matter distinction, the view that basic ontology includes both form and matter. Plato’s version is patently dualist. He holds that form is primary being, that it is mind- and matter-independent, and that formal being acts on material being such that matter can only be said to be something to the degree that it is involved in form. Aristotle, objecting to what he saw as Plato’s ontological promiscuity, argued that substance, a union of matter and form, was primary being. Among other advantages this resolved the interaction problem that afflicts Plato’s dualism. On the other hand, the price of collapsing matter and form together into substance in this axiomatic way was that one had to accept that primary being was heterogeneous. This is counter-intuitive, but that doesn’t make it wrong. Close attention to Aristotle’s metaphysical differences with Plato is rewarded with any number of insights into subtleties of the mind-body problem (for example notice the resonance with Spinoza). We will return to Aristotle and De Anima, his own great work on the philosophy of mind, in Chapter Four.

However I will argue that these differences, significant as they are, are not relevant to the present, relatively broad point I want to make about the form-matter distinction, materialism, and the problem of rationality. Ultimately I’m more of an Aristotelian than a Platonist, but I think Plato’s more explicitly dualist discussion makes this broad point best so I will discuss two passages from Plato, the “analogy of the sun” at Republic 507b-509c and the treatment of the materialist argument that “soul is an attunement of the body” at Phaedo 93a-94e.

The Sun, Plato says, makes the universe a visible place. Our eyes take advantage of this (Plato and Aristotle resisted Empedocles’ arguments for natural selection, which they saw as reductive, but the reader should join me in helping ourselves to evolutionary biology wherever it helps to fill things in here). We can see each individual visible thing because the whole universe is suffused with that one element, light, which emanates from the Sun. Analogously Plato claimed that something he called “the Good” suffused the universe with order and made it an intelligible place. The Sun is to vision as the Good is to rationality: both vision and rationality are possible because of the existence of a more general feature of the universe. Plato takes the analogy farther. The Sun’s light is necessary for the growth of plants and the Good’s order is necessary for the emergence of definite (definable, intelligible) things. The Sun is the source of warmth; the Good is the source of value. Darkness is the absence of light; badness is the absence of order.

Describe any concrete particular thing. You will describe it (you can only describe it) in terms of its properties. Concrete particulars, as Heraclitus pointed out, are constantly coming-to-be and passing away. Properties (forms, universals) are eternal. The epistemological challenge posed by Heraclitus’ doctrine of universal flux is met with the Platonic doctrine that formal knowledge (knowledge of formal properties), as distinct from material knowledge (knowledge of concrete particulars), constitutes true understanding.

However there are properties and then there are properties. I stated at the beginning of the book that I don’t like a lot of loose talk about “properties” and that ultimately I think that physical properties are the only kind of properties that there are. If I am going to qualify that at all (and at the end of this discussion you will be left with your own judgment to decide how far I have gone in that direction, and if too far), then I had better try to be a good deal more precise about what I mean by “formal properties.”

Consider two putative properties: the property of “cowness” (or “being-a-cow” or what you will) and the property of circularity. According to Plato, as matter approaches nearer to form it comes to be something, “being” meaning “being intelligible,” which to Plato is a legitimate ontological category (Plato posits degrees of being, contrary to the materialist’s zero-sum understanding of being). However, while there are certainly well-formed cows and malformed cows, even a cow still-born with deformity is a cow (if someone comes into the barn and asks, “What is that?” the right answer is “That’s a cow.”). Plato and Aristotle thought that species were fixed natural kinds (to use the standard phrase), but we (well, I) don’t think so: species are the kinds of things that come-to-be and pass away, just as individuals do. With circularity the situation is different. Being a circle just is having (instantiating) that property, and there is a threshold of trueness short of which we will say that the concrete particular isn’t a circle in a sense that it cannot be said, of any animal born of cows, that it “isn’t a cow.” Once a cow, always a cow, but a concrete particular can gain and lose the property of circularity.

The extension of the set of all formal properties can only be understood in the context of Plato’s central metaphysical thesis of the Good. Plato is clear on the difference between material being and formal being. Material being is divisible (Socrates’ body can be chopped up into pieces and scattered like leaves or burnt and blown away like smoke), it is a multiplicity (I am one body, you are another), and it comes-to-be and passes away (“All men are mortal, Socrates is a man…”). What part of reality is indivisible, a unity (oneness), and eternal?

Imagine (if this is the sort of thing that can be imagined) that one’s sole mathematical practice was to name one set, {x,x}, let’s call it “2.” Now we reflect on our named set and it occurs to us that we need a name for the constituent set, {x}, so we call it something: “1.” It is now impossible not to notice a pair of functions, “+” and “=.” From these we will inevitably get to the other functions, and we also now have a practice of naming all sets; we have the set of natural numbers. In fact all of mathematics is entailed by any part of mathematics. Mathematics cannot be cut into pieces. To have it is to have, at least implicitly, all of it, including all of those proofs that no human has as yet discovered (it is mind-independent). Nor can any part of mathematics be considered, as physical objects can, in isolation from the rest. I can imagine a universe consisting only of this desk chair floating in the vast emptiness of space (I think), but if the proof of the infinity of prime numbers is floating out there, so is all the rest of mathematics. It is one, not a multiplicity of separable propositions. Not only that, but it looks like it is floating out there, since we discover the entailments. And those proofs would be valid, undoubtedly, whether or not there was any matter and energy at all. Mathematics is indivisible, a unity and eternal.

At this point it is possible to be more specific about what a “formal property” is. I take formal properties to be mathematical properties, essentially. For what it’s worth, I even think that this may not be far from Plato’s actual theory, reflecting as it does the metaphysical influence of Pythagoras and Parmenides. To say that a thing has a formal property is to say that there is an aspect or part of that thing that can only be described in terms of mathematical or logical relationships that can be formalized without reference to the contingent physical properties of the thing. For example the property of circularity is a formal property. The set of circular things includes wooden things, clay things, bone things and metal things, but circularity is supervenient: its mathematical description is about the spatial relationship between one of its parts and another and this formalizable (mathematical) relationship does not “reduce” to any contingent properties of wood cells or clay particles etc. That is, “formal properties” are properties that can be formalized. All formal properties are supervenient on matter: there is no physical criterion that fixes the extension of the set of physical things that instantiate the property.

Another way of saying the same thing is to say that any physical object might potentially be involved in any formal property. Formal properties are universal (sometimes they are called “universals”). A critical point here is that strictly speaking there is only one formal property, that property that the universe has of being formally organized by the Good. To speak of a plurality of “forms” (“circularity,” “rationality”) is figurative. There is only one form in which all formally organized things participate; only its expression in matter is multifarious as for example in the various geometrical shapes. (In the next section I will discuss whether and how much this literalist Platonism can coexist with materialism in general and particularly with the Wittgenstein-influenced eliminativism about mental content that I sketched above.)

At Phaedo 93a-94e Socrates is responding to a kind of materialist theory suggested by Simmias. Simmias acknowledges that Socrates can raise difficulties for the identification of the soul with the body by pointing out apparently metaphysical differences between them (for example with the argument from “recollection,” which is Socrates’ term of art for innate knowledge), but Simmias argues that the soul might nonetheless be a kind of “attunement” of the body. This is an emergentist view: when all of the physical properties come together in the right way, a non-physical property emerges, not identical to but dependent on (caused by) the underlying physical properties. Emergentism is a creature of that murky area, populated by refugees and smugglers, where “non-reductive materialism” and “epistemological dualism” share a hopelessly porous border. People who wind up here wanted the goodness of materialism without the badness. Plato’s (dualist) response to the emergentist challenge provides the last link in my argument for a Platonic resolution (I don’t say “solution”) to the problem of rationality.

Consider a musical instrument and the harmonious sounds it makes. On Simmias’ view the harmonious sounds are caused by the particular physical properties of the instrument. Thus while it’s true that the harmony is not identical to the body of the instrument, it is also true that with the passing away of the instrument’s body there will be a simultaneous passing away of the harmony. Socrates responds that harmony is a formal property. That is, harmony itself is not more or less harmonic, any more than circularity is more or less circular. It is physical particulars that can gain or lose circularity, gain or lose harmony. One can get more or less harmonious, but once a lyre always a lyre. The harmony, then, is nothing particular to the lyre; the lyre may have a particular sound in some other aspect, but qua harmonious it participates in the same harmony as every other harmonious object. “Harmonious” is the type, and the extension of the set of physical tokens (musical instruments) cannot be fixed with physical criteria; harmony is formalized in musical notation.

In fact causation runs the other way. Instruments were developed (over a more or less long period of time involving trial and error) according to how well various materials, constructions, forms and so forth achieved harmony. Musical instruments come to be, and are caused to have the physical properties that they have, by virtue of the principles of harmonics. Music is a clear case where the formal property (of harmony) is the antecedent cause of the formation of a set of physical particulars (musical instruments) that exist because they participate in the property. If someone asks, “Why is the lyre shaped like that?” the right answer is, “Because that shape is harmonic.”

Here is the argument towards which I have been working: Consider the three properties circularity, harmony and rationality. They are all formal properties: they are all supervenient and they are all formalizable. The property of rationality is a very fancy formal property compared to circularity, to be sure. But rationality does not constitute, relative to circularity and harmony, any new ontological category. A circular object is an example of an object that possesses both physical and formal properties (in fact both Plato and Aristotle thought that all physical objects possessed formal properties). Meanwhile “immortality of soul” is neither more nor less than “immortality of form.” Remember that ontologically speaking there is only one form: form is a unity, matter a multiplicity. That both a rational human and a circular piece of chalk are involved in the same dualism of form and matter seems difficult to dispute.

Although Plato never, to my knowledge, uses panpsychist language to the effect that non-living objects such as pieces of chalk have souls (a view more explicit in the double-aspect ontology of Spinoza), neither does he say they don’t. Anyway he could be using the word “soul” to refer specifically to rationality and that wouldn’t affect the basic argument here. Socrates comforts his human friends with the argument that humans are constituted out of both matter and rationality, a formal property, and as form is immortal, so that element of humans will never pass away. But obviously a circular object is constituted out of both matter and circularity, and so anything said about a rational object also follows for a circular object as both are understood as possessing a formal property, and the argument turns on the immortality of form.

The result is that what we have been calling “the problem of rationality” turns out to be an instance of a quite general metaphysical problem, the form/matter problem. Now I can discuss the “resolution” to the problem of rationality that this constitutes, but first there are two discussions that are owed to those who have read up to here. The first discussion is about the relationship between the form-matter distinction and materialism: is materialism unable to give a naturalistic account of the formal properties of the universe, including the mind? The second discussion is about whether or not an eliminativist, externalist solution to the problem of representation (such as the one I proposed in the first half of this chapter) can coexist with a Platonic resolution to the problem of rationality.


  1. "Plato posits degrees of being, contrary to the materialist’s zero-sum understanding of being."

    I don't think "zero-sum" is exactly the adjective you want there. If I understand the term, it's a category in game theory. Poker is a zero-sum game, because every dollar one player wins, another player loses. Bargaining for employment conditions is a positive sum game, because at the end of the day (one hopes) one party will have gained a valuable employee and the other a desired job, although the particular distribution of the positive result is at issue in the negotiations. War is a negative-sum game, because much of what is lost isn't a gain for anyone.

    I'm not sure you mean to say a materialist has a zero-sum understanding of being in anything like that sense. If you do mean that, you've lost me.

    What you more likely mean here is that a materialist has a "binary" conception of being. Either the cow is or it isn't: 0 or 1. Right?

  2. Christopher, You are right, the phrase i want is "binary," not "zero sum." This is one of the reasons I post these sections, to get comments and corrections. I'll change that passage in the manuscript today. Thanks.