Sunday, February 6, 2011

Wittgenstein and Aristotle?

I’m afraid that some readers will be growing impatient as they read the foregoing discussion of a kind of Platonic resolution to the problem of rationality. Hadn’t I just, in the first half of this same chapter, argued for an operational theory of intentional predicates? Not only that, but when one suggests that the non-physical property of “meaning” can be washed out of the ontology of mind and language (replaced with an externalist account of intentional predicates as describing relations between persons and environments), that would be about as nominalist as one could go, surely?

Maybe not. The Platonism that I am offering has only one element of basic ontology besides matter. Form is indivisible, not divisible; a unity, not a multiplicity. There is only one form really: only one (perhaps inexplicable) ontological fact beyond the fact of the existence of something rather than nothing. Putting the question of Plato and Aristotle’s own views of species as “fixed natural kinds” to the side in favor of a view of species informed by evolutionary biology, it can be seen that putative “forms” such as the property of “cowness” or “lyrehood” are not genuine examples of form. Some categories (types of species, types of artifacts) come-to-be and pass away.

In its Aristotelian version Platonic form-matter dualism becomes a kind of non-reductive materialism: primary being is substance, the unity of form and matter. From the doctrine of the unity of form, though, it appears that this must be a kind of “non-reductive formalism” as well, as every particular with a formal property has that property, not by virtue only of the formally-organized parts of that particular, but by virtue of the entire formal organization of the material world: all geometric shapes (for example) are tokens of the one thing.

We know that by this point Wittgenstein would be fuming, but as usual with him we might not be certain exactly why. Of course Wittgenstein would have none of this Platonic talk. “The idea that in order to get clear about the meaning of a general term one had to find the common element in all its applications has shackled philosophical investigation; for it has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him to understand the usage of the general term. When Socrates asks the question, ‘what is knowledge?’ he does not even regard it as a preliminary answer to enumerate cases of knowledge.” (Blue and Brown Books; italics in original). Wittgenstein’s operationalist account of functional-role semantics is an arch-nominalist position: there is human behavior, a highly-adaptive and plastic process that changes over time, whose constants are determined by the biological (probably the best choice) nature of the human body and the human “mode of life.” “Property” names (like all names) really pick out parts of language, and the criteria for the proper application of language are essentially operational. Insofar as this line is developed as a strategy to naturalize meaning I think it’s a good one.

But I have never thought that philosophy of mathematics was a particularly strong point for empiricists, and that is troubling considering that Wittgenstein devoted a considerable portion of his writings to the development of an operationalist theory of mathematics. In any event I am unpersuaded by Wittgenstein’s view that extending the known proofs of mathematics is nothing more than an elaboration of a kind of “language game,” specific to humans by virtue of our particular “form of life,” such that there was no such system of entailments until some human (for example) elaborated it. It’s counterintuitive: isn’t the fact, that we can work our way from one part of mathematics to another, evidence that mathematical reasoning is coherent? Doesn’t Wittgenstein’s ultra-nominalist view of mathematics overstate the possibility space: the different ways “mathematics” could go?

However, it may be that the two treatments of the two different parts of intentionality - an eliminativist, operationalist argument to the effect that mental representation/content is not part of the reference of intentional predicates, on the one hand, and an Aristotelean argument to the effect that rationality is nothing more nor less than a formal property and that formal properties, if they exist at all, are ubiquitous – are compatible. According to Wittgenstein there are no abstract entities, of course, but it is important to appreciate how far Wittgenstein went in his naturalization of meaning, and how central to this were his ideas about mathematics. Wittgenstein saw mathematical behavior as a “technique,” a technique for living. “Living” is the operational verb that replaces the Cartesian verb “knowing”: a case of knowing how rather than knowing that. Wittgenstein rejected the passivity of the representational theory and insisted on viewing language as a physical behavior that aimed at getting on with the business of life.

Granted that the Aristotelean world is one where every concrete particular is a union of matter and form, the “form of life,” understood as the vital activities of a being of that kind, would exhibit formal properties. In fact “behavioral ecology” develops an entire narrative, largely mathematical, about the ratio of nutrients per square meter to species population per square meter, showing the correlations between these functions and genetic transmission and so forth. The human “form of life,” if it is anything at all, is a product of the same natural history as that of the human organism; the rationality of humans, like the harmony of musical instruments, is an expression of form.

Within this form of life, that stress made no more emphatically by anyone than Wittgenstein himself, the criteria for use of psychological predicates can be understood operationally such that no mental content is implied. In fact Wittgenstein and Aristotle come together in a sense around “form of life” or what Aristotle would call the telos of an organism. They both suspected that explanations about what sort of thing a thing was and what sort of life a thing led were more informative than explanations about what sort of things a thing thought. Wittgenstein thought that the notion of mental content made no sense. I take the argument from the form-matter distinction to show that “computation” need not necessarily entail mental representations; organizational complexity equivalent to the syntactical complexity of language is found throughout nature. Finally, Wittgenstein’s functional-role semantics and Aristotle’s teleological account of biological explanation are very similarly motivated. They come together in the area where functionalism replaces reductive materialism as a response to the supervenient nature of the functional property.


  1. Do That Stuff AHHHHH Do That Stuff The angle of the dangle is increased by the heat of the beat

  2. Might there be something like an experiential argument for Platonism, at least as to mathematical phenomena?

    Mathematicians (with rare exceptions such as Brouwer) certainly believe that they are discovering facts that have been waiting for them. This has been their experience from Pythagoras to Mandelbrot.

    Heinrich Hertz put it well. "One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put into them."

    Who was Hertz that we should pay heed to his views on math? A physicist who obtained his Ph.D. from the University of Berlin in 1880, and whose work helped refine the mathematical theory of electromagnetism developed before him by Faraday and Maxwell. He earned his bones in terms of the relationship between physical reality and abstract formulae employed to describe it. If he believed (as have many others of equal eminence) that the formulae have an independent sort of existence, this isn't testimony that those of us who have shown less facility in their use than he should take lightly!

  3. 1) Hello Paul. I believe it's "The angle of the dangle is increased by the heat of the meat," if I am not mistaken.
    2) Christopher, I very much agree, see the post on Plato's metaphysics and the problem of rationality.