The Aristotelian Categories
On pages 123-35 of Metaphysics: A Contemporary Introduction, Michael Loux argues that both bundle theory and substratum theory provide unsatisfactory descriptions of the nature of objects. Bundle theory, he says, is empirically sound but requires us to accept the illogical Principle of the Identity of Indiscernibles. Substratum theory evades the PII but requires us to accept the existence of bare particulars. No one can say what a bare particular is, and none appear in the world, so this concept seems to violate the Correspondence Theory of Truth. Loux claims that we can evade the problems of both theories if we accept the existence of categories, Aristotle’s name for irreducibly complex concrete particulars. These categories include living organisms and any irreducible physical objects, such as quarks and photons, which exist. James Van Cleve, in his “Three Versions of The Bundle Theory,” characterizes category theory as a form of bundle theory which contains the same difficulties as bare particulars (Red Book page 125). In this paper, I will argue that Van Cleve’s criticism shows that he does not understand the categories. I will first explain how the categories differ from bundles and then how they differ from substrata. To conclude, I will give some reasons why categories surpass them both.
Van Cleve describes a category as an object F with a bundle of essential properties “X” and a bundle of non-essential properties “Y.” Whereas the X properties are necessary for the continued identity of F, the Y properties came to F accidentally; F can possess as many or as few of them as he likes. This description, innocent as it is, is incorrect. A category is neither a bundle of properties nor a set of bundles. Bundle theory, after all, stipulates that objects are dependent upon their properties for existence. Categories, however, are not dependent on their properties. They are clearly not dependent on the non-essential set of properties “Y.” As for the essential set of properties “X,” these things are actually dependent on the category. The category theory denies the basic assumption of bundle theory. It asserts that an object has properties because it belongs to a category, not vice versa. Just as a caterpillar develops into a butterfly, so a category develops its own properties.
Van Cleve also describes the category as something similar to a bare particular. He argues that the set of essential properties X is too small to instantiate any actual individuals. His example of this is the category “human,” which he imagines would contain the properties “rational” and “animal.” He argues that there is no human whom we would reduce to these traits alone. I agree with him that these two are not the only essential traits for humans. I would at least include emotions and self-awareness in this set. Van Cleve’s incomplete assessment of the essential qualities of humanity does not disprove the existence of essential qualities, though.
Certainly, there are necessary properties for each category which are not filled until the instantiation itself. For instance, every human must have a mother, but the identity of each mother is not included in a human being’s category description. Rather, the property of having a mother is a necessary part of being a mammal, and the specific identity of the mother is a non-essential fact which we determine later. Any traits which seem to be lost in a category’s description are probably folded into the complex universals which the category possesses.
Van Cleve further argues that the many empty spaces within the categories could lead their instantiations to fill their blank property spaces with contradictions. For instance, one instantiation of humans could be wise while another could be foolish. The category “human” would contradict itself.
I do not understand this particular criticism of the category theory. Yes, different instantiations of categories could have contradictory properties, but this seems to mirror the real world. There are both wise and foolish humans. It would be a bigger concern if the same instantiation could have two contradictory properties – a dog that is both sick and healthy, for instance – but this still seems impossible. Contradictory essential properties would indicate serious problems with our classifications, but contradictory non-essential properties are feasible. Each human has a unique genome, so we all contradict each other in this property, but we do all have genomes.
I am sure that Van Cleve meant well in his criticism of category theory; he simply didn’t understand it. In my opinion, category theory is the most satisfactory account of concrete particulars which we have. With categories, we can have objects which are as irreducible as substrata but far more coherent, breaking our dependence upon properties. We can account for change in objects without committing ourselves to the Heraclitean view that objects constantly lose their identities. We can give a satisfactory answer to Descartes’s wax example: the wax can burn all it likes, but if it changes its properties in the radical way which he describes, it is no longer the same object, regardless of its spatiotemporal continuity. If it changes color, shape, hardness, and so forth, but still is a wax, it is the same thing. If a piece of paper is burned, the pile of ashes which it leaves behind shares continuity with the paper, but it is no longer paper. The paper is gone. Only ashes remain.
I think Aristotle’s insight that living beings are irreducible particulars is especially profound. We can create tools, pictures, even lakes and mountains with their hands. We cannot produce life in the same way. Each living being is the product of a cycle of natural reproduction. Only frogs and make frogs; only oak trees can make oak trees, and so forth. When a tool breaks, we can fix it, but when a living being dies, we cannot revive it. I believe that this lends inductive evidence to Aristotle’s contention that animals, plants, and so forth are irreducibly complex. It seems that bundle theorists and substratum theorists, rather than sitting in their ivory towers and assuming they had each solved the mystery of objects, should have spent more time examining the world outside their windows. Category theory explains the mystery of life in a way the other two theories do not.