DOI: 10.4324/9780415249126-N065-1
Version: v1,  Published online: 1998
Retrieved June 16, 2024, from

1. Sources in ancient mathematics and biology

Plato looked to mathematics as a model to find ideal ‘forms’ which can be grasped by the intellect and which we find to be imperfectly reflected in the world of the senses. Moral and political ideals too, Plato thought, are reflected only very imperfectly in the world of appearances. Aristotle’s conception of universals was tailored to fit not mathematics but biology. Individual animals and plants fall into natural kinds, or species, such as pigs or cabbages. Various different species, in turn, fall under a genus.

Universals impose a taxonomy on the plurality of different individuals in the world. Regularities in the world can then be understood by appeal to the universals, or species, under which individuals fall, explaining why pigs never give birth to kittens, for instance, and in general why each living thing generates others of its kind.

Plato conceived of universals as transcendent beings, ante rem in Latin (‘before things’): the existence of universals does not depend on the existence of individuals which instantiated them. This is a natural thought if your model of universals lies in mathematics: geometrical truths about circles, for instance, do not depend on the existence of any individuals which really are perfectly circular. Aristotle, in contrast, held a theory of universals as immanent beings, in rebus (‘in things’): there can be no universals unless there are individuals in which those universals are instantiated. This is a natural thought if your model of universals lies in biology: a species cannot exist, for instance, if there are no animals of that species. Thus, one of the key distinctions between Plato’s transcendent and Aristotle’s immanent realism is that the Platonist allows, and Aristotle does not allow, the existence of uninstantiated universals (see Aristotle §15; Plato).

Citing this article:
Bigelow, John C.. Sources in ancient mathematics and biology. Universals, 1998, doi:10.4324/9780415249126-N065-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2024 Routledge.

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