Nominalism

William of Ockham's case for nominalism rests on the principle now named for him, that entities should not be multiplied beyond necessity: if every particular red object, a rose, a ruby, a sunset, can be adequately explained and classified without positing a further, separately existing universal, redness, that all of them somehow share or participate in, then that further entity is explanatorily idle and should be eliminated from one's ontology, leaving only the particular things themselves and the general words and concepts the mind uses to sort them into groups based on resemblance. This was a direct challenge to the realist tradition running from Plato's theory of Forms through much of medieval scholastic philosophy, which held that universals are genuinely real, existing either independently of particulars, as Plato argued, or at least really present in particulars themselves, as Aristotle's more moderate realism held.

Ockham's nominalism did not deny that things resemble one another, or that general words are useful and even necessary for thought and language, only that this resemblance and usefulness require a separately existing universal entity to explain them, arguing instead that resemblance among particulars is itself a brute, unanalyzed fact, or at most a matter of particulars sharing similar, but still entirely particular, properties, a further refinement called trope theory that later nominalists developed to avoid resting everything on unexplained resemblance alone.

The medieval debate over universals that nominalism belongs to was never a purely abstract exercise, since it bore directly on how theologians could speak of God's attributes, goodness, wisdom, justice, being shared, whether literally or only by analogy, across God and creatures, and nominalism's insistence that general terms name no further real, shared entity pushed theology in this period toward treating divine attributes as either radically unique to God, or as convenient labels rather than descriptions of any real, common property; this theological stake is a major reason the dispute mattered so intensely to figures who were, first and foremost, working theologians rather than detached metaphysicians. Realists about universals answer nominalism's parsimony argument by insisting that shared resemblance itself, real red things genuinely being similar to one another in a way that is not just a matter of a shared name, is exactly the phenomenon that needs explaining, and that nominalism, for all its economy, ultimately explains classification by simply redescribing it rather than accounting for why the classifications track anything real at all; nominalists reply that this demand for a further explanation of resemblance is precisely the unnecessary posit their razor is designed to cut away.