William of Ockham

On Quantity

Excerpted from Tractatus de corpore Christi, OTh 10: 157-9

It remains after this to show that not only can a substance be quantified without a quantity added to it, but also that a substance is quantified through its essential parts without any quantity which is another separate entity in reality, distinct from substance and quality.

Let me persuade you first in this way: it is pointless to explain by supposing many things what can be explained by supposing fewer. For this is a principle which should not be denied, because no plurality must be supposed unless it is by reasoning or by experience or by the authority of one who cannot be deceived, nor be mistaken, nor be overcome. But since substance can be quantified, and similarly quality can be quantified, without such a quantity distinct from substance and quality, therefore neither reason nor experience can convince us that there is another such distinct quantity.

Original Latin

Nec hoc invenitur expressum ab aliquo auctore qui non potest errare, quia non invenitur a Deo fuisse revelatum; igitur non est necesse ponere talem quantitatem, et ita frustra poneretur.

Omnia enim quae possent salvari per talem rem, possunt salvari sine ea, per hoc quod substantia [materialis est] habens partes substantiales distinctas realiter, natas distare localiter, quae partes tam substantiae quam qualitatum virtute causae efficientis et finalis sicut in esse producuntur, ita fiunt distantes. Eadem enim virtute qua diversae partes substantiae et qualitatum de non esse procedunt ad esse, etiam in distinctis locis capiunt esse. Et ideo sicut nihil praeter causam efficientem, finalem, formalem et materialem necessario requiritur nec praeexigitur ad hoc quod substantia et partes substantiae de non esse producantur ad esse, ita nihil praeter praedictas causas requiritur necessario ad hoc quod una pars substantiae sit extra aliam partem vel distans ab alia parte.

Quis enim prohiberet Deum producere unam substantiam vel qualitatem sine omni accidente distincto a substantia et qualitate? Et quis prohiberet Deum ponere unam partem illius substantiae vel qualitatis extra aliam absque dissolutione illius substantiae vel qualitatis absque re alia absoluta, distincta realiter, si possit hoc facere mediante tali re distincta? Hoc enim videtur nimis artare divinam potentiam dicere quod una re producta a Deo habente partes distinctas realiter Deus non possit facere eas distare localiter nisi dando eis rem novam vel nisi unitatem rumpat vel dissolvat.