What is the absolute maximum and absolute minimum?

Nicholas of Cusa, answered from the texts and cited to the page.

Nicholas of Cusa answers

The absolutely Maximum is that than which nothing greater can be conceived, and the absolutely Minimum is that than which nothing lesser can be conceived.1 At first hearing, these sound like two distinct things standing at opposite poles of some scale — the largest and the smallest. But the whole force of what I argue in De Docta Ignorantia (the three-book treatise of 1440 on learned ignorance and the boundless universe) is that this appearance deceives us, because the very opposition between greater and lesser belongs only to the domain of finite, comparable things.

Consider quantity. Maximum quantity is maximally large; minimum quantity is maximally small. These are genuinely opposed — one is at the top of the scale, the other at the bottom. But now perform the mental operation I propose: remove quantity from both terms, strip away the large and the small, and what remains? What remains is the superlative itself, in absolute simplicity, freed from all contraction to mass or power.1

And when the superlative is freed from the finite scale that made the two poles distinct, they collapse into one another. The Maximum coincides with the Minimum because opposing features belong only to things that can be comparatively greater and lesser; they do not befit the absolutely Maximum at all, since it is beyond all opposition.2 This is why the absolutely Maximum is beyond both all affirmation and all negation.2

To say "God is light" is to say "God is maximally light in such way that He is minimally light" — which is to say that the finite predicate, applied absolutely, overreaches itself and cancels its own limitation.2 The Maximum is all that which can be, and precisely because it is altogether actual, there can be no lesser either, for the Minimum is that than which there cannot be a lesser, and the Maximum already is such.1

The same structure governs number. Ascending the scale of numbers, we never arrive at an actually infinite number, because such a number would be no number at all — to be infinite number and to be minimally number amount to the same thing.3 Descending, we arrive necessarily at oneness, the minimum than which there cannot be a lesser.3 The infinite and the one thus mirror each other as the transcendent bounds of the number-series, neither of them a member of the series they bound.

What this means for theology is not a paradox to be swallowed but a structural consequence to be understood: the absolutely Maximum cannot be bounded by any of the things it encompasses, and so it is infinite; and because it is infinite, nothing is opposed to it, and the Minimum coincides with it.1 The principle of non-contradiction is not violated — it holds at the level of ratio, of discursive reason working among finite comparable things.

What I am pointing toward is the level of intellectus, the higher faculty that grasps the coincidence by seeing that the contrastive relations of finite reason simply do not bind the unconditioned ground from which those relations derive.

Sources

  1. since it is not of the nature of those things which can be comparatively greater and lesser, it is beyond all that we can conceive... the absolutely Maximum is all that which can be, it is altogether actual. And just as there cannot be a greater, so for the same reason there cannot be a lesser, since it is all that which can be. But the Minimum is that than which there cannot be a lesser. And since the Maximum is also such, it is evident that the Minimum coincides with the Maximum.
    De Docta Ignorantia I, p. 9
  2. Therefore, because the absolutely Maximum is absolutely and actually all things which can be (and is so free of all opposition that the Minimum coincides with it), it is beyond both all affirmation and all negation... to say 'God, who is Absolute Maximality, is light' is no other than 'God is maximally light in such way that He is minimally light.'
    De Docta Ignorantia I, p. 9
  3. maximum and minimum, as used in this book, are transcendent terms of absolute signification, so that in their absolute simplicity they encompass—beyond all contraction to quantity of mass or quantity of power—all things... to be infinite number and to be minimally number amount to the same thing. Therefore, in numbering, it is necessary to come to a minimum than which there cannot be a lesser, viz., oneness.
    De Docta Ignorantia I, p. 10