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What the Absolute Minimum is.
The Absolute Maximum and Minimum coincide without any contradiction.
Boethius, the author of this striking statement original: "epiphonematis," a rhetorical term for a pithy or concluding exclamation, says clearly in Book 1 of his Arithmetic, as does Cardinal Cusanus in his book On Learned Ignorance original: "de docta ignor." referring to Nicholas of Cusa’s famous 15th-century work "De Docta Ignorantia", that the absolute maximum coincides with the absolute minimum—indeed, that they are the same. Let us see how this is to be understood. The "absolute maximum" in this context denotes nothing other than the greatest possible thing, than which nothing greater can be provided; it is infinite truth, incomprehensible to any human or angelic intellect. For since this maximum is not at all of the nature of those things which admit "the exceeding" and "the exceeded" meaning things that can be compared as more or less, it must necessarily be above everything that can be expressed by the concept of our mind. For all things, whatever they may be, that are apprehended by us through reason or intellect differ so much among themselves and from one another that no precise equality can ever be assigned between them. However, that "greatest equality" is that which is neither other than nor different from anything else, nor does it imply any excess or defect. Thus, being placed above all intellect, it deservedly exceeds every concept of the mind, and so is absolutely the same as the maximum. Furthermore, since this absolute maximum is everything that can possibly be, and the "absolute minimum" is that than which a smaller cannot be conceived, it is clear that the absolute maximum coincides with the absolute minimum. Therefore, the oppositions which the apprehension of our weak mind establishes only have a place in those things that allow for "more" and "less." But the maximum and minimum, just as they are above all opposition, so they can contain no excess or defect in their concept, as Cusanus learnedly proves.
Boethius’s statement is proved.Since, therefore, the absolute maximum is absolutely all things in actuality original: "actu," a philosophical term meaning fully realized or "in act," as opposed to "in potential" that can possibly exist, it is necessary that it coincide with the minimum without any opposition. And thus, that which exists above every affirmation and negation, and above all that can be conceived, is conceived "to be" no more than "not to be"; and everything that is conceived "not to be" is no more "not to be" than it "is." Truly, this is so, that it is all things; and so all things, that it is none; and so the maximum that it is the minimum; so light, that it is darkness; original: "vti enim tenebræ eius, ita & lux eius" for as his darkness is, so also is his light A reference to Psalm 139:12, suggesting that from God's perspective, opposites are identical. Otherwise, God could not be all possible things in actuality if He were not infinite and the boundary of all. This, however, transcends all intellect, which cannot combine contradictories in its own source through the path of reason; for we walk by those things known to us by nature itself, which—falling far short of this infinite power—cannot simultaneously connect the very contradictories that are separated by an infinite distance. Therefore, above every path of reason, we see that incomprehensible absolute or infinite maximum, to which nothing is opposed, coincide with the minimum. Thus, "Maximum" and "Minimum" in this place are transcendent terms of absolute meaning which, in their absolute simplicity, encompass all things above every "contraction" original: "contractionem," a technical term used by Cusanus to describe how the infinite is limited or "contracted" into specific, finite forms to a quantity of bulk or power. And this maximum