SHAWORDS

But as the Pythagoreans define a point to be unity having position, le — 1 (number)

Home›1 (number)›Quote
"But as the Pythagoreans define a point to be unity having position, let us consider what they mean. That numbers, indeed, are more immaterial and more pure than magnitudes, and that the principle of numbers is more simple than the principle of magnitudes, is manifest to every one: but when they say that a point is unity endued with position, they appear to me to evince that unity and number subsist in opinion: I mean monadic number. On which account, every number, as the pentad and the heptad, is one in every soul, and not many; and they are destitute of figure and adventitious form. But a point openly presents itself in the phantasy, subsists, as it were, in place, and is material according to intelligible matter. Unity, therefore, has no position, so far as it is immaterial, and free from all interval and place: but a point has position, so far as it appears seated in the bosom of the phantasy, and has a material subsistence. But unity is still more simple than a point, on account of the community of principles. Since a point exceeds unity according to position; but appositions in incorporeals produce diminutions of those natures, by which the appositions are received."
1
1 (number)
1
1 (number)
1 (number)
author25 quotes

1 is a number, numeral, and grapheme. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, and represents a single thing. The representation of 1 e

More by 1 (number)

View all →
Quote
"When do centuries end?—at the termination of years marked 99 (as common sensibility suggests), or at the termination of years marked 00 (as the narrow logic of a peculiar system dictates)?... the source of all our infernal trouble about the ends of centuries may be laid at the doorstep of a sixth-century monk named , or (literally) Dennis the Short. ...Dennis neglected to begin time with year zero, thus discombobulating all our usual notions of counting. During the year that Jesus was one year old, the time system that supposedly started with his birth was two years old. (Babies are zero years old until their first birthday; modern time was already one year old at its inception.) The absence of a year zero also means that we cannot calculate algebraically (without making a correction) through the B.C.-A.D. transition. ...The problem of centuries starts from Denniss unfortunate decision to start with year one, rather than year zero... logic and sensibility do not coincide, and since both have legitimate claims upon our decision, the great and recurring debate about century boundaries simply cannot be resolved. ...One might argue that humans, as creatures of reason, should be willing to subjugate sensibility for logic; but we are, just as much, creatures of feeling. And so the debate has progressed at every go-round."
1
1 (number)
Quote
"Those numbers... independent of the particular things which happen to undergo counting—of what are these... ? To pose this question means to raise the problem of "scientific" arithmetic or logistic. ...we are no longer interested in the requirements of daily life ...now our concern is rather with understanding the very possibility of this activity, with understanding... that knowing is involved and that there must... be a corresponding being which possesses that permanence of condition which first makes it capable of being "known." But the souls turning away from the things of daily life, the changing of the direction... the "conversion" and "turning about"... leads to a further question... What is required is an object which has a purely noetic character and which exhibits at the same time... the countable... This requirement is exactly fulfilled by the "pure" units, which are "nonsensual," accessible only to the understanding, indistinguishable from one another, and resistant to all participation. The "scientific" arithmetician and logistician deals with numbers of pure monads. And... Plato stresses emphatically that there is "no mean difference" between these and the ordinary numbers. ...Only a careful consideration of the fact... forces us into the further supposition that there must indeed be a special "nonsensual" material to which these numbers refer. The immense propaedeutic importance... within Platonic doctrine is immediately clear, for is not a continual effort made in this doctrine to exhibit as the true object of knowing that which is not accessible to the senses? Here we have indeed a "learning matter"... "capable of hauling [us] toward being". It forces the soul to study, by thought alone, the truth as it shows itself by itself. ...ability to count and to calculate presupposes the existence of "nonsensual" units. Thus an unlimited field of "pure" units presents itself to the view of the "scientific" arithemetician and logistician."
1
1 (number)
Quote
"The first definition of number is attributed to Thales, who defined it as a collection of units... following the Egyptian view. The Pythagoreans made number out of one [Aristotle, Metaph. A. 5, 986 a 20]; some of them called it a progression of multitude beginning from a unit and a regression ending in it [, p. 18. 3-5]. Stobaeus credits Modoratus, a Neo-Pythagorean of the time of Nero, with this definition.) Eudoxus defined number as a determinate multitude... has yet another definition, a flow of quantity made up of units... Aristotle gives a number of definitions equivalent to one or other of those just mentioned, limited multitude, multitude (or combination) of units, multitude of indivisibles, several ones... multitude measurable by one, multitude measured, and multitude of measures (the measure being the unit)."
1
1 (number)