“These objects are commonly called points; but to remove all notion of space relations, it may be better to name them monads.”

—  Charles Sanders Peirce

Source: Mathematical Monads (1889), p. 268
Context: As the mathematics are now understood, each branch — or, if you please, each problem, — is but the study of the relations of a collection of connected objects, without parts, without any distinctive characters, except their names or designating letters. These objects are commonly called points; but to remove all notion of space relations, it may be better to name them monads. The relations between these points are mere complications of two different kinds of elementary relations, which may be termed immediate connection and immediate non-connection. All the monads except as serve as intermediaries for the connections have distinctive designations.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "These objects are commonly called points; but to remove all notion of space relations, it may be better to name them mo…" by Charles Sanders Peirce?
Charles Sanders Peirce photo
Charles Sanders Peirce 121
American philosopher, logician, mathematician, and scientist 1839–1914

Related quotes

Alfred Korzybski photo

“From this point of view, all language can be considered as names for unspeakable entities on the objective level, be it things or feelings, or as names of relations.”

Alfred Korzybski (1879–1950) Polish scientist and philosopher

Source: Science and Sanity (1933), p. 20.
Context: The only link between the verbal and objective world is exclusively structural, necessitating the conclusion that the only content of all "knowledge" is structural. Now structure can be considered as a complex of relations, and ultimately as multi-dimensional order. From this point of view, all language can be considered as names for unspeakable entities on the objective level, be it things or feelings, or as names of relations. In fact... we find that an object represents an abstraction of a low order produced by our nervous system as the result of a sub-microscopic events acting as stimuli upon the nervous system.

Isaac Newton photo

“I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Definitions - Scholium
Philosophiæ Naturalis Principia Mathematica (1687)

Iamblichus photo

“The dyad gets its name from passing through or asunder; for the dyad is the first to have separated itself from the monad, whence also it is called "daring." For when the monad manifests unification, the dyad steals in and manifests separation.”

Iamblichus (240–320) Syrian philosopher

On the dyad
The Theology of Arithmetic

Bertrand Russell photo

“Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

Leonardo Da Vinci photo

“The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and this being its nature it occupies no space. Therefore an infinite number of lines may be conceived of as intersecting each other at a point, which has no dimensions and is only of the thickness (if thickness it may be called) of one single line.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), II Linear Perspective

Denis Diderot photo

“Time, matter, space — all, it may be, are no more than a point.”

Denis Diderot (1713–1784) French Enlightenment philosopher and encyclopædist

Dying words of Nicholas Saunderson as portrayed in Lettre sur les aveugles [Letter on the Blind] (1749)
Variant translation:
What is this world of ours? A complex entity subject to sudden changes which all indicate a tendency to destruction; a swift succession of beings which follow one another, assert themselves and disappear; a fleeting symmetry; a momentary order.
Context: What is this world? A complex whole, subject to endless revolutions. All these revolutions show a continual tendency to destruction; a swift succession of beings who follow one another, press forward, and vanish; a fleeting symmetry; the order of a moment. I reproached you just now with estimating the perfection of things by your own capacity; and I might accuse you here of measuring its duration by the length of your own days. You judge of the continuous existence of the world, as an ephemeral insect might judge of yours. The world is eternal for you, as you are eternal to the being that lives but for one instant. Yet the insect is the more reasonable of the two. For what a prodigious succession of ephemeral generations attests your eternity! What an immeasurable tradition! Yet shall we all pass away, without the possibility of assigning either the real extension that we filled in space, or the precise time that we shall have endured. Time, matter, space — all, it may be, are no more than a point.

John Dee photo

“Neither the circle without the line, nor the line without the point, can be artificially produced. It is, therefore, by virtue of the point and the Monad that all things commence to emerge in principle.
That which is affected at the periphery, however large it may be, cannot in any way lack the support of the central point.”

John Dee (1527–1608) English mathematican, astrologer and antiquary

Theorem II
Monas Hieroglyphica (1564)

Iamblichus photo

“The Pythagoreans called the monad "intellect" because they thought that intellect was akin to the One; for among the virtues, they likened the monad to moral wisdom; for what is correct is one.”

Iamblichus (240–320) Syrian philosopher

On the Monad
The Theology of Arithmetic
Context: The Pythagoreans called the monad "intellect" because they thought that intellect was akin to the One; for among the virtues, they likened the monad to moral wisdom; for what is correct is one. And they called it "being," "cause of truth," "simple," "paradigm," "order," "concord," "what is equal among the greater and the lesser," "the mean between intensity and slackness," "moderation in plurality," "the instant now in time," and moreover they call it "ship," "chariot," "friend," "life," "happiness."

Iamblichus photo

“Anatolius says that it is called "matrix" and "matter," on the grounds that without it there is no number.
The mark which signifies the monad is the source of all things.”

Iamblichus (240–320) Syrian philosopher

On the Monad
The Theology of Arithmetic
Context: Likewise, they call it "Chaos," which is Hesiod's first generator, because Chaos gives rise to everything else, as the monad does. It is also thought to be both "mixture" and "blending," "obscurity" and "darkness" thanks to the lack of articulation and distinction of everything which ensues from it.
Anatolius says that it is called "matrix" and "matter," on the grounds that without it there is no number.
The mark which signifies the monad is the source of all things.

Alan Keyes photo

“Sex itself only exists in relation to procreation. That's one of the reasons why I sometimes object — and it's just a theoretical objection, but it's worth thinking about — to the whole notion that one calls what people of the same sex do "sexual relations." As a matter of fact, they have precisely turned their back on sexual relations, in order to engage in acts of mutual pleasure that have nothing whatsoever to do with sexuality.”

Alan Keyes (1950) American politician

National Federation of Republican Assemblies, NYC, August 31, 2004. http://renewamerica.us/archives/speeches/04_08_31nfra.htm.
2009

Related topics