"The concept-systems of antithesis are concepts that are indeed thoroughly determined by negative predicates but are not positively representable. Just because a precise and complete representation of these concept-systems is impossible, they are inaccessible to direct investigation and elaboration by our reflection. They may, however, be regarded as lying at the limit of the representable, i.e., we can form a concept-system lying within the representable, which passes over into the given system by simple change of magnitude ratio. By abstracting from the ratios of the quantities, the concept-system remains unchanged in case of transition to the limit. At the limit itself, however, some of the correlative concepts of the system lose their susceptibility of being represented, and those, indeed, that mediate the relation between other concepts."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
General Relation of the Concept System of Thesis and Antithesis
https://en.wikiquote.org/wiki/Bernhard_Riemann
Revision History
No revisions have been submitted for this quote.
Categories
Bernhard Riemann
Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry.
69 quotes on TrueQuotesView all quotes by Bernhard Riemann →
Related Quotes
"As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was…"
"Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisat…"
"Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison wi…"
"If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisa…"
"Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only b…"
"For Space, when the position of points is expressed by rectilinear co-ordinates, ds = \sqrt{ \sum (dx)^2 }; Space is …"
"Let us imagine that from any given point the system of shortest lines going out from it is constructed; the position …"
"With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appea…"
"Mind-masses entering the soul appear to us as ideas, the quality of the latter depending on the inner state of the fo…"
"Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordanc…"