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The Collaborative International Dictionary
Manifoldness

Manifoldness \Man"i*fold`ness\, n.

  1. Multiplicity.
    --Sherwood.

  2. (Math.) A generalized concept of magnitude.

Wiktionary
manifoldness

n. 1 The quality of being manifold, diversity. 2 (context mathematics English) multiplicity 3 (context mathematics English) A generalized concept of magnitude.

Usage examples of "manifoldness".

All the manifoldness of things consist only of so many modes of limiting the concept of the highest reality that forms their common substratum, in the same way as all figures are only different modes of limiting endless space.

The manifoldness of things would not depend on the limitation of the original being, but on its complete effect, and to this also would belong all our sensibility, together with all reality in phenomenal appearance, which could not, as an ingredient, belong to the idea of a supreme being.

These laws have therefore a certain utility in this respect also, yet it is easily seen that they regard the parsimony of causes, the manifoldness of effects, and an affinity between the parts of nature arising from thence, as both rational and natural, so that these principles carry their recommendation direct, and not only as aids towards a proper method of studying nature.

It is quite possible to form a definite thought of what is greatest and absolutely complete, when all restrictive conditions that lead to an undefined manifoldness have been omitted.

But this difference of the two maxims of manifoldness or unity in nature may easily be adjusted, though as long as they are taken for objective knowledge they cause not only disputes, but actually create impediments which hinder the progress of truth, until a means is found of reconciling the contradictory interests, and thus giving satisfaction to reason.

It is quite true, no doubt, that empirical laws, as such, cannot derive their origin from the pure understanding, as little as the infinite manifoldness of phenomena could be sufficiently comprehended through the pure form of sensuous intuition.

The world's manifoldness was felt to be not a juxtaposition of single things, externally connected, but the content of this unity, and therefore derived from it.

Now that which connects the manifold of sensuous intuition is the faculty of imagination, which receives from the understanding the unity of its intellectual synthesis, and from sensibility the manifoldness of apprehension.

But this difference of the two maxims of manifoldness and unity in nature, may easily be adjusted, though as long as they are taken for objective knowledge they cause not only disputes, but actually create impediments which hinder the progress of truth, until a means is found of reconciling the contradictory interests, and thus giving satisfaction to reason.