On the Abstract Idea of a Triangle

Everything in nature is individual,
and it is utterly absurd to suppose a triangle really existent, which has no precise proportion of sides and angles.
If this therefore be absurd in fact and reality, it must also be absurd in idea; since nothing of which we can form a clear and distinct idea is absurd and impossible.
But to form the idea of an object, and to form an idea simply, is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character.
Now as it is impossible to form an idea of an object, that is possest of quantity and quality, and yet is possest of no precise degree of either; it follows that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars.
Abstract ideas are therefore in themselves individual, however they may become general in their representation.
The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal.

About Matthew Arnold

English poet and cultural critic. His elegiac verse, including "Dover Beach," captures Victorian spiritual uncertainty.

More poems by Matthew Arnold

View all Matthew Arnold poems →

More Solitude & Reflection poems

View all Solitude & Reflection poems →