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scalenon and instead of “ all and none of these at once ” (“all” denoting 
several particulars united by the conjunction “and,” and “none” denoting 
several particulars disjoined by the particle “ nor ”), he should have said 
“ some one of these at a time, and no more.” Abstract ideas, like their 
signs (which in ordinary language are words or names, and in algebraic 
language are letters or symbols), can only be presented to the mind singly. 
If we think of man in the abstract, we do not think of him as a human 
being without any features, nor, on the other hand, as possessing all the 
various features at once that a human being can have, but as having one 
set of features out of many, — those of either Peter, James, or John, for 
example. And if we think of any algebraic question involving numbers, we 
take a letter (<z, for instance) not to represent at the same time all numbers 
or none , but some particular number {either 3, 5, 10, &c.), and it must 
denote the same number throughout the calculation. Thus, abstract ideas 
and the words or symbols which represent them are, as Locke confesses, 
“ fictions and contrivances of the mind.” They serve for convenience in 
reasoning or speech, but have no objective existence. 
And if this is so with respect to ideas, still more is it the case with 
the objects they are supposed to represent. To avoid confusion, however, 
it should be remarked that there are two kinds of abstraction 1. We 
may think of a subject without reference to certain of the qualities 
belonging to it. This is the kind of abstraction which leads up from indi- 
viduals to species and genera. Or, 2. We may think of a certain quality 
without reference to the subject to which it belongs, as of whiteness, for 
example, which may belong to several different materials. I am disposed 
to think that some philosophical errors have arisen from not observing this 
distinction. As an example of the second kind of abstraction, existence is 
a quality common to all objects of thought, and may therefore be thought 
of in the abstract. This, however, does not mean that it can be thought of 
apart from everything existing , but as belonging to some one of the innumer- 
able things that exist, no matter which ; and we may think of it at one 
moment as belonging to a book, at another as belonging to a man, or at a 
third as belonging to God. But to think of existence without anything 
that exists is to me impossible. Perhaps some of the philosophical errors 
about the Absolute, and the Unconditioned, and so forth, might have been 
avoided if this distinction had been more attended to. In a similar manner, 
motion apart from anything that moves, whiteness apart from anything 
that is white, &c., are, I venture to think, impossible conceptions, and 
resemble those abstract ideas which, as Mr. Lias justly observes, have no 
objective existence. The term “ Absolute,” denoting existence under no 
relations, and the term “Unconditioned,” denoting existence under no 
conditions, seem to have much the same signification as existence without 
anything that exists. In short, such words, really meaningless, have a kind 
of philosophical ring, calculated only to bewilder and mislead. 
