AN ENUMERATION OF 77 fE SCIENCES 19

it pertains to every other, and no other can be pursued

without it.

Nevertheless, another science can advance a claim seem-

ingly as unanswerable in another respect as is the claim of

Mathematics, as just stated. Xo science can claim to be

absolutely primary which has to depend on another science

for explanation and comprehension. Mathematics is a science

of "number"; but what is "number"? Moreover, numbers are

alike or not unlike, and a perception of " likeness and unlike-

ness " was declared, in our introductory chapter, to be at the

base of all the sciences. What, then, it must be further asked,

is " likeness " ? May not the science which can solve these

riddles justly claim to underlie, and be prior to, the science

of Mathematics?

The idea of " number " implies comparison, together with a

recognition that the things compared are similar, and yet not

identical. Things which are quite dissimilar such as, e.g.,

"a violet blossom" and "a fall in consols" cannot be said

to be two, unless it be two expressions or two thoughts in

which respects they are alike. But the idea of number, inas-

much as it recognizes things as similar but not identical,

implies many things besides similarity and identity. In every

perception of number there are, and must be, latent the ideas

of " existence," " distinction," " similarity," " unity," and

' truth," as a little reflexion will show. Thus, to say " there

are two sheep," implies that they are not merely imaginary,

but that they actually exist ; that they are not seen double

by some optical delusion, but are really distinct ; that they

are certainly both sheep and not one of them a goat i.e. t that

they are similar, and that they have that unity of nature

which we have just seen to be necessary in order that they

should be susceptible of numeration, and finally the assertion

implies that the thought of the assertion corresponds with

objective reality, that is, it implies truth.

it pertains to every other, and no other can be pursued

without it.

Nevertheless, another science can advance a claim seem-

ingly as unanswerable in another respect as is the claim of

Mathematics, as just stated. Xo science can claim to be

absolutely primary which has to depend on another science

for explanation and comprehension. Mathematics is a science

of "number"; but what is "number"? Moreover, numbers are

alike or not unlike, and a perception of " likeness and unlike-

ness " was declared, in our introductory chapter, to be at the

base of all the sciences. What, then, it must be further asked,

is " likeness " ? May not the science which can solve these

riddles justly claim to underlie, and be prior to, the science

of Mathematics?

The idea of " number " implies comparison, together with a

recognition that the things compared are similar, and yet not

identical. Things which are quite dissimilar such as, e.g.,

"a violet blossom" and "a fall in consols" cannot be said

to be two, unless it be two expressions or two thoughts in

which respects they are alike. But the idea of number, inas-

much as it recognizes things as similar but not identical,

implies many things besides similarity and identity. In every

perception of number there are, and must be, latent the ideas

of " existence," " distinction," " similarity," " unity," and

' truth," as a little reflexion will show. Thus, to say " there

are two sheep," implies that they are not merely imaginary,

but that they actually exist ; that they are not seen double

by some optical delusion, but are really distinct ; that they

are certainly both sheep and not one of them a goat i.e. t that

they are similar, and that they have that unity of nature

which we have just seen to be necessary in order that they

should be susceptible of numeration, and finally the assertion

implies that the thought of the assertion corresponds with

objective reality, that is, it implies truth.