AN ENUMERATION OF THE SCIENCES 21

a fortiori, its groundwork. But the science of Mathematics

enables us to prove a vast quantity of truths which would

be inaccessible to the human mind without its aid. By its

help truths, applicable to all existing things, can be deduced

from other truths by means of various processes of inference.

But can Mathematics, which thus makes use of "proofs,"

dispense with the aid of that science upon which it thus

leans : which tells us in what proof consists, and lays down

the laws by obedience to which alone valid inference can

be carried on and truth attained? Now, such a science is

Logic. Surely, then, Logic may advance a strong claim

to be the most fundamental, and, therefore, to head our

list of the sciences.

But to comprehend Logic, speech is necessary, and though,

as we shall hereafter see, there are strong grounds for con-

cluding that speech was posterior to thought, nevertheless

here and now, the use of, and a considerable knowledge about,

speech is long anterior to our comprehension of, or even to

the very first application of our minds to, Logic. Therefore,

the science which treats of human speech could also advance

a claim to priority.

But, as before said, Logic is essentially the science of the

art of proof, and all proof must repose upon certain data.

Therefore, such data must, in the first place, be either per-

ceptions which we have concerning our own mental states

and operations, or perceptions concerning external things,

or conceptions of, and reflexions about, one or the other, or

both of these.

But all these are forms of psychical activity, or are the

direct results of different forms of psychical activity. Now

these psychical activities must be anterior to any processes

of reasoning, and form the data whence all reasonings

proceed. But the elucidation of these data is the business

of Psychology. Surely, then, the science which deals with

a fortiori, its groundwork. But the science of Mathematics

enables us to prove a vast quantity of truths which would

be inaccessible to the human mind without its aid. By its

help truths, applicable to all existing things, can be deduced

from other truths by means of various processes of inference.

But can Mathematics, which thus makes use of "proofs,"

dispense with the aid of that science upon which it thus

leans : which tells us in what proof consists, and lays down

the laws by obedience to which alone valid inference can

be carried on and truth attained? Now, such a science is

Logic. Surely, then, Logic may advance a strong claim

to be the most fundamental, and, therefore, to head our

list of the sciences.

But to comprehend Logic, speech is necessary, and though,

as we shall hereafter see, there are strong grounds for con-

cluding that speech was posterior to thought, nevertheless

here and now, the use of, and a considerable knowledge about,

speech is long anterior to our comprehension of, or even to

the very first application of our minds to, Logic. Therefore,

the science which treats of human speech could also advance

a claim to priority.

But, as before said, Logic is essentially the science of the

art of proof, and all proof must repose upon certain data.

Therefore, such data must, in the first place, be either per-

ceptions which we have concerning our own mental states

and operations, or perceptions concerning external things,

or conceptions of, and reflexions about, one or the other, or

both of these.

But all these are forms of psychical activity, or are the

direct results of different forms of psychical activity. Now

these psychical activities must be anterior to any processes

of reasoning, and form the data whence all reasonings

proceed. But the elucidation of these data is the business

of Psychology. Surely, then, the science which deals with