254 THE GROUNDWORK OF SCIENCE

Such cases are, however, most rare. No one can pretend

to know by a complete induction that all the radii of a

circle are equal. It is absolutely impossible to examine

all existing circles ; besides, the assertion that all the radii

of a circle are equal applies not only to all existing, but

also to all possible, circles.

Similarly, if we are shown a triangular figure and are

asked, " Are its angles equal to two right angles ? " we

may not be able at once to answer the question by

directly inspecting the figure. If, however, we already

know that the angles of every triangle are together equal

to two right angles, then we should be able at once to

infer the truth, and to say that in so far as the figure

approximated to an ideally perfect triangle, would its

three angles approximate to two absolutely perfect right

angles. We should arrive at this truth mediately, and

reach the conclusion by the combined help of a major

and minor premiss.

A very great part of the knowledge we acquire throughout

our whole lives is acquired, in this indirect way, by the help

of that mental process which is expressed by the word

" therefore."

But we have no special reason to be proud of that

word, since it implies that we are compelled to get at truth

by a very roundabout process. Were our intellect of a

much higher order,* it is conceivable that we might be

able to see equally well, and at one and the same time,

all those truths which a proposition may contain implicitly

as well as explicitly. In that case, of course, we should

be saved the trouble of any process of inference. The

truths we now have to gather indirectly, would then be

directly evident to us, just as our own actual mental activity

is evident to us. Only having, however, the imperfect

* See ante, p. 102.

nature we possess, we must be content with the more

laborious, though practically sufficient, process of inference

or ratiocination. We must be content to gain actual

knowledge from implicit truth by placing propositions

side by side, and so evolving explicit truth as a consequence

of that process properly performed.

Reasoning, then, is an indirect process of attaining truths,

and one which, when properly carried out, is necessarily

and self-evidently true. It is not, however, the highest

kind of act our intellect is capable of. Its highest possible

act is the direct apprehension, or intellectual intuition, of

a universal and necessary truth or of a concrete fact as

absolutely certain and self-evident.

Just, however, as certainty, self-perception, the principle of

contradiction and axiomatic truths, may be perceived directly

with reflex advertence to each, so also correct reasoning can

be carried on, and the force of the term " therefore " (as the

expression of a truth which is a consequent from truths ante-

cedently known) appreciated, without any reflex consciousness

of ratiocination as a process, and a process performed by us.

It is, of all things, important to note and keep in mind

the truth, that " thought," as we know and experience it,

is our only means of arriving at knowledge, and gives the

highest certainty thereto. It is evidently necessary to state

this very distinctly, since there are men who profess to be

philosophers and yet ignore or deny this truth. To suppose

that by any kind of reasoning we can come to understand what

we can never think, may seem an utterly incredible folly ; yet

at a meeting of a metaphysical society in London, a speaker,

a few years ago, expressly declared " thought " to be a mis-

leading term, the use of which should be avoided.

"Thoughts" may be, and should be, carefully examined

and criticised ; but however much we may do so, and what-

ever the results we may arrive at, such results can, manifestly,

Such cases are, however, most rare. No one can pretend

to know by a complete induction that all the radii of a

circle are equal. It is absolutely impossible to examine

all existing circles ; besides, the assertion that all the radii

of a circle are equal applies not only to all existing, but

also to all possible, circles.

Similarly, if we are shown a triangular figure and are

asked, " Are its angles equal to two right angles ? " we

may not be able at once to answer the question by

directly inspecting the figure. If, however, we already

know that the angles of every triangle are together equal

to two right angles, then we should be able at once to

infer the truth, and to say that in so far as the figure

approximated to an ideally perfect triangle, would its

three angles approximate to two absolutely perfect right

angles. We should arrive at this truth mediately, and

reach the conclusion by the combined help of a major

and minor premiss.

A very great part of the knowledge we acquire throughout

our whole lives is acquired, in this indirect way, by the help

of that mental process which is expressed by the word

" therefore."

But we have no special reason to be proud of that

word, since it implies that we are compelled to get at truth

by a very roundabout process. Were our intellect of a

much higher order,* it is conceivable that we might be

able to see equally well, and at one and the same time,

all those truths which a proposition may contain implicitly

as well as explicitly. In that case, of course, we should

be saved the trouble of any process of inference. The

truths we now have to gather indirectly, would then be

directly evident to us, just as our own actual mental activity

is evident to us. Only having, however, the imperfect

* See ante, p. 102.

nature we possess, we must be content with the more

laborious, though practically sufficient, process of inference

or ratiocination. We must be content to gain actual

knowledge from implicit truth by placing propositions

side by side, and so evolving explicit truth as a consequence

of that process properly performed.

Reasoning, then, is an indirect process of attaining truths,

and one which, when properly carried out, is necessarily

and self-evidently true. It is not, however, the highest

kind of act our intellect is capable of. Its highest possible

act is the direct apprehension, or intellectual intuition, of

a universal and necessary truth or of a concrete fact as

absolutely certain and self-evident.

Just, however, as certainty, self-perception, the principle of

contradiction and axiomatic truths, may be perceived directly

with reflex advertence to each, so also correct reasoning can

be carried on, and the force of the term " therefore " (as the

expression of a truth which is a consequent from truths ante-

cedently known) appreciated, without any reflex consciousness

of ratiocination as a process, and a process performed by us.

It is, of all things, important to note and keep in mind

the truth, that " thought," as we know and experience it,

is our only means of arriving at knowledge, and gives the

highest certainty thereto. It is evidently necessary to state

this very distinctly, since there are men who profess to be

philosophers and yet ignore or deny this truth. To suppose

that by any kind of reasoning we can come to understand what

we can never think, may seem an utterly incredible folly ; yet

at a meeting of a metaphysical society in London, a speaker,

a few years ago, expressly declared " thought " to be a mis-

leading term, the use of which should be avoided.

"Thoughts" may be, and should be, carefully examined

and criticised ; but however much we may do so, and what-

ever the results we may arrive at, such results can, manifestly,