250 THE GROUNDWORK OF SCIENCE

appear to be "truths" at all. A straight line for them

would not be the shortest line between two points, while

two parallel lines prolonged would enclose a space.

But beings so extraordinarily defective might well be

supposed incapable of perceiving geometrical truths evident

enough to others less imperfect such as ourselves. Never-

theless, if they could at all conceive of the things we denote

by the terms " straight lines " and " parallel lines," then

there is nothing to show that they could not also perceive

those same necessary truths concerning them which are

evident to us.

It is strange that the very men who brought forward this

fanciful objection actually showed, by the way they made it,

that they themselves perceive the necessary truths of those

very geometrical relations the necessity of which they

verbally denied. For how, otherwise, could they affirm what

would or would not be the necessary results attending such

imaginary conditions? How could they confidently declare

what perceptions such conditions would certainly produce,

unless they were themselves convinced of the validity of the

laws regulating the experiences of such beings? Anyone

who should affirm (as they did) that they can perceive what

would necessarily be the truth with regard to the perceptions

of such beings, would thereby implicitly assert the existence

of some necessary truths, or else their own argument itself

must fail as utterly futile.

There is one more general principle which, for the end

we have in view, we must endeavour to depict as fully as

we can, namely, the principle of causation. It is, however,

so important in our eyes that we will reserve its treatment

for the following chapter, and terminate the present one by

presenting to our readers the remarks we have yet to make

with respect to the process of reasoning.

The process of deduction, its validity, and the force of the

appear to be "truths" at all. A straight line for them

would not be the shortest line between two points, while

two parallel lines prolonged would enclose a space.

But beings so extraordinarily defective might well be

supposed incapable of perceiving geometrical truths evident

enough to others less imperfect such as ourselves. Never-

theless, if they could at all conceive of the things we denote

by the terms " straight lines " and " parallel lines," then

there is nothing to show that they could not also perceive

those same necessary truths concerning them which are

evident to us.

It is strange that the very men who brought forward this

fanciful objection actually showed, by the way they made it,

that they themselves perceive the necessary truths of those

very geometrical relations the necessity of which they

verbally denied. For how, otherwise, could they affirm what

would or would not be the necessary results attending such

imaginary conditions? How could they confidently declare

what perceptions such conditions would certainly produce,

unless they were themselves convinced of the validity of the

laws regulating the experiences of such beings? Anyone

who should affirm (as they did) that they can perceive what

would necessarily be the truth with regard to the perceptions

of such beings, would thereby implicitly assert the existence

of some necessary truths, or else their own argument itself

must fail as utterly futile.

There is one more general principle which, for the end

we have in view, we must endeavour to depict as fully as

we can, namely, the principle of causation. It is, however,

so important in our eyes that we will reserve its treatment

for the following chapter, and terminate the present one by

presenting to our readers the remarks we have yet to make

with respect to the process of reasoning.

The process of deduction, its validity, and the force of the