222 THE GROUNDWORK OF SCIENCE

proof, as also that to accept as true anything which is

incapable of proof, is to accept a conviction blindly.

Of course it is common enough and reasonable enough

to ask for proof to be given with respect to any new or

extraordinary statement, and it is most reasonable not to

assent to any proposition which does not possess sufficient

evidence,

It is also true that the greater part of our knowledge is

gained by us indirectly, by inference or testimony of some

kind. And thus it has come about that many persons (as

before said) have acquired, half unconsciously, a persuasion

that to believe anything which cannot be proved is an act

of irrational credulity, and thus a tendency has arisen to

distrust any assertion for which no proof is offered.

But, as we before pointed out,* however long our processes

of proof may be, they must stop somewhere. We cannot

go on reasoning for ever if anything is ever to be proved.

Therefore, every valid process of reasoning must ultimately

depend upon propositions which need no proof, and are

undemonstrable not "undemonstrable"' because, like matters

which have to be taken on trust, we can obtain no evidence

for them, but because they are so luminously self-evident

that they admit of no demonstration, nothing else being

so clearly and necessarily true as they are. We have,

indeed, just said that it is most reasonable to demand

sufficient evidence for any proposition to which our assent

is demanded. But that evidence need not be external

evidence, and the evidence of those ultimate propositions

which need no proof is, and must be, internal evidence. They

carry with them their own evidence, and so are evident in

and by themselves.

Thus the reasoning of our supposed sceptic his syllogism

reposes on premisses which are accepted by him as true

* See ante, p. 103.

proof, as also that to accept as true anything which is

incapable of proof, is to accept a conviction blindly.

Of course it is common enough and reasonable enough

to ask for proof to be given with respect to any new or

extraordinary statement, and it is most reasonable not to

assent to any proposition which does not possess sufficient

evidence,

It is also true that the greater part of our knowledge is

gained by us indirectly, by inference or testimony of some

kind. And thus it has come about that many persons (as

before said) have acquired, half unconsciously, a persuasion

that to believe anything which cannot be proved is an act

of irrational credulity, and thus a tendency has arisen to

distrust any assertion for which no proof is offered.

But, as we before pointed out,* however long our processes

of proof may be, they must stop somewhere. We cannot

go on reasoning for ever if anything is ever to be proved.

Therefore, every valid process of reasoning must ultimately

depend upon propositions which need no proof, and are

undemonstrable not "undemonstrable"' because, like matters

which have to be taken on trust, we can obtain no evidence

for them, but because they are so luminously self-evident

that they admit of no demonstration, nothing else being

so clearly and necessarily true as they are. We have,

indeed, just said that it is most reasonable to demand

sufficient evidence for any proposition to which our assent

is demanded. But that evidence need not be external

evidence, and the evidence of those ultimate propositions

which need no proof is, and must be, internal evidence. They

carry with them their own evidence, and so are evident in

and by themselves.

Thus the reasoning of our supposed sceptic his syllogism

reposes on premisses which are accepted by him as true

* See ante, p. 103.