Practice with CP

At the end of Chapter 14 I promised to prove that I should use induction, for these reasons: a

I want to make reliable predictions and general statements.

b

If induction is a reliable method, I can: what I have not experienced will be like what I have (if what I have experienced is a good sample). If induction is not reliable, I cannot.

c

If I bet that induction is not reliable, I lose out either way. If I am right, there is no chance of basing predictions or general statements on experience; if I am wrong there is a chance, but I do not take it.

d

If I bet that induction is reliable and I am wrong, I lose again. But this bet also gives me a chance to win, which the other does not. For if I am right, reliable general statements and predictions are possible, using induction.

a

gives us the premise:

'I want to make reliable predictions and general statements'

and surely we can assume:

'If I want to do this and it requires induction, I should use induction'.

b

, (c) and (d) yield:

'If I use induction and it's reliable, I'll make reliable predictions and general statements'

'If I use it and it's not reliable, I won't make reliable predictions and general statements'

'If I don't use it, I won't make reliable predictions and general statements'.

And

'Either I use induction and it's reliable; or I use it and it's not; or I don't use it'.

is a logical truth: it covers all the possibilities.