Induction, as applied in the physical sciences, is always uncertain, because it rests on the belief in a general order in the universe, an order outside of us. On the contrary, mathematical induction, I.e., demonstration by recurrence, imposes itself as a necessity, because it is only a property of the mind itself …

We can ascend only by mathematical induction, which alone can teach us something new. Without the aid of this induction, different from physical induction but just as fertile, deduction would be powerless to create a science.

Henri Poincare, “The nature of mathematical reasoning”

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s