The Positive Heuristic Of The Programme Saves

The History Of Mathematics, Lacking The Guidance Of Philosophy, [is] Blind, While The Philosophy Of Mathematics, Turning Its Back On The Most Intriguing Phenomena In The History Of Mathematics, Is Empty.

It Would Be Wrong To Assume That One Must Stay With A Research Programme Until It Has Exhausted All Its Heuristic Power, That One Must Not Introduce A Rival Programme Before Everybody Agrees That The Point Of Degeneration Has Probably Been Reached.

That Sometimes Clear ... And Sometimes Vague Stuff ... Which Is ... Mathematics.

Blind Commitment To A Theory Is Not An Intellectual Virtue: It Is An Intellectual Crime.

Belief May Be A Regrettably Unavoidable Biological Weakness To Be Kept Under The Control Of Criticism: But Commitment Is For Popper An Outright Crime.