Source: The New Ethics (1907), Conclusion, p. 211
The Foundations of Mathematics (1925)
Journals IV A 164 (1843)
See Phenomenology: Critical Concepts in Philosophy, by Dermot Moran (2002)
Variants:
We live forward, but we understand backward.
Life can only be understood backwards; but it must be lived forwards.
1840s, The Journals of Søren Kierkegaard, 1840s
Recent Work on the Principles of Mathematics, published in International Monthly, Vol. 4 (1901), later published as "Mathematics and the Metaphysicians" in Mysticism and Logic and Other Essays (1917)
1900s
Context: Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
Source: 1850s, An Investigation of the Laws of Thought (1854), p. 165; As cited in: James Joseph Sylvester, James Whitbread Lee Glaisher (1910) The Quarterly Journal of Pure and Applied Mathematics. p. 350
Epilogue
The Hero with a Thousand Faces (1949)
Source: A Brief History of Time (1988), Ch. 1
Context: It has certainly been true in the past that what we call intelligence and scientific discovery have conveyed a survival advantage. It is not so clear that this is still the case: our scientific discoveries may well destroy us all, and even if they don’t, a complete unified theory may not make much difference to our chances of survival. However, provided the universe has evolved in a regular way, we might expect that the reasoning abilities that natural selection has given us would be valid also in our search for a complete unified theory, and so would not lead us to the wrong conclusions.
“To "postulate" a proposition is no more than to hope it is true.”
The Doctrine of Necessity Examined (1892)
Context: When I have asked thinking men what reason they had to believe that every fact in the universe is precisely determined by law, the first answer has usually been that the proposition is a "presupposition " or postulate of scientific reasoning. Well, if that is the best that can be said for it, the belief is doomed. Suppose it be " postulated " : that does not make it true, nor so much as afford the slightest rational motive for yielding it any credence. It is as if a man should come to borrow money, and when asked for his security, should reply he "postulated " the loan. To "postulate" a proposition is no more than to hope it is true. There are, indeed, practical emergencies in which we act upon assumptions of certain propositions as true, because if they are not so, it can make no difference how we act. But all such propositions I take to be hypotheses of individual facts. For it is manifest that no universal principle can in its universality be compromised in a special case or can be requisite for the validity of any ordinary inference.
