“Tautologies and contradictions are not real propositions, but degenerate cases. …Clearly, by negating a contradiction we get a tautology, and by negating a tautology a contradiction. …A genuine proposition asserts something about reality, and it is true if reality is as it is asserted to be. But a tautology is a symbol constructed so as to say nothing whatever about reality, but to express total ignorance by agreeing with every possibility.”

Certain, possible, impossible: here we have the first indication of the scale that we need in the theory of probability.
4.464
Original German: Die Wahrheit der Tautologie ist gewiss, des Satzes möglich, der Kontradiktion unmöglich
Source: 1920s, Tractatus Logico-Philosophicus (1922)

Art after Philosophy, 1969

Part III, Section 31 <br class="br"> Principles of Philosophy of the Future http://www.marxists.org/reference/archive/feuerbach/works/future/index.htm (1843)

Source: Striking Thoughts (2000), p. 15 - 16

Source: Mind and Nature, a necessary unity, 1988, p. 27

Source: Chainfire

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.

Part Seven “The Demagogue”, Chapter vi “Hello, Stranger”, Section 2 (p. 307)
(1987), BOOK TWO: THE FUGUE

§ 4.8
An Enquiry Concerning Human Understanding (1748)