“It is quite impossible for a proposition to state that it itself is true.”

4.442
Original German: Ein Satz kann unmöglich von sich selbst aussagen, dass er wahr ist.
1920s, Tractatus Logico-Philosophicus (1922)

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Ludwig Wittgenstein 228
Austrian-British philosopher 1889–1951

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“Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.) (5)”

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Original German: Der Satz ist eine Wahrheitsfunktion der Elementarsätze
1920s, Tractatus Logico-Philosophicus (1922)

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“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.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

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)
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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.

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“A tautology's truth is certain, a proposition's possible, a contradiction's impossible.”

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)

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“The proposition that economist Ludwig von Mises was a feminist is an apodictic impossibility.”

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“God could not make the creature to be great and glorious in itself; this is as impossible, as for God to create beings into a state of independence on himself.”

William Law (1686–1761) English cleric, nonjuror and theological writer

¶ 8 - 9.
An Humble, Earnest and Affectionate Address to the Clergy (1761)
Context: God could not make the creature to be great and glorious in itself; this is as impossible, as for God to create beings into a state of independence on himself. "The heavens," saith David, "declare the glory of God"; and no creature, any more than the heavens, can declare any other glory but that of God. And as well might it be said, that the firmament shows forth its own handiwork, as that a holy divine or heavenly creature shows forth its own natural power.
But now, if all that is divine, great, glorious, and happy, in the spirits, tempers, operations, and enjoyments of the creature, is only so much of the greatness, glory, majesty, and blessedness of God, dwelling in it, and giving forth various births of his own triune life, light, and love, in and through the manifold forms and capacities of the creature to receive them, then we may infallibly see the true ground and nature of all true religion, and when and how we may be said to fulfill all our religious duty to God. For the creature's true religion, is its rendering to God all that is God's, it is its true continual acknowledging all that which it is, and has, and enjoys, in and from God. This is the one true religion of all intelligent creatures, whether in heaven, or on earth; for as they all have but one and the same relation to God, so though ever so different in their several births, states or offices, they all have but one and the same true religion, or right behavior towards God. Now the one relation, which is the ground of all true religion, and is one and the same between God and all intelligent creatures, is this, it is a total unalterable dependence upon God, an immediate continual receiving of every kind, and degree of goodness, blessing and happiness, that ever was, or can be found in them, from God alone. The highest angel has nothing of its own that it can offer unto God, no more light, love, purity, perfection, and glorious hallelujahs, that spring from itself, or its own powers, than the poorest creature upon earth. Could the angel see a spark of wisdom, goodness, or excellence, as coming from, or belonging to itself, its place in heaven would be lost, as sure as Lucifer lost his. But they are ever abiding flames of pure love, always ascending up to and uniting with God, for this reason, because the wisdom, the power, the glory, the majesty, the love, and goodness of God alone, is all that they see, and feel, and know, either within or without themselves. Songs of praise to their heavenly Father are their ravishing delight, because they see, and know, and feel, that it is the breath and Spirit of their heavenly Father that sings and rejoices in them. Their adoration in spirit and in truth never ceases, because they never cease to acknowledge the ALL of God; the ALL of God in the whole creation. This is the one religion of heaven, and nothing else is the truth of religion on earth.

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“To "postulate" a proposition is no more than to hope it is true.”

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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.

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“Some philosophers fail to distinguish propositions from judgments; … But in the real world it is more important that a proposition be interesting than that it be true.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

Source: 1920s, Process and Reality: An Essay in Cosmology (1929), p. 259.
Variant: It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occasion of experience is its interest, and its importance. But of course a true proposition is more apt to be interesting than a false one.
As extended upon in Adventures of Ideas (1933), Pt. 4, Ch. 16.
Context: Some philosophers fail to distinguish propositions from judgments; … But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.

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