Lukasiewicz's keywords


Polivalent logic and indeterminism

"I have declared a spiritual war upon all coercition that restricts man's creative activity.
There are two kinds of coercition. One of them is physical [...].
The other kind of coercition is logical. We must accept self evident principles and the theorems resulting therefrom. This coercition is much stronger than the physical; there is no hope for liberation. No physical or intellectual force can overcome the principles of logic and mathematics.
That coercition originated with the rise of Aristotelian logic and Euclidean geometry. The concept was born of science as a system of principle and theorems connected by logical relationship. [...]
In the universe conceived in this way there is no place for a creative act resulting not from a law but from a spontaneous impulse [...].
The creative mind revolts against this concept of science, the univers and life. A brave individual, conscious of his value, does not want to be just a link in the chain of cause, but wants himself affect the course of events.
This was always been the background of the opposition between science and art. [...]
He has two paths to choose from: either to submerge himself in scepticism and abandon research, or to come to grips with the concept of science based on Aristotelian logic.
I have chose that second path. [...]
In striving to transform the concept of science based on Aristotelian logic I had to forge weapons stronger than that logic. It was symbolic logic that became such a weapon for me.
(Farewell lecture by Prof. Jan Lukasiewicz, delivered in the Warsaw University Hall on March 7, 1918, in Selected Works, North Holland, Amsterdam 1970, pp. 84-5).

"[...] it can assume one and only one of two truth-values: truth and falsity. I call this principle the principle of bivalence. In ancient times this principle was emphatically defended by Stoics and opposed by the Epicurean, both parties being fully aware of the issue involved. Bacause it lies at the very foundation of logic, the principle under discussion cannot be proved. One can only believe it, and he alone who consider is self-evident believe it. To me, personally, the principle of bivalence does not appear to be self-evident. Therefore I am entitled not to recognize it, and to accept the view that besides truth and falsehood exist other truth-values, including at least more, the third truth-value.
What is this third-value? I have no suitable name for it. But after the preceding explanations it should not be difficult to understand what I have in mind. I maintain that there are propositions which are neither true nor false but indeterminate. All sentences about future facts which are not yet decided belong to this category. Such sentences are neither true at present moment, for they have no real correlate. If we make use of philosophical terminology which is not particularly clear we could say that ontologically there corrisponds to these sentences neither being nor non-being but possibility. Indeterminate sentences, which ontologically have possibility as their correlate, take the third value.
If third value is introduced into logic we change its very foundations. A trivalent system of logic, whose first outline I was able to give in 1920 [see the previous fragment], differs from ordinary bivalent logic, the only one known so far, as much as non-Euclidean systems of geometry differ from Eucildean geometry. in spite of this, trivalent logic is as consistent and free from contradictions as is bivalent logic. Whatever form, when worked out in detail, this new logic assumes, the thesis of determinism will be no part of it"
("On determinism" [1946], in op. cit., p. 126).

"In my view the age-old arguments in support of determinism do not withstand the test of critical examination. this does not at all imply that determinism is a false view; the falsehood of the arguments does not demonstrate the falsehood of the thesis. Taking advantage of my preceding critical examination, I should like to state only one thing, namely that determinism is not a view better justified than indeterminism.
Therefore, without exposing myself to the charge of thoughtlessness, I may declare myself for indeterminism. I may assume that not the whole future is determined in advance."
(Ib., p. 127).

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