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The concept of confirmation occupies a central position in the methodology of empirical science. For it is the distinctive characteristic of an empirical hypothesis to be amenable, at least in principle, to a test based on suitable observations or experiments; the empirical data obtained in a test—or, as we shall prefer to say, the observation sentences describing those data—may then either confirm or disconfirm the given hypothesis, or they may be neutral with respect to it. To say that certain observation sentences confirm or disconfirm a hypothesis, does not, of course, generally mean that those observation sentences suffice strictly to prove or to refute the hypothesis in question, but rather that they constitute favorable, or unfavorable, evidence for it; and the term “neutral” is to indicate that the observation sentences are either entirely irrelevant to the hypothesis, or at least insufficient to strengthen or weaken it.

1. The problem. The aim of the following considerations is to introduce a new type of non-Aristotelian logic by generalizing the truth-table methods so far employed for establishing non-Aristotelian sentential calculi. We shall expound the intended generalization by applying it to the particular set of pluri-valued systems introduced by J. Łukasiewicz. One will remark that the points of view illustrated by this example may serve to generalize quite analogously any other plurivalued systems, such as those originated by E. L. Post, by H. Reichenbach, and by others.2. J. Łukasiewicz's plurivalued systems of sentential logic. First of all, we consider briefly the structure of the Łukasiewicz systems themselves.As to the symbolic notation in which to represent those systems, we make the following agreements: For representing the expressions of the (two- or plurivalued) calculus of sentences, we make use of the Principia mathematica symbolism; however, we employ brackets instead of dots. We call the small italic letters “p”, “q”, “r”, … sentential variables or elementary sentences, and employ the term “sentence” as a general designation of both elementary sentences and the composites made up of elementary sentences and connective symbols (“~”, “ν” “.”, “⊃” “≡”).Now, the different possible sentences (or, properly speaking, the different possible shapes of sentences, such as “p”, “p∨q”, “~p.(q∨ r)”, etc.) are the objects to which truth-values are ascribed; and just as in every other case one wants a designation for an object in order to be able to speak of it, we want now a system of designations for the sentences with which we are going to deal in our truth-table considerations.

In 1923 I was asked by the editors of the "Handbuch der Physik" to write an article about the philosophy of physics. Since one of the points I wanted to discuss in this article was the reality of the physical world, I used the occasion of a trip to the Bavarian mountains to see Moritz Schlick at his summer vacation place and to talk with him about this problem. I told him that I had recently discussed these questions with a young philosopher who was writing a book entitled "Der logische Aufbau der Welt", and who advanced the idea that Mach's positivism could be given a strict logical form by regarding any statement about the physical world as logically equivalent to a combination of statements about sense data. I myself objected to this equivalence ; I thought that only a probability relation ship could be maintained. Schlick supported me in this view; he argued that the positivistic equivalence was untenable. That was in 1923. A few years later, after Schlick had invited Rudolf Carnap to become a member of his department and had succeeded in attaching Ludwig Wittgenstein to his circle in Vienna, Schlick changed his views completely and turned posi tivist. In this environment, those views were elaborated which culminate in the thesis that the meaning of a sentence is the method of its verification. Mainly as the achievement of Carnap,1 the verifiability theory of meaning was thus given an elaborate logical form ; for the first time in its long history, which goes back to William of Occam and Leibniz, this theory was set forth with the precision tools of modern symbolic logic. My article written in 1923 had to wait for publication until 1929, when the volume of the Handbuch finally came out.2 My refusal to accept the equivalence interpretation was based on the distinction between a complex (Gebilde) which is "artgleich" to its elements from a complex which is "artverschieden" to its elements, a thesis which I took over into a later book of mine as the distinction between a reducible and a protective complex of elements.3 But I knew that it was vain to go into a further elaboration of my conception before I had been able to con