Logicians From Poland

"According to Husserl, that 'act of meaning', or the use of a given phrase as an expression of a certain language, consists in the fact that a sensory content appears in consciousness, by means of which one might think visually about that phrase, should that content be joined by an appropriate intention directed to that phrase. But when a given phrase is used as an expression belonging to a certain language, then that sensory content is joined by another intention, not necessarily a representative one, which is however in principle directed to something other than that phrase itself. Together with the sensory content in question, that intention makes up a uniform experience, but neither the experiencing of that sensory content, nor that intention is a complete, independent experience. Both the one and the other are non-independent parts of the experience as a whole. The meaning of a given expression (as a type) would be, according to Husserl, the type under which that intention joined to the sensory content must fall if the given phrase is to be used as an expression belonging precisely to that language"

"The fundamental thesis of ordinary , represented for instance by Poincare, states that there are problems which cannot be solved by appeal to experience unless one introduces a certain convention, since only such a convention, together with experimental data, makes it possible to solve the problem in question. The judgements which combine to make up such a solution are thus not forced on us by empirical data alone, but their adoption depends partly on our recognition, since the said convention which co-determines the solution of the problem can be arbitrarily changed by us so that as a result we obtain different judgements."

"By spreading logical culture, we prepare the foundation for a scientific world-view and by doing this we enable development."

"However, the voice of the rationalist is a sound social reaction, it is an act of self-defense by society against the dangers of being dominated by uncontrollable forces such as a saint proclaiming a revelation or a madman affirming the products of his sick imagination, and finally a fraud who wants to convert others to his views for the sake of his egoistic and unworthy purposes. It is better to rely on the safe but modest nourishment of reason than, in fear of missing the voice of ‘Truth’, to let oneself be fed with all sorts of uncontrollable nourishment which may more often be poisonous than healthy and beneficial."

"What then is the content of the concept of God common to all monotheistic religions? What remains, it seems, is only the emotional content: the highest enthusiasm and respect, humility and submissiveness"

"All through these attempts to give the traditional concept of God a more explicit content philosophers did not mind if, in making the content more explicit, they departed from the original, highly emotionally charged, concept of deity."

"If he [the metaphysician] takes an empiricist position in regard to the source of knowledge and a realist one in regard to the limits of knowledge, he will see no need or even possibility of seeking a world-view other than that provided by science as based on experience. If he inclines towards an aprioristic position, or even more, if he is convinced by the arguments of irrationalists, he will seek his world-view in an aprioristic way, or he will appeal to intuition or mystical experience"

"Ajdukiewicz's view, published in the Erkenntnis, certainly did not fail to influence the opinions held by the neo-positivist supporters of semantic philosophy. But Ajdukiewicz was not alone in his opinions which fitted Carnap's principle of tolerance and, e.g., the theories of C. G. Hempel."

"Ajdukiewicz was one of the most distinguished and important philosophers of the contemporary Poland. He produced important ideas in logic, epistemology, philosophy of language, and ontology. He influenced Polish analytic philosophy very much."

"Ajdukiewicz’s philosophy was strongly inspired by the rationalism of Kazimierz Twardowski as well as by some ideas of the Vienna Circle. However, in contrast to the latter's logical empiricism, Ajdukiewicz could be interpreted as holding that beliefs constituting our world-view have both logical value and cognitive content—they cannot be construed as mere expression of some emotions."

"The present article is almost wholly devoted to a single problem—the definition of truth. Its task is to construct—with reference to a given language—a materially adequate and formally correct definition of the term 'true sentence. This problem, which belongs to the classical problems of philosophy, raises considerable difficulties. For although the meaning of the term 'true sentence' in colloquial language seems to be quite clear and intelligible, all attempts to define this meaning more precisely have hitherto been fruitless, and many investigations in which this term has been used and which started with apparently evident premisses have often led to paradoxes and antinomies (for which, however, a more or less satisfactory solution has been found). The concept of truth shares in this respect the fate of other analogous concepts in the domain of the semantics of language."

"Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws."

"There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and infer correctly."

"It is perhaps worth while saying that semantics as conceived in this paper (and in former papers of the author) is a sober and modest discipline which has no pretensions to being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflicts. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense."

"If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes."

"For reasons mentioned at the beginning of this section, we cannot offer here a precise structural definition of semantical category and will content ourselves with the following approximate formulation: two expressions belong to the same semantical category if (I) there is a sentential function which contains one of these expressions, and if (2) no sentential function which contains one of these expressions ceases to be a sentential function if this expression is replaced in it by the other. It follows from this that the relation of belonging to the same category is reflective, symmetrical and transitive. By applying the principle of abstraction, all the expressions of the language which are parts of sentential functions can be divided into mutually exclusive classes, for two expressions are put into one and the same class if and only if they belong to the same semantical category, and each of these classes is called a semantical category. Among the simplest examples of semantical categories it suffices to mention the category of the sentential functions, together with the categories which include respectively the names of individuals, of classes of individuals, of two-termed relations between individuals, and so on. Variables (or expressions with variables) which represent names of the given categories likewise belong to the same category."

"Tarski tried to publish his theorem (the equivalence between AC and "every infinite set A has the same cardinality as A × A") in Comptes Rendus, but Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known (true) propositions is not a new result, and Lebesgue wrote that an implication between two false propositions is of no interest. And Tarski said that after this misadventure he never tried to publish in the Comptes Rendus."

"It's interesting... Tarski, although his English was weak, had a very good sense of language and he kept on asking me "Is that really good English?" Not in the sense of being grammatically correct, but, well for example, Helmer was very fond of using the word "tantamount" and Tarski got the feeling that somehow it's not a word used very often. Actually his instincts for language were extremely good. I suppose that was connected with his general work on formalizations and metalanguages. Anyway, I was just a proofreader."

"In 1931, Tarski proved quite simply that... there is no complete language of science. ...Tarski's proof... essentially consists in showing that, as soon as you not only exhibit the statements but add to them the statement, "is true," you are in trouble because you are bound to be landed in contradictions like the one which arises in the ."

"I think that I have learned more from you than from any other living thinker, except perhaps Alfred Tarski... but not even excepting Russell."