This paper investigates relations between truth and consistency. The basic intuition is that truth implies consistency, but the reverse dependence fails. However, this simple account leads to some troubles, due to some metalogical results, in particular the Gödel-Malcev completeness theorem. Thus, a more advanced analysis is required. This is done by employing the concept of ω-consistency and ω-inconsistency. Both concepts motivate that the concept of the standard truth should be introduced as well. The results are illustrated by an interpretation of (...) the well-known logical square and its generalization. (shrink)
This paper discusses the distinctions indicated in its title. It is argued that the distinction between syntax and semantics is much more important for the present situation in logic than other distinctions. In particular, doing formal syntax and formal semantics requires the use of an informal melanguage based on ordinary mathematics.
This paper examines the problem of genesis of logic in the light of naturalism as a philosophical view about the nature of knowledge and reality. The main difficulty of naturalism as far as applied to logic consists in reconciling genetic empiricism (all cognition starts with experience) and abstract nature of logic. Anti-naturalism (Platonism, for example) maintains than empiricism is not able to explain how logical theorems as a priori assertions are accumulated. To defend naturalism one should note that experiential character (...) of knowledge can be understood phylogenetically or ontogenetically. The former account is more suitable for naturalism and allows us to investigate genesis of logic by glasses of evolutionary theory. This way can be supplemented by an appeal to genetics. Both theories can explain how logical competence, that is ability to use deduction, arose in humans. The author claims that the structure of the genetic coded has some properties that became transformed into logical rule. Some analogies between consequence operation and topological closure are employed in analysis. (shrink)
For decades Ryszard Wójcicki has been a highly influential scholar in the community of logicians and philosophers. Our aim is to outline and comment on some essential issues on logic, methodology of science and semantics as seen from the perspective of distinguished contributions of Wójcicki to these areas of philosophical investigations.
This paper comments Susan Haack’s remarks about Twardowski’s criticism of relativism in the theory of truth. The author summarizes Twardowski’s arguments for truth-absolutism and tries to show that that their presentation by Haack is incomplete. The defense of Twardowski’s position in the paper uses ideas developed by Tarski and Kokoszyñska.
Roman Ingarden offered a strong criticism of the verifiability principle in his talk delivered at the 8th International Congress in Prague in 1934. Ingarden argued that this principle either violates itself or smuggles a hidden sense. In this paper I show that Ingarden-like arguments about smuggled (but this pejorative qualification is skipped) meaning apply not only to the criteria of sense, but also to other semantic assertions within language-hierarchies in Tarski’s sense.
This volume portrays the Polish or Lvov-Warsaw School, one of the most influential schools in analytic philosophy, which, as discussed in the thorough introduction, presented an alternative working picture of the unity of science.
. This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.
This paper critically discusses two points concerning some recent views about the concept of truth. Firstly, contrary to Davidson, it shows that meaning of sentences cannot be explicated by T-equivalences. In particular, “is true” is an extensional predicate, but “means that” an intensional one. Secondly, the minimalist account of truth does not provide a satisfactory analysis of the concept of falsity. In this respect, minimalism does not satisfy Russell’s claim that any adequate truth-theory must be a theory of falsity as (...) well. (shrink)
This paper proposes a formal framework for the cognitive relation understood as an ordered pair with the cognitive subject and object of cognition as its members. The cognitive subject is represented as consisting of a language, conequence relation and a stock of accepted theories, and the object as a model of those theories. This language allows a simple formulation of the realism/anti-realism controversy. In particular, Tarski’s undefinability theorem gives a philosophical argument for realism in epistemology.
The theory of double truth was proposed in the Middle Age by Latin Averroists as a solution of how the relation between faith (religion, theology) and reason (science) should be conceived. In general terms, according to this theory, there are two orders, one dictated by faith and second dictated by reason. Both are epistemologically different and cannot mutually remain in logical relations such as (in)consistency or entailment. This view was used in the Middle Ages for defending science against a claim (...) that it is the ancilla thelogiae only. The author compares the theory of double truth with other solutions like the model of identity of science and theology or the model of two overlapping regions (Thomas Aquinas). It is argued that the substantial difference of the language of faith and the language of reason makes logical relations between statements of science and statements of theology impossible. In particular, all cosmological proofs of God's existence as well as projects of intelligent design fail if the theory of double truth is adopted. (shrink)
This paper examines how the work of Frege was known and received in Poland in the period 1910?1935 (with one exception concerning the later work of Suszko). The main thesis is that Frege's reception in Poland was perhaps faster and deeper than in other countries, except England, due to works of Russell and Jourdain. The works of ?ukasiewicz, Le?niewski and Cze?owski are described.
Finland is internationally known as one of the leading centers of twentieth century analytic philosophy. This volume offers for the first time an overall survey of the Finnish analytic school. The rise of this trend is illustrated by original articles of Edward Westermarck, Eino Kaila, Georg Henrik von Wright, and Jaakko Hintikka. Contributions of Finnish philosophers are then systematically discussed in the fields of logic, philosophy of language, philosophy of science, history of philosophy, ethics and social philosophy. Metaphilosophical reflections on (...) the nature of philosophy are highlighted by the Finnish dialogue between analytic philosophy, phenomenology, pragmatism, and critical theory. (shrink)
This paper examines two arguments againstpsychologism advanced by Frege andHusserl. The first argument says that thelaws of logic cannot be justified by thelaws of psychology, because the formerand a priori and certain, but the latterare probable only. The second argumentpoints out that the status of logicallaws as universal principles of thinking isnot intelligible on the psychologisticinterpretation of logic. The author tries toshow how to examine both arguments bymetalogical devices.
This paper reports some attempts undertaken in Poland in the 1930s to modernize Thomism by means of modern logic. In particular, it concerns J.M. Bocheski and J. Salamucha, the leading members of the CracowCircle. They attempted to give precise logical form to the Five Ways of Thomas Aquinas. Other works concerned the concept of transcendentals, the levels of abstraction, and the concept of essence.
Klemens Szaniawski has been dealing with many philosophical problems, but the philosophical foundations of statistics and theory of decision were his main interest. Unfortunately, he did not present his results and considerations in a synthetic monograph. One can suppose, however, that it would be an attempt to look at science from the point of view of someone who makes epistemic decisions and to regard statistical inferences as paradigmatic scientific procedures. The material concerning that subject contained in Szaniawski's published papers justifies (...) the claim that it would be an extremely interesting synthesis. The author presents consequences for naturalism and antinaturalism that the discussions surrounding the foundations of statistics and decision theory has brought about. He often employs the results obtained by Szaniawski. (shrink)
The paper is a reply to Jan Czerniawski's paper „On epistemic impotence of analytical philosophy” (Filozofia Nauki 3-4/1998). Czerniawski argues that the analytic method consists either in arbitrary stipulations or in the appeal to linguistic intuitions. He claims that the latter are subjective and moreover they cannot help deciding objective problems, while the former are an arbitrary creation of truth. Hence, the analytic method has to be assisted by an intuitive insight into objective situations. However, Czerniawski forgets one quite elementary (...) circumstance. For there is something else between linguistic intuitions and arbitrary terminological stipulations - namely precisation of intuitions. And this is what the analytic philosophers care for the most; those analytic philosophers who are logicians at the same time, in particular. According to the analytic philosophers philosophically relevant intuitive insight into objective situations is always achieved through language. Therefore, we do not need an epistemic viagra in the form of the extra-linguistic insight directly into the objective situation. (shrink)
Władysław Witwicki was first of all a psychologist, but he graduated in philosophy from Lvov University, being one of the earliest pupils of Kazimierz Twardowski. He was a representative of the descriptivistic branch of the Lvov-Warsaw School. In the area of phsychology he put into practice the important postulate of his teacher, who persuaded his students to write original handbooks, giving Polish scholar contributions their due: it is how the work on Witwicki's Psychology began. In the area of philosophy he (...) was particularly interested in the foundations of (descriptive) psychology. Witwicki's ontological and epistemological views are close to realism. In ethics he defended the absolute character of moral norms against scepticism and relativism. In general, Witwicki subscribed to anti-irrationalism, the common standpoint in his School. (shrink)
Two different kinds (or levels) of information are distinguished and compared: physical and semantical. The author indicates that semantic information cannot be reduced to physical information, and that the former is more diffiult to explain than the latter, while the latter is less useful and less interesting.
In this article the author first described the developments which brought to focus the importance of consistency proofs for mathematics, and which led Hilbert to promote the science of metamathemat-ics. Further comments and remarks concern the (partly analogous) beginnings of the work on the decision problem, Gödel?s theorems and related matters, and general metamathematics. An appendix summarizes a text by the author on completeness and categoricity.
Non-existence provides big problems for ontology and modest for logic. Logical problems of non-existence consist in licensing inferences in which sentences with empty terms are involved. The standard predicate logic solves this question by presupposing that every individual constant has an object to which it refers. This means that empty domains are excluded from semantics for the first-order logic. However, there is a temptation to consider logic without existential presuppositions.The ontological problem of non-existence leads to the question of the meaning (...) of 'nothing'. We encounter "various conceptions of nothing" in the history of philosophy from Parmenides to our times. However, nothing (or nothingness) is always a negation of being. Since we have distributive and collective (mereological) concepts of being, we also should distinguish nothing in the distributive and mereological meaning. This difference is important because only the former leads to the paradox of nothing of all nothings, analogical to the paradox of all sets. A closer analysis of the nothing in the distributive sense shows that any meaningful talk about non-existence requires a relativisation to a fixed domain of discourse. This seems; to entail that the empty set is the formal model of nothing what means that the concept of absolute nothing in the distributive sense is simply inconsistent. To some extent, being and nothing are mutually dual. This motivates that the concept of nothing is governed by so-called dual logic connected with processes of rejection. More specifically, statements on "nothing" are not asserted but rejected. (shrink)