Jan Wolenski

This paper offers a logical analysis of scepticism. It is shown that dogmatism, academism and scepticism as characterized by Sextus Empiricus in Outlines of Pyrronism form a variety of views which can be ordered by an interpretation of the classical logical square. In particular, scepticism appears as a conjunction of the negations of dogmatism and academism. The next problem concerns the logic proper for scepticism. Logic based on a dual of the consequence operation is proposed as satisfying intuitive requirements associated with doubting. Finally, the attitude of the sceptic toward logic is discussed. In particular, it is argued that the principle of isosteny trivializes scepticism if it is applied to logic

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

Kazimierz Twardowski is most commonly known as the teacher of great philosophers and the founder of the Lvov-Warsaw School. As a philosopher however, he is primarily remembered for his famous comparison of the contents and objects of various kinds of representations, a comparison that remains enshrined in European thought.In fact, he attained important results in many other branches of philosophy as well. For instance, in ontology, he laid the foundations for the modern theory of formal structure of objects, and he introduced the theoretically fruitful pair of terms, action-product. In epistemology, he developed a profound analysis of the notion and criteria of truth; and he provided a forceful account of the errors underlying relativist theories of truth. In methodology, he drew an explicit distinction between the processes of discovering, systematising, and grounding in science, and he offered accurate descriptions of the nature of psychology and other humanities. In logic, he offered decisive arguments on behalf of the idiogenetic conception of judgement, and he improved the traditional typology of adjectives.These achievements are of significance that is not only historical. Kazimierz Twardowski's work, formulated in plain, precise language, are instructive and inspiring for contemporary students of philosophy

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

The relevance of metamathematical researches for philosophy of math- ematics is an indubitable matter. In the paper I shall speak about impli- cations of metamathematics for general philosophy, especially for classical epistemological problems. Let us start with a historical observation con- cerning Hilbert's programme, the rst research programme in metamathe- matics as a separate study of formal systems. This programme was strongly in uence by epistemological considerations. In fact, Hilbert wanted to se- cure all classical mathematics against inconsistencies and this aim had be achieved with the help of nitary consistency proof. Hilbert's claim is like the Cartesian project of reduction of all concepts to clarae et distinctae ideae. The epistemological commitment of original Hilbert's programme may be treated as a prelim- inary heuristic motivation for looking for epistemological implications of metamathematical results. It seems reasonable to examine in this respect three so-called limitative theorems: the rst Godel's incompleteness theo- rem , the second Godel's incom- pleteness theorem consistency of S, cannot be proved in S, providing that S is consistent) and Tarski's undenability theorem ; \S" stands for formal system containing elementary number theory. From the above-mentioned theorems we obtain an important, from philosophical point of view, conclusion: semantics of S cannot be expressed in S. Now, I shall present three applications of limitative theorems to the analysis of classical epistemological problems

Traces of the coherence theory are to be found in rationalistic epistemological systems of Leibniz, Spinoza, Kant, Hegel and Fichte. However, the first fully advanced coherence theory was proposed by Bradley in XIX century. He was followed by Joachim, McTaggart, and particularly Blanshard and Ewing. The coherence theory later became popular among philosophers of the Vienna Circle, notably in Neurath and Hempel.2 Recently, Rescher tried to combine various proposals of coherentists into one fully unified view.

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.

This paper outlines an approach to the principle of bivalence based on very general, but still elementary, semantic considerations. The principle of bivalence states that “every sentence is either true or false”. Clearly, some logics are bivalent while others are not. A more general formulation of uses the concept of designated and non-designated logical values and is captured by “every sentence is either designated or non-designated”. Yet this formulation seems trivial, because the concept of non-designated value is negative. In order to refine the analysis, the class of anti-designated values has been distinguished. The non-trivial version of the principle of bivalence is expressed by “every sentence is either designated or anti-designated”. The last part of the paper mentions some extralogical reasons for considering the principle of bivalence with truth being a designated value as intimately connected to human thinking and behavior

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.

Formal semantics is understood either as a formal analysis of semantical features of natural language or as model-theoretic semantics of formal(ized) languages. This paper focuses on the second understanding. The problem is how to identify the formal aspects of formal semantics, if we understand ‘formal’ as ‘independent of content’. This is done by showing that the form of semantical interpretation of a language L is given by its syntax and the parallelism of the signature of L and its interpretative structure SI. However, the content of interpretation, that is, the way of correlating of L-expressions with extralinguistic items depends of informal factors. The discussion shows that semantics is prior to syntax