The third/fourth issue:
Analytic Aposteriority and its Relevance to Twentieth-Century Philosophy
One of the central features of Kant’s ground-breaking Critique of Pure Reason is its introduction of a new framework for classifying propositions according to their epistemological status, based on two dyadic distinctions: first, between propositions that evince an “analytic” structure and those with a “synthetic” structure; and second, between “a priori” modes of justifying such propositions and “a posteriori” modes.1 This gives rise to four possible kinds of propositional knowledge-claim, two of which are relatively non-controversial: analytic a priori propositions establish logical knowledge, whereas synthetic a posteriori propositions establish empirical knowledge.
The Adjustment of Identity: Inquiries into Logic and Semantics of an Uncertain World
What is the truth, for man to search for it so much, and what is man, to be searching for the truth so much? Truth is a moving target in philosophy and science, but it is perhaps in art and literature that it moves at its fastest. The distance between us and the truth is also problematic: at times it is so near that our senses fail to recognize it; and sometimes it is so far that our mind only sees it in images itself produces. How, then, does the truth adjust itself to man, and how does man adjust himself to the truth? What is the relationship between identity and the truth?
Is Identity a Logical Constant and Are There Accidental Identities?
Propositional connectives and quantifiers are logical constants without any doubt. On the other hand, we speak about first-order logic with or without identity. Even this way of speaking suggests that identity has a special status to some extent. In fact, the status of identity is controversial.
There Is No Metaphysical a Posteriori Necessity
Water is H2O. Is it simply so? Or must it be so? Kripke believes the second: If true at all, it must be that water is H2O. What, however, are his reasons why it must be so? Roughly, they are as follows: If two things are identical to each other, then they are necessarily so. The necessity of identity can be proved from the necessity of self-identity and the Leibniz’s Law.
Abstract Incompleteness Theorems and Their Influence in Methodology
Gödel theorem of incompleteness and Chaitin theorem of incognizable are affecting many philosophical speculations and many branches of Western philosophy. Due to their importance it is reasonable to clarify whether they deal with one kind of precisely defined structures or with a wide class of such (and maybe not fully defined) structures. So we start with a popular outline of proof of their very common and abstract nature making them in essence basic and inevitable restrictions of precise thinking.
Intensio: Leibniz in Creating a New Term for the Modal Logic
Leibniz’s achievements and intuitions in the field of intensional logics were evaluated, for the first time, by no other than the creator of the modern modal logic Clarence I. Lewis, whose seminal 1918 monograph contains a very important historical essay on Leibniz with addition of two translations of his pertinent works (published for the first time in 1903, but not acknowledged as important even then).
On Axiomatization of Non-Cartesian Logics
Nowadays it is generally accepted as a kind of truism by a significant part of logicians that Belnap's four-valued logic B4 (the definition see below) is a good logical system, which is both useful in practice and fruitful in theory. Lots of papers and monographs deal with the syntactic analogue of B4, which is a well-known system of First Degree Entailment (FDE), and with its algebraic correlate, id est the class of De Morgan algebras.
Pragmatico-Linguistic and Semiotic Tools in Analysis of Electronic Conversation
CMC-studies researchers do not pay their attention on methods of pragmatics (here theory of conversation) probably because the Internet in its communicative aspect is treated as textual medium or hypertextual one, and because communication via the Internet is often seen as impersonal (Wood, Smith ). Users of the electronic communication channel usually do not see each other, hence there is no non-verbal communication between them – they send text messages constructed and displayed with the use of given software. Pragmatico-linguistic analyses have been developed in an area of philosophy of language (J. Austin, J. Searle, H.P. Grice) and psycholinguistics (H.H. Clarke) and those scientific disciplines did not (and obviously could not) deal with online communication/conversation, and they were out of the scope of interest of CMC-studies scientists.
The Dial of the Circular Complementarity of the Designated and Antidesignated Pairs
“Let None But Geometers Enter Here” – that was a motto of Platonic Academy. The founder of the higher geometry chair in Sorbonne M. Chasles said that the geometry “is considered as a basis of mathematical sciences, and the best thinkers of all times considered it, as an excellent exercise in the logics, extremely suitable for development of great minds” [17, p. 515]. Lobachevsky's works have focused scientists’ attention on the problem of the relationship between various geometrical constructions. “When analyzing formation of a principle of compliance in the history of geometry, usually the value of ideas of N.I. Lobachevsky for identification of relationship between Euclidean and not Euclidean geometry is appreciated” [12, p. 234].
Interview: Is the Polish Logic One of the Best Traditions Still?
The interview of Andrew Schumann, the managing editor of Studia Humana with Roman Murawski, Professor at Faculty of Mathematics and Computer Science of Adam Mickiewicz University.
Review: Charting the Sea of the a fortiori
The Talmud is a sea, a sea into which one can dive or be drowned in or simply observe carefully from the shore. And this is not any sea, but one of the most opaque seas. Indeed, one definitely should be accompanied in the sea of Talmud. This is the purpose of this excellent book. However, while methods of explaining the Talmud are usually textual, Yisrael Ury’s method is different; he creates Diagrams to explain difficult topics.