The issue of the emergence of formal axiomatic logical systems due to the emergence of logical antinomies in formal axiomatic systems, specifically the issue of developing formal logical axiomatics in the calculus of considerations was investigated in the considered research. At the same time, in order to determine the characteristics of the implementation of the logical-methodological principles and provisions of the deductive reasoning obviously, conceptual-logical foundations of the calculus of considerations was studied and the main propositions of the calculus of (...) considerations and the analysis of the initial logical operations on them were given in the study. The basic laws of logic and the expression of one logical act with another one were also explained in the research work by giving the concepst of proportional form and tautology in the calculus of considerations. At the same time, main properties and the procedure of setting of the formal deductive theory in the calculus of considerations were studied in the article. In order to provide an adequate characterization of the conceptual and methodological bases of the calculus of considerations in the research work, the basic logical laws of the calculus of considerations developed by the German mathematician and thinker P. Hilbert were also given. In addition, the main principles and methodological provisions of the deductive method were investigated, and the rules of deriving new conclusions from the axioms were interpreted. At the end of the reviewed article, the main principles and methods of the formal axiomatic mathematical systems built on a deductive basis, specifically the calculus of considerations, were studied and a logical-methodological analysis of the calculus of considerations was carried out on this basis. In this framework, the syntactic and semantic analysis of formalized language in formal axiomatic logical systems was carried out separately, the constituent parts of those systems, including the construction scheme, were given. (shrink)

Gordon Baker and I had been colleagues at St John’s for almost ten years when we resolved, in 1976, to undertake the task of writing a commentary on Wittgenstein’s Philosophical Investigations. We had been talking about Wittgenstein since 1969, and when we cooperated in writing a long critical notice on the Philosophical Grammar in 1975, we found that working together was mutually instructive, intellectually stimulating and great fun. We thought that we still had much to say about Wittgenstein’s philosophy, and (...) it seemed to us that misinterpretations of passages in the Investigations were so extensive that it would be worth trying to write a detailed analytical commentary. It is difficult to recapture the excitement of those early days in being among the first to work on the microfilms and, subsequently, on the photocopies of Wittgenstein’s Nachlass. We spent many hundreds of hours poring over the typescripts and the often only semi-legible manuscripts, fascinated and privileged to be able to try to follow the development of the thoughts of a great philosophical genius. We talked endlessly about what we had found in Wittgenstein’s manuscripts and typescripts, and debated how it should be understood. The first fruit of our labours was Wittgenstein – Understanding and Meaning. Its guiding idea was to draw attention to the manner in which Wittgenstein linked the concepts of meaning, understanding and explanation, and so to bypass the connections between meaning, truth and truth-conditions that so fascinated philosophers of the 1970s, and to abandon the red-herring of assertion-conditions and anti-realism. After a hiatus of four years, during which time we wrote a controversial book entitled Frege – Logical Excavations and a polemical book on contemporary philosophy of language – Language, Sense. (shrink)

This article explores three ways in which a cognitively entrenched mindreading (or 'theory of mind') system may bias our thinking as cognitive scientists. One issues in a form of tacit dualism, impacting scientific debates about phenomenal consciousness. Another leads us to think that our own minds are easier to know than they really are, influencing debates about self-knowledge, and about mindreading itself. And the third results in a bias in favour of empiricist over nativist accounts of cognitive development. The discussion (...) throughout is tentative and speculative, and can be regarded as an appeal for caution, as well as a call for further research. (shrink)

In what sense can the sciences be said to constitute a (set of) specific cultural tradition(s) within broader culture? This is the proper way of posing the problem of the 'two cultures' today. For G. Bachelard the opposition between 'poem' and 'theorem' was fundamental, the elements of poetical imagination being radically different from the symbolical constructions of conceptual invention. In this article a sophisticated version of this point of view is proposed. The nowadays popular attempts to bridge all gaps between (...) the cultures by an appeal to creative imagination ('science as art', 'mathematics and poetry') are criticized. The real basis of considering research traditions nevertheless as cultural realities in a nontrivial sense is not to be found in a mediation between cognitive faculties, but has to be revealed by a comparative analysis of their respective products. In fact, science, as well as other cultural practices, is subject to variations of style (Granger, Hacking ...). Research styles are not in the first place due to external, sociological determinants, but to such factors as the necessity of individuating any idea in a work, the presence of changing images of science within each discipline, and the fundamental role of the not-yet-explicit, given the specific temporal structure of conceptual innovation with its „essential tension” (Kuhn) between the old and the new. (shrink)