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1993, Bryn Mawr College B.A. Honors Thesis
This paper is intended as a contribution to the history and philosophy of logic. Its aim is to present the logical views of an important and long-neglected Russian philosopher, Nikolai Andreyevich Vasil'ev [1880-1940], and ot explain the significance of those views for the development of so-called "deviant," or non-classical, logics. Vasil'ev produced a series of four articles on the topic of "non-Aristotelian logic" between the years 1910 and 1914. The third article in the series, and the focus of this paper, is entitled "Voobrazhaemaia (nearistoteleva) logika" ["Imaginary (non-Aristotelian) Logic";1 912]: it is here that Vasil'ev articulates his notion of a "non-classical" ("non-Aristotelian") logic. In this paper, I hope to establish (1) that Vasil'ev did not explicitly 2 develop a system of many-valued logics, but (2) that the arguments he gives to support his views might be used to motivate the development of such logics. I will further suggest that there is a natural connection between Vasil'ev's logical intuitions and some problems related to the underlying logic of quantum mechanics.
2017 •
The paper deals with intellectual legacy of Kazan University professor N.A. Vasiliev (June 29, 1880–December 31, 1940), the forerunner of modern nonclassical logic. A thinker with a wide range of interests, he worked in poetry, philosophy, ethics, psychology, and history. N.A. Vasiliev’s path to imaginary logic is presented, along with the revival of his ideas in the early 1960s and their contemporary development.
Studies in Soviet Thought
The fate of one forgotten idea: N. A. Vasiliev and his imaginary logic1990 •
2017 •
This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers.
Brief summaries of selected sections of Graham Priest’s Introduction to Non-Classical Logic: From If to Is, chosen for their relevance to a study of the logic of Gilles Deleuze
This paper explores the modal interpretation of Lukasiewicz' n-truth-values, his conditional, and the puzzles they generate by exploring his suggestion that by 'necessity' he intends the concept used in traditional philosophy. Scalar adjectives, used in ancient and mediaeval modality, form families with nested extensions over the left and right fields of an ordering relation described by an associated comparative adjective, e.g. increasingly less happy broader sets referred to by ecstatic, happy, content, so-so, down, sad, miserable are associated with the comparative is happier than. Also associated is a privative negation that reverses the "rank" of a predicate within the field, e.g. unhappy is synonymous with sad. If the scalar semantics is interpreted over a totally ordered domain of cardinality n and metric , an n-valued Lukasiewicz algebra is definable. Privation is analyzed in terms of non-scalar adjectives: a scalar of a given rank holds exactly when a family of standard predicates interpreted over a finite Boolean algebra applies. Any Boolean algebra of 2n "properties" determines an n+1 valued Lukasiewicz algebra, e.g. {sighted-in-the-right-eye, sighted-in-the-left-eye} determines a 4-element Boolean algebra of three ranks, and a corresponding 3-valued Lukasiewicz algebra that interprets scalar predicates for blindness, Aristotle's paradigm privative property: The Neoplatonic "hierarchy of Being" is essentially the order presupposed by natural language modal scalars in series like necessary, likely/probable, possible, unlikely/improbable, impossible. Relations to product logics and frequency interpretations of probability are sketched.
Logica Universalis
Non-Classical Stems from Classical: N. A. Vasiliev’s Approach to Logic and his Reassessment of the Square of Opposition2008 •
ABSTRACT In the XIXth century there was a persistent opposition to Aristotelian logic. Nicolai A. Vasiliev (1880–1940) noted this opposition and stressed that the way for the novel – non-Aristotelian – logic was already paved. He made an attempt to construct non-Aristotelian logic (1910) within, so to speak, the form (but not in the spirit) of the Aristotelian paradigm (mode of reasoning). What reasons forced him to reassess the status of particular propositions and to replace the square of opposition by the triangle of opposition? What arguments did Vasiliev use for the introduction of new classes of propositions and statement of existence of various levels in logic? What was the meaning and role of the “method of Lobachevsky” which was implemented in construction of imaginary logic? Why did psychologism in the case of Vasiliev happen to be an important factor in the composition of the new ‘imaginary’ logic, as he called it?
Kazania świętokrzyskie w perspektywie tekstowej i ogólnojęzykowej
Kazania świętokrzyskie w perspektywie tekstowej i ogólnojęzykowej2018 •
2023 •
Neuroscience Letters
Vertical disconjugacy during reading in dyslexic and non-dyslexic children2018 •
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