Philosophy of Logic

Cet article prouve que les paradoxes appelés « cercles vicieux » comme celui de Russell exigent une logique classique, puisque l'élimination de la double négation joue un rôle clé dans leur dérivation. Mots-clés. Paradoxe, cercle vicieux, Russell, logique classique, double négation. ‫ملخص‬. ‫أن‬ ‫إلثبات‬ ‫الورقة‬ ‫هذه‬ ‫تسعى‬ ‫اة‬ ّ ‫املسم‬ ‫املفارقات‬ " ‫مفرغة‬ ‫حلقات‬ " ‫يلعب‬ ‫املزدوج‬ ‫في‬ ّ ‫الن‬ ‫إلغاء‬ ّ ‫ألن‬ ‫ا‬ ّ ‫كالسيكي‬ ‫منطقا‬ ‫ي‬ ‫تفتض‬ ‫ل‬ ّ ‫رس‬ ‫إليها‬ ‫أشار‬ ‫كالتي‬ ‫ها‬ ّ ‫حل‬ ‫في‬ ‫ا‬ ّ ‫أساسي‬ ‫ا‬ ‫دور‬. ‫مف‬ ‫كلمات‬ ‫اتيح‬. ‫نفي‬ ‫كالسيكي،‬ ‫منطق‬ ‫ل،‬ ّ ‫رس‬ ‫مفرغة،‬ ‫حلقة‬ ‫مفارقة،‬ ‫مزدوج‬. Abstract. This paper proves that paradoxes called "vicious circles" like Russell's, require classical logic, since the double negation elimination plays a key role in their derivation.

It is known from history of mathematics, that Gödel submitted his two theorems called incompleteness theorem, which can be considered one of hallmark of modern mathematics in 20 th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert's axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz's three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective.

A Logic Values Sketch

Logic values are appropriated in any number of ways. Does that truly make them right or wrong?

A logical argument must develop its theorem within an articulated matrix in order to focus on its true identity where it ends up or adds up to. ...

This is a long paper I wrote quite a while ago. I've tried to submit it to few Western journals but eventually unsuccesful.
This is my reading of a famous thought experiement by Thomas Nagel. If his "bat experiment" states the complete alien nature of "other minds" I claim that from some point of view, if we assume our mind is connected to a computational structure, every one from us actually knows "what it is like to be a bat". In other words it is the "mathematics" that disproofs "other minds" problem.

Estudiamos la lógica de Lukasiewicz infinitovalorada repasando algunos puntos importantes para demostrar el teorema de completud débil. Para ello estudiamos la algebraización mediante MV-álgebras (también veremos las álgebras de Wajsberg), y repasamos las MV-cadenas mediante grupos abelianos totalmente ordenados. Ademas resumimos los origenes de la lógica fuzzy, borrosa o infinitovalorada

One of the central logical ideas in Wittgenstein's Tractatus logico-philoso-phicus is the elimination of the identity sign in favor of the so-called "exclusive interpre-tation" of names and quantifiers requiring different names to refer to different objects and (roughly) different variables to take different values. In this paper, we examine a recent development of these ideas in papers by Kai Wehmeier. We diagnose two main problems of Wehmeier's account, the first concerning the treatment of individual constants, the second concerning so-called "pseudo-propositions" (Scheinsätze) of classical logic such as a = a or a = b ∧ b = c → a = c. We argue that overcoming these problems requires two fairly drastic departures from Wehmeier's account: (1) Not every formula of classical first-order logic will be translatable into a single formula of Wittgenstein's exclusive notation. Instead, there will often be a multiplicity of possible translations, revealing the original "inclusive" formulas to be ambiguous. (2) Certain formulas of first-order logic such as a = a will not be translatable into Wittgenstein's notation at all, being thereby revealed as nonsensical pseudo-propositions which should be excluded from a "correct" conceptual notation. We provide translation procedures from inclusive quantifier-free logic into the exclusive notation that take these modifications into account and define a notion of logical equivalence suitable for assessing these translations.

Objective of the present Dissertation will be to examine the evolution of Wittgenstein’s concept of nonsense throughout his works, from his Tractarian, ‘ideal’ conception of what would idealistically count as ‘nonsense’ - as I will put it - to a gradual declining interest of the same question of nonsensicality in Wittgenstein’s later years. My thesis will be that Wittgenstein’s conception of nonsense, although pivotal at the very beginning of his career, loses his central importance throughout his later works. Of course, I will not deny that Wittgenstein ceases to be interested in the detachment of cases of nonsense in later years. But as I will explain, he will do so by following a completely new, ‘pragmatic’ - as I will define it - method.
In stark opposition to the evolving Wittgenstein I have above sketched, stands the (nowadays leading) Resolute Reading’s interpretative view, and its main supporters. Point by point, the aim of my dissertation will also be an analysis of it, in order to show why such view relies on a completely untenable set of interpretative claims. Unlike the RR, indeed, the Wittgenstein I will sketch shows all his irresoluteness.
As I will conclude, the evolution of Wittgenstein’s renewed conception of nonsense will be proved to be a direct consequence of his later, new views on language.

The discipline of philosophy and thinking facilities generally focus on the subjects, objects and devices of thought, and this facility turns into something high in intellectual when thinking about the thinking itself occurs. Thinking about and concretizing the thinking process, generally induces people to dig deep in the fields of logic and language. This article firstly aims to clarify the relationship of thought with the logic and language which has been established by the thought during the process of its resolution, then, in doing so, it focuses on the fact that the field of language takes logic's place in the course of time and thus a philosophical activity as a product of logic gives its place to a literary activity as a product of language. This paper also aims at pointing out the causes and the results of this process. It clarifies the transformation of the categories of the field of logic into that of linguistics. THE JOURNEY OF THE THOUGHT FROM LOGIC TO LANGUAGE, FROM PHILOSOPHY TO LITERATURE 1-ON THE THOUGHT One of the subjects, on which people have been thinking at least as much as they did on the existence and the knowledge of the existence, since the ancient ages of the history, has been the thought itself. Information process emerged as the result of the realization of the thinking activity on the existence, and epistemology appeared as the audit of this process in terms of correctness-incorrectness, suitability and consistency criteria. Whether the science of logic has

Zeidler begann seine Dissertation, wie er im Vorwort schreibt, „als Untersuchung der ‚Logic of Discovery‘ Norwood R. Hansons und verschiedener anderer Ansätze zur Heuristik“, wandte sich aber „nach anfänglichen Irrfahrten in den Labyrinthen gegenwärtiger Wissenschaftstheorien und Methodologien“ dem „Problem des synthetischen Erkennens“ und damit „der Sache selbst zu: dem ‚abduktiven Schlusse‘ bei Peirce, der die Grundlage der ‚Forschungslogik‘ Hansons bildet.“ „Dem Studium der Philosophie Peircens und dem glücklichen Zufalle der Entdeckung der formalen Identität von ‚Abduktion‘ bei Peirce und ‚Analogie‘ bei Hegel, verdankt diese Arbeit“, so Zeidler, „denn auch ihrer jetzige Gestalt und ihren Inhalt.“ Bereits in dieser frühen Arbeit entwirft er im Anhang eine „Theorie der Grundlagen rationaler Vermittlung, eine ‚Logik des Erkenntnisprozesses‘ “ im Anschluss an Hegels und Peirce’ transzendentallogische und begriffsrealistische Interpretation der Aristotelischen Syllogistik. Zeidler geht in seiner Dissertation zunächst von dem vor dem Hintergrund der „Kuhn-Popper-Debatte“ unternommenen Versuch der Überwindung des Gegensatzes von Wissenschaftslogik und Wissenschaftsgeschichte durch die Bestimmung der Wissenschaftstheorie als Rekonstruktion der Wissenschaftsgeschichte seines Lehrers Erhard Oeser aus, wendet sich aber schließlich der fundamentalphilosophischen Aufgabe einer „logischen und erkenntnistheoretischen Klärung der wissenschaftstheoretischen Begründungsproblematik“ zu, die Oeser, v.a. in Anknüpfung an Schelling und Aristoteles, als Aufgabe einer „elementare[n] Erkenntnistheorie als Abstraktions- oder Begriffsbildungstheorie“ begreift, und kommt damit von Peirce und Hegel zu Kant und dem Problem einer transzendentalen Logik. Beide Problemstellungen, sowohl die wissenschaftstheoretische oder methodologische als auch die im engeren Sinn philosophische oder transzendentallogische, verfolgt er in seiner Habilitationsschrift Vernunft und Erfahrung: Untersuchungen zum Erkenntnisproblem in Philosophie und Wissenschaftstheorie weiter, aus deren beiden Hauptteilen später der Grundriß der transzendentalen Logik und die Prolegomena zur Wissenschaftstheorie hervorgegangen sind. Insofern Zeidlers Auseinandersetzung mit der Schlusslogik von Peirce und Hegel auch für seine Kantinterpretation und -kritik bestimmend ist, wird uns diese zum Leitfaden dienen, anhand dessen wir seinen Weg von der Dissertation bis zum Grundriß nachzuzeichnen versuchen wollen, wobei wir mit Blick auf seine schluss- und begriffslogische Rekonstruktion der Kritik der reinen Vernunft im zweiten Teil von Vernunft und Erfahrung und im Grundriss, die die transzendentale Dialektik als Prinzipien- und Begründungstheorie systematisch voranstellt und damit die Kantische Vernunftarchitektonik umkehrt, deren Herzstück, die transzendentale Ästhetik und Analytik, die er in einer genetischen Entfaltung der Kategorienlehre im Rückgriff auf Kants „subjektive Deduktion“ und das Schematismuskapitel miteinander verbindet, wobei er sich v.a. an Schelling orientiert, weitgehend unberücksichtigt lassen müssen.
https://www.peterlang.com/view/9783631817247/html/ch08.xhtml

Short abstract of the work

PART 1: Generativism: A new logical philosophy
In the first part of the book, I deal with the creation and formulation of some “intellectual and investigative tools” derived from inferential logic. During this phase, I will suggest the reevaluation of some fundamental philosophical concepts: existence, perception, truth, illusion (falsehood), Cartesian dualism, monisms, determinism, time and indeterminism. My proposal for new "reformulations" of these concepts is condensed into what I call Generativism: a new philosophy of logic.

PART 2: Vitalism: A new moral and politico-economic philosophy (post-capitalism)
In the second part of the book, I propose a new reevaluation of the concepts of freedom, as well as good and evil. In redefining them I propose a new prescriptive ("moral") philosophy. I want to offer this specific and reformulated prescriptive philosophy in the fervent hope that it may somehow be an inspiration for the contribution of necessary changes to an economy and a global policy that in no way do I support. You may say my intention is highly ambitious. Indeed, I maintain that it is not individuals themselves that change the world, but rather the ideas they formulate that can do so. The world is beautiful but it can certainly be made better. However, in order to do so, we need to have a good idea. This idea, which, in writing this book, I hope to give to my daughter and her children, doesn’t seem to be too shabby. Of course, time will tell whether it will be successful: such a bet may come to no avail. Yet, hoping for something better is part of my way of approaching things, and, above all, of living life. Why shouldn’t I try?

PART 3: Cognitive Generativism: A cognitive theory of language and emotions
In this part I propose a cognitive theory of language and emotions. In reality, as we shall see, it is a broader theory, which describes the functioning of the mind from perception to imagination. It is not a cognitive theory of child development, but rather a descriptive theory of the psyche, emotions, language and identity. Psychology is now no longer self-sufficient: it has to merge better with the richness of linguistics, neuroscience and philosophy. Cognitivism is a new discipline, which merges different disciplines in a creative way: a new comprehensive theory of mind can come to life. 

PART 4: MATHgen: A functional generative grammar
Mathgen is not exactly a theory, but rather a logical tool; an instrument. It is an attempt to formulate a series of "functional principles" of what Chomsky calls "generative grammar". The tool, if functional, allows us to create "derivative" tools to complement existing technologies: for example, the creation of a perfect language translator (software). Mathgen is a highly creative, powerful and generative tool.

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn't been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton's fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position.

These are the lecture notes of a course on the applications of modern mathematical logic to ancient Buddhist logic as exemplified by Dharmakirti's Nyaya Bindu. The lecture come in three parts. First, modern logic is introduced. Second, Buddhism is described superficially. Third, the Nyaya Bindu is analyzed in some detail using modern logical language.

De Morgan on Euclid’s fourth postulate

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831.
Today it is difficult to accept the proposition that Aristotle was blind to the fact that, for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical.
This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that as late as 1831 De Morgan was still in the grips of the allegedly Aristotelian relation-free paradigm.
This paper complements work showing that Boole’s 1847 and 1854 masterpieces were not intended to overthrow Aristotle’s syllogistic paradigm but to extend it and to provide it with modern algebraic foundations.
https://www.academia.edu/8840970/Aristotle_s_Prior_Analytics_and_Boole_s_Laws_of_Thought

CORCORAN ON COMMENSURABILTY OF ANCIENT, TRANSITIONAL, AND MODERN SCIENCES
Review of: Smith, Sheldon, Incomplete understanding of concepts: the case of the derivative.
MIND, 124 (2015), no. 496, 1163—1199. 


The article under review, “Incomplete understanding of concepts: the case of the derivative”, hereafter IUC, investigates foundational phenomena spanning the entirety of mathematics: the past and the present. These perennial phenomena involve the increasing clarity of objective mathematical concepts in themselves and the evolving subjective understanding of these concepts by individual mathematicians. But only recently these phenomena have started to attract attention.
They become more vivid as the gap widens between the relative vagueness of ancient mathematics and the relative precision of modern mathematics. Large domains of modern geometry and number theory contain results achieved long ago, sometimes many centuries ago, or at least results having analogs which were achieved earlier. Yet modern mathematics has concepts far more precise than those of ancient mathematics and a modern mathematician has an understanding of mathematical concepts that is far more rigorous than that an ancient mathematician had.
Comparing the clarity and precision of Alfred Tarski’s geometry with the vagueness and imprecision of Euclid’s raises the question of whether the ancient results are literally what are recognized as true today (or only relatively crude forerunners of modern theorems). If the ancient results survived intact, the question concerns how Euclid’s predecessors—whose results Euclid catalogued—achieved results still recognized as true.
This article continues studies of these phenomena as they relate to the concepts of derivative in calculus from Newton and Leibniz to Weierstrass and later analysts.

A lógica menor, parva, ou simplesmente formal de Fray Alonso de Vera Cruz é de matriz terminística. Visa diagnosticar a estrutura, a natureza e o significado das proposições, motivo pelo qual integra o rol das principais obras de logica modernorum da segunda escolástica, em especial pelo tratamento conferido aos temas: significatio, propositio e suppositio, usualmente presentes nos cursos de artes em Paris, Salamanca e outras partes do continente europeu.