We develop some of Williamson’s ideas regarding how propositional calculus aids in comprehending Aristotelian logic. Specifically, we enhance the utilisation of truth tables to examine the structure of opposition diagrams. Using ‘conditioned truth tables’, we establish logical dependency relationships between the truth values of different propositions. This approach proves effective in interpreting various texts of the Organon concerning the doctrine of opposition.

In Metaphysics Λ.6-7 Aristotle argues that an unmoved substance causes the outermost sphere to rotate. His argument has puzzled and divided commentators from ancient Greece to the present. I offer a novel defense of Aristotle's argument by highlighting the logic of classification that Aristotle deploys. The core of Aristotle's argument is the identification of the unmoved substance on the 'table of opposites' as simple and purely actual. With this identification in place, Aristotle argues that the outermost sphere activates (...) its capacity to relocate its body by rotating because this is how it can be a simple and actual substance. But unlike traditional attempts to rehabilitate Aristotle's argument, I argue that the sphere does not rotate in order to imitate the Prime Mover. Rather, the sphere rotates because that is good for it to do, and the Prime Mover is a metaphysically necessary source of simple and actual substantial being, which the sphere acts for the sake of. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

In Plato’s dialogues, Socrates calls things like justice, piety, and largeness “forms.” In several of these dialogues, he makes clear that forms are very different from familiar objects like tables and trees. Why, exactly, does he think that they differ and how are they supposed to do so? This chapter argues that in the Phaedo Socrates does not assume that they are different, but rather, over five stages of the dialogue, provides an account of how and why they do so. (...) To fully understand the claims made in the first stage, one must look to the next stage, and so on until the final stage. Socrates' ultimate reason for distinguishing forms from ordinary objects does not depend on our intuitions about things like justice and largeness, nor on the distinction between universals and particulars. Ultimately, forms cannot be ordinary objects because the form of f-ness must cause every f-thing to be f, but no ordinary object could serve as such a cause. They cannot do so because they have multiple parts and are receptive of opposites; by contrast, the form of f-ness must be simple and unchanging, since it causes every f-thing to be f. (shrink)

Ludwig Wittgenstein is the most famous philosopher of modern times but very few understand his pioneering work and there has been a collective amnesia regarding him in recent decades. Most of the essays are new but some date as far back as 1979 and whether they give a new view of his ideas depends on one’s understanding of what he said. For me, the interpretations are not new and mostly just as confused as nearly all the other commentary on W (...) and on human behavior throughout the behavioral sciences and by the general public. As usual, nobody seems to grasp that philosophy is armchair psychology, and that W was (in my view) the greatest natural psychologist of all time. He laid out the general structure of how the mind works, which is often referred to as intentionality and is roughly equivalent to cognition or personality or thinking and willing or higher order thought (HOT). He can thus be regarded as a pioneer in evolutionary psychology, although hardly anyone but me seems to realize it. W was thus nearly 50 years ahead of his time as the first to reject (though not entirely consistently) the blank slate or cultural view of human nature, though this has gone unrecognized and he has generally been interpreted as supporting a communal consensus view of psychology—exactly the opposite of his overall thrust (e.g., see Short’s comment on p 115). -/- I provide my recent (2016) table of intentionality for a current frame of reference from the two systems point of view before remarking on each of the essays. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

Ludwig Wittgenstein is the most famous philosopher of modern times but very few understand his pioneering work and there has been a collective amnesia regarding him in recent decades. Most of the essays are new but some date as far back as 1979 and whether they give a new view of his ideas depends on one’s understanding of what he said. For me, the interpretations are not new and mostly just as confused as nearly all the other commentary on W (...) and on human behavior throughout the behavioral sciences and by the general public. As usual, nobody seems to grasp that philosophy is armchair psychology, and that W was (in my view) the greatest natural psychologist of all time. He laid out the general structure of how the mind works, which is often referred to as intentionality and is roughly equivalent to cognition or personality or thinking and willing or higher order thought (HOT). He can thus be regarded as a pioneer in evolutionary psychology, although hardly anyone but me seems to realize it. W was thus nearly 50 years ahead of his time as the first to reject (though not entirely consistently) the blank slate or cultural view of human nature, though this has gone unrecognized and he has generally been interpreted as supporting a communal consensus view of psychology—exactly the opposite of his overall thrust (e.g., see Short’s comment on p 115). -/- I provide my recent (2016) table of intentionality for a current frame of reference from the two systems point of view before remarking on each of the essays. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

An analogy is made between two rather different domains, namely: logic, and football. Starting from a comparative table between the two activities, an alternative explanation of logic is given in terms of players, ball, goal, and the like. Our main thesis is that, just as the task of logic is preserving truth from premises to the conclusion, footballers strive to keep the ball as far as possible until the opposite goal. Assuming this analogy may help think about logic in (...) the same way as in dialogical logic, but it should also present truth-values in an alternative sense of speech-acts occurring in a dialogue. The relativity of truth-values is focused by this way, thereby leading to an additional way of logical pluralism. (shrink)

This article appeals to the table of nothingness (Nichts) occurring within Kant's Critique of Pure Reason to assess three recent accounts of nothingness - by Graham Priest, Filippo Costantini, and Filippo Casati & Naoya Fujikawa - under the light of folk preconceptions about nothingness. After defining the two strongest preconceptions as the absence of unrestrictedly everything (nihil absolutum) and the idea of nothingness as a self-contradictory item (nihil negativum), I argue that both might be read as two Aristotelian connected (...) homonyms, rather than conflating them into a single item (as Priest's and Casati and Fujikawa's accounts seem to do), or dropping the idea of the nihil absolutum, as Costantini's account does. (shrink)

Nietzsche’s Ecce homo, Notebooks and Letters: 1888-1889 / Translation by Daniel Fidel Ferrer. ©2023 Daniel Fidel Ferrer. All rights reserved. -/- Ecce homo: How One Becomes What One Is (Ecce homo: Wie man wird, was man ist). -/- Who should read Nietzsche? You can disagree with everything Nietzsche wrote and re-read Nietzsche to sharpen your attack. Philosophy. Not for use without adult supervision (required). Philosophy is a designated area for adults only. Read at your own risk. You have the pleasure (...) of reading and of course disagree with all philosophy. Warning philosophical ideas are present. Reading Nietzsche does not mean you will gain anything, in fact, you might lose your previous ideas. -/- Nietzsche does not call this book an autobiography (he has written many short autobiographical sketches before); but rather, uses the expression “I tell myself my life”. -/- Nietzsche was the past philosopher who wrote about our future, “The time is coming when the struggle for the domination of the earth will be waged - it will be waged in the name of basic philosophical doctrines.” KGWB/NF-1881, 11[273]. The world has seen plenty of wars and death, since 1881. The process of the domination of the earth and world is still on-going. -/- What is Nietzsche’s overall project with Ecce homo? -/- Main Leitmotifs in Ecce homo. -/- Christianity as the denial of the will to life, revaluation of all values (Umwerthung aller Werthe), Amor fati, Dionysus as a god and his philosophy (future project for Nietzsche), overthrowing idols, two worlds (“true world" finally became a fable) against Plato eternal world and forms, eternal recurrence or the eternal return of the same (Nietzsche heaviest thought, also his most abysmal thought “abgründlichsten Gedanken”), opposite and counterpart to type of person decadent (décadent), “I count the overcoming of pity among the noble virtues”, against the concept of God (Christian), overman or superman (Übermensch), Will to Power (Wille zur Macht), great politics, immoralist, morality of the Christian church, and Declaration of war (“Kriegserklärung”). -/- Table of Contents -/- Motto [page 3]. Epigraph [pages 4-6]. -/- Preface to the Translation of Ecce homo [pages 7-16] -/- Major Leitmotifs in Nietzsche [pages 17-24]. -/- Translations from Nietzsche’s German to English include. -/- 1). Ecce homo: How One Becomes What One Is (Ecce homo: Wie man wird, was man ist. [pages 25-113]. -/- 2). This poem was included in the first publications of Ecce homo (1908). Glory and Eternity (Ruhm und Ewigkeit). [pages 114-124]. -/- 3). These are all of Nietzsche’s last notebooks (complete) they are numbered 21, 22, 23, and 24. There are a total of 82 notes. Final notes by Nietzsche from the Nachlass (Nachlaß). Sometime in German called the Notizheft. Nietzsche’s notebooks that include some drafts for Ecce homo and other topics he was thinking during his last writings. Dating from October 1888 until early Janurary 1889. [pages 125-191]. -/- 4). Nietzsche’s Letters Regarding Ecce homo. Nietzsche’s letters starting at the end of October 1888 discussing Ecce homo. These are not always the complete letters but include all of the passages of Nietzsche discussing Ecce homo. Complete translation of the last letter Nietzsche wrote. Dated until BVN-1889. #1256. Letter to Jacob Burckhardt in Basel. Turin, about 6 January 1889. [pages 192-223]. -/- Bibliographies [pages 224-254]. -/- Nietzsche’s Philosophy Final Thoughts [pages 255-259]. -/- Enjoy reading Nietzsche's last book. (shrink)

● Sergio Cremaschi, The non-existing Island. The chapter discusses how the cleavage between the Continental and the Anglo-American philosophies originated, the (self-)images of both philosophical worlds, the converging rediscoveries from the Seventies, and recent ecumenic or anti-ecumenic strategies. I argue that pragmatism provides an important counter-instance to the familiar self-images and the fashionable ecumenic or anti-ecumenic strategies. The conclusions are: (i) the only place where Continental philosophy exists (as Euro-Communism one decade ago) is America; (ii) less obviously, also analytic philosophy (...) does not exist, or does no more exist as a current or a paradigm; what does exist is, on the one hand, philosophy of language and, on the other, philosophy of mind, that is, two disciplines; (iii) the dissolution of analytic philosophy as a school has been highly fruitful, precisely in so far as it has left room for disciplines and research programmes; (iv) what is left, of the Anglo-American/Continental cleavage is primarily differences in styles, depending partly on intellectual traditions, partly owing to sociology, history, institutional frameworks; these differences should not be blurred by rash ecumenism; besides, theoretical differences are alive as ever, but within both camps; finally, there is indeed a lag (not a difference) in the appropriation of intellectual techniques by most schools of 'Continental' philosophy, and this should be overcome through appropriation of what the best 'analytic' philosophers have produced. ● Michael Strauss, Language and sense-perception: an aspect of analytic philosophy. To test an assertion about one fact by comparing it with perceived reality seems quite unproblematic. But the very possibility of such a procedure is incompatible with the intellectualistic basis of logical positivism and atomism (as it is for example to be found in Russell's Analysis of Mind). According to the intellectualistic approach pure sensation is meaningless. Sensation receives its meaning and order from the intellect through interpretation, which is performed with the help of linguistic tools, i.e. words and sentences. Before being interpreted, sensation is not a picture or a representation, it is neither true nor false, neither an illusion nor knowledge; it does not tell us anything; it is a lifeless and order-less matter. But how can a thought (or a proposition) be compared with such a lifeless matter? This difficulty confronts the intellectualist, if on the one hand he admits the necessity of comparing thought with sense-perception, and on the other hand presupposes that we possess only intellectual and no immediate perceptual understanding of what we see and hear. In this paper I give a critical exposition of three attempts, made by Russell, Neurath and Wittgenstein, to solve this problem. The first attempt adheres to strict conventionalism, the second tends to naturalism and the third leads to an amended, very moderate version of conventionalism. This amended conventionalism looks at sense impressions as being a peculiar language, which includes primary symbols, i.e. symbols not founded on convention and not being in need of interpretation. ● Ernst Tugendhat, Phenomenology and language analysis. The paper, first published in German in 1970, by which Tugendhat gave a start to the German rediscovery of analytic philosophy. The author stages a confrontation between phenomenology and language analysis. He argues that language analysis does not differ from phenomenology as far as the topics dealt with are concerned; instead, both currents are quite different in method. The author argues that language-analytic philosophy does not simply lay out of the mainstream of transcendental philosophy, but that instead it challenges this tradition on the very level of foundations. The author criticizes the linguistic-analytic approach centred on the subject as well as any object-centred approach, while proposing inter-subjective understanding through language as the new universal framework. This is, when construed in so general terms, the same program of hermeneutics, though in a more basic version. ● Jürgen Habermas, Language game, intention and meaning. On a few suggestions by Sellars and Wittgenstein. The paper, first published in German in 1975, in which Habermas announces his own linguistic turn through a discovery of speech acts. In this essay the author wants to work out a categorical framework for a communicative theory of society; he takes Wittgenstein's concept of language game as a Leitfade and, besides, he takes advantage also of Wilfried Sellars's quasi-transcendental account of the genesis of intentionality. His goal is to single out the problems connected with a theory of consciousness oriented in a logical-linguistic sense. ● Zvie Bar-On, Isomorphism of speech acts and intentional states. This essay presents the problem of the formal relationship between speech acts and intentional states as an essential part of the perennial philosophical question of the relation between language and thought. I attempt to show how this problem had been dealt with by two prominent philosophers of different camps in our century, Edmund Husserl and John Searle. Both of them wrote extensively about the theory of intentionality. I point out an interesting, as it were unintended, continuity of their work on that theory. Searle started where Husserl left off 80 years earlier. Their meeting point could be used as the first clue in our search. They both adopted in effect the same distinction between two basic aspects of the intentional experience: its content or matter, and its quality or mode. Husserl did not yet have the concept of a speech act as contradistinguished from an intentional state. The working hypothesis, however, which he suggested, could be used as a second clue for the further elaboration of the theory. The relationship of the two levels, the mental and the linguistic, which remained for Husserl in the background only, became the cornerstone of Searle' s inquiry. He employed the speech act as the model and analysed the intentional experience by means of the conceptual apparatus of his own theory of speech acts. This procedure enabled him to mark out a number of parallelisms and correlations between the two levels. This procedure explains the phenomenon of the partial isomorphism of speech acts and intentional states. ● Roberta de Monticelli, Ontology. A dialogue among the linguistic philosopher, the naturalist, and the phenomenological philosopher. This paper proposes a comparison between two main ways of conceiving the role and scope of that fundamental part of philosophy (or of "first" philosophy) which is traditionally called "ontology". One way, originated within the analytic tradition, consists of two main streams, namely philosophy of language and (contemporary) philosophy of mind, the former yielding "reduced ontology" and the latter "neo-Aristotelian ontology". The other way of conceiving ontology is exemplified by "phenomenological ontology" (more precisely, the Husserlian, not the Heideggerian version). Ontology as a theory of reference ("reduced" ontology, or ontology as depending on semantics) is presented and justified on the basis of some classical thesis of traditional philosophy of language (from Frege to Quine). "Reduced ontology" is shown to be identifiable with one level of a traditional, Aristotelian ontology, namely the one which corresponds to one of the four "senses of being" listed in Aristotle's Metaphysics: "being" as "being true". This identification is justified on the basis of Franz Brentano's "rules for translation" of the Aristotelian table of judgements in terms of (positive and negative) existential judgments such as are easily translatable into sentences of first order predicate logic. The second part of the paper is concerned with "neo-Aristotelian ontology", i.e. with naturalism and physicalism as the main ontological options underlying most of contemporary discussion in the philosophy of mind. The qualification of such options as "neo-Aristotelian" is justified; the relationships between "neo-Aristotelian ontology" and "reduced ontology" are discussed. In the third part the fundamental tenet of "phenomenological ontology" is identified by the thesis that a logical theory of existence and being does capture a sense of "existing" and "being" which, even though not the basic one, is grounded in the basic one. An attempt is done of further clarifying this "more basic" sense of "being". An argument making use of this supposedly "more basic" sense is advanced in favour of a "phenomenological ontology". ● Kuno Lorenz, Analytic Roots in Dialogic Constructivism. Both in the Vienna Circle ad in Russell's early philosophy the division of knowledge into two kinds (or two levels), perceptual and conceptual, plays a vital role. Constructivism in philosophy, in trying to provide a pragmatic foundation - a knowing-how - to perceptual as well as conceptual competences, discovered that this is dependent on semiotic tools. Therefore, the "principle of method" had to be amended by the "principle of dialogue". Analytic philosophy being an heir of classical empiricism, conceptually grasping the "given", and constructive philosophy being an heir of classical rationalism, perceptually providing the "constructed", merge into dialogical constructivism, a contemporary development of ideas derived especially from the works of Charles S. Peirce (his pragmatic maxim as a means of giving meaning to signs) and of Ludwig Wittgenstein (his language games as tools of comparison for understanding ways of life). 7. Albrecht Wellmer, "Autonomy of meaning" and "principle of charity" from the viewpoint of the pragmatics of language. In this essay I present an interpretation of the principle of the autonomy of meaning and of the principle of charity, the two main principles of Davidson's semantic view of truth, showing how both principles may fit in a perspective dictated by the pragmatics of language. I argue that (I) the principle of the autonomy of meaning may be thoroughly reformulated in terms of the pragmatics of language, (ii) the principle of charity needs a supplement in terms of pragmatics of language in order to become really enlightening as a principle of interpretation. Besides, I argue that: (i) on the one hand, the fundamental thesis of Habermas on the pragmatic theory of meaning ("we understand a speech act when we know what makes it admissible") is correlated with the seemingly intentionalist thesis according to which we understand a speech act when we know what a speaker means; (ii) on the other hand, to say that the meaning competence of a competent speaker is basically a competence about a potential of reasons (or also of possible justifications) which is inherently connected with the meaning of statements, or with their use in utterances. ● Rüdiger Bubner, The convergence of analytic and hermeneutic philosophy This paper argues that the analytic philosophy does not exist, at least as understood by its original programs. Differences in the analytic camp have always been bigger than they were believed to be. Now these differences are coming to the fore thanks to a process of dissolution of dogmatism. Philosophical analysis is led by its own inner logic towards questions that may be fairly qualified as hermeneutic. Recent developments in analytic philosophy, e.g. Davidson, seem to indicate a growing convergence of themes between philosophical analysis and hermeneutics; thus, the familiar opposition of Anglo-Saxon and Continental philosophy might soon belong to history. The fact of an ongoing appropriation of analytical techniques by present-day German philosophers may provide a basis for a powerful argument for the unity of philosophizing, beyond its strained images privileging one technique of thinking and rejecting the remainder. Actual philosophical practice should take the dialogue between the two camps more seriously; in fact, the processes described so far are no danger to philosophical work. They may be a danger for parochial approaches to philosophizing; indeed, contrary to what happens in the natural sciences, Thomas Kuhn's "normal science" developing within the framework of one fixed paradigm is not typical for philosophical thinking. And in philosophy innovating revolutions are symptoms more of vitality than of crisis. ● Karl-Otto Apel, The impact of analytic philosophy on my intellectual biography. In my paper I try to reconstruct the history of my Auseinandersetzung mit - as I called it - "language-analytical" philosophy (including even Peircean semiotics) since the late Fifties. The heuristics of my study was predetermined by two main motives of my beginnings: the hermeneutic turn of phenomenology and the transformation of "transcendental philosophy" in the light of the "language a priori". Thus, I took issue with the early and the later Wittgenstein, logical positivism, and post-Wittgensteinian and post-empiricist philosophy of science (i.e. G.H. von Wright and the renewal of the "explanation vs understanding controversy" as well as the debate between Th. Kuhn and Popper/Lakatos); besides, with speech act theory and the debate about "transcendental arguments" since Strawson. The "pragmatic turn", started already by C.L. Morris and the later Carnap, led me to study also the relationship between Wittgensteinian "use" theory of meaning and of truth. This resulted on my side in something like a program of "transcendental semiotics", i.e. "transcendental pragmatics" and "transcendental hermeneutics". ● Ben-Ami Scharfstein, A doubt on both their houses: the blindness to non-western philosophies. The burden of my criticism is that contemporary European philosophers of all kinds have continued to think as if there were no true philosophy but that of the West. For the most part, the existentialists have been oblivious of their Eastern congeners; the hermeneuticians have yet to stretch their horizons beyond the most familiar ones; and the analysts remain unaware of the analyses and linguistic sensitivities of the ancient non-European philosophers. Briefly, ignorance still blinds almost all contemporary Western philosophers to the rich, variegated philosophical traditions outside of their familiar orbit. Both Continental and Anglo-Americans have lost the breadth of view that once characterized such thinkers as Herder and the Humboldts. The blindness that has resulted is not simply that of individual Western philosophers but of our whole, still parochial philosophical culture. (shrink)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition (...) is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.

This article considers distinct ways of understanding the world, referred to in psychology as Functions of Consciousness or as Cognitive Modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung's Simile of the Spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an Hexagon of Opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

We show that we in ways related to the classical Square of Opposition may define a Cube of Opposition for some useful statements, and we as a by-product isolate a distinct directive of being inviolable which deserves attention; a second central purpose is to show that we may extend our construction to isolate hypercubes of opposition of any finite cardinality when given enough independent modalities. The cube of opposition for obligations was first introduced publically in a lecture for the Square (...) of Opposition Conference in the Vatican in May 2014. -/- A COLORFUL ERRATUM: The article Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability, suffered a couple of mishaps when it was published in Logica Universalis, ISSN 1661-8297, 10(2-3), p. 373–376. The worst of them was that the colorful cube was printed in shades of grey, instead of decorating the sides with two transparent sides, and then a red, a yellow, a blue and a green side. The text of the article is not quite understandable because of this mishap, so I avail a colorfully updated version of the original article here. -/- . (shrink)

This article considers distinct ways of understanding the world, referred to in psychology as functions of consciousness or as cognitive modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung’s simile of the spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an hexagon of opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically (...) consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

This article focuses on the distinction between psychosocial types and conceptual personae advanced by Gilles Deleuze and Félix Guattari in What is Philosophy? The conceptual persona is the tool that a philosopher invents in order to create new concepts with which to bring forth new events. Although they present it as one of the three elements of philosophy, its nature and function and, above all, its conjunctions with psychosocial types have been overlooked by scholars. What is Philosophy? contains a list (...) of character traits of which each conceptual persona is composed. The central argument of this article is that this list can well be regarded as a table of categories that enable the exercise and experience of philosophy’s creative thinking. Since the character traits of a conceptual persona match the characteristics of the given psychosocial types, it is necessary to keep inventing new conceptual personae always starting from the historical presuppositions. The philosopher requires the conceptual persona to transfer his or her movements of thought to philosophy’s plane of immanence and thereby transform them in such a manner that philosophy can unfold as a creative power. It emerges as the subject of creative thinking at the same time as the concepts that subject creates, with which it coincides in the moment of creation. With the conceptual persona in What is Philosophy?, Deleuze and Guattari determine the one element of philosophy that makes the transcendental empiricism a method of creation that appears as a precise operation with all its convincing and transparent results. (shrink)

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I will (...) conclude with some consideration on scope interactions between quantifiers. (shrink)

The Table of Contents to the Philosophy of Happiness book by Martin Janello. The Introduction, individual Chapters, and the Conclusion and Epilogue of the book can be downloaded from PhilArchive as well. Audio versions corresponding to these sections of text, an entire on-line review copy, and a host of other pertinent materials are available without charge at the referenced website.

The heart of Aristotelian Logic is the square of opposition. This study engaged on further [re]investigation and meta-logical analysis of the validity of the square of opposition. Further, in this paper, it has been modestly established, with greater clarity, the exposition of the strengths, more than the presentation of the defects, loopholes and weaknesses, of the Aristotelian Logic in a descriptive and speculative manner. The unconcealment of the breakdown of the square of opposition marked a rupture and the opening of (...) avenues of alternative reasoning. The critical and analytical exposition of the loopholes of the square of opposition led to a realization that things around us could have been and still be different; and there could have been better alternative reasoning than what we have called, adopted, and worshipped [Greek] logic. Results show that the downfall of the oppositional relationships in the square of opposition provided a proof of the logical illusion of Aristotle or the loophole of Traditional Logic. The laws of opposition, that have been considered the measures of logically deductive inferences, are practically almost totally logical deceptions. By implication, if the laws of subcontrariety, contrariety, and subalternation [and may be contradiction] have collapsed, the square of opposition has also collapsed; hence, Aristotle‟s square of opposition is a fallacy. This means that the square of opposition has errors and in itself an error. (shrink)

Determinismus und Indeterminismus in der modernen Physik is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements”. A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen, to Substanzbegriff und Funktionsbegriff, a seminal (...) work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation. (shrink)

This cosmological model considers our observable universe as part of an expanding volume, produced by an explosion inside a black hole, while other, similar, expanding volumes exist beyond our observation. Such expanding volumes emerge into the space beyond them, initially appearing there as white holes. Then, over time as they continue to expand, their matter meets up, creating contracting volumes of space that eventually form hypermassive black holes — ones containing more mass than is in the observable universe. When a (...) tipping point is reached, such as a critical mass, these hypermassive black holes explode producing new expanding volumes. Considered at a suitably large scale, this model can be consistent with the perfect cosmological principle. This model is distinct from existing cyclical models as it has multiple explosions (big bangs) spatially spread out across the universe. It is consistent with Smoller and Temple’s Shockwave Cosmology Inside a Black Hole, which integrates shockwave cosmology with general relativity to produce a universe essentially like the one we observe, including cosmological redshift and a cosmic microwave background. (shrink)

Kant’s derivation of the table of categories from logical functions of judgments in the metaphysical deduction remains one of the least convincing arguments of the Critique of Pure Reason. This article presents an alternative approach to the question of the a priori origin of the table of categories. By circumventing the metaphysical deduction, I show the possibility of demonstrating the exact functions and necessity of the twelve categorial forms as emerging from the interaction of the synthetic unity of (...) apperception with the manifold content of the a priori intuition of space and time. I argue that this a priori material of cognition imposes a constraint on the spontaneity of understanding, thus giving rise to the specific rules of synthesis that make up the table of categories. On the reading I suggest, the table of categories can be understood as expressing the a priori form of self-consciousness in the face of space and time. (shrink)

Abstract: The main purpose of this paper is to find Artin's characters table of the group (Q2n×D3)when n=p_1.p_2….p_n,and p_1,p_2,…,p_n are primes number, which is denoted by Ar(Q2n×D3) where Q2m is denoted to Quaternion group and D3 is the Dihedral group of order 6 .

The aim of this paper is to make sense of the Keynes–Johnson octagon of oppositions. We will discuss Keynes' logical theory, and examine how his view is reflected on this octagon. Then we will show how this structure is to be handled by means of a semantics of partition, thus computing logical relations between matching formulas with a semantic method that combines model theory and Boolean algebra.

The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to (...) the system to which the atom at issue is related as a true part of it. The paper follows previous publications of mine stating that “dark matter” and “dark energy” are projections of arbitrarily entangled states on the cognitive “screen” of Einstein’s “Mach’s principle” in general relativity postulating that gravitational field can be generated only by mass or energy. (shrink)

This book is about whether reference to an individual is the essential feature of a proper name -- a widely held view -- or whether referring to an individual is simply a contingent feature. Three questions need resolving, then. First, whether all names in particular contexts are themselves referring devices. Second, whether recognizing names types and the consequent issue of their ambiguity can be resolved simply by distinguishing between name types and tokens thereof. Last, whether names are ever referential in (...) the way Kripke and others have convincingly argued. The answer to first two questions is negative. The answer to third is a qualified "yes." I explain the theory that allows for these answers in the manuscript, as well as addressing other issues such as: the problem of fictional names; descriptive names; empty names; what an act of naming consists of; an account of ontological commitment; and the data that suggests that names are predicates. (shrink)

This chapter gives an overview of the evolution of the position of the rare-earth elements in the periodic system, from Mendeleev’s time to the present. Three fundamentally different accommodation methodologies have been proposed over the years. Mendeleev considered the rare-earth elements as homologues of the other elements. Other chemists looked upon the rare earths as forming a special intraperiodic group and therefore clustered the rare-earth elements in one of the groups of the periodic table. Still others adhered to the (...) intergroup accommodation of the rare earths, according to which the rare-earth elements do not show any relationship with the other elements, so that they had to be placed within the periodic table as a separate family of elements. The intergroup accommodation became the preferred one in the twentieth century. The advantages and disadvantages of the different representations of the modern periodic table are discussed. (shrink)

An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.

This study aims to examine the Islamic Theological School that was opened in Nicosia back in 1932 to meet the chaplain needs of the Cypriot Muslims. In this context, how the Islamic Theological School was welcomed among the groupings of the period, its physical structure, teaching staff, and students were all addressed within the framework of the education program and the closure process. The "Foundation Files" in the National Archives and Research Department in the TRNC and the newspaper collections of (...) the period and the "British Colonial Documents" in the Archives of the General Directorate of the Foundations of Cyprus are the main sources of our research. Documentation method, which is one of the qualitative research methods, was used in the study. In this context, the documents that could be accessed in the researches related to the subject of the study are examined and described for the objectives of the study. In conjunction with the madrasas in Cyprus becoming dysfunctional until the end of the 1920s, the wrecked Great Madrasah building in Nicosia, which had the purpose of training personnel such as imams, preachers, chaplains and muezzins for the mosques, was demolished and a school called Islamic Theological School was built instead. The opening of the Islamic Theological School led to important debates between the two opposition groups of the time, the Halkçılar and the Evkafçılar. Halkçılar are the group of people who advocate the adoption of the revolutions and reforms of the newly established Turkish Republic also by Turkish Cypriots. For this reason, they strongly criticized the opening of the Islamic Theological School on the grounds that it would cause reactionism and bigotry. On the other hand, the concept of Evkafçılar is used for people who represent tradition and are close to the current British rulers. Evkafçılar advocated the opening of the Islamic Theological School by stating that it was a social need. Accordingly, both groups used the press effectively as a means of conveying their own thoughts. The halkçı group used the newspapers called "Söz" and "Masum Millet" and the evkafçılar group used the newspaper called "Hakikat" as a means to convey their views to the society. In the shadow of the discussions between the two groups, the Islamic Theological School, which was built in 1932 in place of the wrecked Great Madrasah building in the northeast of Selimiye (Hagia Sofia) Mosque in Nicosia, was built as a single-floor building and a gable roof system was used on its roof. Funds were appropriated by Education (Hatib Ahmed Efendi) Foundation for supplying the school's materials such as tables, chairs, cabinets, sofas, and armchairs. In 1932, when the Islamic Theological School began educating, there were only three professors and one teacher in its teaching staff. Hürremzâde Hakkı Efendi, one of the professors, was both the school director and the Fatwa Emin. One of the other professors was an imam and the other one was a fatwa clerk. And Muallim Ahmed Fehim Efendi undertook the duty of imamate. According to the documents examined, the aforementioned faculty members have taught religious and human sciences-oriented courses in the school. As far as we can identify from the documents open to research in the archives, in the years between 1932 and 1950, when the Islamic Theological School was open, a total of 11 students were educated in this school. In the first year of this school, which started education with three students only, students were given a monthly scholarship of 15 shillings. In addition, the students were both able to practice as assistants to muezzins in the mosques during the month of Ramadan and they were also provided with economic support. After graduation, the students were nominated as imams, muezzins and devirhan. The Islamic Theological School was closed in 1950 because there was no student demand. Despite the fact that 11 people received education in 18 years between the school's opening year 1932 and 1950, and the annual reports published by General Directorate of Foundations stated that the Islamic Theological School continued its services satisfactorily under the upervision of its Fatwa Emin, these statements were unrequited in reality. The Islamic Theological School started to serve in the shadow of the debates between the opposition groups of its time. The parties of the discussions are divided into two groups: Halkçılar and Evkafçılar. The first group opposed the opening of the school by claiming that the financial resources of the General Directorate of Foundations would be spent unnecessarily and that the students to be educated would be raised with reactionism and bigoted ideas. The second group, Evkafçılar, approached the issue with a need-centred approach and defended the necessity of a school to educate religious officials. The mentality of the populist group reflects the ideology of the young Turkish Republic and this is clearly seen in their defence mechanisms. Evkafçılar, on the other hand, did not pay the required attention to the Theological School despite their discourses of necessity. As a result, the power struggle of these two groups aiming to hold the leadership of the Turkish Cypriots caused the Theological School to be adversely affected. Very low salaries of religious officials working in existing mosques and low fees being paid to the graduates of the Theological School who were employed in mosques were other factors that reduced the demand for Theological School. As a result, those who saw low-paid religious officials who had difficulty even getting along did not seek education to become religious officials and their families never pointed such way to them. The fact that a very limited number of students attended Theological School did not lead General Directorate of Foundations to alternative solutions. As the Islamic Theological School was not well organized, the issue of religious officials was felt more and more by the muslim people in the following years in Cyprus where many villages do not even have religious officials. (shrink)

Axel Honneth reconstructs Hegel’s social and political philosophy on the basis of the concept of recognition. For Honneth, recognition is a constitutive relation between individuals that is in principle symmetrical. By conceiving recognition through symmetry, Honneth effectively bans the inclusion of power within recognitive relation. He thus regards the relations of power as cases of non-recognition or misrecognition. In this paper, I develop an alternative theory of the constitutive relation between individuals for Hegel, one that is based on the asymmetrical (...) relation of power. To this aim, I focus on the chapter of “determinations of reflection” in the Science of Logic. Through a close analysis of Hegel’s Logic, I argue that the most fundamental form of relation between individuals is the relation of opposition, that individuals are solely constituted in and through the relation of opposition, and that the relation of opposition is essentially asymmetrical. Together, these claims establish... (shrink)

According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...) the propositions that contradict this proposition are true” does not have the contrary proposition and does not have the contradictory proposition. In fact: FEX “All the propositions that contradict this proposition are not true” has a different subject: the subject of the proposition X is constituted by all the propositions that contradict the proposition X; by contrast, the subject of the proposition FEX is constituted by all the propositions that contradict the proposition FEX. And FOX “Not all the propositions that contradict this proposition are true” has a different subject: the subject of the proposition X is constituted by the propositions that contradict the proposition X; by contrast, the subject of the proposition FOX is constituted by the propositions that contradict the proposition FOX. According to Aristotle, a singular proposition (in his example: "Socrates is white") which is true must have its negative proposition ("Socrates is not white") which is false. I agree with Aristotle, but there are singular propositions which do not have the corresponding negative proposition. The proposition (or, rather, the pseudo-proposition) L “This same statement is not true” does not have the negative proposition because the proposition FNL “This same statement is true” has a different subject from the subject of the proposition L: the subject of the proposition L is the proposition L; by contrast, the subject of the proposition FNL is the proposition FNL. L and FNL cannot have the same subject. By contrast, the proposition M “This mount is entirely in Swiss territory” and the proposition NM “This mount is not entirely in Swiss territory” can have the same subject (for example, the Mount Eiger): in case the subject of the proposition M and the subject of the proposition NM is the same, M and NM are opposite propositions, NM is the negative proposition of M. By contrast, the proposition (or, rather, the pseudo-proposition) L "This same statement is not true" cannot have the corresponding negative proposition because FNL "This same statement is true" has a different subject: the subject of L is L ; by contrast, the subject of FNL is FNL. Then the paper continues by analyzing some variants of the liar’s paradox: L1 “The statement L1 is not true”; the so-called liar cycle; and the so-called Yablo’s paradox. (shrink)

Saba Mahmood’s anthropological work studies the gain in skills, agency and capacity building by the women’s dawa movement in Egypt. These women increase their virtue toward the goal of piety by following dominant, often patriarchal norms. Mahmood argues that “teleological feminism” ignores this gain in agency because this kind of feminism only focuses on opposition or resistance to these norms. In this paper I defend Mahmood’s “anti-teleological” feminist work from criticisms that her project valorizes oppression and has no vision for (...) a nonoppressive feminist future. I argue the future envisioned by teleological feminists gets caught in “the Hegelian” trap of replicating past oppression in their feminist future. I find in Mahmood’s work the tools to escape this trap. I argue, rather than a movement of overcoming oppression, Mahmood’s work suggests an immanent and creative movement that emphasizes difference for a truly new future. I turn to a Bergsonian metaphor and argue that this movement can be seen as akin to the movement of biological evolution. I conclude using the work of Eve Sedgwick that the Egyptian women that Mahmood studies are being read in a “paranoid” fashion and demonstrate using Leila Ahmed a better “reparative” reading of these women. (shrink)

THESIS ABSTRACT The life of Catholic reformer Jacques Lefèvre d’Étaples, 1455- 1536, spanned the threshold between Medieval and Renaissance eras. Like other humanists, Lefèvre synthesized philosophical, theological and scientific theories and practices — of such is his unpublished treatise De Magia naturali, On Natural Magic. I elucidate Lefèvre’s focus on universal mystical metaphors of divine union, in order to offer a simpler view into the evolution of his writings. Engaging historic-intellectual background in critical analysis of Book II, I address the (...) conflicting political, religious, and academic opinions of natural magic, demonstrating that current Academia is poised to expand the historical, “theoretical” treatment of natural magic to engage it as a phenomenological, “practical” human experience. In De Magia naturali Book II, Lefèvre decloaks mythology, philosophy, astrology, literature and religion to a scientific theory, practice and experience of number as Idea. He reveals how the limit of metaphorical imagery is duality, the binary Coincidence of Opposites, symbolized by the number 2. The magic in Lefèvre’s number mysticism is human experience of numerical ascension from man to God, achieved through the number 3, the love-nexus re-uniting 2 into One, duality into unity. Renaissance humanists conceived of this prisca theologia, pristine or ancient theology, as embodied in the Christian Trinity through the Spirit of Christ. Current Academia is responsible to teach this wisdom tradition from a multicultural, interdisciplinary worldview, as I posit the humanists intended. (shrink)

A disregard for human traditions, the brutality of predation, sacrifice, and sexual desire are ingrained in languages across cultures. This paper concerns a key linguistic feature reflecting this predicament: utterances that encapsulate their opposite and effectuate a U-turn in meaning. This mode of communication stands out as a representation of the friction between incommensurable worlds—conceived together. An enemy’s perspective or an unpalatable reality finds a host within language. I embark upon a multidisciplinary search for examples of such utterances and present (...) an assemblage of five pertinent images. Each of these makes a distinct conceptual contribution. Vigilance and an awareness of other points of view underpin most of the utterances under study, which I propose to call “sharp communication” at the intersection of opposing perspectives. (shrink)

A critique is given of the attempt by Hettema and Kuipers to formalize the periodic table. In particular I dispute their notions of identifying a naïve periodic table with tables having a constant periodicity of eight elements and their views on the different conceptions of the atom by chemists and physicists. The views of Hettema and Kuipers on the reduction of the periodic system to atomic physics are also considered critically.

Proof of the Opposition Between Consciousness and Matter logically. Please refer to the document for specific content. An independent research work by a 16-year-old high school student. I support open collaboration. Contact me if there's any question.

A formal theory of oppositions and opposites is proposed on the basis of a non- Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows. After recalling the historical background, oppositions and opposites are compared from a mathematical perspective: the first occurs as a relation, the second as a function. Then the main point of the paper appears with a calculus of oppositions, by (...) means of a non-Fregean semantics that redefines the logical values of various sorts of sentences. A num- ber of topics are then addressed in the light of this algebraic semantics, namely: how to construct value-functional operators for any logical opposition, beyond the classical case of contradiction; Blanché's "closure problem", i.e., how to find a complete structure connecting the sixteen binary sentences with one another. All of this is meant to devise an abstract theory of opposition: it encompasses the relation of consequence as subalternation, while relying upon the use of a primary "proto- negation" that turns any relatum into an opposite. This results in sentential negations that proceed as intensional operators, while negation is broadly viewed as a difference-forming operator without special constraints on it. (shrink)

We propose in this article some new elements for the interpretation of Heraclitus' doctrine, concerning in particular the role of the opposition of contraries as generator of harmony, that results from Fragments 8DK and 51DK. This interpretation is based on the conceptual tool of matrices of concepts. After having described the basic elements that govern the latter, we set out to define in this conceptual framework the notions of opposition and contrary, as well as of harmony. This allows us to (...) give an interpretation and also a justification of Heraclitus' specific doctrine, according to which the opposition of contraries generates harmony. (shrink)

The 1960s and 1970s in Britain was a time of revolution in attitudes towards sex, especially in the public education system. The campaign to see sex education established as a subject in primary and secondary schools was gaining traction despite fierce opponents like Mary Whitehouse. This article focuses on the story of a traditionalist Catholic couple named Mr Derrick Taylor and Mrs Irene Taylor who set up a campaign to defend their children against what they saw as the encroachment of (...) immorality, promiscuity and pornography. Mrs Taylor worked to spread the message that sex education was wrong by building a network of mothers who shared her views while Mr Taylor defended in court his decision to remove his children from school altogether. This article gives an account of the lengths Mr and Mrs Taylor went to in order to try to stop sex education and describes the impacts this campaign had on their children. (shrink)

Developing a suggestion of Wittgenstein, I provide an account of truth tables as formulas of a formal language. I define the syntax and semantics of TPL (the language of Tabular Propositional Logic), and develop its proof theory. Single formulas of TPL, and finite groups of formulas with the same top row and TF matrix (depiction of possible valuations), are able to serve as their own proofs with respect to metalogical properties of interest. The situation is different, however, for groups of (...) formulas whose top rows differ. For them I provide (i) a tree-style system of ‘row tree proofs’, which is shown to be sound and complete, and (ii) an alternative, re-writing strategy. (shrink)

At the heart of chemistry lies the periodic system of chemical elements. Despite being the cornerstone of modern chemistry, the overall structure of the periodic system has never been fully understood from an atomic physics point of view. Group-theoretical models have been proposed instead, but they suffer from several limitations. Among others, the identification of the correct symmetry group and its decomposition into subgroups has remained a problem to this day. In an effort to deepen our limited understanding of the (...) periodic law, we have extended the traditional Lie algebraic framework to account for the peculiar degeneracy structure of the periodic system. Starting from the four-dimensional hidden symmetry and accidental degeneracy of the hydrogen atom, as first revealed by Fock in 1935, our research has mainly focussed on the way this SO(4) symmetry of the Coulomb potential gets broken in the periodic system as a consequence of the transformation of the hydrogenic (n, l) filling order to the Madelung (n+l, n) order due to electronic repulsions, relativistic effects and spin-orbit couplings. In this PhD dissertation, a new left-step format of the periodic table is first proposed on the basis of the Madelung rule. Following the particle physics tradition, the chemical elements are then considered as various states of some 'atomic matter', which is described by a non-compact spectrum-generating dynamical Lie group. The chemical elements are shown to form a basis for a single infinite-dimensional degeneracy space of the SO(4,2) ⊗ SU(2) group. An explanation for the period doubling is then proposed in terms of a particular symmetry breaking of the SO(4,2) group to the anti de Sitter SO(3,2) group. The Madelung rule is rationalised on the basis of nonlinear Lie algebras which reflect the screening of the Coulomb hole. This opens new perspectives for a symmetry-based understanding of how the periodic law emerges from its quantum mechanical foundations, and holds the future promise of complementing our current phenomenological approach by a direct atomic physics approach. (shrink)

A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric (...) sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth. (shrink)

This paper discusses knowledge of opposites. In particular, attention is given to the linguistic notion of antonymy and how it represents oppositional relations that are commonly found in perception. The paper draws upon the long history of work on the formalisation of antonymy in linguistics and formal semantics, and also upon work on the perception of opposites in psychology, and an assessment is made of the main approaches. Treatments of these phenomena in linguistics and psychology posit that the (...) principles of minimal difference and invariance are centrally important. It will be suggested that the standard approach employing meaning postulates fails to capture the relevant notion of antonymy, in part because it is not informed by these principles, and in part due to a number of other problems with this kind of approach, many of which may be overcome by building in the central principles from the beginning. The paper also discusses the issue of whether we can know that opposites necessarily exclude each other and, if so, how. This issue is intertwined with what is known as the colour incompatibility problem that Wittgenstein wrangled with at various times during his life. The paper assesses various solutions to these problems including an approach that was first put forward by Jerrold J. Katz. The relation between this approach and the theory of determinables and determinates is also examined. A further development upon this approach is proposed and then applied to the case of the formalisation of antonymy. It is argued that this approach avoids the problems suffered by the main approaches discussed earlier in the paper. (shrink)

High grade chromite ore has been decreased constantly due to the importance of chromium element in industrial uses such as metallurgical, chemical, and refractory industries. Therefore, beneficiation of low grade has been more significant .Response Surface Methodology (RSM) is combination of statistical and mathematical methods used for modeling and analyzing problems. In this study, the Central Composite Design (CCD) was applied by using Design-Expert (version 6.0.5) for modeling and optimizing the effect of operating variables on the performance of gravity separation (...) via pilot plant shaking table for chromite ore. Three operating variables were studied, namely feed rate, tilt angle, and flow rate during the tests. The sample under study is low grade chromite ore, containing (30.21%, Cr2O3). The mathematical model equations of ANOVA model revealed that the grade of concentrate is more sensetive for feed rate (g/min) compered to water flow rate (l/min).whereas , recovery of concentrate is more sensetive for tilt angle compered to water flow rate (l/min) and feed rate (g/min). Optimized responses for the beneficiation process were found at concentrate with 48.52% Cr2O3 in with 83.09% recovery and it was achieved at water flow rate 15.33 l/min, tilt angle 2.16 ≈ 2.00 degree, and feed rate of 195.38 g/min. (shrink)