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)

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.

. 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)

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.

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)

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)

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)

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)

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.

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)

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.

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)

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)

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.

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 opposites generates harmony. (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)

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)

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)

This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...) notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

We argue that while the new opposition in Azerbaijan between 2005 and 2013 did not realize all the goals set, it influenced a new generation of young activists who became the loudest supporters of democratic and secular values in Azerbaijan. This grassroots activation of the youth brought noticeable changes to some parts of Azerbaijani society by questioning the authority of traditional values. Many young people, especially students found a platform to discuss their problems concerning everyday basic issues such as intimate (...) relationships as well as their freedom to live in accordance with their personal choices and desires without the family interference in the light of theoretical questions such as the importance of liberal democratic values, individual liberties, and the rule of law. The successfully established connections between material problems and transcendental ideals encouraged some young people to participate in the open discussions and seminars organized by the new opposition. Because of the emergence of this new generation of active youth, the government was forced to incorporate some elements of this new discourse at least by making some cosmetic changes within its structures. The government became successful in its attempts of weakening the new opposition by hijacking its ideas and creating similar but pro-government organizations; neutralizing or buying some well-known opposition figures such as writers and journalists; and finally, persecuting the leading members of the youth organizations. (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)

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)

The aim of this article is to demonstrate the thesis that the stabilization of Nigeria’s complicated political situation is furthered by the functioning in that country of institutions based on two models of interethnic power-sharing – consociationalism and centripetalism – and that the two are to some extent complementary in Nigerian practice, despite the fact that political theory sees the two as opposites of each other. The article begins with a short analysis of the political situation in Nigeria. This (...) is followed by a presentation of the problem of defining the notion of political stability and an assessment of the same in the Nigerian context. The article then goes on to discuss the nature of centripetalism and consociationalism and specific centripetal and consociational institutions involved in the stabilization of the political situation in Nigeria. The article ends with the author’s conclusions about the initial thesis. The article has been published in "Politeja" 2016, vol. 42, no. 3, pp. 53-73. For more on combining institutions of different models of power-sharing see: Krzysztof Trzcinski, Hybrid Power Sharing: On How to Stabilize the Political Situation in Multi-Segmental Societies, "Politeja" 2018, vol. 56, no. 5, pp. 86-107. (shrink)

Following a previous article (cf. Costa-Leite, A. (2018). Oppositions in a line segment, South American Journal of Logic, 4(1), pp.185-193) in which logical oppositions are defined in a line segment, this article goes one step further and proposes a method defining them using a zero-dimensional object: a point.

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)

It is claimed hereby that, against a current view of logic as a theory of consequence, opposition is a basic logical concept that can be used to define consequence itself. This requires some substantial changes in the underlying framework, including: a non-Fregean semantics of questions and answers, instead of the usual truth-conditional semantics; an extension of opposition as a relation between any structured objects; a definition of oppositions in terms of basic negation. Objections to this claim will be reviewed.

According to Greimas, the semiotic square is far more than a heuristic for semantic and literary analysis. It represents the generative “deep structure” of human culture and cognition which “define the fundamental mode of existence of an individual or of a society, and subsequently the conditions of existence of semiotic objects” (Greimas & Rastier 1968: 48). The potential truth of this hypothesis, much less the conditions and implications of taking it seriously (as a truth claim), have received little attention in (...) the literature. In response, this paper traces the history and development of the logical square of opposition from Aristotle to Greimas and beyond, to propose that the relations modelled in these diagrams are embodied relations rooted in gestalt memories of kinesthesia and proprioception from which we derive basic structural awareness of opposition and contrast such as verticality, bilaterality, transversality, markedness and analogy. To make this argument, the paper draws on findings in the phenomenology of movement (Sheets-Johnstone 2011a, 2011b, 2012, Pelkey 2014), recent developments in the analysis of logical opposition (Beziau & Payette 2008), recent scholarship in (post)Greimasian semiotics (Corso 2014, Broden 2000) and prescient insights from Greimas himself (esp. 1968, 1984). The argument of the paper is further supported through a visual and textual content analysis of a popular music video, both to highlight relationships between the semiotic square and mundane cultural ideologies and to show how these relationships might be traced to the marked symmetries of bodily movement. In addition to illustrating the enduring relevance of Greimasean thought, the paper further illustrates the neglected relevance that embodied chiasmus holds for developments in anthropology, linguistics and the other cognitive sciences. (shrink)

From 1) the main ideas of the Kantian CRP - 2) a reinterpretation of the concept of transcendental subject and - 3) the logical principle of Individuation, we propose a new ontology in which subject and object are of the same reality. We describe the dynamic principle by which the Existence of the subject emerges from formless meta-substance and separates into an animated representation of the world.

I present an argument Marilyn Strathern makes against characterizing Elmdon villagers as innately lazy. It looks as if the eventual direction of this material is going to be a rational actor model.

There are four ways in which things are said to oppose (ἀντικεῖσθαι) each other: as relatives (τὰ πρός τι), as contraries (τὰ ἐναντία), as privation and possession (στρέσις καὶ ἓξις) and as affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) Aristotle’s examples are: double and half for relatives, good and bad for contraries, blindness and sight for privation and possession and ‘He is sitting’ and ‘he is not sitting’ for affirmation and negation. We discussed relatives separately thus we (...) ignore it here. A. Contraries Contraries (ἐναντία) have the following features: 1) They are not said of each other (οὐδαμῶς πρὸς ἄλληλα λέγεται) as relatives are said of each other. (Cat., 10, 11b15-23) 2) Contraries are of two kinds: a) Non-intermediables: Those that it is necessary for one or the other of them to belong to the things they naturally occur in or predicated of and accept no intermediate between themselves. Since it is necessary for one of e.g. health and sickness to occur in an animal’s body or odd and even to belong to a number, there is no intermediate between health and sickness or odd and even. (Cat., 10, 11b38-12a9; 12b28-34) b) Intermediables: Those that it is not necessary for one of them to belong to the things they naturally occur in or predicated of and accept intermediates between themselves. It is not necessary for one of e.g. black and white to belong to a body and there may be some intermediates between them. (Cat., 10, 12a9-25; 12b34-40) 3) Contraries can change to one another when the thing capable of receiving them is there. (Cat., 13a18-21) The only exception is when one of the contraries belongs to something by nature. In such cases, change is not possible as the hotness of fire cannot change to coldness while fire is still there. 4) Contraries belong to the same thing, either the same in species or in genus as e.g. sickness and health in an animal’s body or whiteness and blackness in body simply. (Cat., 10, 14a15- ) In Metaphysics (I, 1058a8-10) Aristotle asserts that contraries are in the same genus. 5) There are three possibilities about the genera of contraries: they either are in the same genus, e.g. black and white, or in the contrary genera, e.g. justice and injustice, or are themselves genera, e.g. good and bad. (Cat., 11, 14a19-25) 6) Doing and being affected admit of contrariety, e.g. heating is contrary to cooling. (Cat., 9, 11b1-4) 7) Substances only are able to receive contraries. (Cat., 5, 4a10-17) 8) There is nothing contrary to a substance, whether primary or secondary. (Cat., 5, 3b24-27) Thus, neither man nor an individual man has a contrary. 9) There is no contrary to a quantity: e.g. four-foot ot ten has no contrary. (Cat., 5, 3b27-32) 10) Otherness in species means to be contraries. (Met., I, 1058a17-20) 11) Contrariety is complete difference. Two things that have the same genus but are different in species are other than one another in the highest degree and their difference is complete, i.e. they cannot be present along with one another. (Met., I, 1058a10-16) 12) One of the contraries is a privation, which is a denial of a predicate to a determinate genus. (Met., Γ, 1011b18-20) 13) ‘Neither true judgments nor true propositions can be contrary the one to the other.’ (OI., II, 14, 24b6-7) B. Privation and possession Privation and possession are said in connection with the same thing in which the possession naturally occurs. Only that thing which is capable of receiving a possession and only when it is entirely absent from that which naturally has it and only at the time when it is natural for it to have it, is called to be deprived of it. (Cat., 10, 12a26-30) A thing is not called e.g. blind if it has never had or was not supposed to have sight. That privation and possession are not relatives is obvious from the fact that none is called just what it is, of its opposite. (Cat., 10, 12b16-21) Moreover, while relatives reciprocate, they do not. (Cat., 10, 12b21-25) That they are not contraries is explained by the classification of contraries to intermediable and non-intermediable contraries. The latter are different from privation and possession because it is necessary for one of such contraries to be predicated of absolutely everything while it is not the case about privation and possession because they are necessary only in things naturally capable of their predication. Intermediable contraries are different from privation and possession because while the former are not necessary the latter are necessary in their subject matters. (Cat., 13a3-17) Unlike contraries for each of which it is possible to change to the other, change in privation and possession is allowed only from possession to privation and not vice versa: neither a blind man gets sight nor a bald man regain his hair. (Cat., 13a18-36) C. Affirmation and negation Aristotle regards the reception of truth and falsity as the main difference affirmation and negation opposition has in respect of other three kinds of opposition: it is only affirmation and negation that it is always necessary for one of them to be true and the other to be false (Cat., 13a37-b26), no matter the subject of affirmation or negation exists or not. (Cat., 10, 13b27-35) ‘It is impossible that contradictory propositions should both be true of the same subject.’ (OI., II, 12, 21b17-18) It is evident both about relatives and those contraries that include no co-positing, e.g. health and sickness. The only cases that resemble affirmation and negation are those contraries that are said with co-positing, e.g. ‘Socrates is well’ and ‘Socrates is sick.’ Yet, Aristotle points, not even with these is it necessary always for one to be true and the other false because if Socrates does not exist, neither will be true. (Cat., 10, 13b12-19) This is true also about privation and possession: neither ‘Socrates has sight’ nor ‘Socrates is blind’ are true if he does not exist. Moreover, it is not necessary for one or the other of them to be true or false even if he exists because until the time when it is natural for Socrates to have sight, both are false. (Cat., 10, 13b20-26) . (shrink)

Aristotle’s philosophy is considered with respect to one central concept of his philosophy, viz. opposition. Far from being a mere side-effect of syllogistic, it is argued in the present paper that opposition helps to articulate ontology and logic through an account of what can be or cannot be in a systematic and structural way. The paper is divided into three main parts. In Section I, the notion of Being is scrutinized through Aristotle’s theory of categories. In Section II, the notion (...) of Non-Being is connected to Aristotle’s theory of oppositions. In Section III, the notion of essence is revisited in order to bring about a holist theory of meaning by individuating through opposite properties. In conclusion, the legacy of Aristotle is depicted as balanced between a powerful reflection around Being and a restrictive ontology of substance. (shrink)

The paradox of persisting opposition raises a puzzle for normative accounts of democratic legitimacy. It involves an outvoted democrat who opposes a given policy while supporting it. The article makes a threefold contribution to the existing literature. First, it considers pure proceduralist and pure instrumentalist alternatives to solve the paradox and finds them wanting — on normative, conceptual, and empirical grounds. Second, it presents a solution based on a two-level distinction between substantive and procedural legitimacy that shows that citizens are (...) consistent in endorsing the upshot of democratic procedures while opposing it. Third, it unpacks three reasons to non-instrumentally endorse such procedures — namely, the presence of reasonable disagreement, non-paternalism, and the right to democratically do wrong. In so doing, the article shows that those accounts of democratic legitimacy that rely on reasonable disagreement as a necessary condition for democratic procedures being called for are flawed, or at least incomplete, and offers a more complete alternative. (shrink)

The purpose of this paper is to consider the ethical, political, and epistemological dimensions of upward mobility, through higher education, from a personal perspective. I explore some of the contradictions exposed in my experience pursuing aphilosophy Ph.D., in light of scholarship highlighting challenges for low socio-economic status (SES) undergraduate students. I evaluate the proposal from the philosopher Jennifer M. Morton (2019) that low-SES students need ‘clear-eyed ethical narratives’ to navigate higher education. I argue that, in order to develop these narratives, (...) low-SES graduate students must self-conceive in a way that incorporates ‘oppositional consciousness’. (shrink)

The article advances a new way of thinking about classifications in general and the classification of mental disorders in particular. By applying insights from measurement practice to the context of classification, I defend a notion of epistemic accuracy that allows one to evaluate and improve classifications by comparing different classifying methods to each other. Progress in classification arises from the mutual development of classification systems and classifying methods. Based on this notion of accuracy, the article illustrates with an example how (...) psychiatric classifications can be improved via circumscribed comparisons of different perspectives on mental disorders, without relying on complete models of their complex aetiology. When applying this strategy, the traditional opposition between symptom-based and causal approaches is of little consequence for making progress in the epistemic accuracy of psychiatric classification. (shrink)

This article deals with the relationship between philosophy and science in the writings of Karl Jaspers and with its reception in the wider scholarly literature. The problem discussed is how to characterize the relationship that exists between science—defined on pure Kantian grounds as a universally valid knowledge of phenomenal objects—and philosophy—conceived by Jaspers as the transcending mode of thinking of personal Existenz rising towards the totality and unity of Being. Two solutions to that problem arise from Jaspers’s writings. The oppositionist (...) view is based in his earlier philosophy of Existenz. It describes the discrepancy between determinateness, bestowed by science to its objects, and freedom of self-determination, which is both a synonym and a condition of possibility for Existenz. The reciprocal view is based in Jaspers’s later works, where he focuses on exploration of his concept of Being (das Umgreifende). By contrast with most of Jaspers’s commentators, the present interpretation is anchored in a developmentaland contextual understanding of Jaspers’s thought. Showing the transcendental background of this topic, the proposed interpretation allows us to abstain from viewing the two solutions as incoherent or contradictory and instead to see them as constitutive of a single philosophical course. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola by outlining a pragmatic logic for assertions and hypotheses. On the (...) basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

This chapter presents a task-based lesson sequence based on Judith Butler's Gender Trouble. Gender Trouble is a great piece of philosophical literature. However, as philosophical literature is a genre rarely found in EFL teaching, this chapter first demonstrates in detail the merits of this genre for the teaching ofEnglish for Academic Purposes. After a brief analysis of the source text, which deconstructs the entire sex-gender link and presents both sex and gender as free-floating, this chapter presents task-based methodology and how (...) it is utilized in a lesson aimed at building gender awareness and acceptance. In the target task students are asked to take the role of an ethics teacher at an Irish high school, in which the discussion arose whether the school should introduce unisex toilets and changing rooms in order to not discriminate against transsexual students. Tue study of Butler's philosophy will provide students with both the knowledge and language to accomplish this task. Open follow-up discussions often lead to powerful ethical insights in the context of gender, homo- and transsexuality. (shrink)

In the standard model of cosmology, λCDM, were introduced to explain the anomalies of the orbital velocities of galaxies in clusters highest according estimated by General Relativity the dark matter and the accelerated expansion of the universe the dark energy. The model λCDM is based in the equations of the General Relativity that of the total mass-energy of the universe assigns 4.9% to matter (including only baryonic matter), 26.8%, to dark matter and 68.3% to dark energy adjusted according observed in (...) Planck mission, therefore, excluding bosonic matter (quantum vacuum). However, the composition of dark matter and dark energy are unknown. Due to that it lacks of a correct physical theory of gravity since General Relativity is only their powerful equations, which in their applications, their results are interpreted arbitrarily. Properties as curvature, viscous fluid, dragging frame and gravity action are attributed mistakenly to the spacetime by the materialist substantivalism, the most credible philosophical interpretation that complements the General Relativity, caused by its absence of physical definition of spacetime and static gravitational field as immaterial, but which violates, the conception of gravity as an effect of coordinates of the generalization of the inertial motion to the accelerated motion and, in particular, the description of the metric tensor of gravity as a geometric field. These properties are really of the quantum vacuum, the main existence form of the matter. In this paper we propose that the quantum vacuum is the source of dark matter and dark energy, therefore, the components of the quantum vacuum are of them. Both are opposite effects of the quantum vacuum that when gravitationally interacts with the cosmic structures, the vacuum it curves and when such interaction tends to cease by declination of the formation of these structures, occurring since near five milliard of years ago, vacuum it maintains quasi plane, since it interacts gravitationally very weakly with itself, accelerating expansion of the universe. (shrink)

"It’s a beautiful thing, the destruction of words. Of course the great wastage is in the verbs and adjectives, but there are hundreds of nouns that can be got rid of as well. It isn’t only the synonyms; there are also the antonyms. After all, what justification is there for a word which is simply the opposite of some other word? A word contains its opposite in itself. Take “good”, for instance. If you have a word like “good”, what need (...) is there for a word like “bad”? “Ungood” will do just as well — better, because it’s an exact opposite, which the other is not." (Syme, in George Orwell's Nineteen Eighty-Four) This chapter is about opposites and Newspeak in Orwell's Nineteen Eighty-Four. (shrink)

It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern of (...) oppositions that proceeds with colored diagrams and an increasing set of bitstrings. (shrink)

Content nonconceptualism and State conceptualism are motivated by different readings of what I want to call here Bermúdez’s conditions on content-attribution (2007). In one read- ing, what is required is a neo-Fregean content to solve problems of cognitive significance at the nonconceptual level (Toribio, 2008; Duhau, 2011). In the other reading, what is required is a neo-Russellian or possible-world content to account for how conspecifics join attention and cooperate, contemplating the same things from different perspectives in the same perceptual field. (...) The solution to this apparent contradiction is the rejection of the real content view and the adherence to what I call here Content-pragmatism: there is no such thing as the content of experience. According to content pragmatism, “proposition” is not as real as a mental state, but rather, it is a term of art that semanticists use, as a matter of theoretical convenience, to classify mental states. What follows from Content-pragmatism is Content- pluralism: there are so many contents that are required to meet Bermúdez’s condition on content attribution. Because both criticism and the defense of State conceptualism overlook the real scope of Bermúdez’s condition on content attribution, they are ineffective. In this paper, I will argue that the opposition between State and Content nonconceptualism is a real one, but only a relative one, that is, relative to the opposite constraints to be met. If we want to solve the problems of cognitive significance, the best we can do is to let the content of experience be modeled as neo-Fregean content, namely, a compound of nonconceptual modes of presentation of objects and properties. In this case, Content-nonconceptualism prevails. In contrast, if we want to account for how conspecifics join attention to the same entities in the same perceptual field from different perspectives, the best we can do is let the content of experience be modeled either as a structured Russellian proposition or as a function from possible worlds to truth-values. In this case, State-nonconceptualism prevails. (shrink)

One of the most well-known and defining characteristics of indigenous Andean thought is its adherence to a “complementary dualism” in which the “opposites” of existence are viewed as interdependent parts of a harmonious whole. This is in many ways in stark contrast to Western philosophical models, which have historically tended towards an “antagonistic dualism,” the view that the opposites are engaged in an eternal struggle for dominance. This paper considers how a culture’s relationship to the opposites—whether seen (...) as a “war” or a “dance”—influences the way an individual creates psychological meaning. The results of my research into Andean complementary dualism are first presented. I then consider how this cultural-philosophical worldview compares to other complementary models, specifically that of G.W. Hegel and C. G. Jung. The paper concludes with a consideration of how the similar ideals of these complementary worldviews might inform the work of transpersonal researchers and practitioners. (shrink)

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)

In the standard model of cosmology, λCDM, were introduced to explain the anomalies of the orbital velocities of galaxies in clusters highest according estimated by General Relativity the dark matter and the accelerated expansion of the universe the dark energy. The model λCDM is based in the equations of the General Relativity that of the total mass-energy of the universe assigns 4.9% to matter (including only baryonic matter), 26.8%, to dark matter and 68.3% to dark energy adjusted according observed in (...) Planck mission, therefore, excluding bosonic matter (quantum vacuum). However, the composition of dark matter and dark energy are unknown. Due to that it lacks of a correct physical theory of gravity since General Relativity is only their powerful equations, which in their applications, their results are interpreted arbitrarily. Properties as curvature, viscous fluid, dragging frame and gravity action are attributed mistakenly to the spacetime by the materialist substantivalism, the most credible philosophical interpretation that complements the General Relativity, caused by its absence of physical definition of spacetime and static gravitational field as immaterial, but which violates, the conception of gravity as an effect of coordinates of the generalization of the inertial motion to the accelerated motion and, in particular, the description of the metric tensor of gravity as a geometric field. These properties are really of the quantum vacuum, the main existence form of the matter. In this paper we propose that the quantum vacuum is the source of dark matter and dark energy, therefore, the components of the quantum vacuum are of them. Both are opposite effects of the quantum vacuum that when gravitationally interacts with the cosmic structures, the vacuum it curves and when such interaction tends to cease by declination of the formation of these structures, occurring since near five milliard of years ago, vacuum it maintains quasi plane, since it interacts gravitationally very weakly with itself, accelerating expansion of the universe. (shrink)

A analysis of some concepts of logic is proposed, around the work of Edelcio de Souza. Two of his related issues will be emphasized, namely: opposition, and quasi-truth. After a review of opposition between logical systems [2], its extension to many-valuedness is considered following a special semantics including partial operators [13]. Following this semantic framework, the concepts of antilogic and counterlogic are translated into opposition-forming operators [15] and specified as special cases of contradictoriness and contrariety. Then quasi-truth [5] is introduced (...) and equally translated as a product of two partial operators. Finally, the reflections proposed around opposition and quasi-truth lead to a third new logical concept: quasi-opposition, borrowing the central feature of partiality and opening the way to a potential field of new investigations into philosophical logic. (shrink)

The perception of brightness differences in Ehrenstein figures and of illusory contours in phase-shifted line gratings was investigated as a function of the contrast polarity of the inducing elements. We presented either continuous lines or line-like arrangements composed of aligned dashes or dots whose spacing was varied. A yes/no procedure was used in which naive observers had to decide whether or not they perceived a brightness difference in a given Ehrenstein figure or an illusory contour in a phase-shifted line grating. (...) The results show that brightness differences are perceived to some extent in Ehrenstein figures with inducers of opposite polarity of contrast; however, the percentage of yes response was systematically lower and response times were longer than for figures with inducers of the same polarity. Phase-shifted line gratings with lines of opposite polarity of contrast yielded stronger illusory contours and shorter response times than those with lines of the same polarity. When the sign of contrast was not the same within a given line of induction, neither differences in brightness nor illusory contours were perceived. The results suggest that the mechanisms that lead to apparent differences in brightness are more sensitive to input of the same contrast polarity, the mechanisms generating illusory contours more sensitive to input of opposite polarity. The data are discussed in the light of a multistage approach to illusory form perception and some implications for cortical models of illusory contour integration are discussed. (shrink)

Rorty finds that my own appropriation of Spinoza toward a re-conception of ideology critique falls short, however, by (a) failing to “take Spinoza’s mind-body identity seriously” and by (b) advocating a “battle of ideas” rather than an enlargement of perspective. She presents an illuminating analysis of how, according to Spinoza, dichotomies serve as blunt provisional tools that become counterproductive once understanding is reached. She suggests that I preserve certain distinctions to the detriment of my own liberation project, such as the (...) distinction between the truth of an idea and its persuasive force. As part of criticism (a), she admonishes me for neglecting the importance of material conditions, and with criticism (b) she suggests that the imagery of battle misconstrues the project of becoming rational and the power of truth. Below I will try to show that we do not disagree about either the importance of material conditions for a project of political transformation or the identity of mind and body in substance. We do disagree, however, about the character of ideology critique. I will offer an example, in an attempt to demonstrate why it is neither a distortion of Spinoza nor strategically counterproductive to understand the project of thinking as an effort of what I call “resistant reconstruction” within the attribute of thought. (shrink)

Throughout her work, Audre Lorde maintains that her self-preservation in the face of oppression depends on acting from the recognition and valorization of her feelings as a deep source of knowledge. This claim, taken as a portrayal of agency, poses challenges to standard positions in ethics, epistemology, and moral psychology. This article examines the oppositional agency articulated by Lorde’s thought, locating feeling, poetry, and the power she calls “the erotic” within her avowed project of self-preservation. It then explores the implications (...) of taking seriously Lorde’s account, particularly for theorists examining ethics and epistemology under nonideal social conditions. For situations of sexual intimacy, for example, Lorde’s account unsettles prevailing assumptions about the role of consent in responsibility between sexual partners. I argue that obligations to solicit consent and respect refusal are not sufficient to acknowledge the value of agency in intimate encounters when agency is oppositional in the way Lorde describes. (shrink)