This book discusses the philosophical work of Décio Krause. Non-individuality, as a new metaphysical category, was thought to be strongly supported by quantum mechanics. No one did more to promote this idea than the Brazilian philosopher Décio Krause, whose works on the metaphysics and logic of non-individuality are now widely regarded as part of the consolidated literature on the subject. This volume brings together chapters elaborating on the ideas put forward and defended by Krause, developing them in many different directions, (...) commenting on aspects not completely developed so far, and, more importantly, critically addressing their current formulations and defenses by Krause himself. Given that Krause’s ideas do connect directly and indirectly with a wide array of subjects, such as the philosophy of quantum mechanics, more broadly understood, the philosophy of logic and logical philosophy, non-classical logics, metaphysics, and ontology, this volume contains important material for the research on logic and foundations of science, broadly understood. All the invited contributors have already worked with the ideas developed by Décio (some of them still work with them), being also distinct authors and extremely relevant in their areas of expertise. The volume is aimed at philosophers, including those of physics and quantum mechanics. (shrink)

This handbook presents a comprehensive introduction to the core areas of philosophy of education combined with an up-to-date selection of the central themes. It includes 95 newly commissioned articles that focus on and advance key arguments; each essay incorporates essential background material serving to clarify the history and logic of the relevant topic, examining the status quo of the discipline with respect to the topic, and discussing the possible futures of the field. The book provides a state-of-the-art overview of philosophy (...) of education, covering a range of topics: Voices from the present and the past deals with 36 major figures that philosophers of education rely on; Schools of thought addresses 14 stances including Eastern, Indigenous, and African philosophies of education as well as religiously inspired philosophies of education such as Jewish and Islamic; Revisiting enduring educational debates scrutinizes 25 issues heavily debated in the past and the present, for example care and justice, democracy, and the curriculum; New areas and developments addresses 17 emerging issues that have garnered considerable attention like neuroscience, videogames, and radicalization. The collection is relevant for lecturers teaching undergraduate and graduate courses in philosophy of education as well as for colleagues in teacher training. Moreover, it helps junior researchers in philosophy of education to situate the problems they are addressing within the wider field of philosophy of education and offers a valuable update for experienced scholars dealing with issues in the sub-discipline. Combined with different conceptions of the purpose of philosophy, it discusses various aspects, using diverse perspectives to do so. Contributing Editors: Section 1: Voices from the Present and the Past: Nuraan Davids Section 2: Schools of Thought: Christiane Thompson and Joris Vlieghe Section 3: Revisiting Enduring Debates: Ann Chinnery, Naomi Hodgson, and Viktor Johansson Section 4: New Areas and Developments: Kai Horsthemke, Dirk Willem Postma, and Claudia Ruitenberg. (shrink)

We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist.We analyze that (...) claim by employing the traditional square of opposition.We suggest that it is difficult to make sense of the idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them. (shrink)

Following J.-Y.Béziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in [1]. Our conclusion was that such states are contraries, contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties. In this chapter we bring the issue once again into the center of the (...) stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible. (shrink)

In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind, what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not (...) concerned with whether entities posited by a specific physical theory are individuals or not, answering this question is part of the quest for a better understanding of physical reality. Here lies, in large measure, the relevance of ontology. (shrink)

In this paper we deal with two applications of the square of opposition to controversial issues in the philosophy of quantum mechanics. The first one concerns the kind of opposition represented by states in superposition. A superposition of “spin up” and “spin down” for a given spatial direction, for instance, is sometimes said to originate particular kinds of opposition such as contradictoriness. The second application concerns the problem of identical particles. Identity and indiscernibility are entangled in discussions of this problem (...) in such a way that a proper conceptual treatment of those issues through the square seems profitable. (shrink)

Sören Halldén’s logic of nonsense is one of the most well-known many-valued logics available in the literature. In this paper, we discuss Peter Woodruff’s as yet rather unexplored attempt to advance a version of such a logic built on the top of a constructive logical basis. We start by recalling the basics of Woodruff’s system and by bringing to light some of its notable features. We then go on to elaborate on some of the difficulties attached to it; on our (...) way to offer a possible solution to such difficulties, we discuss the relation between Woodruff’s system and two-dimensional semantics for many-valued logics, as developed by Hans Herzberger. (shrink)

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book (...) describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science. (shrink)

Principled discussions of civil rights became inherently less likely as a direct result of the observation by Earl Warren, in Brown v. Board of Education, that, respecting freedmen, “Education of Negroes was almost non-existent, and practically all of the race were illiterate,” and in proportion as that observation increasingly became the foundation of common opinion on the subject. Warren's observation was not true in any meaningful or non-trivial sense. Nevertheless, it served to perpetuate the myth of a backward people needing (...) help to catch up instead of the truth of a people being held back. That is the perspective – the disadvantaged group perspective – that ultimately infected all discussion of civil rights, even after the designation of so-called “disadvantaged groups” had been extended beyond American blacks. To define civil rights, we may well begin with what all mankind would likely recognize. Thus the dictionary definition of “civil rights” stands: “the rights that belong to all individuals in a nation or community touching property, marriage, and the like.” In that definition the term “rights” may be further expanded to mean “legitimate claims,” following the definition of right as law – as “a claim or title or interest in anything whatever that is enforceable by law.” This definition applies with minimal distinction of regimes intruding and, therefore, without the host of recent complications in the United States that create the impression that civil rights have something to do with pluralism. Previously, the generic definition was thought to exhaust the meaning of the term in the United States. (shrink)

Liar-like paradoxes are typically arguments that, by using very intuitive resources of natural language, end up in contradiction. Consistent solutions to those paradoxes usually have difficulties either because they restrict the expressive power of the language, or else because they fall prey to extended versions of the paradox. Dialetheists, like Graham Priest, propose that we should take the Liar at face value and accept the contradictory conclusion as true. A logical treatment of such contradictions is also put forward, with the (...) Logic of Paradox, which should account for the manifestations of the Liar. In this paper we shall argue that such a formal approach, as advanced by Priest, is unsatisfactory. In order to make contradictions acceptable, Priest has to distinguish between two kinds of contradictions, internal and external, corresponding, respectively, to the conclusions of the simple and of the extended Liar. Given that, we argue that while the natural interpretation of LP was intended to account for true and false sentences, dealing with internal contradictions, it lacks the resources to tame external contradictions. Also, the negation sign of LP is unable to represent internal contradictions adequately, precisely because of its allowance of sentences that may be true and false. As a result, the formal account suffers from severe limitations, which make it unable to represent the contradiction obtained in the conclusion of each of the paradoxes. (shrink)

In his “The simple argument for subclassical logic,” Jc Beall advances an argument that led him to take FDE as the one true logic (the latter point is explicitly made clear in his “FDE as the One True Logic”). The aim of this article is to point out that if we follow Beall’s line of reasoning for endorsing FDE, there are at least two additional reasons to consider that FDE is too strong for Beall’s purposes. In fact, we claim that (...) Beall should consider another weaker subclassical logic as the logic adequate for his project. To this end, we first briefly present Beall’s argument for FDE. Then, we discuss two specific topics that seem to motivate us to weaken FDE. We then introduce a subsystem that will enjoy all the benefits of Beall’s suggestion. (shrink)

"Bibliographical notes": pages [243]-244.

Everyone knows the statement of Servius that Virgil was compelled by Augustus to alter the second half of the Fourth Georgic after the fall of Gallus, and that he substituted the story of Aristaeus for the laudes Galli. This statement, often doubted by older generations, has had such a remarkable success in recent years that anyone who ventures to impugn it must feel that he is pleading with a halter round his neck before a one-sided jury. It is notable, however, (...) that these jurors, though one-sided, are by no means united, save in their determination to uphold the credit of Servius. One group will assure us that the episode of Aristaeus shows obvious signs not only of haste but of immaturity, and they draw a pathetic picture of the grief-stricken Virgil, ordered to bring out a second edition minus the praises of his friend Gallus, and half-heartedly throwing together some bits of juvenile stuff which he happened to have handy. Others assure us that the tale of Aristaeus shows us a more mature Virgil, nearer to the Virgil of the Aeneid. But the Servians really cannot have it both ways. They must make up their minds in the one direction or in the other if they are to be taken seriously. They make it doubly difficult for us to take them seriously when they try to tell us what Servius meant—but of that more anon. The present paper is an attempt by a converted Servian to examine frankly the arguments which have been advanced in support of Servius. Most of these may be found in Skutsch, Aus Vergils Frühzeit, pp. 140–147. One is very reluctant to use disparaging words about an eminent scholar who has served the cause of learning in so many ways; but it can scarcely be denied that the work just mentioned, in spite of its ingenuity and enthusiasm, shows a lamentable lack of three great essentials—a judicial temper, accurate statement of facts, and cogent reasoning. There is also at times a regrettable vagueness of expression, suggesting that the author is concealing inward doubts or shrinking from thought. All these deficiencies are to some extent present in the section with which this paper is concerned. (shrink)

Ever since its beginnings, standard quantum mechanics has been associated with a metaphysical view according to which the theory deals with non-individual objects, i.e., objects deprived of individuality in some sense of the term. We shall examine the grounds of the claim according to which quantum mechanics is so closely connected with a metaphysics of non-individuals. In particular, we discuss the attempts to learn the ‘metaphysical lessons’ required by quantum mechanics coming from four distinct roads: from the formalism of the (...) theory, treating separately the case of the physics and the underlying logic; from the ontology of the theory, understood as the furniture of the world according to the theory; and, at last, we analyze whether a metaphysics of non-individuals is indispensable from a purely metaphysical point of view. We argue that neither non-individuality nor individuality is to be found imposed on us in any of these levels so that it should be seen as a metaphysical addition to the theory, rather than as a lesson from it. (shrink)

Open peer commentary on the article “Developing a Dialogical Platform for Disseminating Research through Design” by Abigail C. Durrant, John Vines, Jayne Wallace & Joyce Yee. Upshot: The question of more appropriate dissemination formats for research through design is important, but secondary. Artefacts are just media in the knowledge-generating process. RTD is a much more powerful concept than presented here.

In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate (...) in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal , for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science. (shrink)

Change of logic is typically taken as requiring that the meanings of the connectives change too. As a result, it has been argued that legitimate rivalry between logics is under threat. This is, in a nutshell, the meaning‐variance argument, traditionally attributed to Quine. In this paper, we present a semantic framework that allows us to resist the meaning‐variance claim for an important class of systems: classical logic, the logic of paradox and strong Kleene logic. The major feature of the semantics (...) is that the connectives have the same meanings in these systems, so that the meaning‐variance argument is straightforwardly blocked. We discuss the effects of this semantics for two uses of the argument of meaning variance, and also consider its impact on related issues. (shrink)

The subject of these lines may be found in Caes. B.C. I. 54, from which they are in part derived, though probably at second hand. The reference is to Caesar's tactics after the floods in the plain around Ilerda. He built a number of coracles after the British fashion, and had them conveyed to a point on the right bank of the Sicoris, twenty-two miles from his camp. In these boats he sent a number of men across the river, who (...) fortified some rising ground. Then he sent a legion across and started the building of a bridge from both sides at once: hue legionem postea traiecit atque ex utraque parte pontem institutum biduo perfecit. (shrink)

The late Jacob Klein’s important book is, remarkably, a lucid presentation of esoteric argument. Dealing with the famed Platonic triad, Theaetetus, Sophist, and Statesman, Klein settles the dispute about the missing dialogue, "The Philosopher," by first denying that it is missing and second showing that it is unnecessary. He argues, in short, that the triad is a dyad. That argument is reinforced by the distinction Klein strongly implies between the Socratic Theaetetus and the Eleatic Sophist and Statesman. "We can now (...) understand why the conversations of the ‘trilogy’ occur in two, not three, days and why the Sophist, the Statesman, and the Philosopher are dealt with in two, not three, dialogues". (shrink)