In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case, a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without equality from (...) those with equality. From the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general propositional logic. (shrink)

Resumo: O presente artigo visa apresentar, sistematizar e analisar, à luz da teoria social crítica, as ações desenvolvidas pelo NESEF (Núcleo de Estudos e Pesquisas sobre o Ensino de Filosofia) ao longo de duas décadas de existência na Universidade Federal do Paraná - UFPR. Procura situar e referenciar as diferentes atividades desenvolvidas coletivamente no campo da pesquisa e da extensão. Parte do entendimento que a Filosofia só é Filosofia à medida que ela se nega e, por conseguinte, se realiza; e (...) ela só se realiza na prática social, cultural e política na e através da ação coletiva. Pretende mostrar o conjunto de ações desenvolvidas (em rede) pelo NESEF que, com o passar do tempo, assume a condição de “intelectual orgânico-coletivo”. Por se tratar de uma descrição de atividades estreitamente ligadas à atuação do autor, o texto revelará sua trajetória profissional entrelaçada ao seu “jeito de caminhar” diante dos embates teórico-práticos do campo acadêmico formando, assim, um contínuo movimento de ondas tensas (laços e nós) que encontraram na ação conjunta – na práxis coletiva – um terreno fértil. Palavras-chave: NESEF; Intelectual Orgânico; Educação Filosófica The NESEF as an organic-collective intellectual: from head to toe Abstract: This article aims to present, systematize and analyze, in the light of critical social theory, the actions developed by NESEF (Center for Studies and Research on Philosophy Teaching) over two decades at the Federal University of Paraná – UFPR. It seeks to point out and reference the different activities developed collectively in the field of research and extension. It is considered that Philosophy is Philosophy only insofar as it negates itself and, consequently, realizes itself; and it is only realized in social, cultural and political practice in and through collective action. It is intended to show the set of actions developed (in a network) by the NESEF which, over time, assumes the condition of “organic-collective intellectual”. As it is a description of activities closely linked to the author's work, the text reveals his professional trajectory intertwined with his "way of walking" in the face of theoretical-practical clashes in the academic field, thus forming a continuous movement of tense waves (ties and knots) that found fertile ground in joint action – in collective praxis. Key words: NESEF; Organic Intellectual; Philosophical Education Le NESEF comme intellectuel organique-collectif : de la tête aux pieds Résumé: Cet article vise à présenter, systématiser et analyser, à la lumière de la théorie sociale critique, les actions développées par le NESEF (Centre d'Études et de Recherche sur l'Enseignement de la Philosophie) pendant deux décennies à l'Université Fédérale du Paraná – UFPR. Il cherche à situer et référencer les différentes activités développées collectivement dans le domaine de la recherche et de l'extension. Il est entendu que la Philosophie n'est la Philosophie qu'en tant qu'elle se nie elle-même et, par conséquent, se réalise; et elle ne se réalise que dans la pratique sociale, culturelle et politique dans et par l'action collective. Il vise à montrer l'ensemble des actions développées (en réseau) par la NESEF qui, au fil du temps, assume la condition d'« intellectuel organique-collectif ». Comme il s'agit d'une description d'activités étroitement liées au cours de travail de l'auteur, le texte révèle sa trajectoire professionnelle entrelacé à sa "façon de marcher" face aux affrontements théoriques-pratiques du champ académique, formant ainsi un mouvement continu d'ondes tendues (liens et nœuds) qui ont trouvé un terreau fertile dans l'action commune – c'est à dire, dans la praxis collective. Mots clés: NESEF; Intellectuel Organique; Éducation Philosophique Data de registro: 23/01/2023 Data de aceite: 18/10/2023. (shrink)

In an earlier paper we proved that a universal Horn class generated by finitely many finite structures has a model companion. If the language has only finitely many fundamental operations then the theory of the model companion admits a primitive recursive elimination of quantifiers and is primitive recursive. The theory of the model companion is ℵ 0 -categorical iff it is complete iff the universal Horn class has the joint embedding property iff the (...) class='Hi'>universal Horn class is generated by a single finite structure. In the last section we look at structure theorems for the model companions of universal Horn classes generated by functionally complete algebras, in particular for the cases of rings and groups. (shrink)

It is well known that the model categories of universal Horn theories are locally presentable, hence essentially algebraic . In the special case of quasivarieties a direct translation of the implicational syntax into the essentially equational one is known . Here we present a similar translation for the general case, showing at the same time that many relationally presented Horn classes are in fact quasivarieties.

In this paper, I distinguish two conceptions of solidarity, which I call solidarity as beneficence and solidarity as mutual advantage. I argue that only the latter is capable of providing a complete foundation for national universal health care programs. On the mutual advantage account, the rationale for universal insurance is parallel to the rationale for a labor union’s “closed shop” policy. In both cases, mandatory participation is necessary in order to stop individuals free-riding on an ongoing system of (...) mutually advantageous cooperation. (shrink)

In this paper we address our efforts to extend the well-known connection in equational logic between equational theories and fully invariant congruences to other–possibly infinitary–logics. In the special case of algebras, this problem has been formerly treated by H. J. Hoehnke [10] and R. W. Quackenbush [14]. Here we show that the connection extends at least up to the universal fragment of logic. Namely, we establish that the concept of universal theory matches the abstract notion of fully (...) invariant system. We also prove that, inside this wide group of theories, the ones which are strict universal Horn correspond to fully invariant closure systems, whereas those which are universal atomic can be characterized as principal fully invariant systems. (shrink)

According to Dignāga, the word “cow” makes one understand all cows in a general form by excluding non-cows. However, how does one understand the non-cows to be excluded? Hattori answers as follows: “On perceiving the particular which is endowed with dewlap, horns, a hump on the back, and so forth, one understands that it is not a non-cow, because one knows that a non-cow is not endowed with these attributes.” Hattori regards observation of a dewlap, etc. as the cause of (...) excluding non-cows. Akamatsu presents a view similar to Hattori’s. Tanizawa, however, criticises Akamatsu by pointing out that then the apohavādin would have accepted positive elements such as a dewlap as defining characteristics of a cow. Stating that X is not a cow because it is not endowed with a dewlap, etc., amounts to accepting that the dewlap, etc. are the defining characteristics of a cow. Instead of a real universal cowness the apohavādin would have accepted a dewlap, etc. Akamatsu’s understanding of apoha, if it was correct, implies Tanizawa, would destroy the essence of the Buddhist theory of apoha. Continuing the view of Hattori and Akamatsu, Yoshimizu recently published two articles on Dignāga’s theory of apoha. He claims that “the word “cow” excludes all horses by virtue of the fact that horns are never seen on them.” Thus, “the word “cow” can exclude all of them collectively by virtue of the fact that none of them has all the members of the set of characteristics that form the worldly definition of “cow”.” Horns, one of the characteristic features of cows, are indeed mentioned by Dignāga in PS 5:43. Yoshimizu understands Dignāga’s semantics as being parallel to the modern semantics of componential analysis. A question arises: what does Dignāga, the founder of the Buddhist theory of apoha, really think regarding this issue? The present article sheds light on the incompatibility of the two interpretations by investigating the relevant source texts. It further shows that the issue Tanizawa deals with was already discussed by Dignāga. Examining Dignāga’s discussions shows that Tanizawa is right in his understanding of apoha. The interpretation by Hattori and other scholars is not supported by Dignāga’s text. The present conclusion is also supported by Mādhava, Uddyotakara and Kumārila. None of them assumes Dignāga’s theory to be as Hattori, etc. take it. (shrink)

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability (...) equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. (shrink)

In the twentieth century, philosophy (especially within the United States) embraced the notion of disciplinary expertise: philosophical research consists of working with and writing for other philosophers. Projects that involve non-philosophers earn the deprecating title of “applied” philosophy. The University of North Texas (UNT) doctoral program in philosophy exemplifies the possibility of a new model for philosophy, where graduate students are trained in academic philosophy and in how to work with scientists, engineers, and policy makers. This “field” (rather than “applied”) (...) approach emphasizes the inter- and transdisciplinary nature of the philosophical enterprise where theory and practice dialectically inform one another. UNT’s field station in philosophy at Cape Horn, Patagonia, Chile is one site for developing this ongoing experiment in the theory and practice of interdisciplinary philosophic research and education. (shrink)

The Birth of String Theory by Cappelli et al. tells the story of the beginnings of string theory and of the evolutionary process it has undergone from its origins in S-matrix theory to its current status as a candidate unification theory. The book is intended for an audience of students and researchers in physics, as well as historians and philosophers of science with some background in quantum field theory.In the 50s and early 60s, theoretical particle (...) physics focused on formulating a theory to explain the strong interactions. Due to issues with the application of perturbative quantum field theory to the strong interactions, theoretical particle physicists shifted their attention to Heisenberg’s ‘S-matrix’ theory, which focused solely on observable quantities. This endeavour led in 1968 to the breakthrough of the famous ‘Veneziano amplitude’, which along with the Dolen–Horn–Schmid duality between the s- and the t-channels led to the dual resonance model . Following Ve .. (shrink)

This paper explores the determiner corner of the ‘any’ land in Romanian, taking Lee and Horn 1994 and Horn 2000a as tour guides. The immediate interest of the task lies in the fact that the work done in English by the over-employed determiner any is carried out in Romanian by a host of more specialized (and, one fears, lower paid) morphemes, which I review in the rest of this section. My aim is to introduce the details of the (...) Romanian facts onto the scene and to show that an ‘indefinitist’ view that generalizes the scalar approach advocated in Horn’s work is useful in helping us understand the much more crowded Romanian field. The theory of any that serves as my starting point is summarized in Section 2. Section 3 proposes a generalization of the scalar view advocated by Horn in terms of an alternative-based approach in the spirit of Krifka 1995, Giannakidou 2001 and Kratzer and Shimoyama 2002, based on a novel way of defining alternatives. Section 4 looks at the consequences of the proposal, Section 5 considers ways of extending it, and Section 6 is a brief conclusion. The approach suggested here falls under what Horn calls quodlibetic theories. Its claim is that the unifying characteristic of both existentially and universally flavored free choice-like items is that they denote a maximal set of alternatives that verify the expression in which the item occurs. The scalar view is the important special case in which these alternatives form an implicational scale with respect to verifying the relevant expression. (shrink)

The first volume presents a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including (...) combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, MacColl). This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic. (shrink)

A hidden-variable model for quantum–mechanical spin, as represented by the Pauli spin operators, is proposed for systems illustrating the well-known no-hidden-variables arguments by Peres (Phys Lett A 151:107–108, 1990) and Mermin (Phys Rev Lett 65:3373–3376, 1990) and by Greenberger et al. (Bell’s theorem, quantum theory, and conceptions of the universe, Kluwer, Dordrecht, 1989). Both arguments rely on an assumption of non-contextuality; the latter argument can also be phrased as a non-locality argument, using a locality assumption. The model suggested here (...) is compatible with both assumptions. This is possible because the scalar values of spin observables are replaced by vectors that are components of orientations. (shrink)

This is the first volume of a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of (...) topics including combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic. This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic. (shrink)

A theory is presented which proposes that knowledge acquisition involves direct perception of schematic information in the form of structural and transformational invariances. Individual components with salient verbal descriptions are considered conscious place-holders for non-conscious invariant schemes. It is speculated that theories positing mental construction have three related causes: The first is a lack of consciousness of the schema processing capacities of the right hemisphere; the second is the paucity of adequate words to express schematic relationships; and the last (...) involves the dominance of verbal processes in consciousness. Philosophical theories are reviewed and schematic data relevant to biological survival is offered. Applications to education are suggested. (shrink)

Equational logic for total functions is a remarkable fragment of first-order logic. Rich enough to lend itself to many uses, it is also quite austere. The only predicate symbol is one for a notion of equality, and there are no logical connectives. Proof theory for equational logic therefore is different from proof theory for other logics and, in some respects, more transparent. The question therefore arises to what extent a logic with a similar proof theory can be (...) constructed when expressive power is increased.The increase mainly studied here allows one both to consider arbitrary partial functions and to express the condition that a function be total. A further increase taken into account is equivalent to a change to universal Horn sentences for partial and for total functions.Two ways of increasing expressive power will be considered. In both cases, the notion of equality is modified and nonlogical function symbols are interpreted as ranging over partial functions, instead of ranging only over total functions. In one case, the only further change is the addition of symbols that denote logical functions, such as the binary projection functionAethat maps each pair ‹a0,a1› of elements of a setAinto the elementa0. An addition of this kind results in a language, and also in a system of logic based on this language, which we callequationalIn the other case, instead of adding a symbol forAe, one admits those special universal Horn sentences in which the conditions expressed by the antecedent are, in a sense, pure conditions of existence. Languages and systems of logic that result from a change of this kind will be callednear-equational. According to whether the number of existence conditions that one may express in antecedents is finite or arbitrary, the resulting language and logic shall befiniteorinfinitary, respectively. Each of our finite near-equational languages turns out to be equivalent to one of our equational languages, and vice versa. (shrink)

We have two polynomial time results for the uniform word problem for a quasivariety Q: The uniform word problem for Q can be solved in polynomial time iff one can find a certain congruence on finite partial algebras in polynomial time. Let Q* be the relational class determined by Q. If any universal Horn class between the universal closure S and the weak embedding closure S̄ of Q* is finitely axiomatizable then the uniform word problem for Q (...) is solvable in polynomial time. This covers Skolem's 1920 solution to the uniform word problem for lattices and Evans' 1953 applications of the weak embeddability property for finite partial V algebras. (shrink)

In 1988 a piece of higher education reform legislation titled The Higher Education Funding Act was devised by the Labor Government and enacted by the Commonwealth of Australia to become law. The te...

It is customary to think that Objective List (“OL), Desire-Satisfaction (“D-S”) and Hedonistic (“HED”) theories of prudential value pretty much cover the waterfront, and that those of the three that are “subjective” are naturalistic (in the sense attacked by Moore, Ross and Ewing), while those that are “objective” must be Platonic, Aristotelian or commit the naturalist fallacy. I here argue for a theory that is both naturalistic (because voluntaristic) and objective but neither Platonic, Aristotelian, nor (I hope) fallacious. In (...) addition, this proposal, called “CHOICE,” is an example of neither an OL, D-S, nor HED theory. It is a theory according to which uncoerced choosings create objective values that we (even everyone) may be wrong about, because valuations are conative rather than epistemic activities. On this view, intrinsic prudential goods necessarily involve likely (pursuant to lawlike regularities) net increases in successful free choosings . (shrink)

Name der Zeitschrift: Kant-Studien Jahrgang: 107 Heft: 1 Seiten: 89-110.

In this paper, I hope to show that by considering connections between Bertrand Russell’s early account of names and C.I. Lewis’s theory of propositions, one can see that propositions (as traditionally understood)—while perhaps not explicitly relying on Russellian names, derive a good deal of their plausibility from them. I argue, however, that the Russellian take on names implies Tractarian restrictions on what may be named that are inconsistent with the traditional theory of structured propositions. That is, (i) it (...) is a mistake to claim that any meaningful string of linguistic (or ‘lexical’) entities—whether concrete or abstract—can name facts; (ii) no putative structured abstracta may be named by anything whatever; and (iii) if propositions may not be named and are not necessary to accomplish such tasks as providing objects for attitudes or being bearers of truth-values, then they would likely have been expelled from philosophical ontologies except for the persistence of an alluring myth. (shrink)

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis (...) and his followers regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail. (shrink)

South Africa has the highest rate of foetal alcohol syndrome (FAS) in the world. The problem of alcohol abuse in pregnancy has very deep historical roots that are intertwined with the injustices of both apartheid and pre-apartheid colonialism. Much of the research that is being done in these communities is focused on identifying the epidemiological variables associated with these patterns of alcohol abuse. The underlying reasons as to why these patterns continue seem to remain largely obscured from view. In this (...) article, I apply the theory proposed by Powers and Faden of social justice as a ‘moral foundation for public health and health policy’ to the problem of FAS in South Africa. The objective of this application is two-fold: first, to critically explore the additional insights and alternative perspectives to the problem of FAS that this approach may provide and second, to assess the utility of the theory when applied directly to a specific public health problem. I conclude by noting that although this approach could result in the kind of ‘public health scope creep’ that has been criticized by various authors, it does provide fresh insights to the problem of FAS in South Africa. (shrink)

Harry Eckstein’s long-standing (but ever-changing) hypothesis that a nation’s political stability is a function of “congruence” between the “authority patterns” exhibited by the government and those displayed by nearly every sort of institution under that government’s aegis involved a highly complex politico-psychological theory. As a result, it was quite difficult either to confirm or disconfirm. While there have been a number of suggested revisions that apparently simplify his thesis, they suffer either from vagueness or a failure to take democracy (...) to be a system that requires an actual commitment to majoritarianism. In this paper a revision is offered that utilizes a small number of completely dichotomous variables that are easily subject to empirical tests. This revised theory (of “consonance” rather than congruence) is also explicitly majoritarian, enabling it to shed light on the essential nature of democratic regimes. (shrink)

Scholars have wrestled with "consciousness", a major scholar calling it the "hard problem". Some thirty-plus years after the Towards a Science of Consciousness, we do not seem to be any closer to an answer to "What is consciousness?". Seemingly irresolvable metaphysical problems are addressed by bootstrapping, provisional assumptions, not unlike those used by logicians and mathematicians. I bootstrap with the same ontology and epistemology applicable to everything we apprehend. Here, I argue for a version of the unity of opposites, a (...) form of neutral monism. Something exists because of what it is not; nothing can exist by itself, singularities (analogous to monads), expressing the model. Applying this most fundamental law to the consciousness problem, the physical (movement) comes into being simultaneously as the mental (stasis), each displayed by a field that is variegated (ranging from creative to entropic processes). Such is in keeping with how the singularity emerged as our universe, the same form that may account for sub-Planck-scale phenomena. Overall, like the most fundamental law, deep structures are imminent in our universe, both as objects and processes. (shrink)

This paper maintains that, for all his ethical interests, his philosophical and theological essays, political treatises and linguistic studies, Dante was primarily a poet; a poet who, moreover, believed that poetry could change the world, and that the Comedy must be read, first, as a poem. This is not a trivial point, because the Comedy remains a text that is endlessly fascinating to philosophers and theologians as well as moralists who read it for its philosophy, theology and ethics and who (...) sometimes fail to see that a poet's imagination, even one as egregiously rational as Dante's, is synthetic rather than analytic. This paper offers an examination of the moral universe of the Comedy, paying particular attention to his presentation of the virtues. It endeavours to show how Dante's entry into the moral universe is by way of beauty through the operation of love, and considers how, for Dante, the inevitability of beauty, when properly understood, opens out on to truth and goodness, which, in turn, fold back upon beauty as the Beatific Vision is reached. (shrink)

"Populism" has long been a dirty word. To some, it suggests the tyranny of the mob, to others, a xenophobic nativism. It is sometimes considered conducive to (if not simply identical to) fascism. In this timely book, Walter Horn acquits populism by "distilling" it, in order to finally give the people the power to govern themselves, free from constraints imposed either by conservatives (or libertarians) on the right or liberals (or Marxists) on the left. Beginning with explanations of what (...) it means to vote and what makes one society better off than another, Horn progresses to issues involving what makes for fair aggregation and appropriate, deliberative representation. From suggesting solutions to contemporary problems like gerrymandering, immigration control, and campaign finance, to offering answers to age-old questions like why dissenters should want to obey the majority and who should have the right to vote in various elections, Horn, using his new theory of "CHOICE Voluntarism," provides solutions to some of the most perplexing problems in the history of democratic theory. -/- The Introduction and first chapter can now be read free at Amazon. (shrink)

In the modern age, the political secret has acquired a bad reputation. With modern democracy’s ideal of transparency, political secrecy is identified with political crime or corruption. The article argues that this repression of secrecy in modern democracies falls short of a substantial understanding of the structure and workings of political secrecy. By outlining a genealogy of political secrecy, it elucidates the logic as well as the blind spots of a current culture of secrecy. It focuses on two fundamental logics (...) of secrecy, deduced from the Latin terms ‘ arcanum’ and ‘ secretum’. Whereas the logic of arcanum regards secrecy as a legitimate dimension of government, a modern logic of secretum is marked by an inextricable dialectics between the withdrawal and communication of knowledge, between secrecy and publicity. Here, the secret is not so much a piece of withheld knowledge as a ‘secrecy effect’ that binds the realm of secrecy to the public sphere by a dialectics of permanent suspicion and scandal. Instead of falling into the trap of this ‘secrecy effect’ it is worth taking a closer look at the tradition of thought on the arcana imperii, from Tacitus to early modern doctrines of raison d’état to Carl Schmitt. What this tradition deals with is the functionality of secrecy and its complicated relation to the law. The arcana tradition elaborates the crucial point of secrecy: its potential, but also its profound ambivalence. Secrecy opens up a discretionary space of action exempt from the rule of law, and, according to Carl Schmitt, ignores the law so as to allow it to become effective. Secrecy serves to protect and stabilize the state, but at the same time it opens a space of exception from the rule of law that breeds violence, corruption and oppression. Instead of seeing secrecy as the opposite of a political culture of transparency, it is more productive to regard secrecy as transparency's complement – a counterpart, however, that is marked by the profound paradox of being both a consolidation of and a threat to democracy. (shrink)

This paper rejects metaphysical realism about structural universals as a basis for mathematical realism about numbers, and argues that one construal of structural universals via non-well-founded sets should be resisted by the mathematical realist.

Many contemporary philosophers consider justice to be the crucial normative concept of ethics and political philosophy. This view goes back to J. S. MillÏs Utilitarianism (ch. 5), and to J. RawlsÏ A Theory of Justice. In this paper, I challenge this view. As I take it, justice is not the core of our normative convictions for many normative convictions do not concern questions of justice. I aim to show that our idea of justice has a very specific content and (...) function. (shrink)

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream (...) arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates. (shrink)

The disavowal of positivist science by many educational researchers has resulted in a deepening polarization of research agendas and an epistemological divide that appears increasingly difficult to span. Despite a turning away from science altogether by some, and thus toward various forms of poststructuralist inquiry, this has not held back the renewed entrenchment of more narrow definitions by policy elites of what constitutes scientific educational research. The new sciences of complexity signal the emergence of a new scientific paradigm that challenges (...) some of the core assumptions of positivism, while offering the potential to develop a new kind of social science that demands both rigour and imagination in coming to understand the emergence and behaviours of social systems and the subsystems that comprise them. The language, concepts and principles of complexity are central to the development of a new science of qualities to complement the science of quantities that has shaped our understanding of the physical and social worlds. Accomplishing this task promises to 1) open up new investigations that have thus far been beyond the purview of scientific study, 2) allow the study of social phenomena as fully embodied, or at least as more robust models than those represented in the abstracted empiricism upon which the sciences of quantities are predicated, and 3) allow for more coarse‐grained explanations and predictions of social phenomena to be legitimated as scientific. Both educational research and educational practice stand to gain from this expansion of the scientific repertoire to include rigorous and imaginative investigations of phenomena characterized by change and transformation. (shrink)

This article examines the foundations for the legitimacy of law from the perspective of Hegel’s philosophy. In a first step, Kant’s justification of law is discussed, as Hegel takes the Kantian model as a central point of reference. Then, in the Section 2, I discuss Hegel’s reasons for rejecting the main strategies of justification of the legal order: natural law, contractarianism and legal positivism. This is further followed by a discussion of the meaning and scope of Hegel’s contextualism, according to (...) which there can be no practical normativity without a certain historical embedding. Finally, I describe a more traditional met-aphysical reading that I consider to be the correct solution, contrasting it with Honneth’s theory of recognition and Bran-dom’s pragmatism. (shrink)

In der Reihe werden herausragende monographische Untersuchungen und Sammelbände zu allen Aspekten der Philosophie Kants veröffentlicht, ebenso zum systematischen Verhältnis seiner Philosophie zu anderen philosophischen Ansätzen in Geschichte und Gegenwart. Veröffentlicht werden Studien, die einen innovativen Charakter haben und ausdrückliche Desiderate der Forschung erfüllen. Die Publikationen repräsentieren damit den aktuellsten Stand der Forschung.