We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical (...) language for combining these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our "Principle of general tovariance" states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our "Equivalence principle" states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos. (shrink)

A short review is given of three experimental works on tests of the Pauli Exclusion Principle (PEP) in which the author has been involved during the last 10 years. In the first work a search for anomalous carbon atoms was done and a limit on the existence of such atoms was determined, $^{12}\tilde{\mathrm{C}}$ /12C <2.5×10−12. In the second work PEP was tested with the NEMO-2 detector and the limits on the violation of PEP for p-shell nucleons in 12C were (...) obtained. Specifically, transitions to the fully occupied 1s 1/2-shell yielded a limit of 4.2×1024 y for the process with the emission of a γ-quantum. Similarly limits of 3.1×1024 y for β − and 2.6×1024 y for β + Pauli-forbidded transition of 12C → 12Ñ( $^{12}\tilde{\mathrm{B}}$ ) are reported. In the third work it was assumed that PEP is violated for neutrinos, and thus, neutrinos obey at least partly the Bose-Einstein statistics. Consequences of the violation of the exclusion principle for double beta decays were considered. This violation strongly changes the rates of the decays and modifies the energy and angular distributions of the emitted electrons. It was shown that pure bosonic neutrinos are excluded by the present experimental data. In the case of partly bosonic neutrinos the analysis of the existing data allows one to put an upper bound for sin 2 χ<0.6. The sensitivity of future measurements is also evaluated. (shrink)

The brief article of 1910 which is translated here is, as the prefatory note explains, significant for understanding both the way in which ?ukasiewicz came to many-valued logic and the influences under which he stood at the time.

In the process that followed the evolution of ancient Greek thought from mythology to a systematic philosophy, Parmenides, the founder of the Elea school, built up his thoughts with theses that were the exact opposite of his time and perhaps common sense in general. His famous poem On Nature, in the light of the logical principles, inferences, and analyses it contains, has profoundly influenced both epistemologies in terms of structure and possibility, and ontologies within the framework of time, space, and (...) movement. In the mentioned period, the logical internal consistency of Parmenides and his followers, and the rational level in their arguments shaped the ancient period. The role he played especially in natural philosophy and metaphysics is undeniable. However, the ambiguities in the context of the theses and their interpretations of his poem, the only work that has been quoted, have not been resolved until today. The dimensions of this mystery are not only related to classical thought. Ontologies related to physics approaches, theoretical and institutional beliefs about them, and various cosmogony and language understandings can be related to Parmenides in some way. It is also possible to find in Parmenides's early forms some of the contents that form the basis of the philosophy of logic and has metaphysical roots constructed by Aristotle in the ancient period and for which he gained a well-deserved reputation. In addition to the deductive approach, especially the law of contradiction, the principle of identity, the law of excluded third, and the principles of sufficient reason are the most important concepts among those mentioned. These principles, which are not directly formulated, have been used in the context of Parmenides’ arguments about knowledge, existence, and related concepts. In our study, by touching on the significant points of the poem written by Parmenides, we will try to examine the conceptual uses and logical structures of the principles we have expressed and follow the traces of the process in question, and examine its effects. The main reason for this effort is that the content presented by Parmenides continues to be discussed today, maintained its influence in many areas mentioned above, and is an important cornerstone in the development of philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:146 BOOK REVIEWS the years passed since Father Garrigou-Lagrange last published his De Revelatione would have allowed Thomistic scholars to retrieve and de· velop Aquinas's theological insights in their fullness. The danger of apologetics is that it can lead one to develop a teaching only along the lines set by those challenging the traditional teaching of the Church. In this particular instance, the Catholic apologists of the antimodernist period (...) were led to overstress the epistemological dimension of the theology of Revelation, leaving unstated that for Saint Thomas the primary term of analysis in this question is the knowledge of God. The need of Revelation for Saint Thomas stems from the call to man to share in the beatific vision. A paper on the relation of finality between faith and the beatific vision would have underlined the originality and true significance of the Thomistic tradition in theology. Saint John's Priory Laredo, Texas JOSEPH D'AMECOURT, F.J. The Eternity of the World in the Thought of Thomas Aquinas and his Contemporaries. Edited by J. B. M. WISSINK. Studien und Texte zur Geistesgeschichte des Mittelalters, edited by A. ZIMMERMAN, vol. 27. Leiden: E. J. Brill, 1990. Pp. viii+ 100. $28.75 (paper). This volume contains six short studies by five different scholars from the Netherlands on a topic accurately indicated by its title. These studies are a product of a symposium held by the Thomas Aquinas Workgroup, a scholarly association dedicated to investigating the thesis " that Aquinas first of all has to be understood as a theologian " and to " a rediscovery of the original Aquinas and his authentic thought" (p. vii). The topic chosen for these studies is a suitable one for the aims of the Workgroup, for it is one that requires a clear dis· tinction to be made between the realms of philosophy and theology, and it is one that has generated much interest and dispute-in the Middle Ages no less than today. This small collection of studies makes a con· tribution to scholarship, although there are weaknesses in some of the studies, as I shall note. F. J. A. de Grijs (pp. 1-8) argues that Thomas's purpose in writing the De aeternitate mundi was theological rather than philosophical in that Thomas provides a meditation on the meaning of eternity. This meditation, so de Grijs argues, is not only about the temporal eternity of the world but is even more about God's eternity. It shows us how BOOK REVIEWS 147 little we grasp of God's duration, or how we do not understand it rather than how we do understand it. J. A. Aertsen (pp. 9-19) ·responds to de Grijs by arguing that the work has a philosophical character. First, Aertsen explains, the fact that Thomas begins the De aeternitate mundi with the supposition on faith that the world had a temporal beginning in the past does not of itself (as de Grijs had thought) mean that the work is theological. Rather, it simply means that all believers agree that in fact the world had a temporal beginning, but the question at issue remains a philosophical one: could the world possibly have existed eternally in the past? Second, Aertsen points out that the reasoning in the De aeternitate mundi is much like that of Thomas's Disputed Question De potentia Dei, q. 3, a. 14, which has an explicitly philosophical character. Third, Thomas has already made it clear in his Commentary on the Sentences, bk. 2, d. 1, q. 1, a. 2, that the doctrine of creation, excluding the part of the doctrine that the world had a temporal beginning, is philosophically knowable in principle and known to philosophers in fact. Since the fact of creation is philosophically knowable and can he demonstrated without prejudice to the question of eternity, it cannot he said that an eternal past existence is incompatible with creation. Hence, the question of the compatibility of being eternal and being created-the very question for the De aeternitate mundi-is regarded by Thomas as philosophical rather than as theological. Aertsen's criticisms of de Grijs are sound, yet de Grijs's central point can he saved. De Grijs... (shrink)

The article examines a fundamental problem in classical Jaina philosophy, namely, the ontological status of dead matter in the hylozoistic and at the same time dualistic Jaina worldview. This question is of particular interest in view of the widespread contemporary Jaina practice of venerating bone relics and stūpas of prominent saints. The main argument proposed in this article is, that, from a classical doctrinal point of view, bone relics of renowned ascetics are valuable for Jainas, if at all, because of (...) their unique physical attributes, rather than the presumed presence of the deceased in the remains as posited in much of the extant literature on relic worship across cultures. The specific focus of the article are Jaina and non-Jaina explanations of the qualities of special matter in terms of karmic and natural processes of transformation. (shrink)

Walter Benjamin called Felix Noeggerath (1885-1960) the “universal genius” or simply “genius.” In his 1916 treatise “Synthesis and the Concept of System in Philosophy,” Noeggerath offered a reading of Kant’s concept of synthesis in an original and radical manner. He dares to confront thought with the incommensurability of atheoretical Being. The linkage between logic and incommensurability is what he calls rationalism. In contradiction to this claim, any attempt to exclude atheoretical Being from the realm of logic is anti-rationalism. Noeggerath elaborates (...) on this in a penetrating discussion and modification of epistemological positions, especially those of the Marburg School and Hermann Cohen. Noeggerath constructs a notion of the philosophical system with the help of Kant’s three tables of transcendental judgements, categories, and principles in the Critique of Pure Reason. Each of these tables is known to contain 12 individual elements in four groups of three each. For the systematic division, the third group under the title “Relation” is decisive. Noeggerath assigns one systemic part to each kind of relation: “For it is to be connected: the categorical relation with ethics, the hypothetical with logic, and the disjunctive with aesthetics.” As a result the classical sequence, beginning with logic, is changed. “The order of the limbs is: a) ethics, b) logic, c) aesthetics.” In Noeggerath’s logical outline, specific mathematical concepts of meta-geometry play a decisive role. According to him, philosophy can resemble their preciseness in building a viable concept of the infinite. The prerequisite is that philosophy does not itself behave mathematically but proceeds along its own path in critical distance to the “specialized, act-kindred thinking” of the mathematician. (shrink)

The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated many studies along the history of Western thought. The aim of this paper is to present the reading of Parmenides’s work offered by Federigo Enriques. It is based on several original theses: (1) Parmenides was the discoverer of abstract geometry; (2) his critics was addressed against the Pythagoreans rather than against Heraclitus; (3) Parmenides discovered and applied the contradiction and the (...) third excluded principles in the context of his research on foundation of geometry; (4) Parmenides’s metaphysical and physical conceptions have their bases in his speculation on geometry; (5) Parmenides used the principle of sufficient reason. Enriques’s reading is worth being expounded and discussed within the historical, philosophical and scientific context in which it is inserted. Since Enriques’s ideas are not widely known and discussed, my research has the purpose to fill this gap. The article also aims to provide elements to illustrate the discussion on Parmenides in the first half of the last century. (shrink)

The project of antirealism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of the excluded third and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity. Using principles of intuitionistic mathematics and employing only intuitionistically correct inferences, we show that prima facie reasonable formulations of (1), (2), and (3) are inconsistent. Therefore, (...) it should not be assumed that the project of anti-realism as it bears upon intuitionistic mathematics and logic can be accomplished. (shrink)

The principle of excluded middle is the logical interpretation of the law V ≤ A v ヿA in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on (...) the very conditions under which propositions can be confirmed by measurements. From the fact that the principle of. excluded middle can be confirmed for elementary propositions which are proved by quantum mechanical measurements, we conclude that this principle is inherited by all finite compound propositions. For this proof it is essential that, in the dialog-game about a connective, a finite confirmation strategy for the mutual commensurability of the subpropositions is used. (shrink)

Epistemic impairment has been the decisive yardstick when excluding infants from political agency. One of the suggestions to bypass the epistemic requirement of political agency and to encourage the inclusion of infants in representative democracies is to resort to proxies or surrogates who share or advocate interests which may be coincidental with their interests. However, this solution is far from desirable, given that it privileges the political agency of parents, guardians and trustees over other adult citizens. This article offers an (...) alternative to this conceptual frame of reference by making a case for the political agency of infants. Firstly, it maintains that political agency can be understood in terms of the several facets involved in political representation. Secondly, it claims that the all-affected principle can be reformulated as an ‘infant-affected-interests principle’ in light of which infants are members of the class of the represented. Thirdly, it explores the ways through which this political agency can occur without having to resort to alternative conceptions of representation. The conclusion ascertains that infant enfranchisement is highly undesirable and that there are more viable forms to promote infant political agency, such as virtual representation, infant-beneficial principles of political action and ombudspersons for infants. (shrink)

In his posthumous book from 1914, "New foundations of logic, arithmetic and set theory", Julius Konig develops his philosophy of mathematics. In a previous contribution, we attracted attention on the positive part (his truth and falsehood predicates being excluded) of his "pure logic": his "isology" being assimilated to mutual implication, it constitutes a genuine formalization of positive intuitionistic logic. Konig's intention was to rebuild logic in such a way that the excluded third's principle could no longer (...) be logical. However, his treatment of truth and falsehood (boiling down to negation) is purely classical. We explain here this discrepancy by the choice of the alleged more primitive notions to which the questioned notions of truth and falsehood have been reduced. Finaly, it turns out that the disjunctive and conjunctive forms of the principles of the excluded third and of contradiction have effectively been excluded, but none of their implicative forms. (shrink)

A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.

The Aristotelian, non-relativistic notion of truth as correspondence with and dependency on actual states of affairs is in principle maintained, but refined and even modified in several different directions. The principal reason for maintaining it is empirical: it seems to reflect the way in which humans deal with the notion "truth" naively or pretheoretically, in ordinary life situations. It is shown that the Kantian crisis in epistemology does not affect this notion, since what is at issue is truth-conditions, not (...) actual truth-values. This great crisis in epistemology does, however, reinforce the requirement that logic, as a vehicle of preservation of assumed truth, be entirely and fundamentally independent of contingent states of affairs. This requirement made it imperative that traditional logic be replaced with a logic of absolute applicability, no matter whether there is or is not an outside world, or, if there is one, how it is or happens to be. The Aristotelian Principle of the Excluded Third is given up, not in favour of truth-value gaps for sentences with reference failure, but rather in favour of three truth-values: truth, minimal falsity , and radical falsity . Truth-value gaps do not occur with sentences that are well-integrated in discourse and context This analysis is linked up with a well-defined trivalent logic. It moreover requires the assumption of entities that are defined by thought processes but do not exist in reality. It is further shown that truth-conditions are not always expressible in autonomously verifiable or falsifiable terms. Many lexical meanings depend, for a complete statement of the associated truth-conditions, on variable cognitive input whose content depends on what is known in general terms, or prototypically, about the things referred to in the discourse at hand. Examples are the whole possessive complex , gradable adjectives, or epistemic modals. This fact does not invalidate the notion of truth as correspondence, but it does shed a new light on how sentences acquire their truth-values. Finally, truth is seen als correspondence not so much with whatever one may assume the world to be in its barest or brütest form, down to its very basics, as with the phenomenal world, that is, the world as it presents itself to human perception and interpretation, with all the projections and reifications that go with it. (shrink)

The principle of excluded middle is more important than is commonly believed for understanding Kant's overall philosophical project. In the article, this principle is examined in the following contexts: kinds of judgments, concepts of opposition, negation, and determination, and apagogic proof. It is first explained how the principle of excluded middle is employed by Kant in distinguishing between the kinds of judgment. Also called the principle of division, it is the principle of disjunctive (...) and apodictic judgments in Kant's famous table of judgments. Next, the Author shows which kind of opposition is related to the principle of the excluded middle. As a merely logical criterion of truth, this principle grounds the logical necessity of a cognition and plays an important role in the use of apagogical proofs. Then Kant's account of logical negation will be investigated briefly. Negative judgment with a negative copula indicates that something is not contained within the sphere of a given concept. This process occurs in accordance with the principle of excluded middle. Finally, an analysis is made of how Kant presents the metaphysical principle of thoroughgoing determination and its differences from the logical principle of excluded middle. (shrink)

In this chapter we consider three philosophical perspectives (including those of Stalnaker and Lewis) on the question of whether and how the principle of conditional excluded middle should figure in the logic and semantics of counterfactuals. We articulate and defend a third view that is patterned after belief revision theories offered in other areas of logic and philosophy. Unlike Lewis’ view, the belief revision perspective does not reject conditional excluded middle, and unlike Stalnaker’s, it does not (...) embrace supervaluationism. We adduce both theoretical and empirical considerations to argue that the belief revision perspective should be preferred to its alternatives. The empirical considerations are drawn from the results of four empirical studies (which we report below) of non-experts’ judgments about counterfactuals and conditional excluded middle. (shrink)

European Journal of Political Theory, Volume 21, Issue 2, Page 368-389, April 2022. Epistemic impairment has been the decisive yardstick when excluding infants from political agency. One of the suggestions to bypass the epistemic requirement of political agency and to encourage the inclusion of infants in representative democracies is to resort to proxies or surrogates who share or advocate interests which may be coincidental with their interests. However, this solution is far from desirable, given that it privileges the political agency (...) of parents, guardians and trustees over other adult citizens. This article offers an alternative to this conceptual frame of reference by making a case for the political agency of infants. Firstly, it maintains that political agency can be understood in terms of the several facets involved in political representation. Secondly, it claims that the all-affected principle can be reformulated as an ‘infant-affected-interests principle’ in light of which infants are members of the class of the represented. Thirdly, it explores the ways through which this political agency can occur without having to resort to alternative conceptions of representation. The conclusion ascertains that infant enfranchisement is highly undesirable and that there are more viable forms to promote infant political agency, such as virtual representation, infant-beneficial principles of political action and ombudspersons for infants. (shrink)

The common cause principle says that every correlation is either due to a direct causal effect linking the correlated entities or is brought about by a third factor, a so-called common cause. The principle is of central importance in the philosophy of science, especially in causal explanation, causal modeling and in the foundations of quantum physics. Written for philosophers of science, physicists and statisticians, this book contributes to the debate over the validity of the common cause (...) class='Hi'>principle, by proving results that bring to the surface the nature of explanation by common causes. It provides a technical and mathematically rigorous examination of the notion of common cause, providing an analysis not only in terms of classical probability measure spaces, which is typical in the available literature, but in quantum probability theory as well. The authors provide numerous open problems to further the debate and encourage future research in this field. (shrink)

European Journal of Political Theory, Volume 21, Issue 2, Page 368-389, April 2022. Epistemic impairment has been the decisive yardstick when excluding infants from political agency. One of the suggestions to bypass the epistemic requirement of political agency and to encourage the inclusion of infants in representative democracies is to resort to proxies or surrogates who share or advocate interests which may be coincidental with their interests. However, this solution is far from desirable, given that it privileges the political agency (...) of parents, guardians and trustees over other adult citizens. This article offers an alternative to this conceptual frame of reference by making a case for the political agency of infants. Firstly, it maintains that political agency can be understood in terms of the several facets involved in political representation. Secondly, it claims that the all-affected principle can be reformulated as an ‘infant-affected-interests principle’ in light of which infants are members of the class of the represented. Thirdly, it explores the ways through which this political agency can occur without having to resort to alternative conceptions of representation. The conclusion ascertains that infant enfranchisement is highly undesirable and that there are more viable forms to promote infant political agency, such as virtual representation, infant-beneficial principles of political action and ombudspersons for infants. (shrink)

Peirce’s principles of excluded middle and contradiction more resembled those of Aristotle than those of contemporary logicians. While the principles themselves are simple and straightforward, many of Peirce’s comments about them have been misunderstood by commentators. In particular, his belief that the principle of excluded middle does not apply to the general and that the principle of contradiction does not apply to the vague have been mistakenly connected to his eventual rejection of the principle of (...) bivalence and development of three-valued logical connectives. An understanding of Peirce’s view of those logical principles shows that those beliefs motivated neither his rejection of bivalence nor his work in triadic logic. (shrink)

In his posthumous book from 1914, “New foundations of logic, arithmetic andset theory”, Julius König develops his philosophy of mathematics. In a previous contribution, we attracted attention on the positive part of his “pure logic”: his “isology” being assimilated to mutual implication, it constitutes a genuine formalization of positive intuitionistic logic. König’s intention was to rebuild logic in such a way that the excluded third’s principle could no longer be logical. However, his treatment of truth and falsehood (...) is purely classical. We explain here this discrepancy by the choice of the alleged more primitive notions to which the questioned notions of truth and falsehood have been reduced. Finaly, it turns out that the disjunctive and conjunctive forms of the principles of the excluded third and of contradiction have effectively been excluded, but none of their implicative forms. (shrink)

Many contemporary thinkers seeking to integrate theistic belief and scientific thought reject what they regard as two extremes. They disavow deism in which God is understood simply to uphold the existence of the physical universe, and they exclude any view of divine influence that suggests the performance of physical work through an immaterial cause. Deism is viewed as theologically inadequate, and acceptance of direct immaterial causation of physical events is viewed as scientifically illegitimate. This desire to avoid both deism and (...) any positing of God as directly intervening in the physical order has led to models of divine agency that seek to defend the reality of divine causal power yet affirm the causal closure of the physical. I argue, negatively, that such models are unsuccessful in their attempts to affirm both the reality of divine causal power acting in the created world and the causal closure of the physical and, positively, that the assumption that underlies these models, namely that any genuine integration of theistic and scientific belief must posit the causal closure of the physical on pain of violating well-established conservation principles, is mistaken. (shrink)

Owing to the problem of inescapable clashes, epistemic accounts of might-counterfactuals have recently gained traction. In a different vein, the might argument against conditional excluded middle has rendered the latter a contentious principle to incorporate into a logic for conditionals. The aim of this paper is to rescue both ontic mightcounterfactuals and conditional excluded middle from these disparate debates and show them to be compatible. I argue that the antecedent of a might-counterfactual is semantically underdetermined with respect (...) to the counterfactual worlds it selects for evaluation. This explains how might-counterfactuals select multiple counterfactual worlds as they apparently do and why their utterance confers a weaker alethic commitment on the speaker than does that of a would-counterfactual, as well as provides an ontic solution to inescapable clashes. I briefly sketch how the semantic underdetermination and truth conditions of mightcounterfactuals are regulated by conversational context. (shrink)

The article analyses recent English publications in Cartesian studies that deal with two problems: the problem of the intrinsic coherence of Descartes’s doctrine of the real distinction and interaction between mind and body and the problem of the consistency of this doctrine with the causal principle formulated in the Third Meditation. The principle at issue is alternatively interpreted by different Cartesian scholars either as the Hierarchy Principle, that the cause should be at least as perfect as (...) its effects, or the Containment Principle, that the cause should contain all there is in its effects. The author argues that Descartes’s claim that it is inconceivable how things of different natures can interact does not conflict with the acknowledgement of interaction between things of different natures in the case of soul and body. The case is made that Cartesian mind-body interaction can agree with both the Hierarchy Principle and the Containment Principle, because the Principle is about total and efficient cause, whereas in the interaction, mental and brain states are only partial causes. In particular, in the case of the causality in the brain-to-mind direction, the mind is conditioned by brain states to form the corresponding specific ideas on the basis of its innate general ideas of movements, forms, colours, etc. Eventually, for Descartes, the most natural way to deal with worries about the possibility of mind-brain interaction is to rely on God’s omnipotence, which certainly enables Him to arrange for such interaction. (shrink)

If critique does not want to be more than just a ‘passion of the head’ it has to engage in dialogue with the worst-off in society. However, there are several mechanisms that hinder the excluded from giving words to their suffering. Furthermore, there are processes of invisibilization that impede even the perception of the excluded and their critique in the public space. The aim of this article is to conceptually explore the mechanisms of formulating critique by the (...) class='Hi'>excluded and of understanding critique in the public space. Therefore, I first provide a brief overview on the meaning of critique before then presenting suffering as a language of critique. In a third step, I explore the multiple mechanisms that hinder suffering from becoming visible and end up discussing some (fragmented) solutions for overcoming these invisibilities. Although the excluded is hindered in formulating public critique in linguistic form, the suffering of the excluded can be understood as the ground for a powerful form of social critique. (shrink)

We start by noting that the set-theoretic and semantic paradoxes are framed in terms of a definition or series of definitions. In the process of deriving paradoxes, these definitions are logically represented by a logical equivalence. We will firstly examine the role and usage of definitions in the derivation of paradoxes, both set-theoretic and semantic. We will see that this examination is important in determining how the paradoxes were created in the first place and indeed how they are to be (...) solved in a uniform way. There are three features that are special about these definitions used in the derivation of most of the above paradoxes. The first is the use of self-reference between the definiens and the definiendum, the second is the generality of the definiendum, and the third is the under-determination and over-determination of concepts that usually occur as a result of these definitions. We will examine the impact of these three features on the logical representation of definitions and show how this representation then leads to a uniform paradox solution using an appropriate logic that is both paraconsistent and paracomplete. However, it is the paracompleteness, exhibited through the rejection of the Law of Excluded Middle, together with the rejection of contraction principles, that enables the solution of the paradoxes to go through. We characterize definitions as involving syntactic identity and/or meaning identity. We point out that some paradoxes do not have explicit self-reference or circularity and some may not utilize the generality of the definiendum, but the general characterizations of definitions that we give will still apply. We also look beyond all this to paradoxes that rely on illicit definitions between objects that are essentially different to start with. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE CONCEPT OF PERSON IN ST. THOMAS AQUINAS: A Contribution to Recent Discussion* ST. THOMAS AQUINAS accepted and consistently defended Boethius' definition of person: "persona est substantia individua rationalis naturae." St. Thomas' analysis of this definition necessarily involves metaphysical questions because of the implications of the terms " substance" and " nature" and moreover it manifests the inescapahle imprint of the theological problematics which surrounded the issue (e.g. the (...) Trinity and the hypostatic union). Both of these influences, metaphysical and theological, have engendered problems of interpretation and criticism. Contemporary discussions of person largely either continue the scholastic controversies or adopt a modern perspective from which to expose apparent contradictions in St. Thomas' doctrine. The purpose of this article will be limited to a consideration of the metaphysical problems concerning the relationship between individual substance, universal, nature, and existence. It is hoped that such a clarification will resolve not only the neoscholastic controversies, but also some of the contemporary problems. I. BOETHIUS' DEFINITION OF PERSON AND ST. THOMAS' EXPLANATION A. BOETHIUS' DEFINITION Boethius develops his definition of person in the Liber contra Eutychen et N estorium after a careful consideration of na- * I have to thank cordially Father Brian Shanley, 0.P. for having revised completely this English version, devoting much time and energy to fit the text and the footnotes to the style of The Thomist. He adapted the version in good style and verified the Latin quotations. 435 436 HORST SEIDL ture and substance.1 In the first chapter he sets out to define nature and discovers four possible meanings. The first and broadest definition, embracing both substances and accidents, describes nature as belonging to all things which by their being can be in some way or another be comprehended by reason: "natura est earum rermn quae, cum sint, quoquo modo intellectu capi possunt." A second definition, comprising substances alone both corporeal and incorporeal, describes nature as anything that can effect or suffer something: " natura est vel quod facere vel quod pati possit." A third sense, taken from the Aristotelian analysis of the motion of natural substances, describes nature as the immanent principle of movement : "natura est motus principium per se et non per accidens." Finally, nature can also refer to the formal cause which provides the specific difference: " natura est unam quamque rem informans specifica differentia" (cf. ST Ia. 29, I ad 4). It is this last sense which is most important. In sum, "nature" is a broad term encompassing both composite beings and their causes. Boethius continues in chapter two by first narrowing the relevant sense of nature to substances (thus excluding accidents ) and then presenting a complete division of substances. The major distinction is between corporeal substances and incorporeal substances. Corporeal subdivides further into inanimate and animate, with animate dividing. into insensitive and sensitive and the latter dividing finally into irrational and rational. Incorporeal subdivides into rational and irrational (the life-principle of animals), with rational incorporeal substances being further distinguished into those that are immutable by nature (the Creator) and those that are not so by nature (the human soul and angels) but may become so by virtue of the immutable substance. Boethius then argues that person cannot be affirmed of inanimate beings or irrational animals. A 1 All citations from Boethius are taken from the Loeb text in Boethius: Theological Tractates and the Consolation of Philosophy, ed. H. F. Stewart and E. K. Rand (Cambridge: Harvard University Press, 1918). THE CONCEPT OF PERSON IN ST. THOMAS AQUINAS 437 final distinction of :substance into universal and particular leads to the conclusion that person must refer to an individual. Thus the background is set for the definition of person which opens the third chapter: " naturae rationalis individua substantia." Person must be an individual substance of a certain nature, namely rational, which nature accounts for the form or specific difference of the particular substance (the fourth meaning of chapter 1). The connection of this definition with Aristotle 's definition of man as a rational animal is unmistakable. It should also be noted that this definition of person is applicable not only to man, in whom the rational nature is not identical with his substance, but also to the... (shrink)

It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist (...) of an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE CONCEPT OF PERSON IN ST. THOMAS AQUINAS: A Contribution to Recent Discussion* ST. THOMAS AQUINAS accepted and consistently defended Boethius' definition of person: "persona est substantia individua rationalis naturae." St. Thomas' analysis of this definition necessarily involves metaphysical questions because of the implications of the terms " substance" and " nature" and moreover it manifests the inescapahle imprint of the theological problematics which surrounded the issue (e.g. the (...) Trinity and the hypostatic union). Both of these influences, metaphysical and theological, have engendered problems of interpretation and criticism. Contemporary discussions of person largely either continue the scholastic controversies or adopt a modern perspective from which to expose apparent contradictions in St. Thomas' doctrine. The purpose of this article will be limited to a consideration of the metaphysical problems concerning the relationship between individual substance, universal, nature, and existence. It is hoped that such a clarification will resolve not only the neoscholastic controversies, but also some of the contemporary problems. I. BOETHIUS' DEFINITION OF PERSON AND ST. THOMAS' EXPLANATION A. BOETHIUS' DEFINITION Boethius develops his definition of person in the Liber contra Eutychen et N estorium after a careful consideration of na- * I have to thank cordially Father Brian Shanley, 0.P. for having revised completely this English version, devoting much time and energy to fit the text and the footnotes to the style of The Thomist. He adapted the version in good style and verified the Latin quotations. 435 436 HORST SEIDL ture and substance.1 In the first chapter he sets out to define nature and discovers four possible meanings. The first and broadest definition, embracing both substances and accidents, describes nature as belonging to all things which by their being can be in some way or another be comprehended by reason: "natura est earum rermn quae, cum sint, quoquo modo intellectu capi possunt." A second definition, comprising substances alone both corporeal and incorporeal, describes nature as anything that can effect or suffer something: " natura est vel quod facere vel quod pati possit." A third sense, taken from the Aristotelian analysis of the motion of natural substances, describes nature as the immanent principle of movement : "natura est motus principium per se et non per accidens." Finally, nature can also refer to the formal cause which provides the specific difference: " natura est unam quamque rem informans specifica differentia" (cf. ST Ia. 29, I ad 4). It is this last sense which is most important. In sum, "nature" is a broad term encompassing both composite beings and their causes. Boethius continues in chapter two by first narrowing the relevant sense of nature to substances (thus excluding accidents ) and then presenting a complete division of substances. The major distinction is between corporeal substances and incorporeal substances. Corporeal subdivides further into inanimate and animate, with animate dividing. into insensitive and sensitive and the latter dividing finally into irrational and rational. Incorporeal subdivides into rational and irrational (the life-principle of animals), with rational incorporeal substances being further distinguished into those that are immutable by nature (the Creator) and those that are not so by nature (the human soul and angels) but may become so by virtue of the immutable substance. Boethius then argues that person cannot be affirmed of inanimate beings or irrational animals. A 1 All citations from Boethius are taken from the Loeb text in Boethius: Theological Tractates and the Consolation of Philosophy, ed. H. F. Stewart and E. K. Rand (Cambridge: Harvard University Press, 1918). THE CONCEPT OF PERSON IN ST. THOMAS AQUINAS 437 final distinction of :substance into universal and particular leads to the conclusion that person must refer to an individual. Thus the background is set for the definition of person which opens the third chapter: " naturae rationalis individua substantia." Person must be an individual substance of a certain nature, namely rational, which nature accounts for the form or specific difference of the particular substance (the fourth meaning of chapter 1). The connection of this definition with Aristotle 's definition of man as a rational animal is unmistakable. It should also be noted that this definition of person is applicable not only to man, in whom the rational nature is not identical with his substance, but also to the... (shrink)

I carry out in this paper a philosophical analysis of the principle of excluded middle (or, as it is often called in the version I favor here, principle of bivalence: any meaningful assertion is either true or false). This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, (...) although excluded middle does indeed rest on certain presuppositions, they do not have the character of hypotheses that may or may not be true, or matters of fact that may or may not be the case. These presuppositions have, I claim, a transcendental character. Hence, the acceptance of excluded middle does not necessarily require, as some have claimed, an allegiance to ontological realism or some sort of cognitive optimism, construed as factual theses concerning the ontological status of domains of objects and our capability of accessing them cognitively. DOI:10.5007/1808-1711.2011v15n2p333. (shrink)

One manifestation of argumentation is in critical discussions where people genuinely strive cooperatively to achieve critical decisions. Hence, argumentation can be recognized as the process of advancing, supporting, modifying, and criticizing claims so that appropriate decision makers may grant or deny adherence. This audience-centered definition holds the assumption that the participants must willingly engage in public debate and discussion, and their arguments must function to open a critical space and keep it open. This essay investigates `ideological pronouncement,' a kind of (...) rhetoric that undermines and limits the possibility of critical discussion among target audiences, as an enemy of sound argumentation. First, the essential characteristics of sound argumentation are explained. Next, the typical characteristics of ideological rhetoric are described. At the same time, the Cardinal Principles of the National Entity of Japan, a Japanese wartime moral education textbook, is examined as a paradigm case of ideological rhetoric. Third, three key pronouncements of the Cardinal Principles are outlined and discussed. Finally, implications from the critical discussion are drawn. (shrink)

The potential for vaccines to prevent the spread of infectious diseases is crucial for vaccination policy and ethics. In this paper, I discuss recent evidence that the current COVID-19 vaccines have only a modest and short-lived effect on reducing SARS-CoV-2 transmission and argue that this has at least four important ethical implications. First, getting vaccinated against COVID-19 should be seen primarily as a self-protective choice for individuals. Second, moral condemnation of unvaccinated people for causing direct harm to others is unjustified. (...) Third, the case for a harm-based moral obligation to get vaccinated against COVID-19 is weak. Finally, and perhaps most significantly, coercive COVID-19 vaccination policies (e.g., measures that exclude unvaccinated people from society) cannot be directly justified by the harm principle. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 35.1 (2002) 1-21 [Access article in PDF] Turning Kant Against the Priority of Autonomy: Communication Ethics and the Duty to Community Pat J. Gehrke Communication ethics scholars afford Immanuel Kant significantly less attention than one might expect. This may be because, as Robert Dostal notes, Kant argues that rhetoric merits no respect whatsoever (223). This rejection of rhetoric, Dostal writes, is grounded in the significant emphasis (...) given to Kant's concept of autonomy (232). The focus on autonomy and, hence, rhetoricians' relative neglect of Kant's ethical theory are both connected to the separation of Kant's Critique of Pure Reason (hereinafter CPuR) from his subsequent ethical and moral philosophy. Kenneth Burke writes that Kant's first critique has no ethical implications, "no 'wills,' 'oughts,' 'shoulds,' or 'thou shalt nots'... nothing but an inevitable is, a description of conditions as they necessarily are for human experience" (191; emphasis in original). Such readings lose much of the richness and complexity of Kant's thought and tend instead to produce simple moral duties, such as Mike Markel's assertion that technical communicators must be truthful.Perhaps the most critical element of Kant's work lost in our focus on autonomy is his articulation of a ground for a duty to community. While Kant makes clear the importance of community for his metaphysics in the first critique (CPuR), the importance of community in Kant's moral philosophy often is overlooked. Some scholars claim that an ethical duty to community is either rejected by Kant's emphasis on the autonomy of will or simply ignored. This article combines a reading of Kant's metaphysics of experience with his moral philosophy to articulate a communication ethic grounded in community. This argument is made in three parts: first, the community of objects in experience—the Third Analogy of Experience—is an organizing principle of and a necessary condition for the possibility of all experience; second, this metaphysical principle of community is relevant [End Page 1] to community as developed in Kant's ethical writings; and finally, Kant's own work undermines the primacy of autonomy and better supports a communication ethic grounded in a duty to community.Scholars interested in Jurgen Habermas's theory of communicative action have special reason to take note of Kant's work. Kant is not only a figure that Habermas sees reflected in his own work, 1 but a constant point of contrast. Craig Calhoun writes that much of Habermas's own philosophy emerges by rejecting Kant's epistemology and elements of his metaphysics while still giving credence to Kantian moral philosophy (2). However, like most communication scholars and philosophers, Habermas believes that autonomy governs Kantian ethics: "Formalistic ethics (Kant) binds the criterion of generality of norms to the further criterion of autonomy, that is, independence from contingent motives" (Habermas, Legitimation 89). Since autonomy excludes or represses the contingent, if our readings of Kant give primacy to autonomy we leave little room for any notion of community as manifest in experience. In no small part, it is the criticism of Kant for privileging autonomy that has given Habermasians their break from Kantian ethics. However, if we turn to the first critique to guide our reading of the moral philosophy, there is another way to understand the role of autonomy and community in Kant's thought. By linking Kant's metaphysics with his moral philosophy, this article turns Kant away from the primacy of autonomy and uses Kant's own works to argue that autonomy is but one half of an antinomy that is organized under the principle of community. Thus, this article recuperates the possibility of deploying Kantian metaphysics and moral philosophy together as grounds for a communication ethic that privileges community and recovers the value of rhetoric.For rhetorical scholars, the resistance to the priority of autonomy may be related to the frequent expression of community through appeal to commonality, sameness, or identification. Today, feminist, race, postmodern, and poststructural communication scholars are questioning the value of commonality as a ground for ethics (e... (shrink)

I carry out in this paper a philosophical analysis of the principle of excluded middle. This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, although excluded middle does indeed rest on certain presuppositions, they do not have the character of hypotheses that may or may not be (...) true, or matters of fact that may or may not be the case. These presuppositions have, I claim, a transcendental character. Hence, the acceptance of excluded middle does not necessarily require, as some have claimed, an allegiance to ontological realism or some sort of cognitive optimism, construed as factual theses concerning the ontological status of domains of objects and our capability of accessing them cognitively. (shrink)

We systematically study the interrelations between all possible variations of \(\Delta ^0_1\) variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.

As regards the issue of futura contingentia, Aquinas's interpretation turns on a phrase that has sometimes been dismissed as irrelevant or even confused: "...non tamen haec vel illa determinatae...". It is shown that this clause is in complete conformity with Aquinas's interpretation of the principles of non-contradiction and of excluded middle. According to this interpretation the meaning of propositional negation derives from the first two principles considered collectively but is not presupposed by them. With respect to time-relative modalities this (...) implies that at the time of announcement, say, of a sea battle both parts of the contradiction could be true, provided one understands "could" in the sense of a counterfactual possibility with respect to the final outcome. It is also shown that Aquinas's interpretation allows one to avoid some perplexities in connection with the controversial beginning of Met. IX, 4. Some final considerations are meant to show the rationale of that interpretation. (shrink)