We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...) LEM is intrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it. (shrink)

This rich and varied collection of essays addresses some of the most fundamental human questions through the lenses of philosophy, literature, religion, politics, and theology. Peter Augustine Lawler and Dale McConkey have fashioned an interdisciplinary consideration of such perennial and enduring issues as the relationship between nature and history, nature and grace, reason and revelation, classical philosophy and Christianity, modernity and postmodernity, repentance and self-limitation, and philosophy and politics.

The Theory of Planned Behavior predicts that a combination of attitudes, perceived norms, and perceived behavioral control predict intentions, and that intentions ultimately predict behavior. Previous studies have found that the TPB can predict students’ engagement in plagiarism. Furthermore, the General Theory of Crime suggests that self-control is particularly important in predicting engagement in unethical behavior such as plagiarism. In Study 1, we incorporated self-control in a TPB model and tested whether norms, attitudes, and self-control predicted intention to plagiarize and (...) plagiarism behavior. The best statistical fit for the path-analytic model was achieved when a direct path from self-control to plagiarism engagement was specified. In Study 2, we added a measure of perceived behavioral control and split the measurement of norms into descriptive and injunctive components. This study found that both self-control and perceived-behavioral control additively contributed to the prediction of plagiarism and the path-analytic model achieved its best fit when direct paths from perceived norms to plagiarism behavior were specified. These studies suggest that setting strong anti-plagiarism norms, such as by the use of honor codes, and seeking to enhance students’ self-control may reduce engagement in plagiarism. (shrink)

The first-order theory of the lattice of recursively enumerable closed subsets of an effective topological space is proved undecidable using the undecidability of the first-order theory of the lattice of recursively enumerable sets. In particular, the first-order theory of the lattice of recursively enumerable closed subsets of Euclidean n -space, for all n , is undecidable. A more direct proof of the undecidability of the lattice of recursively enumerable closed subsets of Euclidean n -space, n ⩾ 2, is provided using (...) the method of reduction and the recursive inseparability of the set of all formulae satisfiable in every model of the theory of SIBs and the set of all formulae refutable in some finite model of the theory of SIBs. (shrink)

The standard Hilbert-style of axiomatic system yields the assertion of axioms and, via the use of rules, the assertion of theorems. However, there has been little work done on the corresponding axiomatic rejection of non-theorems. Such Hilbert-style rejection would be achieved by the inclusion of certain rejection-axioms (r-axioms) and, by use of rejection-rules (r-rules), the establishment of rejection-theorems (r-theorems). We will call such a proof a rejection-proof (r-proof). The ideal to aim for would be for the theorems and r-theorems to (...) bemutually exclusive and exhaustive. That is, if a formula A is a theorem then it is not an r-theorem, and if A is a non-theorem then it is an r-theorem. In this paper, I present a rejecion system for the first-degree formulae of a large number of relevant logics. (shrink)

We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with respect (...) to a content semantics, which embraces the concept of meaning containment. (shrink)

We assess Meyer’s formalization of arithmetic in his [21], based on the strong relevant logic R and compare this with arithmetic based on a suitable logic of meaning containment, which was developed in Brady [7]. We argue in favour of the latter as it better captures the key logical concepts of meaning and truth in arithmetic. We also contrast the two approaches to classical recapture, again favouring our approach in [7]. We then consider our previous development of Peano arithmetic (...) including primitive recursive functions, finally extending this work to that of general recursion. (shrink)

We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with respect (...) to a content semantics, which embraces the concept of meaning containment. (shrink)

The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...) logic R of relevant implication. A further aim is the use of metavaluations in a new context, expanding the range of application of this novel technique, already used in the context of negation and arithmetic, thus providing an alternative to traditional model theoretic approaches. (shrink)

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A 1 .A 2 . ... .A n B, the conjunctive form,A 1&A 2 & ...A n (...) B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A 1&A 2& ...A n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C. (shrink)

“The sublime is a massive concept,” Emily Brady states in her book’s first sentence. Her lucid study of the sublime should interest scholars from a wide range of disciplines, from environmental philosophy and aesthetics to the history of philosophy, art history, and literary criticism. Although its title refers to modern philosophy, the book examines not only the period typically classified in philosophy as “modern,” but also romanticism and contemporary aesthetics. Brady aims “to reassess, and to some extent reclaim, (...) the meaning of the sublime as developed during its heyday in eighteenth-century aesthetic theory by the likes of Addison, Burke, Kant, and others, and mark out its relevance for contemporary debates... (shrink)

On the Dvaita (dualistic) school of Vedanta philosophy propounded by Madhva, 13th cent.

This article aims to provide a response to the problem of suffering through an explication of a new theodicy termed the Exemplarist Theodicy. This specific theodicy will be formulated in light of the moral theory provided by Linda Zagzebski, termed the Exemplarist Moral Theory, the notion of transformative experience, as explicated by L.A. Paul, Havi Carel and Ian James Kidd, and the virtue-theoretic approach to suffering proposed by Michael Brady, which, in combination with some further precisifying philosophical concepts—namely, compensation, (...) total empathy, and infinitely valuable connections—will provide us with a possible, morally sufficient reason for why God allows individuals to experience suffering. (shrink)

In this article, we consider two independently appealing theories—the Growing-Block view and Humean Supervenience—and argue that at least one is false. The Growing-Block view is a theory about the nature of time. It says that past and present things exist, while future things do not, and the passage of time consists in new things coming into existence. Humean Supervenience is a theory about the nature of entities like laws, nomological possibility, counterfactuals, dispositions, causation, and chance. It says that none of (...) these entities are fundamental, since if they were, this would entail the existence of irreducible necessary connections between matters of fact. Instead, these entities supervene on a fundamental, non-nomological ‘Humean mosaic’ of property instances at spacetime points. We will further explain and motivate the Growing-Block view and Humean Supervenience in Sects. 2 and 3, but first, we turn to our master argument. (shrink)

The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some (...) conditions are fulfilled. The aim of this note is to prove BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely. (shrink)

The author's motivation for constructing the calculi of this paper\nis so that time and tense can be "discussed together in the same\nlanguage" (p. 282). Two types of enriched propositional caluli for\ntense logic are considered, both containing ordinary propositional\nvariables for which any proposition may be substituted. One type\nalso contains "clock-propositional" variables, a,b,c, etc., for\nwhich only clock-propositional variables may be substituted and that\ncorrespond to instants or moments in the semantics. The other type\nalso contains "history-propositional" variables, u,v,w, etc., for\nwhich only history-propositional variables may (...) be substituted and\nthat correspond to maximally linearly ordered subsets of instants.\nThis second type is for tense logics in which time is not linear\nand where at any moment there may exist alternative future courses\nof events. Quantifiers are included in both types but only for clock-\nand history-propositional variables. However, these quantifiers are\ngiven an essentially substitutional interpretation. In addition,\nbesides each clock-propositional variable being true at exactly one\ninstant, the semantics requires that for each instant there be at\nleast one clock-propositional variable true at that instant, which\nin effect amounts to having each instant of the model "denoted" in\nthe formalism by some clock-propositional variable. Thus it is not\nsurprising that quantification over clock-propositional variables\nturns out to have a "well behaved first-order semantics" (p. 284).\n{One axiom relating history- with clock-propositions seems to need\nrevision: CKTauTbuAUabUba. Since the clock-propositional variables\nmight be true at the same instant the consequent should include an\nalternative, namely, LCab.} Besides the standard truth-functional\nand tense operators G,H,F,P, the author includes L for "it is\nalways the case that". The model-theoretic earlier-than relation\nordering instants and the semantic truth-at (an instant) relation\nare formalized by Uab and Taα (for a wff α) which\nare defined respectively as LCbPa (whenever the clock-proposition\nb is the case the clock-proposition a was the case) and LCaα\n(α is the case whenever the clock-proposition a is the case).\nBecause the future tense operators are definable in terms of U\nand T and the latter are definable in terms of L and P, the\ndual of H, the author notes that his completeness proofs can be\nrestricted to L and H as primitive and with the future tense\noperators used for other interpretations, especially Prior, A.'s\nindeterminist "it will be the case that", where time is not linear.\nThe author concludes with some rather technical observations showing\nthat "in ordinary tense logics the instants are nonstandard elements\nof the models. This provides", according to the author, "a semantic\npressure to build the instants into tense logic, so that they will\nappear as standard elements in the models" (p. 283). (shrink)

This paper proposes an ethical framework for rationing publicly financed health care. We begin by classifying alternative rationing criteria according to their ethical basis. We then examine the ethical arguments for four rationing criteria. These alternatives include rationing high technology services, non-basic services, services to patients who receive the least medical benefit, and services that are not equally available to all. We submit that a just health care system will not limit basic health care to persons unable to pay for (...) it. Furthermore, justice in health care requires limiting publicly-financed non-basic health care, striving for equality in access to basic health care, and relying on medical benefit to ration non-basic health care. (shrink)

The logic BN4 was defined by R.T. Brady in 1982. It can be considered as the 4-valued logic of the relevant conditional. E4 is a variant of BN4 that can be considered as the 4-valued logic of entailment. The aim of this paper is to define reduced general Routley-Meyer semantics for BN4 and E4. It is proved that BN4 and E4 are strongly sound and complete w.r.t. their respective semantics.

The third book in the Criminalization series examines the constitutionalization of criminal law. It considers how the criminal law is constituted through the political processes of the state; how the agents of the criminal law can be answerable to it themselves; and finally how the criminal law can be constituted as part of the international order.

Little previous research has examined attitudes about societal and ethical issues (SEI) among interns participating in research experience for undergraduate programs (REUs) in nanotechnology, thus neglecting an important population for understanding the burgeoning views of the next generation of nanotechnology researchers. This study surveyed a sample of interns (N = 85) participating in the National Nanotechnology Infrastructure Network’s (NNIN) REU program during the summer of 2012. Our questions focused on interns’ experiences with education on ethical issues, as well as their (...) attribution of responsibility for considering ethical issues, motivations to talk about ethical issues, and comfort level of discussing ethical issues with faculty, mentors, lab staff, and other REU students. Among key findings was that lab culture related to the extent to which REU interns felt comfortable discussing ethical issues. In addition, those who reported more discussions about ethical issues with their mentors were more likely to consider themselves as responsible for considering ethical issues. We conclude with recommendations and future research directions. (shrink)

Suetonius quotes at Tiberius 21. 4–7 a number of passages from letters of Augustus to Tiberius showing the high regard in which he professed to hold him, despite his reservations about the darker side of his character, once he had decided to adopt him ‘rei publicae causa’ in a.d 4. They seem to have attracted little critical comment, although Seager connects them with the handling by Tiberius of the Pannonian revolt in a.d. 6–9. suggesting that in view of their fulsome (...) character they were probably written towards the end of this period, when the crisis was past, rather than earlier when Augustus may have been critical of Tiberius’ caution in prosecuting the war. But he does not attempt a more detailed appraisal of the possible dates of the individual letters quoted. Sections 21. 4 and 5 in particular present interesting textual difficulties, mainly arising from the transmission of Greek in a predominantly Latin text: this article discusses these with a view to throwing greater light on the historical significance of the letters. First, the text, to which I have appended a limited apparatus which concentrates on the points of greatest difficulty. (shrink)