We prove that for sufficiently large N, there are tautologies of size O that require proofs containing Ω lines in axiomatic systems of propositional logic based on axioms and the rule of substitution for single variables. These tautologies have proofs with O lines in systems with the multiple substitution rule.

It was noted recently in [4] that the definitions in a certain system of protothetic cease to be creative if one extends the rule of substitution so that direct substitution of the so called incomplete expressions for functor variables becomes possible. However, precise formulations were omitted in [4]. Here, we describe the new rule in some details and formulate some relevant theorems. For more circumstantial discussion, see [5].

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that (...) class='Hi'>Substitution ought to fail. (shrink)

Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery f, 0.5b> is strictly preferred to the compound lottery f, 0.5a>. Using tiebreak rules the following is shown here: In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a and b at (...) certain choice nodes, i.e., indifference between a and b is not stable. Using this result, I answer a question posed by Rabinowicz (1997) concerning admissibility in sequential decisions when indifferent options are substituted at choice nodes. (shrink)

This chapter contains sections titled: Odysseus's Iron Soul Socrates' Wild Claim The Treasure Parable How Socrates Teaches the World The Incommensurable Objection Socrates Restates the Absurdity Augustine's Tormented Decision The Brute‐Desire Objection Further Reading.

This study focuses on the devices implemented in classical Indian texts on ritual and language in order to develop a structure of rules in an economic and systematic way. These devices presuppose a spatial approach to ritual and language, one which deals for instance with absences as substitutions within a pre-existing grid, and not as temporal disappearances. In this way, the study reveals a key feature of some among the most influential schools of Indian thought. The sources are Kalpasūtra, Vyākaraṇa (...) and Mīmāṃsā, three textual traditions which developed alongside each other, sharing - as the volume shows - common presuppositions and methodologies. The book will be of interest for Sanskritists, scholars of ritual exegesis and of the history of linguistics. - Cover. (shrink)

Raymond Kelly’s widely cited _Warless Societies and the Origin of War_ (University of Michigan Press, 2000) seeks to explain the origins of two central signatures of human society: war and segmented—i.e., multilevel—societies. Both, he argues, arose with the emergence of a social-substitutability principle, a rule that establishes a collective identity among a set of individuals such that any one member becomes equivalent to, and responsible for the actions of, the others. This principle emerged during the Holocene, when population increase (...) gave rise to the first lethal ambushes. By its nature, ambush obscures attackers’ identities. Those attempting to retaliate for the ambush were therefore obliged to target members of the ambushers’ group indiscriminately—i.e., based on a social-substitutability principle. Kelly’s proposals draw welcome attention to a widespread, deeply influential, and unsettling human behavior, the disposition to hold everyone in a group culpable for the actions of a few, a proclivity that all too often results in mass slaughter. His general argument, however, is logically and empirically deficient, and cross-cultural evidence on ambush in contact-era New Guinea undermines his anonymity-of-ambush hypothesis. What then accounts for war and multilevel society? The New Guinea evidence strongly supports a contention that social-substitutability behavior arose not from offensive military action (i.e., ambush) but from the defensive military response to ambush. These findings render the social-substitutability argument’s unconventional definition of war superfluous, undermine its chronology for the emergence of war, and underwrite an alternative scenario for the origins of multilevel, segmented society. (shrink)

If p(x 1 ,...,x n ) and q(x 1 ,...,x n ) are two logically equivalent propositions then p(π (x 1 ),...,π (x n )) and q(π (x 1 ),...,π (x n )) are also logically equivalent where π is an arbitrary permutation of the elementary constituents x 1 ,...,x n . In Quantum Logic the invariance of logical equivalences breaks down. It is proved that the distribution rules of classical logic are in fact equivalent to the meta-linguistic rule (...) of universal substitution and that the more restrictive structure of the substitution group of Quantum Logic prevents us from defining truth in a classical fashion. These observations lead to a more profound understanding of the Logic of Quantum Mechanics and of the role that symmetry principles play in that theory. (shrink)

I examine the theoretical difficulties of Aristotle’s syllogism and the traditional syllogism. I propose a more unified ordinary thinking logic different from the syllogism. I show that the new logic based on the substitution of thinking elements can be used to describe the reasoning process of human minds more properly, bypassing rigid figures, moods and cumbersome rules of the syllogism. I also show that the new logic combines the categorical inference with relation and modal inferences, expanding the scope of (...) the syllogism so that more complex quantification inferences can be captured. I conclude that the substitution of thinking elements is the basic characteristics of human thinking, and the substitutions can be further applied not only to all research fields of abstract and image thinking but also to practical fields of action methodology. (shrink)

Frances Kamm's Principle of Secondary Permissibility specifies a class of exceptions to the general rule not to kill as a means. The principle allows us to harm as a means some of those who would have been otherwise harmed as side effects. ‘For example, suppose it is impermissible to paralyze A's legs as a means to a greater good. It would still be permissible to do this as the alternative to permissibly killing A as a mere indirect side effect.’ (...) I argue that, despite of its great appeal, PSP is incorrect; it is simply not true that the victims of substitutive harm are not worse off than they would otherwise permissibly have been. In fact, there is no moral difference between the purportedly substitutive harm licensed by PSP and the standard sort of harming as means repudiated by nonconsequentialists. (shrink)

This note presents a point of view upon the notions of programsubstitution which are the tools for proving properties of programs of algorithmic logics [5], [3] being sufficiently strong and universal to comprise almost all previously introduced theories of programming, and the so-called extended algorithmic logic [1], [2] and algorithmic logic with nondeterministic programs [4]. It appears that the mentioned substitution rule allows us to examine more deeply algorithmic properties of terms, formulas and programs. Besides the problem of (...) Post-completeness and structural completeness of algorithmic logics strengthened additionally by the rule of substitution is raised. (shrink)

The particular problem which will concern us here is raised by "Leibniz's Rule": Eadem sunt quorum unum in alterius locum substitui potest, salva veritate. The puzzle arises from the following inference.

Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz (...) and for the intuitionistic calculus H is decidable, intuitionistic propositional calculus H is decidable with respect to admissibility . A semantical criterion for the admissibility of rules of inference in Grz is given. (shrink)

Kripke’s substitutional interpretation of quantifiers is usually said to be unsatisfactory for independence-friendly (IF) languages. The purpose of this paper is to question this claim. Two accounts of substitutional semantics for IF sentences will be written down, and the objection of the so-called ‘dummy variables’ will be ruled out. Moreover, it will be argued, against the traditional view, that Game-Theoretical Semantics (GTS) should be conceived of as substitutional. The paper ends with some remarks concerning the reasons why substitution is (...) especially suitable for dynamic semantics. (shrink)

Abstract:The kind of commitment to moral rules that characterizes effective interaction between persons in among others places, manufacturing and commercial settings is characteristically treated by economists and game theorists as a public good, the securing of which requires the expenditure of scarce resources on surveillance and enforcement mechanisms. Alternatively put, the view is that, characteristically, rational persons cannot voluntarily guide their choices by rules, but can only be goaded into acting in accordance with such rules by the fear of social (...) and formal sanctions. On this way of thinking, rational individuals are condemned to having to settle for the “second-best” results that are thereby implied. This conclusion rests not only on an appeal to a consequentialist perspective, but also a separability principle. Against this, it is argued that consequentialism itself offers a basis for the rejection of the separability principle, and a defense of the thesis that, for a wide range of realistic cases, being disposed to voluntarily guide one’s choice by rules (on the condition that others can be expected to do so as well) is a necessary condition of engaging in rational interaction.Most people do not trust most other people, unmonitored, to honor obligations completely. Because of this they use substantial amounts of resources to specify the details of agreements, and to police them. Use of these resources … could be greatly reduced, if transacting parties would agree to honor the spirit of their agreement and simply shake hands. The resource saving to the two parties combined, from substituting this mode of “enforcing” agreements to those currently used, is clear. Why, then, does not this more efficient mode of transacting drive out the more costly methods through the normal competitive process? … The underlying rationale for this … is that it is privately profitable to engage in some degree of “cheating” on agreements, and to use resources to disguise this fact. — M. W. Reder, “The Place of Ethics in the Theory of Production”. (shrink)

The aim of this paper is to propose a criterion of finite detachment-substitutional formalization for normal modal systems. The criterion will comprise only those normal modal systems which are finitely axiomatizable by means of the substitution, detachment for material implication and Gödel rules.

The follow-up research of Aristotle’s syllogism has different approaches. The traditional syllogism follows Aristotle’s conceptual system and hopes to make improvements within Aristotle’s theory. Mathematical logic proposes a new conceptual system to accurately interpret Aristotle’s syllogism. Lei Ma puts forward an extended syllogism whose conceptual system is different from Aristotelian logic and mathematical logic. He thinks that Aristotle’s syllogism and traditional syllogism have tedious figures, moods, and reasoning rules, which are difficult for us to memorize. It is a theoretical conclusion (...) of the human reasoning process but does not conform to the actual human thinking process. Ma’s syllogism is called substitution logic, which mainly concerns the substitution characteristics of a human thinking process, and summarizes the substitution rules in the reasoning process. Substitution logic appropriately describes the actual human reasoning process, thus inspiring us to establish a unified scientific theory of thinking and carry out normative research on the unity of abstract thinking and imaginative thinking. Substitution logic may be applied to the field of artificial intelligence, making artificial intelligence closer to the reality of human thinking. It seems that the research direction of substitution logic will give birth to human-like AI systems and promote the revolutionary transformation of AI research. (shrink)

The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the (...) community, as well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games. (shrink)

A term td is called a ternary deductive term for a variety of algebras V if the identity td≈r holds in V and ∈θ yields td≈td for any A∈V and any principal congruence θ on A. A connective f is called td-distributive if td)≈ f,…,td). If L is a propositional logic and V is a corresponding variety that has a TD term td, then any admissible in L rule, the premises of which contain only td-distributive operations, is derivable, and (...) the substitution r↦td is a projective L-unifier for any formula containing only td-distributive connectives. The above substitution is a generalization of the substitution introduced by T. Prucnal to prove structural completeness of the implication fragment of intuitionistic propositional logic. (shrink)

What is an inference rule? This question does not have a unique answer. One usually finds two distinct standard answers in the literature; validity inference $(\sigma \vdash_\mathrm{v} \varphi$ if for every substitution $\tau$, the validity of $\tau \lbrack\sigma\rbrack$ entails the validity of $\tau\lbrack\varphi\rbrack)$, and truth inference $(\sigma \vdash_\mathrm{t} \varphi$ if for every substitution $\tau$, the truth of $\tau\lbrack\sigma\rbrack$ entails the truth of $\tau\lbrack\varphi\rbrack)$. In this paper we introduce a general semantic framework that allows us to investigate the (...) notion of inference more carefully. Validity inference and truth inference are in some sense the extremal points in our framework. We investigate the relationship between various types of inference in our general framework, and consider the complexity of deciding if an inference rule is sound, in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and first-order logic. (shrink)

Open-source communities that focus on content rely squarely on the contributions of invisible strangers in cyberspace. How do such communities handle the problem of trusting that strangers have good intentions and adequate competence? This question is explored in relation to communities in which such trust is a vital issue: peer production of software (FreeBSD and Mozilla in particular) and encyclopaedia entries (Wikipedia in particular). In the context of open-source software, it is argued that trust was inferred from an underlying ‘hacker (...) ethic’, which already existed. The Wikipedian project, by contrast, had to create an appropriate ethic along the way. In the interim, the assumption simply had to be that potential contributors were trustworthy; they were granted ‘substantial trust’. Subsequently, projects from both communities introduced rules and regulations which partly substituted for the need to perceive contributors as trustworthy. They faced a design choice in the continuum between a high-discretion design (granting a large amount of trust to contributors) and a low-discretion design (leaving only a small amount of trust to contributors). It is found that open-source designs for software and encyclopaedias are likely to converge in the future towards a mid-level of discretion. In such a design the anonymous user is no longer invested with unquestioning trust. (shrink)

One of the principal lessons of The Concept of Law is that legal systems are not only comprised of rules, but founded on them as well. As Hart painstakingly showed, we cannot account for the way in which we talk and think about the law - that is, as an institution which persists over time despite turnover of officials, imposes duties and confers powers, enjoys supremacy over other kinds of practices, resolves doubts and disagreements about what is to be done (...) in a community and so on - without supposing that it is at bottom regulated by what he called the secondary rules of recognition, change and adjudication. Given this incontrovertible demonstration that every legal system must contain rules constituting its foundation, it might seem puzzling that many philosophers have contested Hart's view. In particular, they have objected to his claim that every legal system contains a rule of recognition. More surprisingly, these critiques span different jurisprudential schools. Positivists such as Joseph Raz, as well as natural lawyers such as Ronald Dworkin and John Finnis, have been among Hart's most vocal critics. In this essay, I would like to examine the opposition to the rule of recognition. What is objectionable about Hart's doctrine? Why deny that every legal system necessarily contains a rule setting out the criteria of legal validity? And are these objections convincing? Does the rule of recognition actually exist? This essay has five parts. In Part One, I try to state Hart's doctrine of the rule of recognition with some precision. As we will see, this task is not simple, insofar as Hart's position on this crucial topic is often frustratingly unclear. I also explore in this part whether the United States Constitution, or any of its provisions, can be considered the Hartian rule of recognition for the United States legal system. In Part Two, I attempt to detail the many roles that the rule of recognition plays within Hart's theory of law. In addition to the function that Hart explicitly assigned to it, namely, the resolution of normative uncertainty within a community, I argue that the rule of recognition, and the secondary rules more generally, also account for the law's dexterity, efficiency, normativity, continuity, persistence, supremacy, independence, identity, validity, content and existence. In Part Three, I examine three important challenges to Hart's doctrine of the rule of recognition. They are: 1) Hart's rule of recognition is under- and over-inclusive; 2) Hart cannot explain how social practices are capable of generating rules that confer powers and impose duties and hence cannot account for the normativity of law; 3) Hart cannot explain how disagreements about the criteria of legal validity that occur within actual legal systems, such as in American law, are possible. In Parts Four and Five, I address these various objections. I argue that although Hart's particular account of the rule of recognition is flawed and should be rejected, a related notion can be fashioned and should be substituted in its place. The idea, roughly, is to treat the rule of recognition as a shared plan which sets out the constitutional order of a legal system. As I try to show, understanding the rule of recognition in this new way allows the legal positivist to overcome the challenges lodged against Hart's version while still retaining the power of the original idea. (shrink)

This article offers a new perspective on the relationship between slurring terms and their neutral counterparts with an inferentialist view of slurs. I argue that slurs and their counterparts are coextensional with contrasting senses. Crucially, the proposed inferentialist view overcomes the combination of two challenges: Kaplanian inferences and the substitution argument. The previous views cannot account for both of them.

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz’s 1973paper ‘Towards a foundation of a general proof theory’ and refined by Schroeder-Heister in ‘Validity concepts in proof-theoretic semantics’ (2006). We will call the new notion generalized proof-theoretic validity and (...) show that the logic of generalized proof-theoretic validity is intuitionistic logic. (shrink)

Open-source communities that focus on content rely squarely on the contributions of invisible strangers in cyberspace. How do such communities handle the problem of trusting that strangers have good intentions and adequate competence? This question is explored in relation to communities in which such trust is a vital issue: peer production of software (FreeBSD and Mozilla in particular) and encyclopaedia entries (Wikipedia in particular). In the context of open-source software, it is argued that trust was inferred from an underlying ‘hacker (...) ethic’, which already existed. The Wikipedian project, by contrast, had to create an appropriate ethic along the way. In the interim, the assumption simply had to be that potential contributors were trustworthy; they were granted ‘substantial trust’. Subsequently, projects from both communities introduced rules and regulations which partly substituted for the need to perceive contributors as trustworthy. They faced a design choice in the continuum between a high-discretion design (granting a large amount of trust to contributors) and a low-discretion design (leaving only a small amount of trust to contributors). It is found that open-source designs for software and encyclopaedias are likely to converge in the future towards a mid-level of discretion. In such a design the anonymous user is no longer invested with unquestioning trust. (shrink)

Condensed detachment is usually regarded as a notation, and defined by example. In this paper it is regarded as a rule of inference, and rigorously defined with the help of the Unification Theorem of J. A. Robinson. Historically, however, the invention of condensed detachment by C. A. Meredith preceded Robinson's studies of unification. It is argued that Meredith's ideas deserve recognition in the history of unification, and the possibility that Meredith was influenced, through ukasiewicz, by ideas of Tarski going (...) back at least to 1939, and possibly to 1930 or earlier, is discussed. It is proved that a term is derivable by substitution and ordinary detachment from given axioms if and only if it is a substitution instance of a term which is derivable from these axioms by condensed detachment, and it is shown how this theorem enables the ideas of ukasiewicz and Tarski mentioned above to be formalized and extended. Finally, it is shown how condensed detachment may be subsumed within the resolution principle of J. A. Robinson, and several computer studies of particular Hilbert-type propositional calculi using programs based on condensed detachment or on resolution are briefly discussed. (shrink)

Transcript of an Interview on the podcast: Irreverend: Faith and Current Affairs.

This book introduces and explores the role of apprehension in reasoning - setting out the problems, determining the vocabulary, fixing the boundaries, and questioning what is often taken for granted. Lynn Holt argues that a robust conception of rationality must include intellectual virtues which cannot be reduced to a set of rules for reasoners, and argues that the virtue of apprehension, an acquired disposition to see things correctly, is required if rationality is to be defensible. Drawing on an Aristotelian conception (...) of intellectual virtue and examples from the sciences, Holt shows why impersonal standards for rationality are misguided, why foundations for knowledge are the last elements to emerge from inquiry not the first, and why intuition is a poor substitute for virtue. By placing the current scene in historical perspective, Holt displays the current impasse as the inevitable outcome of the replacement of intellectual virtue with method in the early modern philosophical imagination. Written in an engaging and jargon-free style, this book is of interest to a wide range of readers, particularly epistemologists and philosophers of science concerned with the fate of reason. (shrink)

The past decade has seen an explosion of work on calculi of explicit substitutions. Numerous works have illustrated the usefulness of these calculi for practical notions like the implementation of typed functional programming languages and higher order proof assistants. It has also been shown that eta-reduction is useful for adapting substitution calculi for practical problems like higher order unification. This paper concentrates on rewrite rules for eta-reduction in three different styles of explicit substitution calculi: λσ, λse and the (...) suspension calculus. Both λσ and λse when extended with eta-reduction rules, have proved useful for solving higher order unification. We enlarge the suspension calculus with an adequate eta-reduction rule which we show to preserve termination and confluence of the associated substitution calculus and to correspond to the eta rules of the other two calculi. We prove that λσ and λse as well as λσ and the suspension calculus are non-comparable while λse is more adequate than the suspension calculus in simulating one-step beta-reduction. After defining the eta-reduction rule in the suspension calculus, and after comparing these three calculi of explicit substitutions , we then concentrate on the implementation of the rewrite rules of eta-reduction in these calculi. We note that it is usual practice when implementing the eta rule for substitution calculi, to mix isolated applications of eta-reduction with the application of other rules of the corresponding substitution calculi. The main disadvantage of this practice is that the eta rewrite rules so obtained are unclean because they have an operational semantics different from that of the eta-reduction of the λ-calculus. For the three calculi in question enlarged with adequate eta rules we show how to implement these eta rules. For the λse we build a clean implementation of the eta rule and we prove that it is not possible to follow the same approach for the λσ and λsusp. (shrink)

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naïve Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's use of Dempster–Shafer updating as a model of belief revision may lead to violations of the AGM axioms (...) for rational belief change. (shrink)

We prove that for sufficiently large \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $n$\end{document}, there are tautologies of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $O(n)$\end{document} that require proofs containing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Omega( n / \log n )$\end{document} lines in axiomatic systems of propositional logic based on the rules of substitution and detachment.

Philosophers have both produced as well as replied to a number of alleged "counter-examples" to the rule of substitution. Recently, Cartwright has urged that the standard reply to at least one of them is inadequate. The counter-example he singles out is:1). Giorgioni is so-called because of his size.2). Giorgiori = Barbarelli :3). Barbarelli is so-called because of his size.Cartwright argues that since 1) and 2) are true while 3) false, substitution has failed. It is argued in reply (...) that, contrary to Cartwright's claim, substitution does not even occur in the above argument. Rather, the meaning of the predicate "is so-called because of his size" changes from 1) to 3), rendering the invalidity the result of equivocation, not the failure of substitution. (shrink)

Research is crucial to advancing knowledge about dementia, yet the burden of the disease currently outpaces research activity. Research often excludes people with dementia and other cognitive impairments because researchers and ethics committees are concerned about issues related to capacity, consent, and substitute decision-making. In Australia, participation in research by people with cognitive impairment is governed by a national ethics statement and a patchwork of state and territorial laws that have widely varying rules. We contend that this legislative variation precludes (...) a consistent approach to research governance and participation and hinders research that seeks to include people with impaired capacity. In this paper, we present key ethical principles, provide a comprehensive review of applicable legal rules in Australian states and territories, and highlight significant differences and ambiguities. Our analysis includes recommendations for reform to improve clarity and consistency in the law and reduce barriers that may exclude persons with dementia from participating in ethically approved research. Our recommendations seek to advance the national decision-making principles recommended by the Australian Law Reform Commission, which emphasize the rights of all adults to make their own decisions and for those with impaired capacity to have access to appropriate supports to help them make decisions that affect their lives. (shrink)

Research is crucial to advancing knowledge about dementia, yet the burden of the disease currently outpaces research activity. Research often excludes people with dementia and other cognitive impairments because researchers and ethics committees are concerned about issues related to capacity, consent, and substitute decision-making. In Australia, participation in research by people with cognitive impairment is governed by a national ethics statement and a patchwork of state and territorial laws that have widely varying rules. We contend that this legislative variation precludes (...) a consistent approach to research governance and participation and hinders research that seeks to include people with impaired capacity. In this paper, we present key ethical principles, provide a comprehensive review of applicable legal rules in Australian states and territories, and highlight significant differences and ambiguities. Our analysis includes recommendations for reform to improve clarity and consistency in the law and reduce barriers that may exclude persons with dementia from participating in ethically approved research. Our recommendations seek to advance the national decision-making principles recommended by the Australian Law Reform Commission, which emphasize the rights of all adults to make their own decisions and for those with impaired capacity to have access to appropriate supports to help them make decisions that affect their lives. (shrink)

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. (...) Among these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

The information explosion and digital modes of learning often combine to inform the quest for the best ways of transforming information in digital form for pedagogical purposes. This quest has become more urgent and pervasive with the ‘turn’ to online learning in the context of COVID-19. This can result in linear, asynchronous, transmission-based modes of teaching and learning which commodify, package and deliver knowledge for individual ‘customers’. The primary concerns in such models are often technical and economic – technology as (...) a cost-effective ‘solution’ to educational challenges. In this paper I argue for the importance of dialogic learning space in teaching and learning by means of Information and Communication Technologies, whether in the form of fully online learning, blended learning or face-to-face encounters using ICT affordances. Although the 20th Century theorists Mikhail Bakhtin (1895–1975) and Hans-Georg Gadamer (1900–2002) produced their seminal works before the advent of ICTs, they were both concerned with the quality and authenticity of human engagement with texts and with other persons and contexts. Besides a shared interest in dialogue as an ontological feature of human life and being, they both used spatiotemporal concepts for understanding and interpreting texts. The article draws on Gadamer’s notions of dialogue and horizon, and Bakhtin’s notions of dialogue and chronotope, to conceptualize dialogic possibilities for online education. Its purpose is to provide a framework, grounded in Bakhtin’s and Gadamer’s ideas, for a dialogic approach to online teaching and learning in higher education. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Fashioning the "Order of Saint Clare." A Rule illuminated by Neri da Rimini:Princeton University Library MS 83 in contextFrances Andrews (bio) and Louise Bourdua (bio)KeywordsRule of Urban IV, Clare of Assisi, Urbanist Clare nuns, Manuscript illumination, Neri da RiminiIntroduction1This interdisciplinary essay is an investigation of an illuminated, early 14th-century copy of the rule of the "Order of Saint Clare" issued by Pope Urban IV in 1263, now (...) in Princeton. It examines the unprecedented visual language adopted in a female Franciscan context to authorize their way of life, and places the manuscript in context, exploring how it relates to other early representations showing Saints Francis and Clare together and documenting the production of this and comparable early rule manuscripts, including a previously unpublished copy now in Venice.2Thousands of manuscript copies of rules of life were produced in and for late medieval religious houses and their members, good numbers of which remain extant, though these are scarce remnants of what must originally have been produced. Rules do sometimes appear in extant library inventories,3 but unlike individual books destined for personal [End Page 75] prayer or study and ultimately deposit in a conventual library, their primary purpose was as legal texts binding all who professed them.4 In their iterative function, read and reread, alone or aloud in the community, they were comparable to liturgical books, though they were not for use in church nor kept in the sacristy.5 In the rule of Urban IV for the Order of Saint Clare investigated here, chapter twenty-four required that the rule be read and explained annually by the visitator, while the final chapter emphasized that it be read once each fortnight lest the sisters neglect it.6 This sort of repetition must have ensured most nuns knew the rule by memory, having first encountered its details as novices, with no need to own the text. Copies were perhaps in the hands of the abbess, a visitator, or other monastic superior, or kept in the chapter room or refectory, ready for routine use.7 Nonetheless, wealthier women may have had a copy prepared or received one as a gift, either on entering the religious life or on becoming a superior responsible for its observance.8Princeton University Library, Manuscripts Division, Department of Rare Books and Special Collections, MS 83, contains a Latin, [End Page 76] professionally made and illuminated copy of the text designed to substitute existing rules, including the 1219 Forma Vitae issued by Cardinal Hugolino and the rule of Innocent IV from 1247.9 Clare's own hard-fought for rule, approved in 1253, was initially for the San Damiano community alone and was followed in subsequent decades by a very small group of houses.10 The making of Urban IV's rule, adopted instead by hundreds of communities, has been much discussed, but the survival of this early illuminated copy has gone unnoticed outside the library catalog.11 The manuscript includes the earliest extant sequence known to us showing Clare of Assisi receiving the rule from the pope and in turn taking the profession of her sisters, images designed to legitimize the new order by building ties to its "founder" while yet acknowledging its papal origins. Among extant imagery it is pioneering. The large, illuminated initials have been recognized as painted by Nerius da Rimini and his workshop but the case has never been set out and PUL MS 83 has [End Page 77] not been included in accounts of this artist's production.12 Better known as "Neri," he is a comparatively well-documented manuscript illuminator whose signatures sometimes survive on his work, a rare practice at this date.13Historians of medieval women religious are by now familiar with books produced by women themselves.14 A beautiful manuscript, for example, containing Bonaventure's Legenda Maior of Saint Francis, the Vita beati Antonii and documents relating to the Portiuncula indulgence was written in Latin in 1337 by two sisters, Elspet von Amberk and Katerina von Purchausen, perhaps living in the Paradies convent in Diessenhofen (Switzerland).15 Other women have been identified as skilled illuminators.16 The prolific activity of... (shrink)

The Corpus Delicti Rule prohibits the introduction of the defendant’s confession to a crime to count as evidence against the defendant in the absence of independent evidence of the crime in question. The common law rule, designed to protect the defendant who confesses to the commission of a fictitious crime, has fallen out of favor with federal courts and a number of state courts. Moreover, the rule has its academic detractors. This essay is an attempt to investigate (...) the value of the rule, the academic criticisms of the rule and to analyze the federal substitute for the rule. If the analysis is not completely astray, the rule serves a most admirable social purpose. The academic arguments are not so telling as to justify jettisoning the rule. Finally, the federal rule is argued to be either completelyinadequate a protection or an adequate protection only to the extent that the federal substitute is coextensive with the rule it is designed to replace, namely, the original Corpus Delicti Rule. (shrink)

The Corpus Delicti Rule prohibits the introduction of the defendant’s confession to a crime to count as evidence against the defendant in the absence of independent evidence of the crime in question. The common law rule, designed to protect the defendant who confesses to the commission of a fictitious crime, has fallen out of favor with federal courts and a number of state courts. Moreover, the rule has its academic detractors. This essay is an attempt to investigate (...) the value of the rule, the academic criticisms of the rule and to analyze the federal substitute for the rule. If the analysis is not completely astray, the rule serves a most admirable social purpose. The academic arguments are not so telling as to justify jettisoning the rule. Finally, the federal rule is argued to be either completelyinadequate a protection or an adequate protection only to the extent that the federal substitute is coextensive with the rule it is designed to replace, namely, the original Corpus Delicti Rule. (shrink)