Many states prohibit patients from appointing their physicians as health care proxies, fearing paternalism and conflict of interest. But the potential for conflict is not unique to physicians, and patients may have compelling reasons to prefer that their doctor make decisions on their behalf. Managing potential conflicts serves patients better than denying them the right to choose who will make health care decisions for them when they are no longer competent.

Drawing on a landscape analysis of existing data-sharing initiatives, in-depth interviews with expert stakeholders, and public deliberations with community advisory panels across the U.S., we describe features of the evolving medical information commons. We identify participant-centricity and trustworthiness as the most important features of an MIC and discuss the implications for those seeking to create a sustainable, useful, and widely available collection of linked resources for research and other purposes.

Vol. 1. Ars logica seu de forma et materia ratiocinandi -- v. 2. Naturalis philosophiae I. pars. De ente mobili in communi. III. pars. De ente mobili corruptibili -- v. 3. Naturalis philosophiae IV. pars. De ente mobili animato.

As a work of a scholarship it seems to me to compare favourably with the best books on the subject, including those by Marcus Singer and Onora Nell.' Prof.

The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...) it. Two such discourse-texts are said to have the same grammatical form, in this sense, if a uniform one-one substitution of content words transforms the one exactly into the other. The sentence ‘Abe properly respects every agent who respects himself’ may be regarded as having the same grammatical form as the sentence ‘Ben generously assists every patient who assists himself’. (shrink)

A Inseparabilidade entre Lógica e a Ética. Philósophos. 18 (2013) 245–259. Portuguese translation by Décio Krause and Pedro Merlussi: The Inseparability of Logic and Ethics, Free Inquiry, Spring 1989, 37–40. This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science of justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless (...) without rigor and objectivity. The logician’s advice to be dispassionate is in resonance and harmony with the ethicist’s advice to be compassionate. (shrink)

"From the 1930 Reiser edition of the Ars logica, itself comprising the first two parts of the five part Cursus philosophicus of 1631-1635, by the same author.".

Em linguística gerativa, distinguem-se várias propriedades formais dos sistemas representacionais: a infinidade discreta, a finitude discreta e a infinidade do contínuo. Não é frequente filósofos aplicarem essas distinções ao estudo da forma lógica. O fato de essas distinções serem raramente aplicadas resultou em os filósofos pressuporem, geralmente sem discutir, que todas as formas lógicas apresentam una infinidade discreta, como o faz a linguagem natural. Este artigo defende a existência de outros tipos de forma lógica, além daquela que apresenta infinidade discreta. (...) Na representação mental é possível encontrar formar apresentando infinidade contínua e finitude discreta, além da infinidade discreta. Além disso, tais representações mantêm relações lógicas entre si, parcialmente em virtude dessas formas. Isso equivale à alegação de que o estudo da lógica natural precisa ir além da faculdade de linguagem, abrangendo formas lógicas pertinentes a representações mentais que não se assemelham a sentenças. Isso incluiria formas lógicas pictóricas. O ponto final é que, no estudo da lógica natural, é preciso considerar as formas lógicas representadas a sistemas mentais que antecedem a evolução da linguagem. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Resumo: Ludwig Wittgenstein tentou desenvolver, desde 1929, uma abordagem à filosofia da lógica em termos de escalas de medição. Embora mostrasse grande sensibilidade a diversos tipos de escalas, Wittgenstein não estava bem posicionado para fazer seu projeto render frutos, porque a teoria das medidas não começou a fazer avanços significativos antes do final da década de 1940, e continuou desfrutando de um progresso relevante, até os anos 80. Não obstante, nas suas obras e palestras dos anos 30, Wittgenstein fez diversas (...) tentativas de entender a lógica, ou a “gramática” da linguagem religiosa e ética relativa à medição. Este artigo é uma tentativa de desenvolver algumas dessas ideias que ocorreram a Wittgenstein, na sua fase intermediária, dentro do contexto da evolução posterior da teoria da medição. Especificamente, defende-se que as linguagens religiosa e ética são formas extremas de medição, não empíricas nem fatuais. Elas representam o caso-limite da medição.: Ludwig Wittgenstein attempted to develop an approach to the philosophy of logic in terms of measurement scales. While he showed great sensitivity to different kinds of scaling, Wittgenstein was not in a good position to bring this project to fruition; measurement theory did not begin to develop significantly until the late 1940s, and only made pertinent advances as late as the 1980s. However, in writings and lectures from the 1930s, Wittgenstein made a number of attempts to understand the logic, or “grammar”, of religious and ethical language in relation to measurement. This article is an attempt to develop some of these nascent ideas in intermediate Wittgenstein in terms of later developments in measurement theory. Specifically, it is argued that religious and ethical language are extreme forms of non-empirical and non-factual forms of measurement; they represent the limit-case of measurement. (shrink)

This book makes available for the first time an English translation of William of Ockham's work on Aristotle's _Posterior Analytics_, which contains his theory of scientific demonstration and philosophy of science. John Lee Longeway also includes an extensive commentary and a detailed history of the intellectual background to Ockham's work. He puts Ockham into context by providing a scholarly account of the reception and study of the _Posterior Analytics_ in the Latin Middle Ages, with a detailed discussion of Robert (...) Grosseteste, Albert the Great, Thomas Aquinas, Duns Scotus, and Giles of Rome. In a series of appendices, Longeway includes shorter translations of some important related work by Giles of Rome and John of Cornwall. In his introductory discussion, Longeway examines the exact character of the highest sort of demonstration, the relations of the empirical sciences to mathematics, natural causation and the manner in which natural laws come to be known, the possibility of natural knowledge, our knowledge of God, and the relation of theology to the other sciences. Longeway discusses the way in which scientific epistemology and theory of demonstration corresponds to the metaphysical position of its interpreter, in particular to the Neoplatonism of Grosseteste, the radical Aristotelianism of Giles of Rome and Albert the Great, the more moderate Aristotelianism of Aquinas, and the nominalistic empiricism of Ockham. Throughout the book, Longeway makes a case for Ockham's importance as the founder of empiricism in the West. _ “The present work is the result of decades of study of Ockham's philosophy of science. The translation and commentary are introduced by a chapter in which Longeway presents an overview of Ockham's thought in this area and highlights its philosophical significance. This introduction is in its own right a significant contribution to the history of philosophy.” — Owen Goldin, Marquette University_ "Like much else in medieval philosophy, medieval theories of demonstrative knowledge are historically important, philosophically interesting, and little understood. There are a few extensive studies into medieval discussions of demonstration and even fewer translations of these important discussions. Longeway's_ Demonstration and Scientific Knowledge in William of Ockham_ is, therefore, an important contribution to the field. This work contains not only an extensive set of translations of Ockham's work on the theory of demonstration, but also a book-length introduction in which Longeway surveys the development of medieval theories of demonstration prior to Ockham and situates Ockham's discussion within that development. The book will be of value to any scholar interested in Ockham's thought as well as to anyone interested more generally in medieval discussions of demonstration, science, and epistemology." —_Susan Brower-Toland, Saint Louis University_. (shrink)

A colleague’s personal recollections of Jean van Heijenoort’s contributions to the editing of volumes I–III of Gödel’s Collected Works and of his interactions with the other editors.

It is argued that indicative conditionals are best viewed as having truth conditions (and so they are in part factual) but that these truth conditions are ‘gappy’ which leaves an explanatory gap that can only be filled by epistemic considerations (and so indicative conditionals are in part epistemic). This dual nature of indicative conditionals gives reason to rethink the relationship between logic viewed as a descriptive discipline (focusing on semantics) and logic viewed as a discipline with a normative import (focusing (...) on epistemic notions such as ‘reasoning’, ‘beliefs’ and ‘assumptions’). In particular, it is argued that the development of formal models for epistemic states can serve as a starting point for exploring logic when viewed as a normative discipline. (shrink)

"From the 1930 Reiser edition of the Ars logica, itself comprising the first two parts of the five part Cursus philosophicus of 1631-1635, by the same author.".

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...) and a deductive logic by which the steps of the deduction proceed. Every demonstration produces knowledge of its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand. (shrink)

I note that the logics of the relevant group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A.AB).AB and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverA B is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.

Italian translation of "Schaum's Outline of Theory and Problems of Logic" (1988).

The species of indeterminist tense logic called Peircean by A. N. Prior is proved to be recursively decidable.

When a belief set is contracted only some beliefs are eligible for removal. By introducing eligibility for removal as a new semantic primitive for contraction and combining it with epistemic entrenchment we get a contraction operator with a number of interesting properties. By placing some minimal constraint upon eligibility we get an explicit contraction recipe that exactly characterises the so called interpolation thesis, a thesis that states upper and lower bounds for the amount of information to be given up in (...) contraction. As a result we drop the controversial property of recovery. By placing additional constraints on eligibility we get representation theorems for a number of contraction operators of varying strength. In addition it is shown that recovery contraction is a special case that we get if eligibility is explicitly constructed in terms of logical relevance. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abailard and the Problem of Universals JOHN F. BOLER ABAILARD t IS A CLEVERman, but in one respect he is just like the rest of us: Given one clear idea of which he is convinced, he tends to become intolerant, thinking the worst of everyone else. Abailard's clear idea goes something as follows. In what does universality consist? It consists, says Abailard, in the signifying of many things (...) by one sign? Abailard's predecessors had been searching for some thing which was universal. But a sign must signify many things to be universal; and furthermore, the sign itself, as a thing--a noise, gesture, or statue--is individual. ~ It may help to describe the model which crops up here and there in Abailard's examples and which, I think, dominates his analysis. Consider, then, a statue which is not meant to stand for any one particular individual: for example, the Minute Man at Concord, Massachusetts.* First of all, the statue is an individual thing. Second, just as a piece of metal, it need not stand for anything--anymore than a bird bath would, had the town council decided to build that instead. What is more, it is information from other sources which leads us to take the statue as "general" rather than as depicting some individual (like Nathan Hale). And even though the statue stands for "all" minute men, not only is the statue an individual thing but all those things for which it stands are (or were) individuals. And finally, we might also point out that the statue must be taken as signifying; it does not have "representative" qualities in quite the same way that it has properties like weight and shape. t The text of Abailard to which I have referred is: Peter Abaelards Philosophische Schrqte, herausgegeben yon Dr. Bernhard Geyer, I Die Logica "Ingredientibus,'" II Die Logica "'Nostrorum Petitioni Sociorum" which is to be found in Beitraege zur Geschichte der Philosophie und Theologie des Mittelalters, Band XXI (1933). A partial translation of this text appears in R. McKeon, Selections from Medieval Philosophers (New York: Scribners, 1929), II, 208-258. Hereafter I shall refer to the latin text as "G" followed by the page number and lines; and to the translation, where possible, as "'M" with the page number. 9Abailard feels that when Aristotle says that a universal is what is fitted for being predicated of many things, it is the signifying of many things which is at stake; and he chides Aristotle for seeming to ascribe universality to things as well as to words. G ~ (M 221). The reference to Aristotle is On Interpretation, 17a (38-40). *See note 7, below. 9I have interpolated on two passages: G 22t~-~ (M 241-242), and G 522*t-=. [37] 38 HISTORY OF PHILOSOPHY The upshot of Abailard's insight is that universality pertains to the interpretation of signs: the effort to locate universal things is misguided. Some want to say that the universal is a collection; but do collections signify their members? ~ Some want to say that the universal is a substance of which individuals are accidents; but is a substance predicated of its accidents? e And some want to say that universals are words--that is noises; but noises are also individual things. ~ In short, to signify or to show ("monstrare") pertains to words; to be signified or shown pertains to things. 8 And to transfer the properties of one to the other leads to hopeless difficulties. ~ One can understand Abailard's exultation (and exaltation) at having shown both sides of a seething controversy to be equally misguided? ~ But what then remains as the problem of universals? It is this: one would expect that every sign would have some subject which it signifies; but universals seem to lack a proper subject. And does this not mean that universals are fictions (like goat-stag or chimera)? = Having thus set out rather baldly what I take to be Abailard's "clear idea," let me now try to show more fully how he goes about establishing the problem and providing for a solution. Abailard's position on universals is set forth in his two logic books, both of which begin... (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Investigamos a lógica de Leonhard Euler com ênfase no papel dos “diagramas de Euler”. Concluímos que os referidos diagramas constituem um instrumento intuitivo, embora não sistemático, para determinar validade na silogística tradicional, isto é, a silogística munida de implicações conversacionais. Nisto, contrastam-se com os diagramas de Venn que constituem um instrumento sistemático, porém menos intuitivo, para determinar validade numa silogística mais voltada para os fundamentos da matemática moderna.: We investigate the logic of Leonhard Euler, giving emphasis to the role of (...) “Euler diagrams”. We conclude that these diagrams are an intuitive, non-systematic instrument for determining validity in the traditional syllogistic, that is, the syllogistic furnished with conversational implications. In this regard, they contrast with Venn diagrams which are a systematic, less intuitive instrument for determining validity in a syllogistic more appropriate for the foundation of modern mathematics. Keywords: History of Logic. Leonhard Euler. Euler Diagrams. Venn Diagrams. (shrink)

English translation of an entry on pages 137–42 of the Spanish-language dictionary of logic: Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta. -/- DEDICATION: To my friend and collaborator Kevin Tracy. -/- This short essay—containing careful definitions of ‘counterargument’ and ‘counterexample’—is not an easy read but it is one you’ll be glad you struggled through. It contains some carefully chosen examples suitable for classroom discussion. -/- Using the word ‘counterexample’ instead of ‘counterargument’ in connection with Aristotle’s invalidity (...) proofs leads to a misinterpretation of Aristotle’s intentions. The two relations expressed by these two words are drastically different—as explained in this essay. There is however a subtle overlap: Every argument that is a counterargument for a given argument is a counterexample to the universal proposition that every argument in the same form as the given argument is valid. The word ‘counterexample’ was coined in the 1800s. The word ‘counterargument’ was given this sense in the 1960s. Saying that one argument is a counterexample for another argument is bad English—taking the word ‘counterexample’ in its Standard English sense. The word ‘counterinstance’ is an exact synonym for ‘counterexample’. Which logic books define ‘counterinstance’ or ‘counterexample’? Who started using ‘counterinstance’ or ‘counterexample’ in the sense of ‘counterargument’? Did they note that they were not using the word in the Standard sense? Why did it catch on? -/- Also see: https://www.academia.edu/8840909/Argumentations_and_logic_1989_ . (shrink)

We begin with an introductory overview of contributions made by more than twenty scholars associated with the Philosophy Department at the University of Buffalo during the last half-century to our understanding and evaluation of Aristotle's logic. More well-known developments are merely mentioned in..

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...) weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself.Em sua forma mais forte e geral, o princípio da referência universalista afirma que toda proposição refere-se ao universo completo do discurso propriamente dito, independentemente de quão limitados sejam os referentes de seus termos não-lógicos ou com conteúdo. Embora Boole mudasse de um modelo monístico de universo-fixo nos seus trabalhos iniciais de 1847 e 1848 para um modelo pluralista de universo-múltiplo no seu tratado maduro de 1854, ele nunca hesitou em sua aceitação franca do princípio da referência universalista, possivelmente em uma forma ligeiramente mais fraca. De fato, ele considerou este princípio como um acompanhamento essencial para a sua teoria de formação de conceitos e de proposições. Visões semelhantes são encontradas em lógicos posteriores, e algumas das mais recentes formulações da lógica clássica de primeira ordem parecem estar de acordo com uma forma deste, se é que elas não implicam, de fato, o próprio princípio. (shrink)

Down through the ages, logic has adopted many strange and awkward technical terms: assertoric, prove, proof, model, constant, variable, particular, major, minor, and so on. But truth-value is a not a typical example. Every proposition, even if false, no matter how worthless, has a truth-value:even “one plus two equals four” and “one is not one”. In fact, every two false propositions have the same truth-value—no matter how different they might be, even if one is self-contradictory and one is consistent. It (...) is not such a big surprise that every true proposition, no matter how worthless, has a truth-value. Every proposition, whether valuable or worthless, has a truth-value.But it is a little strange that every two true propositions, no matter how different they might be, have the same truth-value. The Pythagorean Theorem has the same truth-value as the proposition that one is one. It is a stretch to think of truth-values as values in any of the normal senses of the word ‘value’. (shrink)

The first mention of the concept of an inconsistency measure for sets of formulas in first-order logic was given in 1978, but that paper presented only classifications for them. The first actual inconsistency measure with a numerical value was given in 2002 for sets of formulas in propositional logic. Since that time, researchers in logic and AI have developed a substantial theory of inconsistency measures. While this is an interesting topic from the point of view of logic, an important motivation (...) for this work is also that some intelligent systems may encounter inconsistencies in their operation. This research deals primarily with propositional knowledge bases, that is, finite sets of propositional logic formulas. The goal of this paper is to extend the concept of inconsistency measure in a formal way to sets of formulas with the modal operators “necessarily” and “possibly” applied to propositional logic formulas. We use frames for the semantics, but in a way that is different from the way that frames are commonly used in modal logics, in order to facilitate measuring inconsistency. As a set of formulas may have different inconsistency measures for different frames, we define the concept of a standard frame that can be used for all finite sets of formulas in the language. We do this for two languages. The first language, AMPL, contains formulas where a prefix of operators is applied to a propositional logic formula. The second language, CMPL, adds connectives that can be applied to AMPL formulas in a limited way. We show how to extend propositional logic inconsistency measures to such sets of formulas. Finally, we define a new concept, weak inconsistency measure, and show how to compute it. (shrink)

Following Quine [] and others we take deductions to produce knowledge of implications: a person gains knowledge that a given premise-set implies a given conclusion by deducing—producing a deduction of—the conclusion from those premises. How does this happen? How does a person recognize their desire for that knowledge of a certain implication, or that they lack it? How do they produce a suitable deduction? And most importantly, how does their production of that deduction provide them with knowledge of the implication. (...) What experienceable sign reveals to the reasoner that they achieved the desired knowledge? If a deduction is an array of inscriptions constructed by following syntactical—mechanical, machine-performable—rules as suggested by Tarski, Carnap, Church, and others, the epistemic question becomes even more pressing and more challenging. Moreover, deduction, the ability to produce deductions and to recognize them when produced, is operational knowledge that presupposes other component operations such as recognizing characters, making assumptions, inferring conclusions from premises, chaining inferences [AL]. (shrink)

A universal proposition is shown false by a known counterexample. A premise-conclusion argument is shown invalid by a known counterargument. The failure to distinguish counterexample from counterargument is like the failure to distinguish falsehood from invalidity.

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It (...) is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories. (shrink)

This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R S4or R M. The technique is to construct an extension of the well known entailment matrix set M 0and show that the model of the deontic formula P (A v B). PA v PB (...) is excluded. (shrink)

The paper presents a brief survey of recent work by Metakides, Nerode and others in the area of effective algebra and makes some comments on the relation between formal presentations, characterizations, etc. of sets and of algebraic structures and their practical presentations.