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1. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection Logics admitting inconsistency (paraconsistent Logics, discussive Logics, etc.) 03B53 Logics and related algebras (e.g., diagonalizable algebras) http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_33.htm

linear integral equations # systems of linear integral equations # systems of nonsingular linear integral equations # systems of singular linear logic and other substructural logics linear logic, Lambek calculus, BCK and BCI logics) # substructural logics (including relevance, entailment, linear mappings, matrices, determinants, theory of equation) # linear algebra. multilinear algebra. (vector spaces, linear models # generalized linear operators linear operators # equations and inequalities involving linear operators # equations with linear operators # general theory of linear operators # groups and semigroups of linear operators # special classes of linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) # functions whose values are linear operators as elements of algebraic systems # individual linear operators) # linear relations (multivalued linear operators, their generalizations and applications # groups and semigroups of linear operators, with operator unknowns # equations involving

2. 03Bxx 03B05 Classical propositional logic; 03B10 Classical firstorder logic 68T37, 94D05; 03B53 Logics admitting inconsistency (paraconsistent Logics, http://www.ams.org/msc/03Bxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions General logic 03B05 Classical propositional logic 03B10 Classical first-order logic 03B15 Higher-order logic and type theory 03B20 Subsystems of classical logic (including intuitionistic logic) 03B22 Abstract deductive systems 03B25 Decidability of theories and sets of sentences [See also 03B30 Foundations of classical theories (including reverse mathematics) [See also 03B35 Mechanization of proofs and logical operations [See also 03B40 Combinatory logic and lambda-calculus [See also 03B42 Logic of knowledge and belief 03B44 Temporal logic ; for temporal logic see ; for provability logic see also 03B48 Probability and inductive logic [See also 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness [See also 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) 03B55 Intermediate logics 03B60 Other nonclassical logic 03B65 Logic of natural languages [See also 03B70 Logic in computer science [See also 68-xx 03B80 Other applications of logic 03B99 None of the above, but in this section

3. List KWIC DDC And MSC Lexical Connection Logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI Logics) substructural 03B47 Logics admitting inconsistency http://www.mi.imati.cnr.it/~alberto/dml_11_29.htm

linear integral equations # systems of singular linear logic and other substructural logics linear models # generalized linear operators linear operators # equations and inequalities involving linear operators # equations with linear operators # general theory of linear operators # groups and semigroups of linear operators # special classes of linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) # functions whose values are linear operators as elements of algebraic systems # individual linear operators) # linear relations (multivalued linear operators, their generalizations and applications # groups and semigroups of linear operators, with operator unknowns # equations involving linear operators, with vector unknowns # equations and inequalities involving linear operators; topological tensor products; approximation properties # spaces of linear optimal control problems linear parabolic PDE; boundary value problems for nonlinear parabolic PDE # nonlinear boundary value problems for linear programming linear programming linear programming (transportation, multi-index, etc.) # special problems of

4. 03Bxx 03B53, Logics admitting inconsistency (paraconsistent Logics, discussive Logics, etc.) 03B55, Intermediate Logics. 03B60, Other nonclassical logic http://www.impan.gov.pl/LIB/MSC/03Bxx.html

General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic Modal logic ; for temporal logic see ; for provability logic see also Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) Intermediate logics Other nonclassical logic Logic of natural languages [See also Logic in computer science [See also 68-XX Other applications of logic None of the above, but in this section

5. HeiDOK 03B53 Logics admitting inconsistency (paraconsistent Logics, discussive Logics, etc.) ( 0 Dok. ) 03B55 Intermediate Logics ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?anzahl=0&la=de&

6. Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical Logic A Currently firstorder language is a redirect to first-order logic, which contains . edit 03B53 Logics admitting inconsistency (paraconsistent Logics, http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathematics/PlanetMath_Exchan

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations From Wikipedia, the free encyclopedia Wikipedia:WikiProject Mathematics PlanetMath Exchange Jump to: navigation search This page provides a list of all articles available at PlanetMath in the following topic: 03-XX Mathematical logic and foundations This list will be periodically updated. Each entry in the list has three fields: PM WP Status status entries are: Status means PM article N not needed A adequately covered C copied M merged NC needs copying NM needs merging Please update the WP and Status fields as appropriate. if the WP field is correct please remove the qualifier "guess". If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link. If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry. If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable. Don't forget to include the relevant template if you copy over text or feel like an external link is warranted See the main page for examples and usage criteria.

7. PlanetMath: Neutrosophic Logic 03B53 (Mathematical logic and foundations General logic Logics admitting inconsistency ). 03B60 (Mathematical logic and foundations General logic http://planetmath.org/encyclopedia/NeutrosophicLogic.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About neutrosophic logic (Definition) A logic , in which each proposition is estimated to have the degree of truth in , the degree of indeterminacy (neither true nor false) in , and the degree of false in , is called neutrosophic logic , where are standard or non-standard real subsets of the non-standard unit interval are called neutrosophic components Now let's explain the previous notations: A number is said to be infinitesimal if and only if for all positive integers one has . Let be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Generally, for any real number one defines which signifies a monad , i.e. a set of hyper-real numbers in

8. MSC2000 03B52 Fuzzy logic; logic of vagueness ( 0 Dok. ) 03B53 Logics admitting inconsistency (paraconsistent Logics, discussive Logics, etc.) ( 0 Dok. http://elib.uni-stuttgart.de/opus/msc_ebene3.php?zahl=03B&anzahl=0&la=de

9. General General Mathematics Mathematics For Nonmathematicians 94D05 Logics admitting inconsistency (paraconsistent Logics, discussive Logics, etc.) Intermediate Logics Other nonclassical logic Logic of natural http://amf.openlib.org/2001/msc2000.xsd

10. 362/369 (Total 5522) NO 107 03C20 Ultraproducts Translate this page 96, 03B60, Other nonclassical logic. 95, 03B55, Intermediate Logics. 94, 03B53, Logics admitting inconsistency (paraconsistent Logics, discussive Logics, http://www.mathnet.or.kr/mathnet/msc_list.php?mode=list&ftype=&fstr=&page=362

11. Os Dois Artigos Abaixo Foram Publicados No Jornal Gazeta Do Povo Translate this page Após 2000, Mathematical Reviews tornou o verbete Paraconsistent Logic mais amplo, 03B53 Logics admitting inconsistency (paraconsistent Logics, http://www.cfh.ufsc.br/~dkrause/LogicaI/paraconsistente.html

Os dois artigos abaixo foram publicados no jornal Gazeta do Povo (Curitiba) em 29 e 30 de Abril de 1998 respectivamente. O interessado pode consultar também ' Sistemas Formais Inconsistentes A LÓGICA PARACONSISTENTE (Parte 1) Faro número 1: em 1997, realizou-se em Gent, na Bélgica, o Primeiro Congresso Mundial sobre Paraconsistência. Fato número 2: a partir de 1991, a celebrada Mathematical Reviews passou a contar com o verbete 00B38: Paraconsistent Logic (Lógica Paraconsistente). O que isso significa? A resposta é que, em termos de ciência, e em especial de ciência brasileira, isso significa muito, como veremos na seqüência. Mathematical Reviews é uma publicação mensal da American Mathematical Society que traz resenhas (que podem ser meramente descritivas ou críticas) de artigos veiculados nas mais importantes publicações (revistas, livros, atas de congressos) do que se considera "matemática" presentemente. É importante frisar que o que é ou deixa de fazer parte de uma disciplina, como a matemática, depende de vários fatores, e muda com o tempo. Para citar um exemplo, no século XVII a astrologia era catalogada como fazendo parte da matemática, o que não ocorre mais hoje em dia. De tempos em tempos, o comitê editorial de Mathematical Reviews (e de sua similar alemã Zentralblatt für Mathematik ) revisa as subdivisões do que se poderia chamar de "matemática do momento", por vezes suprimindo assuntos que deixaram de ter interesse ou acrescentando outros que se evidenciaram como importantes a ponto de constar como uma nova subdivisão de alguma área, como é o caso da Lógica Paraconsistente (que faz parte da Seção 03: Lógica e Fundamentos). Portanto, o Fato 2 acima atesta que tais lógicas e, de modo mais amplo, os trabalhos que podem ser qualificados sob tal código, passaram a constituir tópico oficial da matemática de hoje. Em suma, criou-se uma nova área da matemática.

12. Recent Publications Here we prove the important theorems of the Logics, and describe and justify the dangers of inconsistency when functions and nondeterminacy intermix. http://www.computing.dcu.ie/~jmorris/recabstracts.html

Joseph M. Morris Selected Research Publications Please e-mail me at "Joseph dot Morris at computing dot dcu dot ie" if you would like a copy of any paper that you cannot get hold of. Term Transformer Semantics , ACM Transactions on Programming Languages and Systems (TOPLAS), submitted for publication, 1999. Many-valued Logics for Programming: Theorems and Proofs , Report R-1999-49 Dept of Computing Science, University of Glasgow, 1999. E EC EB , and are members of a family of many-valued logics for reasoning equationally about programs and specifications. EC is also three-valued, but designed to accommodate nondeterminacy rather than partiality. is a four-valued logic that accommodates both partiality and nondeterminacy. EB is also four-valued, and supports nondeterminacy and miracles (i.e. empty choices); it is designed to support bunch theory. All of them are derived from the logic E of Dijkstra and Feijen. Their theory has been described elsewhere (see ''Partiality and Nondeterminacy in Program Proofs''; ''E3: A Logic for Reasoning Equationally in the Presence of Partiality'', and ''A Theory of Bunches''). Here we prove the important theorems of the logics, and describe and justify the proof techniques that allow them to be used effectively in proof engineering. The paper is a reference manual written partly as a definitive record of the family of logics, and partly in response to the requests we have received to prove this or that theorem.

13. J Logic Computation -- Sign In Page C also has as extensions a host of wellknown Logics admitting the weakening axiom Paraconsistent Logic Essays on the Inconsistent , Philosophia pp. http://logcom.oxfordjournals.org/cgi/content/full/16/4/405

@import "/resource/css/hw.css"; @import "/resource/css/logcom.css"; Skip Navigation Oxford Journals Contact Us My Basket ... Volume 16, Number 4 Pp. 405-422 This item requires a subscription* to Journal of Logic and Computation Online. * Please note that articles prior to 1996 are not normally available via a current subscription. In order to view content before this time, access to the Oxford Journals digital archive is required. If you would like to purchase short-term access you must have a personal account. Please sign in below with your personal user name and password or register to obtain a user name and password for free. Full Text Proof Theory for Casari's Comparative Logics Metcalfe J Logic Computation. To view this item, select one of the options below: Sign In User Name Sign in without cookies. Can't get past this page? Help with Cookies. Need to Activate? Password Forgot your user name or password? Purchase Short-Term Access Pay per View - If you would like to purchase short-term access you must have a personal account. Please sign in with your personal user name and password or register to obtain a user name and password for free. You will be presented with Pay per Article options after you have successfully signed in with a personal account.

14. Weber, S.: Investigations In Belnap's Logic Of Inconsistent And Unknown Informat DISCUSSION 57 { An inconsistency adaptive logic, which { according to Batens identified sublanguages Li of LM each admitting unique preferred models, http://lips.informatik.uni-leipzig.de/pub/1998-13/en

Category Value Available via http://lips.informatik.uni-leipzig.de:80/pub/1998-13/en Submitted on 3rd of December 1998 Author Weber, S. Title Investigations in Belnap's Logic of Inconsistent and Unknown Information Date of publication 19th of October 1998 Citation Number of pages Language English Organization The Faculty of Mathematics and Computer Science The Institute of Computer Science Type Ph.D. thesis Subject group Mathematics; Computer Science, Data Processing Abstract Keywords Multi-valued Logic, Nonmonotonic Logic, Paraconsistency Contact address mailto:s-weber@itsec-debis.de Source(s) Postscript ( ps ps.gz [ 506224 bytes ] , ps.zip PDF ( pdf pdf.gz [ 859148 bytes ] , pdf.zip Plain text ( text text.gz [ 332059 bytes ] , text.zip Pagewise preview Management of the document by diss@ub.uni-leipzig.de ... Leipzig University Multimedia Publication Server

15. Sample Chapter For Hannan, M.T., Pólos, L., Carroll, G.R.: Logics Of Organizati Perhaps the reason for sociologists’ reluctance to admit that their theoretical The parallel to inconsistency in a classical logic shows up in the http://press.princeton.edu/chapters/s8550.html

Book Search: Keywords Author Title or ISBN More Options Power Search Search Hints Google contents of this website: Google full text of our books: Logics of Organization Theory: Audiences, Codes, and Ecologies Book Description Endorsements Table of Contents Class Use and other Permissions . For more information, send e-mail to permissions@press.princeton.edu This file is also available in Adobe Acrobat PDF format Chapter One Language Matters Sociological theorists rarely give explicit attention to the language used in formulating arguments and drawing conclusions. We argue that attention ought to be paid to the choice of a theoretical language. This chapter discusses such language matters; and it also argues that choice of a language matters for what a theory can express and whether (and how) it can unify fragmentary knowledge. 1.1 LANGUAGES FOR THEORY BUILDING Sociological theories can be built and arguments can be unified without any special tools or methodologies. However, we believe that attempts in this direction face daunting challenges. The essential problem lies with language, with the natural language used in most sociological theory. Natural languages such as English and Hungarian are less-than-perfect tools for eliminating ambiguity in the claims that one might wish to make. In fact, ambiguity normally comes in two varieties.

16. Discriminations: John Edwards’ Inconsistency Regarding Privilege And Preference The fact that race prefs usually result in admitting less qualified applicants Yet we all keep hoping that rational arguments and logic and common sense http://www.discriminations.us/2004/01/john_edwards_inconsistency_reg.html

Discriminations cogitations declarations contemplations inspirations conversations ruminations Main John Edwards’ Inconsistency Regarding Privilege And Preferences In a USA Today column today, John Edwards once again eloquently assails legacy preferences as virtually un-American. In America, the kind of family you come from should never determine your destiny. All children in America should have the same opportunities — wherever they come from or whatever their backgrounds.... Equal opportunity is the birthright of every American. Legacy preferences get in the way. It's time for them to go. In John Edwards’ America, however, it is apparently acceptable for race to “determine your destiny,” for students to have greater or lesser opportunities because of their race, and for the birthright of “equal opportunity” to co-exist comfortably with the practice of judging individuals of different races by different standards. Overstated? I don’t think so. Edwards not only supports “diversity,” but along with some of the most liberal Senators (Daschle, Kennedy, Clinton, Corzine, Durbin, Kerry, Schumer, Lautenberg, Landrieu, Stabenow) he co-signed an amicus brief in Gratz supporting the University of Michigan’s policy of awarding 20 admission points (out of 150 needed) to minority applicants on the basis of their race alone. (That same policy awarded only 4 points to legacies.)

17. Toward A New Landscape Of Systems Management In An Autonomic Computing Environme Ontologies and description Logics. Ontologies are metadata schemas, Observe that, if this is not the case, then there is an inconsistency in the class http://www.entrepreneur.com/tradejournals/article/98695293_2.html

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18. Toward A New Landscape Of Systems Management In An Autonomic Computing Environme One of the most expressive description Logics studied so far is DER. form of knowledge assertions while still admitting decidable reasoning procedures. http://findarticles.com/p/articles/mi_m0ISJ/is_1_42/ai_98695293/pg_5

@import url(/css/us/pub_page_article.css); @import url(/css/us/template_503.css); @import url(/css/us/tabs_503.css); @import url(/css/us/fa_bnet.css); @import url(http://i.bnet.com/css/fa.css); BNET Research Center Find 10 Million Articles BNET.com Advanced Search Find in free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology Explore Publications in: all Arts Autos Business ... Technology Content provided in partnership with FIND IN free and premium articles free articles only premium articles only this publication Arts Autos Business Health News Reference Sports Technology Advanced Search print share ... link Toward a new landscape of systems management in an autonomic computing environment IBM Systems Journal March, 2003 by Giovanni Lanfranchi Pietro Della Peruta Antonio Perrone Diego Calvanese ... < Page 1 Continued from page 4. Previous Next 1. A description language, which specifies how to construct complex concept and relation expressions, by starting from a set of atomic concepts and relations and by applying suitable constructs 2. A knowledge specification mechanism, which specifies how to construct a description logic knowledge base, in which properties of concepts and relations are specified by means of suitable assertions

19. Accident Can military command be charged with the fallacy of inconsistency? PC The Charter of Twin Oaks Country Club expressly forbids admitting Jews and http://www.drury.edu/ess/Logic/Informal/Accident.html

FALLACY OF ACCIDENT I. Case studies A. The "rules of war" developed in the West (by way of Just War theory) include the principle: noncombatants are not legitimate targets of violence. Attacks on civilian targets are hence immoral. This is called the principle of immunity for noncombatants. Our military command is faced with the following situation in war: one of the enemy's key military headquarters is situated directly across the street from a civilian hospital. The headquarters is a legitimate, indeed, critical target. But the nature of conventional bombing techniques means that any attack on the headquarters is certain to also involve hits on the hospital and thus result in civilian deaths. Military command issues a statement: we uphold just war theory, and remain committed to the principle of immunity for noncombatants. We are also ordering a bombing attack on enemy headquarters, which will result in civilian deaths. Can military command be charged with the fallacy of inconsistency B. Traditional Catholic moral theory insists that the legal/moral/spiritual person begins at the moment of conception; to kill the conceptus/fetus/unborn baby is thus to commit murder. Consequently, abortion is strongly opposed.

20. Intuitionistic Arithmetic - Sci.logic | Google Groups inconsistency. Just in case of confusion, he means two meanings of function . admitting that the orthodox line has (for now at least) http://groups.google.co.vi/group/sci.logic/msg/f38527d6461bbd80

Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Intuitionistic Arithmetic The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful Herman Jurjus View profile More options Nov 15, 7:58 am Newsgroups: sci.logic From: Date: Thu, 15 Nov 2007 12:58:47 +0100 Local: Thurs, Nov 15 2007 7:58 am Subject: Re: Intuitionistic Arithmetic Reply Reply to author Forward Print ... Find messages by this author Bill Taylor wrote: >>> of intuitionistic analysis that prove "every function is continuous" >>> whereas in classical analysis you prove "not every function is >>> continuous". That seems pretty inconsistent to me. > Just in case of confusion, he means - two meanings of "function". > For the intuitionist, the pairs must be related by a "constructive" > meaning: "If you want to get n dec-places of output, you must

21. Contents Of Krisis, Nr. 7/1998 In particular, the interpretation in terms of threevalued Logics offered . We want to suggest that admitting types and degrees of possibility (assumed http://fil.unibuc.ro/krisis/krisis7/krisis7eng.html

KRISIS Philosophical Review n o 7/1998, fourth year ISSN 1224-0044 (paper format only) Originally issued in paper format in December 1997 with the support of SOROS Foundation for an Open Society POSSIBILIA SECOND COVER, PRESENTATION AND CONTENTS IN ROMANIAN (PDF) CONTENTS IN ROMANIAN (HTML) CONTENTS PAPERS Adrian Miroiu: Indexed Propositions and Possible Worlds ABSTRACT : In this paper I shall investigate some logical properties of modal languages containing world-indexed sentences. In general, if phi is a sentence, then that phi is the case at world w, i.e.: at w, phi (or w phi for short) is a w-indexed sentence. So, sentences like: „In world w, Quine is a distinguished philosopher”, or even „In world w’, that Quine is a distinguished philosopher is the case in world w”, etc. will be of our concern. Walter A. Carnielli: The Logical Way of Inconsistency (trans. by T. Ioachim) ABSTRACT: This paper offers an introduction to some philosophical and logical questions concerned with the problem of consistency in logic, as well as a comparison between some distinct positions, their logical approaches and reciprocal criticisms. A brief account of the history of the subject is also sketched. In particular, some recent results about the so-called

22. Toward A New Landscape Of Systems Management In An Autonomic Then we introduce basic concepts in ontology and description Logics and .. Observe that, if this is not the case, then there is an inconsistency in the http://www.research.ibm.com/journal/sj/421/lanfranchi.html

Home My account Select a country Journals Home ... Contact Us Related links: Autonomic Computing IBM AC Research IBM eServer and AC IBM Tivoli Monitoring ... DMTF Volume 42, Number 1, 2003 Autonomic Computing Table of contents: HTML PDF This article: HTML PDF DOI: 10.1147/sj.421.0119 Toward a new landscape of systems management in an autonomic computing environment by G. Lanfranchi , P. Della Peruta , A. Perrone , and D. Calvanese Problems cannot be solved at the same level of awareness that created them To minimize the business downtime, the speedy execution of the appropriate corrective action is needed. An important component of performance and availability management is the monitoring of the system in order to detect anomalies as soon as they occur and to take the necessary corrective actions (e.g., restore the failing objects to their desired state, or activate backup resources). The monitoring and the taking of corrective action should be optimized with respect to the overall objectives of the entire business system. Whenever feasible, systems management tools with predictive capabilities should be used in order to detect future problem states, and to allow action to be taken before a failure occurs and adversely impacts users. When the tools monitoring the system resources simply collect raw data (e.g., performance metrics), it can be difficult to draw any conclusion about the health of a system. A graphical performance monitor or an event viewer tool can be useful, but only if a skilled administrator is able to interpret the information provided, and to determine if a problem exists or not. Only an experienced administrator has the ability to correlate the appropriate domain knowledge with the data collected, such as metrics and events, and come up with answers to questions such as: Is there a memory bottleneck?, What is its cause?, and How can I fix it? In the current monitoring environment, the system administrator inherently owns the best practices and applies them in order to identify and cure problems.

23. JSTOR Curry S Paradox But these Logics are in many ways strange in other respects, and at least the finitely manyvalued versions of these Logics admit more subtle versions of http://links.jstor.org/sici?sici=0003-2638(197906)39:3<124:CP>2.0.CO;2-E

24. Does Logic Presuppose The Existence Of The Christian God? There does not seem to be anything inconsistent in asserting that deductive Logic and Metaphysic. However, it is a long way from admitting that the http://www.infidels.org/library/modern/michael_martin/logic.html

Library Modern Michael Martin : Does Logic Presuppose the Existence of the Christian God? (2000) Does Logic Presuppose the Existence of the Christian God? (2000) Michael Martin The Transcendental Argument for the Existence of God (TAG)the argument that logic, science, and objective ethical standards presuppose the existence of the Christian Godhas been repeatedly used by a small group of Christian apologists operating within the Orthodox Presbyterian tradition. In the recent past I showed that Greg Bahnsen, the leading advocate of TAG, failed to demonstrate that induction presupposes the existence of the Christian God.[ ] In the present paper I consider another part of TAGthe claim made by Bahnsen in this debates with Gordon Stein[ ] and George Smith[ ]that deductive logic presupposes the existence of the Christian God.[ Deductive Logic and the Claim of TAG Let us understand deductive logic to be the study of valid deductive arguments; that is, arguments in which the premises necessitate the conclusion. On this common understanding IF the premises of an argument are true, THEN the conclusion must be true. Deductive validity is determined by the form of the argument and not the content of the premises. An example of a valid deductive argument is: All dogs are brown Rover is a dog Therefore, Rover is brown.

25. The Naturalistic Fallacy: The Logic Of Its Refutation An extract from Logic And The Basis Of Ethics by AN Prior. the significance of this assertion by sacrificing its certainty, admitting that its denial, http://www.utilitarian.org/texts/prior.html

THE NATURALISTIC FALLACY: THE LOGIC OF ITS REFUTATION Arthur N. Prior IF there is any contribution to moral philosophy which is more likely than any other to become permanently associated with the name of Professor G. E. Moore, it is the identification and refutation, in his Principia Ethica of what he calls the 'naturalistic fallacy'. I propose now to explain what it is to which Professor Moore gives this name, and what he considers to be involved in its fallaciousness; and I shall offer reasons for regarding his argument, not as disproving ethical naturalism itself, but as exposing an inconsistency into which some naturalists have fallen. What Professor Moore means by the 'naturalistic fallacy' is the assumption that because some quality or combination of qualities invariably and necessarily accompanies the quality of goodness, or is invariably and necessarily accompanied by it, or both, this quality or combination of qualities is identical with goodness. If, for example, it is believed that whatever is pleasant is and must be good, or that whatever is good is and must be pleasant, or both, it is committing the naturalistic fallacy to infer from this that goodness and pleasantness are one and the same quality. The naturalistic fallacy is the assumption that because the words 'good' and, say, 'pleasant' necessarily describe the same objects, they must attribute the same quality to them. We might, with Mill, call the objects to which a term is applicable the denotation of the term, and the characteristics which an object must have for the term to be applicable to it, the connotation of the term.

26. HAMLET INCONSISTENT If it is justifiable to look for logic and consistency in Hamlet, as Eliot did, one can find a far greater inconsistency in the play than the inadequate http://www.cosmos-club.org/web/journals/2000/safer.html

HAMLET INCONSISTENT JOHN SAFER Logical or not, Shakespeare’s prince has a lasting appeal William Shakespeare undoubtedly achieved one of his greatest characterizations when he created the role of Hamlet, the gloomy Prince of Denmark. Hamlet’s appeal to audiences almost certainly stems from his many human weaknesses. The one for which he is best known is indecisiveness, but his inconsistency may well be an even more outstanding characteristic. T. S. Eliot, in 1932, wrote an essay on Hamlet that is still cited as a noted critique of Shakespeare’s great tragedy. Eliot argued that Hamlet is an artistic failure, due to a basic weakness in the play. It was his contention that a playwright owes a duty to the audience to write dialogue appropriate to characters as they have been developed in the drama. Eliot made the point that in the “Closet Scene,” when Hamlet confronts Queen Gertrude, his mother, in her bedchamber, his words demonstrate an animosity and a vindictiveness for which the audience is totally unprepared. Since Eliot’s charge against Hamlet is self-evidently valid, actors and directors attempting to stage Shakespeare’s tragedy have struggled with the problem Eliot’s essay highlighted, both prior to and after its publication. The conventional approach in the 20th century has been to imply, on Hamlet’s part, a frustrated, incestuous love for his mother, which may justify the words Hamlet speaks, but for which Shakespeare gives no background whatsoever. As a result, rather than solving the problem, this approach creates yet another inconsistency. Still, in spite of these inconsistencies, and in spite of Eliot’s accusation of artistic failure, Hamlet continues to walk the stage and fascinate theatergoers.

27. Hit Seg[eth] On Halgum Bocum: The Logic Of Composite Old English Homilies. Indus Although I know of no scholarly attempt to reconcile this inconsistency, Even the most credulous person will admit that there are false books out in http://goliath.ecnext.com/coms2/gi_0199-4364259/Hit-seg-eth-on-halgum.html

We have detected that your web browser does not have JavaScript enabled. To view Goliath's company profiles, news and business information, please enable JavaScript now. About Us My Account View Cart Browse ... View article excerpt Read this article now - Try Goliath Business News - FREE! You can view this article PLUS... Over 5 million business articles Hundreds of the most trusted magazines, newswires, and journals ( see list Premium business information that is timely and relevant Unlimited Access Now for a Limited Time, try Goliath Business News - Free for 7 Days! Tell Me More Terms and Conditions Already a subscriber? Log in to read full article Publication: Philological Quarterly Publication Date: 22-SEP-02 Delivery: Immediate Online Access Author: Thompson, Nancy M. Article Excerpt The vernacular homilies can be frustrating, the flotsam of the ages coming down through sometimes battered manuscripts, corrected perhaps, but more often riddled with absurdities or error. Many are composite, assembled from multiple sources translated from Latin or taken from earlier vernacular works. The homilists who compiled them borrowed here and there, often without regard for internal consistency. As a result, many homilies seem confused, repetitive, even self contradictory. They wander from one topic to another. Frequently it seems as though the only thing holding them together is the compiler's piety; there is no other clear organizing principle.

28. Plato's Dialogues, By B.Jowett, M.A. Thus far we admit inconsistency in Plato, but no further. He lived in an age before logic and system had wholly permeated language, and therefore we must http://ancienthistory.about.com/library/bl/bl_text_plato_dialogues_intro.htm

zGCID=" test0" zGCID=" test0 test14" zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') You are here: About Education Ancient / Classical History Ancient / Classical History ... Help The Dialogues of Plato Primary Texts Plato's Texts Index Translated into English with Ananlyses and Introductions by B. Jowett, M.A. Master of Balliol College Regius Professor of Greek in the University of Oxford Doctor in Theology of the University of Leyden To My Former Pupiles in Balliol College and in the University of Oxford who during fifty years have been the best of friends to me these volumes are inscribed in grateful recognition of their never failing attachment. The additions and alterations which have been made, both in the Introductions and in the Text of this Edition, affect at least a third of the work. Having regard to the extent of these alterations, and to the annoyance which is naturally felt by the owner of a book at the possession of it in an inferior form, and still more keenly by the writer himself, who must always desire to be read as he is at his best, I have thought that the possessor of either of the former Editions (1870 and 1876) might wish to exchange it for the present one. I have therefore arranged that those who would like to make this exchange, on depositing a perfect and undamaged copy of the first or second Edition with any agent of the Clarendon Press, shall be entitled to receive a copy of a new Edition at half-price. Preface to the First Edition.

29. Quodlibet Online Journal: Is The Trinity A True Contradiction? - By Randal Rause That is, admit one contradiction as true, and all statements follow from it; .. 3 The Logic of inconsistency A Study in NonStandard Possible-World http://www.quodlibet.net/rauser-trinity.shtml

Quodlibet Journal: Volume 4 Number 4, November 2002 http://www.Quodlibet.net Is the Trinity a True Contradiction? The Liar Paradox and Beyond Paraconsistency and Theology Though such a deprecation of consistency is a novelty for logicians, it is in a sense well familiar to theologians who have generally preferred biblical fidelity to logical consistency. Among the first rank of these is Paul who proclaimed: "Has not God made foolish the wisdom of the world?" (I Cor. 1:20d NRSV) and "For God's foolishness is wiser than human wisdom, and God's weakness is stronger than human strength." (I Cor. 1:25 NRSV) A crucial aspect of Christian theology has always been humility in the face of the divine mystery. As such, one might think the ethos of Christian theology is amenable to the possibility of true contradictions. David Cunningham, Trinity, and True Contradiction David Cuningham's recent book These Three are One: The Practice of Trinitarian Theology , [6] is a creative and provocative contribution to the current trinitarian "renaissance". What makes the work of present interest is Cunningham's penchant for making what appear to be contradictory statements about the Trinity. In what follows I will attempt to develop a paraconsistency interpretation of these particular passages. To be sure, we will face a significant hermeneutical obstacle given Cunningham's version of conceptual relativism. Cunningham appears to hold that everything has meaning only with respect to a particular conceptual world. Hence, while he makes statements that sound contradictory, it is not clear whether he is arguing they only appear contradictory from one particular conceptual world, but are not contradictory in another, or whether they are a false contradiction in one world, and a true contradiction in another. In order to gain insight from Cunningham on the possibility of contradictions in theology, I will defend the second interpretation.

30. The Laws Of Thought All of us often do so – as when we refuse to look at or admit the evidence or a logical .. ‘internal inconsistency’ and ‘the logic of paradoxes’. http://www.thelogician.net/5b_ruminate/5b_chapter_01.htm

TheLogician.net RUMINATIONS Sundry notes and essays on Logic © Avi Sion, 2005. Part I - Chapter 1 About the Laws of Thought The three “Laws of Thought” may be briefly explicated as follows: Thesis : there are certain appearances; appearances appear. Antithesis : there are incompatibilities between certain of these appearances; in such cases, one or both of them must be false. Synthesis : some remaining appearances must be true; find out which! We can in this perspective consider dialectic as a fundamental form of thought, through which knowledge is made to progress on and on. It is not a mere detail, an occasional thought-process, but a driving force, an engine, of thought. The laws are not mere information, but calls to cognitive action. They enjoin proactive and curative cognitive measures, to ensure (as much as possible at any given time) continued verification, consistency and completeness. The law of identity tells us to seek out the facts and sort them out as well as we can. The purpose of this law is to instill in people a healthy respect for facts, in the course of observation and judgment. It is essentially a call to honesty, and submission to the verdict of truth. Some people think that it is impossible for us to ignore that “A is A”. Far from it! All of us often do so – as when we refuse to look at or admit the evidence or a logical demonstration; when we avoid reality or evade it having glimpsed it; when we lie to ourselves or to others; and so forth. If the law of identity were always obeyed by us, there would be no need to formulate it.

31. An Examination Of Brahma-Sutra However, the purpose of this aphorism is to examine the Jaina logic of seven free from inconsistency and Contradiction, i.e., valid in Hamilton s sense. http://www.jainworld.com/jainbooks/ramjees/brahmasutra.htm

www.jainworld.com A Perspective in Jaina Philosophy and Religion Prof. Ramjee Singh AN EXAMINATION OF BRAHMA-SUTRA ( II. 2. 33) ( From the Jaina Standpoint ) The Four-cornered Negation and Contradiction - The four-cornered negation of the Madhyamika Buddhists throws light on the problem. According to them, Reality is not (neither B, nor not B nor both B and not B, nor neither B and not B). Now, if Reality is, neither being nor non-being can be negated. But, the Madhyamikas hold that though the Reality is not Being or Non-being it can not be different from them. Thus even the neither nor (i.e. neither Being nor non-Being) has to be negated, and consequently there has to be a double negation. This looks like violating the Law of Contradiction, for the denial of the contradictories suggests the possibility of a possible in between the two contradictories. Professor Raju, however, suggests a technical device for the relief of the Buddhists to meet this charge of the possible violation of the Law of Contradiction. In the doctrine of four-cornered negation if we distinguish between contrary and contradictory opposition in the manner of western logic, we will see that two contraries can be negated but not the two contradictories. Law of Contradiction and the Advaita Vedanta - To Sankara, Being and Non-being are contraries not contradictories. Reality is Being; Non-being is unreal; but there is the third order of reality which is neither Being nor Non-being, This is the phenomenal word which is neither real nor unreal but phenomenal, this is Maya.

32. Uranus Vs. Saturn And The Value Of Inconsistency | Rudhyar Archival Project | As Saturn The Value of inconsistency. When a nation or, as today, . and the arguments are contained within the framework of a well-tested logic. http://rudhyar.com/astroarticles/inconsistency.php

@import url(astroarticlesstyle.css); Home Bio Art Music ... Astrology URANUS vs. SATURN The Value of Inconsistency Dane Rudhyar First Published Horoscope Magazine December 1960 Today one hears so much about "inconsistency", as if to be trusted one's outlook on life or any situation must be entirely fixed - inflexible and unchanging, even in the light newly acquired experience and knowledge. Is such a stance justified, or is it just another way saying "My country right or wrong" and a subterfuge to avoid admitting one's own mistakes and shortcomings? In this article, as significant today as when it first appeared in 1960, Rudhyar states that when a nation or, as today, the whole of humanity, has been shaken up by a crisis of extreme gravity, certain kinds of psychological reactions - symbolized by Uranus and Saturn - are almost inevitable. Read it and discover the Value of Inconsistency ADDED 24 October 2004. The All-Seeing Eye knows if you haven't made a voluntary donation to view the online collection of Astrological Articles by Dane Rudhyar . The suggested contribution is $12, but you may offer as little as $3 or as much as $50. The

33. Shebanation: The Death Of UI Consistency More seriously, I think I was pretty honest about admitting that CS3 isn t . The interface suggests both can be on at once, when logic says they can t. http://blogs.adobe.com/shebanation/2007/04/the_death_of_ui_consistency.html

Shebanation Discussions of: collaboration; dynamic media; Microsoft technologies; dynamic languages; and anything else that captures my eye. Main The Death of UI Consistency Yesterday, John Gruber posted a gripe about the new CS3 panels and palettes and how horrible it is that Adobe put the close box on the right side. To John, this seemed horribly un-Mac-like, and in trademark style he concludes his gripe with an elitist and unsubstantiated slap at Windows users (but hey, at least it was funny): Ends up the title bar controls for palette windows in CS3 are on the right side, Windows-style. “X” for close, “_” for collapse. God, that just looks so wrong – how did this ever get approved? If Adobe really wanted to put these controls in the same location on both platforms, why not do it the Mac way? If Windows users cared about consistency, they wouldn’t be using Windows. I wrote him an email where I explained what I thought the actual motivation for the close box on the right decision was: the desire to save vertical space by putting the close box to the right of the palette tab panel interface. look The trend towards Rich Internet Applications using Apollo and its ilk will further cement this trend, as web applications come down to the desktop with their web UI conventions intact. To me, this is a good thing.

34. Bristol University - Department Of Philosophy - Philosophy And History Of Scienc Logicism is the view that mathematics is reducible to logic alone , for and the risks that arose in admitting this intangible agency to their homes. http://www.bristol.ac.uk/philosophy/department/events/phohos.html

skip menus Philosophy home contact us help ... DEPARTMENT OF PHILOSOPHY Prospective Students Undergraduates Postgraduates Continuing Education Current Students Undergraduates Postgraduates Staff Student Committee Resources About the Department Staff/Faculty Susan Hurley Events Research and Projects ... Philosophy Society Other links British Society for the Philosophy of Science Institute of Philosophy University home Department of Philosophy ... Events Philosophy and History of Science Seminars This series incorporates existing and new seminar series in: philosophy of physics logic and philosophy of mathematics history, philosophy, and sociology of science Please note: philosophy of physics seminars will recommence in the New Year Series (see key Date Speaker Title Time Location Tuesday 18th October Dr Volker Halbach New College, Oxford abstract 5.15 pm Common Room, Department of Philosophy, 9 Woodland Road Tiesday 1 November Prof. Greg Restall Melbourne abstract 5.15 pm Common Room, Department of Philosophy, 9 Woodland Road Tuesday 22 November Dr Jim Bennett Museum of the History of Science, Oxford

35. Lycan On Lewis And Meinong Though standard modal Logics may trade just in possible states of affairs, the semantics of conditionals must deal with inconsistent beliefs. http://users.ox.ac.uk/~shil0124/mystuff/lycan.html

Lycan on Lewis and Meinong Do I contradict myself? Very well then I contradict myself (I am large, I contain multitudes). (Walt Whitman) In his 1988 review of On the Plurality of Worlds (Lycan [1988]), William Lycan argued that what he called Lewis's 'mad-dog modal realism' (also 'rape-and-loot modal realism' and 'nuclear-holocaust modal realism' - I suspect that some reference to the supposed extremity of Lewis's position is intended) rested upon an unanalysed modal notion. Lycan accepted that actualists all seemed to be stuck with such unanalysed notions (adding that his own was the notion of compatibility as applied to pairs of properties), but argued that Lewis's notion of worlds was also a modal primitive: 'World' for him has to mean ' possible world', since the very flesh-and-bloodiness [which relieves him of the sort of abstraction indulged in by actualists] prevents him from admitting impossibilia. (Lycan [1988], p.46) Lycan's main concerns in this review go back to his earlier paper 'The Trouble with Possible Worlds' (Lycan [1979]), and are taken up again in his PAS paper: The ruling out of impossible worlds is a serious liability [...] For semantics needs impossible worlds. Though standard modal logics may trade just in possible states of affairs, the semantics of conditionals must deal with inconsistent beliefs. (Lycan [1991], p.224)

36. Supreme Court Of Canada - Decisions - R. V. Rockey The defence having requested the admission of these additional statements as evidence of inconsistency, it became necessary to admit all statements made on http://csc.lexum.umontreal.ca/en/1996/1996rcs3-829/1996rcs3-829.html

Judgments of the Supreme Court of Canada Search Fran§ais Home Contact Us Important Notices ... Advanced Search Citation: R. v. Rockey [1996] 3 S.C.R. 829 Date: November 21, 1996 Docket: Other formats: PDF WPD Printer Friendly R. v . Rockey, [1996] 3 S.C.R. 829 Shaun Edward Rockey Appellant v. Her Majesty The Queen Respondent Indexed as: R. v . Rockey File No.: 24784. 1996: June 13; 1996: November 21. on appeal from the court of appeal for ontario Criminal law Evidence Hearsay Exceptions Evidence of children Accused charged with sexual assault of two-and-a-half-year-old child Child five years old at time of trial Crown not calling child as witness but instead tendering out-of-court statements he had made to others Whether trial judge erred in admitting hearsay statements without express inquiry into their necessity Whether trial judge erred in admitting certain out-of-court statements without a voir dire Whether trial judge erred in failing to charge jury on which statements it could use for truth of their contents and which went to credibility only Whether verdict would necessarily have been the same Criminal Code, R.S.C., 1985, c. C-46, s. 686(1)(b)(iii). Khan . On the initial voir dire on the admissibility of these statements, the trial judge ruled that two would be admitted and rejected the other five. On a second

37. The Panda's Thumb: ID's Irreducible Inconsistency Revisited However, with Dembski’s habitual irreducible inconsistency, the mousetrap is claimed to . But I admit, his overall position is now exceedingly confused. http://www.pandasthumb.org/pt-archives/000774.html

Navigation Main Weekly Archive Category: Assault on Science Comments (30) ... Printer-friendly version Authors are solely responsible for the content of their articles on PandasThumb.org. Linked material is the responsibility of the party who created it. Commenters are responsible for the content of comments. The opinions expressed in articles, linked materials, and comments are not necessarily those of PandasThumb.org. Recent Comments Mark Perakh on February 5, 2005 11:10 AM Richard Wein on February 5, 2005 01:53 AM RBH on February 1, 2005 09:43 PM Bob Maurus on February 1, 2005 08:40 PM pennathur on February 1, 2005 08:30 PM Dr Zen on February 1, 2005 08:12 PM Mark Perakh on February 1, 2005 05:35 PM Bayesian Bouffant on February 1, 2005 03:29 PM Ginger Yellow on February 1, 2005 03:21 PM theophylact on February 1, 2005 02:43 PM Recent Trackbacks The Panda's Thumb: Bill Dembski and the case of the unsupported assertion Recommend this entry to a friend Friend's email address: Your email address: Message (optional): Site Traffic ID's irreducible inconsistency revisited Posted by Mark Perakh on January 31, 2005 11:30 AM

38. Clear Conclusions When we acknowledge the logic and scripturalness of this change we will no longer have the hobgoblins of our inconsistency staring us in the face, http://www.freedomsring.org/permit/chap19.html

HOME "I Permit Not a Woman . . ." To Remain Shackled Table of Contents Acknowledgements and Dedication Introduction 1. "Mind Control - Male and Female" 2. "Self-Examination" ... Our Java Chat Room Chapter 19 Clear Conclusions The truth is that the ministry of Christ is open to Jews and Greeks, bond men and free men, males and females. All have the equal responsibility and task of teaching and preaching the redeeming power of Jesus Christ. Women prayed, sang, prophesied, spoke in tongues, interpreted tongues, evangelized, witnessed, and taught in the total life of the church in New Testament days. They were deaconesses and fellow workers in the gospel with the apostles. They ministered. Today, women in worship services and in public classes sing, teach, exhort, encourage, read (at least responsively), say "Amen", pass communion, pass collection trays, make announcements, confess faith, confess fault, greet visitors, greet members, etc. We have decided that certain activities are men's jobs and that women are not in subjection if they do them. This is purely human reasoning and has nothing to do with what the Bible teaches. An example is waiting on the table during the Lord's Supper. What authority is exercised in "waiting on the table" or in "passing out the trays?" There is none. Rather, it is a sign of servitude, not dominion. What authority is there in passing the collection trays or picking up attendance cards? There is none! In fact, these also are acts of servitude and not dominion!

39. E. A. Poe Society Of Baltimore Every other science than Logic is the science of certain concrete relations. admitting, as well as we can, for argument’s sake, that the succession of http://www.eapoe.org/works/ESSAYS/EUREKA5.HTM

Last Update: July 12, 1998 Navigation: Main Menu Poe's Misc Next Section Prev Section [Text: Edgar Allan Poe, "[Section 5]," Eureka; A Prose Poem , 1848, pp. 63-81.] [page 63, continued:] I maintain, first, that only in the mode described is it conceivable that Matter could have been diffused so as to fulfil at once the conditions of radiation and of generally equable distribution. I maintain, secondly, that these conditions themselves have been imposed upon me, as necessities, in a train of ratiocination as rigorously logical as that which establishes any demonstration in Euclid; and I maintain, thirdly, that even if the charge of “hypothesis” were as fully sustained as it is, in fact, unsustained and untenable, still the validity and indisputability of my result would not, even in the slightest particular, be disturbed. To explain: — The Newtonian Gravity — a law of Nature — a law whose existence as such no one out of Bedlam questions — a law whose admission as such enables us to account for nine-tenths of the Universal phenomena — a law which, merely because it does so enable us to account for these phenomena, we are perfectly willing, without reference to any other considerations, to admit, and cannot help admitting, as a law — a law, nevertheless, of which neither the principle nor the modusoperandi of the principle has ever yet been traced by the human analysis — a law, in short, which, neither in its detail nor in its generality, has been found susceptible of explanation

40. Paraconsistent Logic (Stanford Encyclopedia Of Philosophy) A most telling reason for paraconsistent logic is the fact that there are theories which are inconsistent but nontrivial. Clearly, once we admit the http://plato.stanford.edu/entries/logic-paraconsistent/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Paraconsistent Logic First published Tue Sep 24, 1996; substantive revision Wed Nov 21, 2007 The development of paraconsistent logic was initiated in order to challenge the logical principle that anything follows from contradictory premises, ex contradictione quodlibet (ECQ) . Let be a relation of logical consequence, defined either semantically or proof-theoretically. Let us say that is explosive iff for every formula A and B A A B . Classical logic, intuitionistic logic, and most other standard logics are explosive. A logic is said to be paraconsistent iff its relation of logical consequence is not explosive. The modern history of paraconsistent logic is relatively short. Yet the subject has already been shown to be an important development in logic for many reasons. These involve the motivations for the subject, its philosophical implications and its applications. In the first half of this article, we will review some of these. In the second, we will give some idea of the basic technical constructions involved in paraconsistent logics. Further discussion can be found in the references given at the end of the article. Motivation and Applications Inconsistent but Non-Trivial Theories Dialetheias (True Contradictions) Automated Reasoning ... Related Entries Motivation and Applications Inconsistent but Non-Trivial Theories A most telling reason for paraconsistent logic is the fact that there are theories which are inconsistent but non-trivial. Clearly, once we admit the existence of such theories, their underlying logics must be paraconsistent. Examples of inconsistent but non-trivial theories are easy to produce. An example can be derived from the history of science. (In fact, many examples can be given from this area.) Consider Bohr's theory of the atom. According to this, an electron orbits the nucleus of the atom without radiating energy. However, according to Maxwell's equations, which formed an integral part of the theory, an electron which is accelerating in orbit must radiate energy. Hence Bohr's account of the behaviour of the atom was inconsistent. Yet, patently, not everything concerning the behavior of electrons was inferred from it. Hence, whatever inference mechanism it was that underlay it, this must have been paraconsistent.

41. MainFrame: Possible Worlds This notion of possible world inherits the position of first order logic in it is necessary to admit that a possible world must identify for every name http://rbjones.com/rbjpub/philos/metap/metap004.htm

Possible Worlds Overview: We discuss some ideas about what "possible worlds" might be, partly to elucidate the character of logical necessity, and partly as an approach to metaphysics and the philosophy of science. Introduction These thoughts on possible worlds are intended to help explicate the notion of logical necessity and the boundary between logic and science. Sets of Sentences Some philosophers have identified "possible worlds" with "maximal consistent sets of sentences". We briefly consider this before passing on to the more flexible idea of a possible world as an interpretation. Interpretations If we identify "possible worlds" with "interpretation of a first order language", then we get a notion of logical necessity which corresponds to that of first order validity. Standard Interpretations Restricting the notion of possible world to interpretations which are consistent with the intended meaning of abstract constants yields a more general notion of necessity which fits better with both the analytic and the a priori. Metaphysics To talk about the world we need abstract (often mathematical) models. We get these by adopting some convenient but otherwise arbitrary abstract ontology, which we use for building abstract models of the real world. Models of the real world require no new concrete ontology but simply the introduction of new constants which are denote abstract surrogates for the real world.

42. Preamble addressing some grey areas in the foundations of mathematics, logic and .. implicitly admit Platonic concepts that are, prima facie, inconsistent with http://alixcomsi.com/Preamble.htm

Index Mathematical Objects and Mathematical Truth Reviewing classical interpretations of Cantor’s, Gödel’s, Tarski’s, and Turing’s reasoning and addressing some grey areas in the foundations of mathematics, logic and computability In the essays on the linked web-pages I highlight some grey areas in foundational concepts - implicitly accepted as intrinsic in classical interpretations of Cantor’s, Gödel’s, Tarski’s and Turing’s reasoning - that may be explicated effectively in non-Platonic interpretations by considering whether, and, if so, when, and how, we may, within classical logic and without inviting inconsistency: a ) define a mathematical object formally The paradoxical element in the mathematical / logical antinomies is effectively eliminated if we recognise that some mathematical concepts, which are effectively definable only non-algorithmically, cannot be introduced into a formal theory without inviting inconsistency, and may, conveniently, be defined as mathematical non-objects relative to the theory. Prima facie, except from a Platonic viewpoint, it would, then, be of little significance whether some concepts are mathematically inconsistent (

43. Dean's World - A Favorite Quote Are my tastes inconsistent? Perhaps. So what? Do I have some obligation to pretend to like other types of pasta if I admit to liking spaghetti? http://www.deanesmay.com/posts/1123592671.shtml

Dean's World Defending the liberal tradition in history, science, and philosophy. A Favorite Quote Dean One of my all-time favorite quotations is: A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. Ralph Waldo Emerson One of the things I like about it is that, read literally, it seems rather contradictory. He's saying there is such a thing as being consistent to the point of foolishness, and that little minds are afraid of foolish consistencies (that's what a hobgoblin is, something you're afraid of), yet that small minds adore foolish consistencies. So are foolish consistencies bad or good? They key to understanding it is to realize first that there is such a thing as foolish consistency. Trying to be 100% consistent at all times is a form of psychosisbut more importantly, you can also accuase someone of being inconsistent over an issue that's trivial or even false. You can scare a little mind by making him think he's being inconsistent in some way when he's really not, and little minds often tell themselves they're perfectly in the right becuase after all they're consistentnever mind whether the consistency actually makes sense. To give an obvious example: I don't much like pasta. I do, however, like spaghetti. Are my tastes inconsistent? Perhaps. So what? Do I have some obligation to pretend to like other types of pasta if I admit to liking spaghetti? Some nattering fool might try to prove some point about my inconsistency about pasta, but what kind of idiot would take that seriously?

44. RENAN'S NEW BOOK.; DESCRIPTION OF THE SCENERY OF NAZARETH. THE KINGDOM... - Arti Drawing a character of transcendent nobleness and loveliness, he has been so inconsistent as to admit a kind of self deception or imposition in this Being http://query.nytimes.com/gst/abstract.html?res=FB0815FE355C1A7493CAA9178AD95F478