ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...) any one logic being privileged, then, on this count partisans across the logical spectrum are in relatively similar dialectical positions. (shrink)

Contains an overall account of morality in its philosophical format particularly with regard to problems of observation, evidence, and truth.

This article explores a case study of a mindfulness teacher, Beth, and her experiences of teaching mindfulness to 11- to 16-year-olds in several English schools. It shows why Beth was drawn to teaching mindfulness, which was both to alleviate the stress amongst her pupils and improve her own mental health. It illustrates how and why she became a confident, successful mindfulness teacher: she learnt about mindfulness at various classes, retreats and teacher-education training sessions, spending thousands of pounds on her own (...) training. It argues that her positioning as a mindfulness teacher in an unmindful school system created an overwhelming demand for her services, but also huge stress upon her. It develops McCaw’s conceptions of ‘thin’ and ‘thick’ mindfulness (2020), arguing that while Beth began by practising ‘thin’ mindfulness – seeing it as a way of solving exam stress amongst her pupils – she became increasingly a ‘thick’ practitioner; her experiences of mindfulness led to profound personal change and, ultimately, to her becoming very disillusioned about teaching mindfulness in an unwelcoming educational, ‘unmindful’ environment. (shrink)

This is a new release of the original 1949 edition.

v. 1. Critical essays.--v. 2. Collected essays, 1929-1968.

Le proslogion de saint Anselme n'est pas une oeuvre tres connue, bien que les commentaires de ses chapitres 2 a 4 sur l'argument appele par Kant ontologique soient en nombre infini.

Beall and Cotnoir (2017) argue that theists may accept the claim that God's omnipotence is fully unrestricted if they also adopt a suitable nonclassical logic. Their primary focus is on the infamous Stone problem (i.e., whether God can create a stone too heavy for God to lift). We show how unrestricted omnipotence generates Curry‐like paradoxes. The upshot is that Beall and Cotnoir only provide a solution to one version of the Stone problem, but that unrestricted omnipotence generates other problems which (...) they do not adequately address. (shrink)

We generalize the notion ofconsequence relationstandard in abstract treatments of logic to accommodate intuitions ofrelevance. The guiding idea follows theuse criterion, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each beusedin some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining betweenmultisets. We motivate and state basic definitions of relevant consequence relations, both (...) in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases). (shrink)

Bi-intuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the first order formulas equivalent to translations of bi-intuitionistic propositional formulas are exactly those preserved under bi-intuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use the machinery of neither saturated models nor elementary (...) chains. (shrink)

In this note we study a counterpart in predicate logic of the notion of logical friendliness, introduced into propositional logic in [15]. The result is a new consequence relation for predicate languages with equality using first-order models. While compactness, interpolation and axiomatizability fail dramatically, several other properties are preserved from the propositional case. Divergence is diminished when the language does not contain equality with its standard interpretation.

First published in 1949, Gilbert Ryle ’s The Concept of Mind is one of the classics of twentieth-century philosophy. Described by Ryle as a ‘sustained piece of analytical hatchet-work’ on Cartesian dualism, The Concept of Mind is a radical and controversial attempt to jettison once and for all what Ryle called ‘the ghost in the machine’: Descartes’ argument that mind and body are two separate entities. This sixtieth anniversary edition includes a substantial commentary by Julia Tanney and is essential (...) reading for new readers interested not only in the history of analytic philosophy but in its power to challenge major currents in philosophy of mind and language today. (shrink)

This is an introduction to the special issue of the AJL on Val Plumwood's manuscript "False Laws of Logic" and her other work in logic.

Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide a fix: we show that $\mathcal {L}_{\omega \omega }^{-} $ is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in [11]), the Löwenheim–Skolem property, and compactness. Furthermore, we show that compactness can be replaced by being recursively enumerable for validity under certain conditions. In the proofs, we (...) use a form of strong upwards Löwenheim–Skolem theorem not available in the framework with identity. (shrink)

This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift (...) to non-classical logic may recast the meanings of these apparently ‘absolute’ theorems. (shrink)

One important concern regarding implantable Brain Computer Interfaces is the fear that the intervention will negatively change a patient’s sense of identity or agency. In particular, there is concern that the user will be psychologically worse-off following treatment despite postoperative functional improvements. Clinical observations from similar implantable brain technologies, such as deep brain stimulation, show a small but significant proportion of patients report feelings of strangeness or difficulty adjusting to a new concept of themselves characterized by a maladaptive je ne (...) sais quoi despite clear motor improvement. Despite the growing number of cases in the DBS literature, there is currently no accepted or standardized tool in neuroethics specifically designed to capture the phenomenological postoperative experience of patients implanted with DBS or BCI devices. Given potential risks of postoperative maladaptation, it is important for the field of neuroethics to develop a qualitative instrument that can serve as a shared method for capturing postoperative variations in patient experience of identity and agency. The goal of this article is to introduce an instrument we have developed for this purpose and call for further neuroethical efforts to assess the phenomenology of implantable brain device use. (shrink)

This paper defines a Sahlqvist fragment for relevant logic and establishes that each class of frames in the Routley-Meyer semantics which is definable by a Sahlqvist formula is also elementary, that is, it coincides with the class of structures satisfying a given first order property calculable by a Sahlqvist-van Benthem algorithm. Furthermore, we show that some classes of Routley-Meyer frames definable by a relevant formula are not elementary.

This paper is devoted to the problem of existence of saturated models for first-order many-valued logics. We consider a general notion of type as pairs of sets of formulas in one free variable that express properties that an element of a model should, respectively, satisfy and falsify. By means of an elementary chains construction, we prove that each model can be elementarily extended to a $\kappa $-saturated model, i.e. a model where as many types as possible are realized. In order (...) to prove this theorem we obtain, as by-products, some results on tableaux and their consistency and satisfiability and a generalization of the Tarski–Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of $\kappa $-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings. (shrink)

In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication $\phi \rightarrow \psi $ with no interpolant. Importantly, this result does not contradict the unfortunately named ‘Craig interpolation’ theorem established by Rauszer in [24] since that article is about the property more correctly named ‘deductive interpolation’ (see (...) Galatos, Jipsen, Kowalski and Ono’s use of this term in [5]) for global consequence. Given that the deduction theorem fails for bi-intuitionistic logic with global consequence, the two formulations of the property are not equivalent. (shrink)

Thepresentwork is arevisedand enlarged English versionofa book originally writtenin Spanish and published in late 1996, La rejlexion de DavidHume en lorno a /a religion. SinceDavidHume is arguablynot only the most important philosopherwhohaseverwrittenintheEnglishlanguage,butthemoststudiedand influential,itisonlynaturalthatsoonerthanlaterIwouldfeelthe urgencyto bring totheattentionofamuchwiderpublicaworkwhoseoutlook is, I think, signifi cantlydifferentfrom that ofother books which deal with the Scottish thinker's worksonreligionandnaturaltheology.Thisdesirewassostrongastoallowmeto overcome the all-too-natural fear that my wavering and uncertain command of English wouldmakethe few valuableinsights theworkmight containappearun clear,andmyphilosophicalerrors,evenmoreastonishing. This book is addressednot only to scholarswhomay beinterested in modem philosophy in (...) generalorHume'sphilosophyofreligion in particular,but also to themoreextensivecompassofreaderseitherintriguedortroubledby religion and themyriadofissuesandproblemsitposes,whichare, as it were, the primematter forphilosophicalanalysisandtheorizing.Inspiteofitsphilosophicaland linguistic limitations,forwhichIamentirelyresponsible,Iferventlyhopethatthisworkmay befoundtocontainsomethingofthatelusivetruthafterwhichHumestrove, andto whichheremainedconstantto theend, particularlyatatime whenthe priceto be paidforthepublicationofcontroversialphilosophicalandreligious views wascon siderablyhigherthanthatofbecominganeasytargetforuniversalridicule. Thecompletionofthisworkhasbeenmadepossible principally by asabbatical leavethattheUniversityofPuertoRico grantedme fortheyear 1999. This leave gavemethenecessarytimeto readandstudy thepertinentliterature,aswell asto writemostoftheEnglish manuscript.Italsoallowedmeto visit Edinburgh and spendmostofJuly andAugust 1999 attheNationalLibraryofScotlandand the EdinburghUniversityLibrary.Although Ihaveincorporatedinto thepresentwork onlyasmallpartofmyresearchatthose libraries,ifthis bookshows agreaterap preciation of the immediate social and religious context of Hume's thought than its Spanish predecessor, it is in no small measure due to the books, articles, and xi xii Preface manuscritsIwasabletoconsultatthe time. Inthis respect, Iwouldliketo thank Professor Peter Jones, Director of the Institute for Advanced Studies in the HumanitiesattheUniversityofEdinburgh, who was very instrumental in making myvisittoEdinburghareality,andgenerouslyputthefacilitiesoftheInstitute at mydisposal. Manythoughts andlinesofargumentcontained in this bookdatebackto my doctoraldissertation,andsomeearlierversionsofanumberofchaptersorsections ofchaptershavebeenpublished in differentphilosophyjournalsor anthologies. I oftheminthebibliographyundermy name. But sincemy previousworks listall onthe subjecthavebeenrevisedandmodifiedsomanytimes in the lightofnew fmdingsortomeetactualorpossiblecriticism,Ican saythatthey havebeeneffec tivelysupersededbythepresentwriting. (shrink)

A long-awaited translation on the philosophical relation between technology, the individual, and milieu of the living.

Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.

This paper argues for a methodological point that bears on a relatively long-standing debate concerning collective beliefs in the sense elaborated by Margaret Gilbert: are they cases of belief or rather of acceptance? It is argued that epistemological accounts and distinctions developed in individual epistemology on the basis of considering the individual case are not necessarily applicable to the collective case or, more generally, uncritically to be adopted in collective epistemology.

Ethics and the Community of Inquiry gets to the heart of democratic education and how best to achieve it. The book radically reshapes our understanding of education by offering a framework from which to integrate curriculum, teaching and learning and to place deliberative democracy at the centre of education reform. It makes a significant contribution to current debates on educational theory and practice, in particular to pedagogical and professional practice, and ethics education.

Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of (...) metalogical properties such as compactness, abstract completeness, the Löwenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value. (shrink)

Surveying nearly seven decades of habitual and obsessive reading, I consider how my character and psychology used reading to shape philosophical questions that move me into forms in which I could pursue them by reading. This became both the method and the substance of my philosophical work. It preserved some core emotional issues but also gave me the way to integrate them into scholarship and into my life.

We show that propositional intuitionistic logic is the maximal abstract logic satisfying a certain form of compactness, the Tarski union property, and preservation under asimulations.

We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraïssé limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.

It's not always the person who is right who wins the arguments, more often it's the person who argues best. Gilbert's practical, clever guide--which also serves as a text for his popular seminars on the art of arguing--shows readers how to hone their polemical skills, and how to counter the verbal weapons that may be in an opponent's arsenal.