In the first part of this investigation we highlight two, seemingly irreconcilable, beliefs that suggest an impending crisis in the teaching, research, and practice of—primarily state-supported—mathematics: (a) the belief, with increasing, essentially faith-based, conviction and authority amongst academics that first-order Set Theory can be treated as the lingua franca of mathematics, since its theorems—even if unfalsifiable—can be treated as ‘knowledge’ because they are finite proof sequences which are entailed finitarily by self-evidently Justified True Beliefs; and (b) the slowly emerging, but (...) powerfully rooted in economic imperatives, belief that only those Justified True Beliefs can be treated as ‘knowledge’ which are, further, categorically communicable as Factually Grounded Beliefs—hence as comprehensible pre-formal ‘mathematical truths’—by any intelligence that lays claims to a mathematical lingua franca. We argue that this seeming irreconcilability merely reflects a widening chasm between an increasing under-estimation of the value to society of ‘semantic arithmetical truth’, and an increasing over-estimation of the value to society of ‘syntactic set-theoretical provability’; a chasm which must be narrowed and bridged explicitly. We thus proffer a Complementarity Thesis which seeks to recognize that mathematical ‘provability’ and mathematical ‘truth’ need to be interdependent and complementary, ‘evidence-based’, assignments-by-convention to the formulas of a formal mathematical language; where (a) the goal of mathematical ‘proofs’ may be viewed as seeking to ensure that any mathematical language intended to formally represent our pre-formal conceptual metaphors and their inter-relatedness is unambiguous, and free from contradiction; whilst (b) the goal of mathematical ‘truths’ must be viewed as seeking to ensure that any such representation does, indeed, uniquely identify and adequately represent such metaphors and their inter-relatedness. Our thesis is that, by universally ignoring the need to introduce goal (b) in our curriculum, the teaching of, and research in, mathematics at the post-graduate level cannnot justify its value to society beyond the mere intellectual stimulation of individual minds. In the second part we appeal to some recent—and hitherto unsuspected—unarguably constructive Tarskian interpretations, of the first-order Peano Arithmetic PA, which establish PA as both finitarily consistent, and categorical. Since we also show that the second order subsystem ACA0 of Peano Arithmetic and PA cannot both be assumed provably consistent, we conclude that there can be no mathematical, or meta-mathematical, proof of consistency for Set Theory. Hence the theorems of any Set Theory are not sufficient for distinguishing between (i) what we can believe to be a ‘mathematical truth’; (ii) what we can evidence as a ‘mathematical truth’; and (iii) what we ought not to believe is a ‘mathematical truth’; whilst the theorems of the first-order Peano Arithmetic PA are sufficient for distinguishing between (i), (ii) and (iii). We conclude from this that the holy grail of mathematics ought to be ‘arithmetical truth’, not ‘set-theoretical proof’. (shrink)

A common style of argument in the literature on free will and moral responsibility is the Manipulation Argument. These tend to begin with a case of an agent in a deterministic universe who is manipulated, say, via brain surgery, into performing some action. Intuitively, this agent is not responsible for that action. Yet, since there is no relevant difference, with respect to whether an agent is responsible, between the manipulated agent and a typical agent in a deterministic universe, responsibility is (...) not compatible with the truth of determinism. In response, some theorists have argued that there is a relevant difference, and have developed two sorts of accounts of that difference: bypassing views, and manipulator-focused views. Manipulator-focused views suggest that the difference concerns the presence of a manipulator, whereas bypassing views suggest that the relevant difference concerns the fact that the action issues from attitudes that the manipulated agent acquired in a way that bypassed her capacities for control over her mental life. One sort of case used to decide between these sorts of accounts is a case of machine induction, which is just like a manipulation case, yet the change in the agent is the result of some natural force. Against the received view, Xiaofei Liu argues that such cases pose problems for bypassing views, and favor manipulator-focused views instead. This paper addresses Liu’s arguments, as well as a variety of cases, concluding that cases of machine induction do not provide motivation for a bypassing theorist to adopt a manipulator-focused view. (shrink)

In Fact, Fiction and Forecast, Nelson Goodman claims that the problem of justifying induction is not something over and above the problem of describing valid induction. Such claim, besides suggesting his commitment to the collapse of the distinction between the context of description and the context of justification, seems to open the possibility that the new riddle of induction could be addressed empirically. Discoveries about psychological preferences for projecting certain classes of objects could function as a criterion for determining which (...) predicates are after all projectible. In this paper, I argue that Goodman's claim must be construed within his project for constructional definitions, which is methodologically oriented by reflective equilibrium. The description of inductive practice is committed to the articulation of the extension of the class selected by the predicate ‘valid induction’. The mutual adjustment between theoretical considerations and inductive practice involved in the proposal of a definition of ‘valid induction’ must preserve that practice as much as possible, there is no way to get rid of entrenchment. Empirical discoveries about the psychological mechanism that underlies projections may help that adjustment but they cannot substitute the role played by the entrenchment of predicates. (shrink)

Developments in the realm of formal sciences and math foundations during the twentieth century were marked by important methodological advances. Such new approaches partialy owe their appearance to the abandonment of the previous paradigm. To identify how this transition occured, in this essay we observe some aspects regarding the works of Gödel and Tarski, who, under a certain interpretations, restructure epistemological bases of math's formalisms. It'll be argued that the theoretical variabilities produced in abstract sciences upon weakening previous viewpoints forced (...) to abandon some of the components of hegemonic programs. (shrink)

Le problème de l’induction (humien) a récemment été abordé par Steel dans son article de 2010. Celui-ci soutient que les théories d’apprentissage formelles permettent de justifier logiquement le principe de l’induction, ce dernier assurant la fiabilité logique des méthodes. Cette proposition a été critiquée par Howson en 2011, ce dernier mettant en doute la possibilité même qu’une méthode puisse être logiquement fiable. Bien que Steel ait offert une réponse à cette critique, il n’y répond pas directement. Dans le présent article, (...) une réponse frontale à celle-ci est offerte en s’inspirant des pratiques de tests d’hypothèses en sciences biologiques. Pour ce faire, une règle de construction des ensembles d’hypothèses est proposée, règle offrant une justification logique au fait qu’une méthode convergera nécessairement vers la vérité. Cet amendement étant cohérent avec l’ensemble de la proposition de Steel, il est ainsi possible d’affirmer que sa thèse est renforcée par cette proposition. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent (...) scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (shrink)

Horwich donne une belle analyse de Wittgenstein (W) et est un érudit W de premier plan, mais à mon avis, ils sont tous en deçà d’une pleine appréciation, comme je l’explique longuement dans cet examen et beaucoup d’autres. Si l’on ne comprend pas W (et de préférence Searle aussi) alors je ne vois pas comment on pourrait avoir plus qu’une compréhension superficielle de la philosophie et de la pensée de l’ordre supérieur et donc de tout comportement complexe (psychologie, sociologie, anthropologie, (...) histoire, littérature, société). En un mot, W a démontré que lorsque vous avez montré comment une phrase est utilisée dans le contexte d’intérêt, il n’y a rien de plus à dire. Je vais commencer par quelques citations notables, puis donner ce que je pense sont les considérations minimales nécessaires pour comprendre Wittgenstein, la philosophie et le comportement humain. Tout d’abord, on pourrait noter que mettre "meta" en face de n’importe quel mot devrait être suspect. W a fait remarquer par exemple, que la métamathématique est mathématiques comme les autres. L’idée que nous pouvons sortir de la philosophie (c’est-à-dire la psychologie descriptive de la pensée de haut ordre) est elle-même une profonde confusion. Une autre irritation ici (et tout au long de l’écriture académique pour les 4 dernières décennies) est le sexisme linguistique inverse constant de «elle» et «la sienne» et «elle» ou «il / elle», etc, où «ils» et «leur» et «eux» ferait bien. De même, l’utilisation du mot Français «répertoire» où le «répertoire» anglais se portera plutôt bien. La lacune majeure est l’échec complet (bien que très commun) d’employer ce que je considère comme la vue extrêmement puissante et intuitive de deux systèmes de HOT et Searle cadre que j’ai décrit ci-dessus. C’est particulièrement poignant dans le chapitre sur le sens p111 et seq. (en particulier dans les notes de bas de page 2-7), où nous nageons dans l’eau très boueuse sans le cadre de l’automatisé vrai seul S1, propositionnelle dispositionnelle S2, COS etc. On peut également avoir une meilleure vue de l’intérieur et de l’extérieur en lisant par exemple, Johnston ou Budd (voir mes commentaires). Horwich fait cependant beaucoup de commentaires incisifs. J’ai particulièrement aimé son résumé de l’importation de la position anti-théorique de W sur p65. Il doit mettre davantage l’accent sur 'On Certainty', récemment l’objet de beaucoup d’efforts de Daniele Moyal- Sharrock, Coliva et d’autres et résumé dans mes récents articles. Horwich est de premier ordre et son travail vaut bien l’effort. On espère qu’il (et tout le monde) étudiera Searle et une certaine psychologie moderne ainsi que Hutto, Read, Hutchinson, Stern, Moyal-Sharrock, Stroll, Hacker et Baker, etc. pour atteindre une large vision moderne du comportement. La plupart de leurs papiers sont sur academia dot edu et philpapers dot org, mais pour PMS Hacker voir http : info dot sjc dot ox dot ac dot uk/ scr / hacker / DownloadPapers dot html. Il donne l’un des plus beaux résumés de l’endroit où une compréhension de Wittgenstein nous laisse que j’ai jamais vu. « Il ne doit y avoir aucune tentative d’expliquer notre activité linguistique/conceptuelle (PI 126) comme dans la réduction de l’arithmétique à la logique de Frege ; aucune tentative de lui donner des fondations épistémologiques (PI 124) comme dans les comptes basés sur le sens d’une connaissance a priori; aucune tentative de caractériser des formes idéalisées de celui-ci (PI 130) comme dans le sens logique; aucune tentative de réforme (PI 124, 132) comme dans la théorie de l’erreur de Mackie ou l’intuitionnisme de Dummett; aucune tentative de rationaliser (PI 133) comme dans le récit de Quine de l’existence; aucune tentative pour le rendre plus cohérent (PI 132) comme dans la réponse de Tarski aux paradoxes menteurs; et aucune tentative pour le rendre plus complet (PI 133) comme dans le règlement des questions d’identité personnelle pour des scénarios hypothétiques bizarres de « téléportation ». Enfin, permettez-moi de suggérer qu’avec la perspective que j’ai encouragée ici, W est au centre de la philosophie et de la psychologie contemporaines et n’est pas obscure, difficile ou non pertinente, mais scintillante, profonde et limpide et que de lui manquer est de manquer l’une des plus grandes aventures intellectuelles possibles. Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deuxemssyst peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (shrink)

Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...) one website. Paste the whole URL. http://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambrid ge.Dictionary.of.Philosophy -/- The 2015 third edition will be available soon. Before you think of buying it read some reviews on Amazon and read reviews of its competition: For example, my review of the 2008 Oxford Companion to Philosophy, History and Philosophy of Logic,29:3,291-292. URL: http://dx.doi.org/10.1080/01445340701300429 -/- Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. The discussion provides an opportunity to bring more flaws to light. -/- Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition. Besides the help received from people in Buffalo, help from elsewhere was received by email. We gratefully acknowledge the following: José Miguel Sagüillo, John Zeis, Stewart Shapiro, Davis Plache, Joseph Ernst, Richard Hull, Concha Martinez, Laura Arcila, James Gasser, Barry Smith, Randall Dipert, Stanley Ziewacz, Gerald Rising, Leonard Jacuzzo, George Boger, William Demopolous, David Hitchcock, John Dawson, Daniel Halpern, William Lawvere, John Kearns, Ky Herreid, Nicolas Goodman, William Parry, Charles Lambros, Harvey Friedman, George Weaver, Hughes Leblanc, James Munz, Herbert Bohnert, Robert Tragesser, David Levin, Sriram Nambiar, and others. -/- . (shrink)

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper concludes with (...) a modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)

The limited aim here is to explain what John Dewey might say about the formulation of the grue example. Nelson Goodman’s problem of distinguishing good and bad inductive inferences is an important one, but the grue example misconstrues this complex problem for certain technical reasons, due to ambiguities that contemporary logical theory has not yet come to terms with. Goodman’s problem is a problem for the theory of induction and thus for logical theory in general. Behind the whole discussion (...) of these issues over the last several decades is a certain view of logic hammered out by Russell, Carnap, Tarski, Quine, and many others. Goodman’s nominalism hinges in essential ways on a certain view of formal logic with an extensional quantification theory at its core. This raises many issues, but the one issue most germane here is the conception of predicates ensconced in this view of logic. (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...) types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)

The monograph contains three works on research on the concept of a rejected sentence. This research, conducted under the supervision of Prof. Jerzy Słupecki by U. Wybraniec-Skardowska (1) "Theory of rejected sentences" and G. Bryll (2) "Some supplements of theory of rejected sentences" and (3) "Logical relations between sentences of empirical sciences" led to the construction of a theory rejected sentences and made it possible to formalize certain issues in the methodology of empirical sciences. The concept of a rejected sentence (...) was introduced by J. Łukasiewicz in the course of his inquiry into Aristotelian Syllogistic. It was essentialy generelized by J. Słupecki who, with reference to Tarski's axiomatic theory of deductive systems (1930), gave the formal definition of the rejection function Cn' according to which a sentence y is rejected on the base of a set of sentences X iff at least one sentence which belongs to X can be deduced from the sentence y. Słupecki proved (1959) that the function Cn', which assignes to the set X the set of sentences rejected on the basis of X, is additive and satisfies the axioms of Tarski's general theory of deductive systems. Work (1) uses not only Tarski's general theory of systems but also his the so-called enlarged theory of systems (1930). It constructs a theory T of rejected sentences (propositions), which is created from Tarski's richer theory of systems by adding one axiom and a number of definitions; among them the definition of the rejection function Cn' is fundamental one. Cn' is a function which assignes to every set X of false sentences the set Cn'X whose members are exclusively false senteces. A number of theorems which describes properties of defined concepts have been proved in T. Some of them are necessary for conducting considertions of the concluding section of (1) devoted to the empirical sentences. Section 2 of (1) deals with the theory of the unit consequenses. It is characterized by an axiom from which follow all axioms of Tarski's general theory of deductive systems, additivity and the property that the unit consequence of the set X of sentences is a unit consequence only one sentence of X. An example of unit consequence is the rejection consequence Cn'. In section 3 of (1) the dual theory T' equivalent to T is presented. In T' the primitive concept is the rejection function Cn'. The fundamental axiom of T' states that Cn' is a unit consequence. The concluding section brings a few examples of applications of the definitions and theorems of T in the domain of the scientific methodology. Work (2) corresonds to J. Słupecki paper (1959) and the theory T of rejected propositions given in work (1). In this paper some suplements of the theory T are given. Work (3) is an extension of the theory of rejected propositios given in the paper (1). It is an attempt of formalization some problems of methodology of the empirical sciences which concern to such concepts as: empirical sentence, similar sentence, generalization, inductive conclusion etc. (shrink)

Cet article cherche à approfondir la conclusion de Hume selon laquelle l’induction, malgré son importance comme méthode inférentielle, est injustifiable. J’argumente en particulier que l’induction devrait être comprise comme un processus psychologique fondamental. Mon plan est le suivant : après un résumé du problème de l’induction humien, j’offre une rapide argumentation en faveur de la conceptualisation de l’induction comme une inférence à la meilleure explication (IME). Ensuite, je propose un argument original visant à montrer que l’IME est un processus psychologique (...) fondamental. Cet argument s’appuie sur une analyse du concept d’explication prouvant qu’une explication nécessite toujours l’existence d’un agent épistémique. J’utilise ce résultat afin de montrer que l’IME est un processus psychologique fondamental. Si l’induction est bel et bien une forme d’IME, l’induction est donc elle aussi un processus psychologique fondamental. (shrink)

This paper provides an interpretation of Aristotle’s criticism to the solution to Meno’s Paradox suggested by Plato. According to Aristotle, when Plato says that reminiscence (anámnēsis) is achieved, what is actually achieved is induction (epagōgê). Our interpretation is based on two aspects: (1) semantic criticism, since Plato’s use of the term anámnēsis is unusual; and (2) the theory is not able to give an adequate explanation of the effective discovery.

Using two examples of ethical choice, Philippa Foot’s snake and the traffic roundabout, this paper offers an account of normative induction that characterizes particularism and generalism as stages of normative inquiry, rather than rival accounts of moral knowledge and motivation. Ethical particularism holds that the evaluative cannot be “cashed out” in propositional form, and that it is descriptively “shapeless.” Drawing on examples from law, this paper claims that, while individual normative inquiry may be viewed as encountering a shapeless particularist context (...) of seemingly unlimited non-moral properties, normativity is driven by repetition of similar situations toward shared practices and descriptive predication. Rather than retention of epistemic status by defeated reasons,this illustrates retirement of relevant properties and accompanying reasons,transformation of the reasons environment, and a pluralist normative ontology. (shrink)

English translation of a paper intially publisdhed in French in Dialogue under the title 'Une solution pour le paradoxe de Goodman'. In the classical version of Goodman's paradox, the universe where the problem takes place is ambiguous. The conditions of induction being accurately described, I define then a framework of n-universes, allowing the distinction, among the criteria of a given n-universe, between constants and variables. Within this framework, I distinguish between two versions of the problem, respectively taking place: (i) in (...) an n-universe the variables of which are colour and time; (ii) in an n-universe the variables of which are colour, time and space. Finally, I show that each of these versions admits a specific resolution. (shrink)

JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised to (...) find out that in normal first-order logic existential import is quite common: some universals “Everything that is S is P” —actually quite a few—imply their corresponding existentials “Something that is S is P”. Anyway, perhaps contrary to its title, this paper is not a cataloging of surprises in logic but rather about the mistakes that did or might have or might still lead people to think that there are no surprises in logic. The paper cataloging of surprises in logic is on our “to-do” list. -/- ► JOHN CORCORAN AND WILIAM FRANK, Surprises in logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] There are many surprises in logic. Peirce gave us a few. Russell gave Frege one. Löwenheim gave Zermelo one. Gödel gave some to Hilbert. Tarski gave us several. When we get a surprise, we are often delighted, puzzled, or skeptical. Sometimes we feel or say “Nice!”, “Wow, I didn’t know that!”, “Is that so?”, or the like. Every surprise belongs to someone. There are no disembodied surprises. Saying there are surprises in logic means that logicians experience surprises doing logic—not that among logical propositions some are intrinsically or objectively “surprising”. The expression “That isn’t surprising” often denigrates logical results. Logicians often aim for surprises. In fact, [1] argues that logic’s potential for surprises helps motivate its study and, indeed, helps justify logic’s existence as a discipline. Besides big surprises that change logicians’ perspectives, the logician’s daily life brings little surprises, e.g. that Gödel’s induction axiom alone implies Robinson’s axiom. Sometimes wild guesses succeed. Sometimes promising ideas fail. Perhaps one of the least surprising things about logic is that it is full of surprises. Against the above is Wittgenstein’s surprising conclusion : “Hence there can never be surprises in logic”. This paper unearths basic mistakes in [2] that might help to explain how Wittgenstein arrived at his false conclusion and why he never caught it. The mistakes include: unawareness that surprise is personal, confusing logicians having certainty with propositions having logical necessity, confusing definitions with criteria, and thinking that facts demonstrate truths. People demonstrate truths using their deductive know-how and their knowledge of facts: facts per se are epistemically inert. [1] JOHN CORCORAN, Hidden consequence and hidden independence. This Bulletin, vol.16, p. 443. [2] LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus, Kegan Paul, London, 1921. -/-. (shrink)

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox. As a consequence, the behavior of things seems to be completely at the mercy of the temporal change of unique absolute (...) temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, - that is my claim - the ontological consequence of a nature results, for which the potentiality of lawfulness is coupled to essentially functionally defined time sequences. (shrink)

The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s (...) Induction-Axiom Schema [23]. Similarly, in first-order set theory, Zermelo’s second-order Separation Axiom is approximated by Fraenkel’s first-order Separation Schema [17]. In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template, a syntactic string composed of one or more “blanks” and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a “template” to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions ‘schema’ and ‘scheme’ in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata. (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)

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

Many commentators on Alfred Tarski have, following Hartry Field, claimed that Tarski's truth-definition was motivated by physicalism—the doctrine that all facts, including semantic facts, must be reducible to physical facts. I claim, instead, that Tarski did not aim to reduce semantic facts to physical ones. Thus, Field's criticism that Tarski's truth-definition fails to fulfill physicalist ambitions does not reveal Tarski to be inconsistent, since Tarski's goal is not to vindicate physicalism. I argue that Tarski's only published remarks that speak approvingly (...) of physicalism were written in unusual circumstances: Tarski was likely attempting to appease an audience of physicalists that he viewed as hostile to his ideas. In later sections I develop positive accounts of: (1) Tarski's reduction of semantic concepts; (2) Tarski's motivation to develop formal semantics in the particular way he does; and (3) the role physicalism plays in Tarski's thought. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of (...) the meaning of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

This paper considers Rumfitt’s bilateral classical logic (BCL), which is proposed to counter Dummett’s challenge to classical logic. First, agreeing with several authors, we argue that Rumfitt’s notion of harmony, used to justify logical rules by a purely proof theoretical manner, is not sufficient to justify coordination rules in BCL purely proof-theoretically. For the central part of this paper, we propose a notion of proof-theoretical validity similar to Prawitz for BCL and proves that BCL is sound and complete respect to (...) this notion of validity. The major difficulty in defining validity for BCL is that validity of positive +A appears to depend on negative −A, and vice versa. Thus, the straightforward inductive definition does not work because of this circular dependance. However, Knaster-Tarski’s fixed point theorem can resolve this circularity. Finally, we discuss the philosophical relevance of our work, in particular, the impact of the use of fixed point theorem and the issue of decidability. (shrink)

Horwich gibt eine feine Analyse von Wittgenstein (W) und ist ein führender W-Stipendiat, aber meinerMeinung nach sind sie alle hinter einer vollen Wertschätzung zurück, wie ich in dieser Rezension und vielen anderen ausführlich erkläre. Wenn man W (und vorzugsweise auch Searle) nicht versteht, dann sehe ich nicht, wie man mehr als ein oberflächliches Verständnis von Philosophie und höherem Denken und damit von allem komplexen Verhalten (Psychologie, Soziologie, Anthropologie, Geschichte, Literatur, Gesellschaft) haben könnte. Kurz gesagt, W hat gezeigt, dass, wenn Sie (...) gezeigt haben, wie ein Satz im Zusammenhang mit Interesse verwendet wird, es nichts mehr zu sagen gibt. Ich beginne mit ein paar bemerkenswerten Zitaten und gebe dann, was ich denke, sind die minimalen Überlegungen notwendig, um Wittgenstein zu verstehen, Philosophie und menschliches Verhalten. Zunächst könnte man feststellen, dass es verdächtig sein sollte, "Meta" vor jedes Wort zu stellen. W bemerkte z.B., dass Metamathematik Mathematik wie jede andere ist. Die Vorstellung, dass wir aus der Philosophie austreten können (d.h. die beschreibende Psychologie des Denkens höherer Ordnung), ist selbst eine tiefe Verwirrung. Eine weitere Irritation hier (und während des akademischen Schreibens in den letzten 4 Jahrzehnten) ist der ständige umgekehrte sprachliche Sexismus von "ihrem" und "ihr" und "sie" oder "er/sie" usw., wo "sie" und "ihre" und "sie" gut machen würden. Ebenso, wird die Verwendung des französischen Wortes "Repertoire", bei dem das englische "Repertoire" recht gut funktioniert. Der größte Mangel ist das (wenn auch sehr häufige) völlige Versäumnis, das zu verwenden, was ich als die enorm leistungsfähige und intuitive Zwei-System-Ansicht von HOT und Searles Framework betrachte, die ich oben skizziert habe. Dies ist besonders ergreifend im Kapitel über die Bedeutung p111 ff. (besonders in den Fußnoten 2-7), wo wir in sehr schlammigem Wasser ohne den Rahmen von automatisierten echten nur S1, propositional DispositionS, COS usw. schwimmen. Man kann auch einen besseren Blick auf das Innere und das Äußere bekommen, indem man z.B. Johnston oder Budd liest (siehe meine Rezensionen). Horwich macht jedoch viele einschneidende Kommentare. Besonders gefiel mir seine Zusammenfassung der Bedeutung von Wes antitheoretischer Haltung auf P65. Er muss "On Certainty" stärker in den Vordergrund stellen, das kürzlich von Daniele Moyal- Sharrock, Coliva und anderen mit viel Aufwand beworfen und in meinen jüngsten Artikeln zusammengefasst wurde. Horwich ist erstklassig und seine Arbeit lohnt sich. Man hofft, dass er (und alle) Searle und einige moderne Psychologie sowie Hutto, Read, Hutchinson, Stern, Moyal-Sharrock, Stroll, Hacker und Baker etc. studieren werden, um eine breite moderne Sicht des Verhaltens zu erreichen. Die meisten ihrer Papiere sind auf academia dot edu und philpapers dot org, aber für PMS Hacker siehe http slash slash info dot sjc dot ox dot ac dot uk slash scr slash hacker slash DownloadPapers dot html Er gibt eine der schönsten Zusammenfassungen, wo uns ein Verständnis von Wittgenstein hinterlässt, das ich je gesehen habe. "Es darf keinen Versuch geben, unsere sprachliche/konzeptionelle Tätigkeit (PI 126) zu erklären, wie in Freges Reduktion der Arithmetik auf logik; kein Versuch, ihr erkenntnistheoretische Grundlagen zu geben (PI 124), wie sie auf der Grundlage von Berichten über ein vormethodikes Wissen beruhen; kein Versuch, idealisierte Formen davon (PI 130) als in gewissem Sinne Logiken zu charakterisieren; kein Reformversuch (PI 124, 132) wie in Mackies Fehlertheorie oder Dummetts Intuitionismus; kein Versuch, sie zu straffen (PI 133) wie in Quines Existenzbericht; kein Versuch, es konsistenter zu machen (PI 132) wie in Tarskis Antwort auf die Lügner-Paradoxien; und kein Versuch, es vollständiger zu machen (PI 133) wie bei der Klärung von Fragen der persönlichen Identität für bizarre hypothetische 'Teleportation'-Szenarien." Abschließend möchte ich vorschlagen, dass W mit der Perspektive, die ich hier gefördert habe, im Zentrum der zeitgenössischen Philosophie und Psychologie steht und nicht obskur, schwierig oder irrelevant ist, sondern schillernd, tiefgründig und kristallklar ist und dass es ist, eines der größten intellektuellen Abenteuer zu verpassen, das möglichist. Wer aus der modernen zweisystems-Sichteinen umfassenden, aktuellen Rahmen für menschliches Verhalten wünscht, kann mein Buch "The Logical Structure of Philosophy, Psychology, Mindand Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019) konsultieren. Diejenigen,die sich für mehr meiner Schriften interessieren, können 'Talking Monkeys--Philosophie, Psychologie, Wissenschaft, Religion und Politik auf einem verdammten Planeten --Artikel und Rezensionen 2006-2019 3rd ed (2019) und Suicidal Utopian Delusions in the 21st Century 4th ed (2019) und andere sehen . (shrink)

The first case of comprehensive Jesuit philosophical textbook, the Cursus Conimbricensis stands as a hallmark of the Jesuit way of teaching philosophy during the second half of the Sixteenth century. After having placed the Cursus conimbricensis in the European philosophical scenario, this paper aims to show how Manuel de Gois, as well as the other contributors, felt to be bound to Aristotle, the major authority according to the Ratio studiorum, in dealing with questions and issues.

In this article we aim to open a new line of debate about religion in public schools by focusing on religious ideals. We begin with an elucidation of the concept ‘religious ideals’ and an explanation of the notion of reasonable pluralism, in order to be able to explore the dangers and positive contributions of religious ideals and their pursuit on a liberal democratic society. We draw our examples of religious ideals from Christianity and Islam, because these religions have most adherents (...) in Western liberal democracies that are the focus of this article. The fifth and most important section ‘‘Reasonable pluralism and the inclusion of religious ideals in public secondary schools’’ provides three arguments for our claim that public schools should include religious ideals, namely that they are important to religious people, that they are conducive for the development of pupils into citizens of a liberal democracy, and that the flourishing of pupils as adults is advanced by encountering religious ideals. We also offer a more practical reason: religious ideals can more easily be included within public education than religious dogmas and rules. (shrink)

Alfred Tarski was a nominalist. But he published almost nothing on his nominalist views, and until recently the only sources scholars had for studying Tarski’s nominalism were conversational reports from his friends and colleagues. However, a recently-discovered archival resource provides the most detailed information yet about Tarski’s nominalism. Tarski spent the academic year 1940-41 at Harvard, along with many of the leading lights of scientific philosophy: Carnap, Quine, Hempel, Goodman, and (for the fall semester) Russell. This group met (...) frequently to discuss logical and philosophical topics of shared interest. At these meetings, Carnap took dictation notes, which are now stored in the Archives of Scientific Philosophy. Interestingly, and somewhat surprisingly, the plurality of notes covers a proposal Tarski presents for a nominalist language of unified science. This chapter addresses the following questions about this project. What, precisely, is Tarski’s nominalist position? What rationales are given for Tarski’s nominalist stance—and are these rationales defensible? Finally, how is Tarskian nominalism of 1941 related to current nominalist projects? (shrink)

Horwich dà una bella analisi di Wittgenstein (W) ed è uno studioso W leader, ma a mio parere, tutti non sono al di sotto di un pieno apprezzamento, come spiego a lungo in questa recensione e molti altri. Se non si capisce W (e preferibilmente anche Searle) allora non vedo come si possa avere più di una comprensione superficiale della filosofia e del pensiero di ordine superiore e quindi di tutti i comportamenti complessi (psicologia, sociologia, antropologia, storia, letteratura, società). In (...) poche parole, W ha dimostrato che quando hai dimostrato come una frase viene usata nel contesto di interesse, non c'è più nulla da dire. Inizierò con alcune citazioni degne di nota e poi darò quelle che penso siano le considerazioni minime necessarie per capire Wittgenstein, la filosofia e il comportamento umano. La prima si potrebbe notare che mettere "meta" davanti a qualsiasi parola dovrebbe essere sospetto. W ha osservato ad esempio, che la metamatematica è matematica come qualsiasi altra. L'idea che possiamo uscire dalla filosofia (cioè la psicologia descrittiva del pensiero di ordine superiore) è di per sé una profonda confusione. Un'altra irritazione qui (e per tutta la scrittura accademica negli ultimi 4 decenni) è il costante sessismo linguistico inverso di "lei" e "suo" e "lei" o "lui/ lei" ecc., dove "loro" e "loro" e "loro" farebbero bene. Allo stessomodo, l'uso della parola francese "repertorio" in cui l'inglese "repertorio" farà abbastanza bene. La carenza principale è il fallimento completo (anche se molto comune) di impiegare quello che vedo come la vista di due sistemi estremamente potente e intuitiva del quadro di HOT e Searle che ho delineato sopra. Questo è particolarmente toccante nel capitolo sul significato p111 et seq. (soprattutto nelle note a piè di pagina 2-7), dove nuotiamo in acqua molto fangosa senza la struttura di vero automatizzato solo S1, proposizionale disposizionale S2, COS ecc. Si può anche ottenere una migliore vista dell'interno e dell'esterno leggendo ad esempio, Johnston o Budd (vedi le mie recensioni). Horwich però fa molti commenti incisivi. Mi è piaciuto soprattutto il suo riassunto dell'importazione della posizione anti-teorica di W su p65. Ha bisogno di dare più enfasi a 'On Certainty', recentemente oggetto di grande sforzo di Daniele Moyal- Sharrock, Coliva e altri e riassunto nei miei recenti articoli. Horwich è di prim'ordine e il suo lavoro vale la pena. Si spera che lui (e tutti) studierà Searle e un po 'di psicologia moderna così come Hutto, Read, Hutchinson, Stern, Moyal-Sharrock, Stroll, Hacker e Baker ecc per raggiungere una vasta visione moderna del comportamento. La maggior parte dei loro documenti sono su academia dot edu e philpapers dot org etc. Egli dà uno dei più bei riassunti di dove una comprensione di Wittgenstein ci lascia che io abbia mai visto. "Non ci deve essere alcun tentativo di spiegare la nostra attività linguistico/concettuale (PI 126) come nella riduzione dell'aritmetica di Frege alla logica; nessun tentativo di dargli basi epistemologiche (PI 124) come nei resoconti basati sul significato di una conoscenza a priori; nessun tentativo di caratterizzarne le forme idealizzate (PI 130) come nelle logiche del senso; nessun tentativo di riformarlo (PI 124, 132) come nella teoria degli errori di Mackie o nell'intuizione di Dummett; nessun tentativo di snellirla (PI 133) come nel racconto dell'esistenza di Quine; nessun tentativo di renderlo più coerente (PI 132) come nella risposta di Tarski ai paradossi bugiar; e nessun tentativo di renderlo più completo (PI 133) come nel sistemare le questioni di identità personale per bizzarri scenari ipotetici di 'teletrasporto'." Infine, lasciatemi suggerire che con la prospettiva che ho incoraggiato qui, W è al centro della filosofia contemporanea e della psicologia e non è oscura, difficile o irrilevante, ma scintillante, profonda e cristallina e che permane lo è mancare una delle più grandi avventure intellettualipossibili. Coloro che desiderano un quadro aggiornato completo per il comportamento umano dalla moderna vista a due systems possono consultare il mio libro 'La struttura logica dellafilosofia, psicologia, Mind e il linguaggio in Ludwig Wittgenstein e John Searle' 2nd ed (2019). Coloro che sono interessati a più dei miei scritti possono vedere 'TalkingMonkeys--Filosofia, Psicologia, Scienza, Religione e Politica su un Pianeta Condannato--Articoli e Recensioni 2006-2019 3rd ed (2019) e Suicidal Utopian Delusions nel 21st Century 4th ed (2019) . (shrink)

This paper advocates a new reading of Nelson Goodman’s new riddle of induction. According to Ian Hacking, this famous problem conveys a “pure nominalism”, as it grounds Goodman’s denial regarding the existence of natural kinds. While this interpretation is somewhat convincing, it suffers the major flaw of not corresponding to what Goodman himself understood by “nominalism”. Nominalism, in a goodmanian sense, is indeed primarily a technical demand, which stems from the so-called “calculus of individuals”. I argue that this mereological definition (...) of nominalism allows to understand the new riddle of induction afresh. As a result, Goodman’s riddle is “hyper-nominalist”, i.e., nominalist in a distinct and stronger sense than what Hacking suggested. (shrink)

It is difficult to advance a point beyond what Keynes himself commented about his own vision in The General Theory of Employment, Interest and Money in 1936 (hereafter TGT) in its Chapter 24. It is also difficult to express a deeper thought than what Skidelsky wrote about Chapter 24 of TGT (cf. Skidelsky, 1997). The purpose of this article is to identify whether Chapter 24 of TGT is the gist of Keynes’s legacy, having set the foundations of macroeconomics in the (...) previous 23 Chapters. Relevant topics included in Chapter 24 are the consequences of full employment, the fate of income distribution, the future of overall wealth, the socialization of investment, saving, expectations, the role of the State in economies, the future of financial markets and the interaction between economics and other disciplines. Indeed this Chapter displays Keynes’s genius as a social philosopher, following the tradition of The Economics Possibilities for our Grandchildren (1930). In Chapter 24 he was taking a glance at his product as did Phillip II when he was observing the construction of his castle El Escorial in XVII Spain. Within his vision, is this piece of work a justification of capitalism? Keynes sees the State as both the spender and the employer of last resort, thereby proposing a new role for the government (Skidelsky, 1998). He also suggests a new role for the private sector and reconsiders the interrelation between the two sectors. He is fully optimistic about this issue, which he considers as evolutionary. In addition, Keynes blurs the distinction between economics and sociology, advancing new interdisciplinary hints in his thinking. Keynes is also concerned on the epistemological role of assumptions in order to obtain defensible conclusions. Thereafter the British economist proposes new methods. He was a neo-realist and was against the inductive method. In addition, it can be stated that TGT is grounded on new psychological laws and motivations, that is, on a new vision of humankind, especially the analyzed chapter. His topics are the bypassing of Classical Economics; the destiny of macroeconomics in both theoretical and policy terms, highlighting new roles for interest rates; savers and rentiers; and the relevance of the concepts of ideas, interests and power. In all these respects Keynes is once again far ahead of his time. Finally a debatable topic dealt with by Keynes in Chapter 24 of TGT is 1 PhD in Economics, Lancaster University, UK; Professor-researcher at ISEC Universidad de Negocios, Mexico City. socialisation of investment. This is in words of Skidelsky, a shift in the balance of social power. Keynes is thus in Chapter 24 of TGT a visionary and an idealist, a reformer, and certainly a trans-generational thinker. When he talks about the passion of thriftiness and the setting of reasonable financial rewards arising from financial instruments he is advancing explications for financial crises in terms of speculation. The open conclusion is that Chapter 24 contains the gist of Keynes’s mature philosophical thinking and legacy, confirming that for him attitudes are one of the most relevant issues in life. In addition, he considers that both social and psychological elements are necessary for a thorough understanding of economic issues and their consequences, such as peace and happiness. Section 1 is an introduction. Section 2 is both a literature review and a summary of Keynes’s general philosophical insights. Section 3 is an analysis of Chapter 24 of TGT in the specific fields of Epistemology, Ethics, Ontology, and Political and Social Philosophy. Section 4 is a conclusion. References are listed at the end of the article. (shrink)

The traditional use of conventional media by businesses for audience targeting has shifted with the rise of influencer marketing, notably on platforms like TikTok, posing challenges in content adaptation and technological adaptation. Albert Bandura's Social Cognitive Theory examines factors shaping purchasing behavior, particularly relevant for young professionals. A quantitative correlational study focused on young professionals engaging with TikTok and influenced by Filipino TikTok creators, revealing education level as a key determinant of purchasing behavior. Extended TikTok engagement positively correlates with increased (...) purchasing likelihood. Filipino TikTok influencers significantly impact young professionals' purchasing decisions, emphasizing the need for tailored marketing strategies targeting this demographic. Recommendations were provided for effective influencer and digital marketing strategies targeting young professionals. (shrink)

Our purpose is to study Aristotle?s solution, in the second book of the Posterior Analytics, for the problem of the apprehension of the principles of science. We attend to the relations between the concepts of induction (epagoge) and intelligence (nous) found in the chapter 19, which seems to confirm that the acquisition of the principles is reached by a process of empirical observation. We examine the method, proposed in chapters 13 to 17, for the right formulation of definitions, which seems (...) to attribute to dialectics the task of finding the principles. Aristotle seems to indicate two different methods ? on one hand, the empirical observation followed by intelligence, on other, the dialectics ? for the apprehension of the principles. Our purpose is to study possible solutions for the problem of the concurrence between these two methods in order to refute as much a strictly empiricist interpretation as a strictly dialectical one. (shrink)

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...) The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

Using semi-structured interviews and an analytic approach based on the grounded theory, this research took on constructing an understanding of the socio-emotional relevance, and the meaning that a group of elder participants of CIAM «Lucía Salas Romo» of Quilicura (Santiago, Chile) ascribe to social discourses regarding aging. Findings showed that, mobilizing the semantic dissonance between what society promotes and the effective opportunities it allows for the elderly, there are two crucial components of the social discourse: social injustice and fear of (...) dependency. In turn, these play a central role in elder affectivity and the reformulation of identity during this developmental stage for this group (DOI: 10.33264/rpa.202101). (shrink)

To improve oneself and grow professionally, career development has been found to be crucial, as it serves as a roadmap for the professional growth of employees. However, a barrier, known as the glass ceiling, hinders the progress of employees, especially those in the LGBTQIA+ community. This study explores the impact of the glass ceiling on the career development of selected LGBTQIA+ individuals, shedding light on the barriers faced by this community in the workplace. The researchers used a qualitative multiple-case study (...) and selected ten (10) LGBTQIA+ participants from large enterprises via the judgmental sampling technique. Through thematic analysis, psychological impact, workplace discomfort, lack of recognition, and career progress challenges emerged as the impacts of the glass ceiling on the participants. Strategies for overcoming glass ceiling barriers, such as resilience, self-reflection, and community support, are identified. Thus, the study found that glass ceilings are really evident in the context of businesses. With this, the proposed advocacy plan in the study suggests interventions like workplace inclusion training, mentorship networks, and seminars on employee rights. Furthermore, it emphasizes the call for ongoing research and advocacy efforts to dismantle barriers and cultivate workplaces that not only embrace diversity but also provide equitable opportunities for career growth. (shrink)

In this paper, I discuss how Newton’s inductive argument of the Principia can be defended against criticisms levelled against it by Duhem, Popper and myself. I argue that Duhem’s and Popper’s criticisms can be countered, but mine cannot. It requires that we reconsider, not just Newton’s inductive argument in the Principia, but also the nature of science more generally. The methods of science, whether conceived along inductivist or hypothetico-deductivist lines, make implicit metaphysical presuppositions which rigour requires we make (...) explicit within science so that they can be critically assessed, alternatives being developed and assessed, in the hope that they can be improved. Despite claiming to derive his law of gravitation by induction from phenomena without resource to hypotheses, Newton does nevertheless acknowledge in the Principia that his rules of reasoning make metaphysical presuppositions. To this extent, Newton has a more enlightened view of scientific method than most 20th and 21st century scientists and historians and philosophers of science. (shrink)

In his seminal work “The Concept of Truth in Formalized Languages”, Alfred Tarski showed how to construct a formally correct and materially adequate definition of true sentence for certain formalized languages. These results have, eventually, been accepted and applauded by philosophers and logicians nearly in unison. Its Postscript, written two years later, however, has given rise to a considerable amount of controversy. There is an ongoing debate on what Tarski really said in the postscript. These discussions often regard Tarski as (...) putatively changing his logical framework from type theory to set theory. In what follows, we will compare the original results with those presented two years later. After a brief outline of Carnap’s program in The Logical Syntax of Language we will determine its significance for Tarski’s final results. (shrink)

RESUMO A bovinocultura sempre esteve atrelada ao desenvolvimento do Brasil e, pensando no avanço, as exigências da máxima eficiência nos sistemas de criação foi pautada na forma de como conseguir realizar a reprodução de bovinos com ênfase na eficiência econômica e reprodutiva. O objetivo deste trabalho é elucidar as principais biotecnologias que auxiliam na maior produtividade reprodutiva de bovinos. Dessa forma, o estudo foi realizado usando artigos do banco de dados do Google acadêmico e SciELO, além de livros do acervo (...) pessoal e sites oficiais. Com o manejo reprodutivo aplicado na bovinocultura, é possível identificar pontos a serem melhorados e implantação de práticas que auxiliam no incremento da eficiência reprodutiva como a estação de monta, que concentra a fertilização dos animais em uma determinada época do ano, o uso do índice de escore corporal, o qual consegue determinar a viabilidade da vaca a ser fertilizada, e a identificação da idade a puberdade, na qual a novilha com 60% de peso vivo quando adulta pode estar apta para reprodução, indicando que a nutrição é um fator importante para reduzir o intervalo entre partos, bem como na indução da precocidade, que ainda pode ser maximizada por uso de bioestimuladores. Assim como a implantação do uso de biotecnologias, que podem adicionar aos planteis, indivíduos geneticamente superiores, saudáveis e eficientes. Dentre as biotecnologias, a inseminação artificial é a mais usada no Brasil, com capacidade de fertilizar vacas com sêmen de touros de genética superior, nacional ou importado. Podem ser citadas ainda as técnicas de transferência de embriões e produção in vitro de embriões como tecnologias a serviço do desenvolvimento da eficiência reprodutiva. A utilização de protocolos hormonais no ciclo estral objetiva a sincronização do estro das vacas para facilitar o emprego das biotecnologias. São vários os protocolos usados para essa finalidade, sendo Ovsynch a base de GnRH e prostaglandina com até 50% de eficácia, protocolos à base de estradiol e progesterona com eficácia de até 86,6%, e protocolos que usam gonadotrofina coriônica equina (eCG), indicados para animais magros por condicionar maior diâmetro folicular, o qual é relacionado com aumento na taxa de prenhez. Dessa maneira, as práticas e tecnologias citadas neste estudo são usadas na reprodução assistida de bovinos. PALAVRAS-CHAVE: Criopreservação. Estro. Gestação. Hipófise. Nutrição. ABSTRACT Cattle farming has always been linked to Brazil’s development and, thinking about advancement, the requirements for maximum efficiency in breeding systems was based on how to achieve the reproduction of cattle with an emphasis on economic and reproductive efficiency. The objective of this work is to elucidate the main biotechnologies that help in the greater reproductive productivity of cattle. Thus, the study was done using articles from the Academic Google and SciELO databases, as well as books from the personal collection and official websites. With the reproductive management applied in cattle farming, it is possible to identify points to be improved and implement practices that help to increase reproductive efficiency, such as the breeding season, which concentrates the fertilization of animals at a certain time of year, use of the body score index, which can determine the viability of the cow to be fertilized, identification of age at puberty, in which the heifer with 60% live weight as an adult may be suitable for reproduction, indicating that nutrition is an important factor in reducing the interval between births, as well as in inducing precocity, which can still be maximized by the use of biostimulators. As well as the implementation of the use of biotechnology, which can add genetically superior, healthy and efficient individuals to the breeding stock. Among the biotechnologies, artificial insemination is the most used in Brazil, with the capacity to fertilize cows with superior genetic bull semen, whether national or imported. Embryo transfer techniques and in vitro embryo production can also be cited as technologies in the service of the development of reproductive efficiency. The use of hormonal protocols in the estrous cycle aims at synchronizing the estrus of cows to facilitate the use of biotechnologies. There are several protocols used for this purpose, with Ovsynch being based on GnRH and prostaglandin with up to 50% efficacy, protocols based on estradiol and progesterone with efficacy of up to 86.6%, and protocols that use equine chorionic gonadotropin (eCG), indicated for lean animals because they condition larger follicular diameter, which is related to an increase in the pregnancy rate. Thus, the practices and technologies mentioned in this study can help the assisted reproduction of cattle. KEYWORDS: Cryopreservation. 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In this article we defend a moral conception of cosmopolitanism and its relevance for moral education. Our moral conception of cosmopolitanism presumes that persons possess an inherent dignity in the Kantian sense and therefore they should be recognised as ends‐in‐themselves. We argue that cosmopolitan ideals can inspire moral educators to awaken and cultivate in their pupils an orientation and inclination to struggle against injustice. Moral cosmopolitanism, in other words, should more explicitly inform the work that moral educators do. Real‐world constraints (...) on moral action and the need to prioritise one’s sometimes conflicting responsibilities will often qualify cosmopolitan justice as supererogatory. This fact does not absolve persons from aspiring to see themselves as having the moral obligation to help others in need, while recognising that their factual obligations are more modest in being bound by what they are actually able to do. (shrink)

Wat betreft economische groei en ontwikkeling van de werkloosheid heeft de Nederlandse economie het sinds 1973 slechter gedaan dan andere OECD-landen. Op de vraag naar de oorzaken van die slechte prestatie zijn in het verleden uiteenlopende antwoorden gegeven door o.m. Bomhoff en Clavaux. Ook zijn er diverse wegen aangegeven om op te rukken naar een betere positie. In dit artikel presenteren de auteurs de resultaten van een internationale doorsnee-analyse om de verschillen in economisch succes tussen landen met behulp van een (...) eenvoudig neo-klassiek macro-economisch model te verklaren. Dit biedt de mogelijkheid om te traceren wat de rol van de exportgroei, de groei van de bevolking, de wisselkoers, de verhouding tussen de binnenlandse en de buitenlandse prijsontwikkeling en de investeringsquote voor verschillen in economische ontwikkeling is geweest. Vooral de uitvoer gecorrigeerd voor de omvang van de bevolking, de investeringsquote en de nominale wisselkoers komen als belangrijke verklarende variabelen naar voren. Op grond van hun analyse komen de auteurs tot de conclusie dat een beleid gericht op het verbeteren van de Nederlandse economische prestatie op lange termijn zich vooral zou moeten concentreren op het benutten van exportkansen en op een hoog investeringsniveau ter bevordering van technologische vernieuwing en daarmee verbetering van de concurrentiepositie. Daarbij moet worden voorkomen dat revaluatie van de gulden het exporteffect teniet doet. (shrink)

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for (...) implication. The general introduction rule for negation has a similar form. Maximal formulas with implication or negation as main operator require reduction procedures of a more intricate kind not present in normalisation for intuitionist logic. (shrink)

In this paper the importance of Tarski's truth definition is evaluated like a productive resource to criticize Nietzsche's nihilistic view and any pragmatic understanding of truth.

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...) infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. -/- Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects. (shrink)

Risk Management Strategies and Investment Behaviors are considered important factors in the investing activities of the retail investors. This study seeks to determine the relationship between Risk Management Strategies and Investment Behavior of Generation Z retail investors. The study is a correlational research and purposive sampling was used to select the respondents for this study. Cochran’s formula was utilized to determine the total sample size or total number of respondents. Spearman’s Rank-Order Correlation was employed to assess the significant relationship of (...) Risk Management Strategies and Investment Behaviors. Based on the results, it showed that risk management strategies have a significant relationship with one or more of the investment behaviors. Risk avoidance has a significant relationship with confirmation bias. Risk reduction has a significant relationship with all of the investment behaviors such as overconfidence, loss-aversion, recency bias, and confirmation bias. Risk transfer shows a significant relationship with only loss-aversion and confirmation bias. And lastly, risk acceptance also has a significant relationship with all of the investment behaviors. This study recommends exploring other types of behavioral biases under cognitive bias and emotional bias to determine their correlation with risk management strategies. Also, broadening the sample size, demographic scope, and geographic scope of the study can improve the generalizability of the study and provide a more comprehensive understanding of the relationship between investment behavior and risk management strategies. The researchers also recommend to utilize interviews and focus group discussions to gain an in-depth understanding of the underlying values and attitudes concerning investment behavior. (shrink)

An estimated 700,000 people in the United States have "long COVID," that is, symptoms of COVID-19 persisting beyond three weeks. COVID-19 and its long-term sequelae are strongly influenced by social determinants such as poverty and by structural inequalities such as racism and discrimination. Primary care providers are in a unique position to provide and coordinate care for vulnerable patients with long COVID. Policy measures should include strengthening primary care, optimizing data quality, and addressing the multiple nested domains of inequity.

This article challenges the prevailing interpretations of Hegel's account of the concept "contradiction" in the Science of Logic by arguing that it is concerned with the principle of Hegel's method rather than with the classical law of non-contradiction. I first consider Hegel's Doctrine of Essence in view of Kant's discussion of the concepts of reflection in the first Critique. On this basis, I examine Hegel's account of the logical principles based on the concepts "identity," "opposition," and "contradiction." Finally, I point (...) out how the principle Hegel derives from the concept of contradiction actually informs his own method. (shrink)

In this paper we provide a defence of cosmopolitanism from a liberal perspective, examining its moral underpinnings, including moral obligations predicated on a belief in common humanity and the fundamental dignity of human people, cultural capacities that include an embrace of pluralism and a fallibilist disposition, and pragmatist resolve in finding humanitarian solutions to real problems that people face. We also scrutinise the ideal of cosmopolitanism by considering the ‘deeply religious’ as the sort of people about whom it may be (...) said that irreconcilable tensions exist between certain types of commitment and/or belonging and what the demands of cosmopolitanism involve. (shrink)