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)

In a recent paper by Tranchini (Topoi, 2019), an introduction rule for the paradoxical proposition ρ∗ that can be simultaneously proven and disproven is discussed. This rule is formalized in Martin-Löf’s constructive type theory (CTT) and supplemented with an inferential explanation in the style of Brouwer-Heyting-Kolmogorov semantics. I will, however, argue that the provided formalization is problematic because what is paradoxical about ρ∗ from the viewpoint of CTT is not its provability, but whether it is a proposition at all.

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)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (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)

The problem of rational prediction, launched by Wesley Salmon, is without doubt the Achilles heel of the critical method defended by Popper. In this paper, I assess the response given both by Popper and by the popperian Alan Musgrave to this problem. Both responses are inadequate and thus the conclusion of Salmon is reinforced: without appeal to induction, there is no way to make of the practical prediction a rational action. Furthermore, the critical method needs to be vindicated if one (...) pretends that its application is suitable for the preference of a hypothesis. I argue that the nature of this vindication is such that it may be applied also to induction. Thus, to be a popperian is a good reason also to be an inductivist. (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)

Ambiguity occurs insofar as a reasoner lacks information about the relevant physical probabilities. There are objections to the application of standard Bayesian inductive logic and decision theory in contexts of significant ambiguity. A variety of alternative frameworks for reasoning under ambiguity have been proposed. Two of the most prominent are Imprecise Bayesianism and Dempster–Shafer theory. We compare these inductive logics with respect to the Ambiguity Dilemma, which is a problem that has been raised for Imprecise Bayesianism. We develop (...) an agent-based model comparison that isolates the difference between the two inductive logics in their updating methods. We find that Dempster–Shafer theory does not avoid the Ambiguity Dilemma. We discuss the implications of this result. (shrink)

This essay presents a point of view for looking at `free will', with the purpose of interpreting where exactly the freedom lies. For, freedom is what we mean by it. It compares the exercise of free will with the making of inferences, which usually is predominantly inductive in nature. The making of inference and the exercise of free will, both draw upon psychological resources that define our ‘selves’. I examine the constitution of the self of an individual, especially the (...) involvement of personal beliefs, personal memories, affects, emotions, and the hugely important psychological value-system, all of which distinguish the self of one individual from that of another. The foundational position that adopted in this essay is that all psychological processes are correlated with corresponding ones involving large scale neural aggregates in the brain, communicating with one another through wavelike modes of excitation and de-excitation. Of central relevance is the value-network around which the affect system is organized, the latter, in turn, being the axis around which is assembled the self, with all its emotional correlates. The self is a complex system. I include a brief outline of what complexity consists of. In reality all systems are complex, for complexity is ubiquitous, and certain parts of nature appear to us to be ‘simple’ only in certain specific contexts. It is in this background that the issue of determinism is viewed in this essay. Instead of looking at determinism as a grand principle entrenched in nature independent of our interpretation of it, I look at our ability to explain and to predict events and phenomena around us, which is made possible by the existence of causal links running in a complex course that set up correlations between diverse parts of nature, in this way putting the stamp of necessity on these events. However, the complexity of systems limits our ability to explain and to predict to within certain horizons defined by contexts. Our ability to explain and predict in matters relating to acts of free will is similarly limited by the operations of the self that remain hidden from our own awareness. The aspects of necessity and determinism appear to us in the form of reason and rationality that explain and predict only within a limited horizon, while the rest depends on the complex operation of self-linked psychological resources, where the latter appear as contingent in the context of the exercise of free will. The hallmark of complex systems is the existence of amplifying factors that operate as destabilizing ones, along with inhibiting or stabilizing factors as well that generally limit the destabilizing influences to local occurrences, while preserving the global integrity of a system. This complex interplay of destabilizing and stabilizing influences lead to the possibility of an enormous number of distinct modes of behavior that appear as emergent phenomena in complex systems. Looking at the particular case of the self of an individual that guide her actions and thoughts, it is the operation of our emotions, built around the psychological value-system, that provide for the amplifying and inhibiting factors mentioned above. The operation of these self-linked factors stamps our actions and thoughts as contingent ones that do not fit with our concepts of reason and rationality. And this is what provides the basis of our idea of free will. Free will is not ‘free’ in virtue of exemption from causal links running through all our self-based processes - ones that remain hidden from our awareness, but is free of what is perceived to be ‘reason and rationality’ based on knowledge and the common pool of beliefs and principles associated with a shared world-view. When we speak of the choice involved in an act of exercise of free will what we actually refer to is the commonly observed fact that various different individuals of a similar disposition respond differently when placed under similar circumstances. In other words, free will is ‘free’ precisely because it is not subject to constraints of a commonly accepted and shared set of principles, beliefs, and values. While it is possible that, in an exercise of free will, the self-linked psychological resources are brought into action when a number of alternatives are presented to the self by the operation of the ingredients of a commonly shared world-view, it seems likely that, that set of alternatives is not of primary relevance in the final response that the mind produces, since the latter is primarily a product of the operation of the self-based psychological resources. What is of greater relevance here is the operation of emotion-driven processes, guided by the psychological value-system based on the activity of the so-called reward-punishment network in the brain. These processes lead the individual to a response that appears to be free from the shackles of determinism precisely because their mechanisms, which are hidden from us, do not conform to commonly accepted and shared rules and principles. In contrast, inductive inference is a process that is based on the ‘cognitive face’ of self, where the self-based psychological resources play a supportive role to the commonly shared world-view of an individual. There is never any freedom from the all-pervading causal links representing correlations among all objects, entities, and events in nature. In the midst of all this, the closest thing to freedom that we can have in our life comes with self-examination and self-improvement. The possibility of self-examination appears in the form of specific conjunctions between our complex self-processes and the ceaseless changes of scenario in our external world. This actually makes the emergent phenomenon of self-examination a matter of chance, but one that keeps on appearing again and again in our life. Once realized, self examination creates possibilities that would not be there in the absence of it, and these possibilities include the enhancement of further self-enrichment and further diversity in the exercise of our free will. (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)

SummaryIn this paper, two different theoretical problems of induction are delineated. The first problem is addressed; the second problem is deferred to the sequel to this paper. The first problem of induction is taken to be the seemingly unformalizable nature of traditional inductive arguments. It is shown that the problem does not arise out of some particularly dubious argument form , but rather from the presupposition that inductive “logic” is, like deductive logic, assertoric. Rather , inductive logic (...) is dialectical in nature.RésuméDans cet article, deux problèmes théoriques de l'induction sont formulés. Le premier est traité, le second le sera dans une suite à cet article. Le premier problème de l'induction est ici la nature apparemment non formalisable des arguments inductifs traditionnels. L'auteur montre que le problème ne provient pas d'une forme d'argumentation particulièrement douteuse , mais au contraire de la présupposition que la «logique» inductive est, comme la logique déductive, assertorique. Il soutient au contraire qu'elle est par nature dialectique.ZusammenfassungIn der vorliegenden Arbeit werden zwei theoretische Probleme der Induktion formuliert, wovon das zweite in einem anderen Artikel behandelt werden soll. Das erste Problem betrifft die scheinbar nicht formalisierbare Natur der üblichen induktiven Argumente. Der Verfasser zeigt dass das Problem nicht von einer besonders zweifelhaften Argumentationsform herrührt , sondern von der Voraussetzung, dass die induktive «Logik» — wie die deduktive Logik — assertorisch sei. Es wird dagegen gezeigt, dass die induktive Logik dialektischer Natur ist. (shrink)

Histoire et utilisation du robot Bien que la robotique soit un marché économique relativement jeune et en pleine croissance, la genèse des robots remonte à l’Antiquité. Le premier robot à être déployé sur des lignes d’assemblage est Unimate, utilisé dès 1961 par General Motors. La robotique, en se di usant dans tous les pans de notre économie, va impacter les business modèles de nombreuses industries comme l’automobile et l’aéronautique mais aussi la construction ou l’agriculture. Aujourd’hui les robots industriels et de (...) service servent à de multiples tâches allant de la logistique à l’usinage en passant par la fonderie. La robotique constitue aussi et surtout un enjeu sociétal contribuant à relever les dé s de la mobilité, de la santé, de l’autonomie, du vieillissement et de l’éducation. Absence de dé nition et de régime juridique spéci que au robot En France, la notion de robot ne fait pas l’objet d’une dé nition juridique qui lui est propre. Les dé nitions relatives à l’environnement robotique peuvent tout de même se retrouver dans la norme ISO 8373:2012. Bien que les robots intéressent les juristes à plusieurs titres, le législateur n’a, à ce jour, pas adopté de régime juridique spéci quement applicable aux robots. Il convient donc de rechercher dans le droit positif le corpus de textes applicables aux robots. Ce corpus pourra alors recevoir l’appellation de « droit de la robotique ». Garanties Le vendeur d’un robot industriel et de service doit se conformer aux garanties légales que sont la garantie des vices cachés et la garantie d’éviction. Il doit également respecter les éventuelles garanties qui ont pu être convenues contractuellement Clauses contractuelles Le fournisseur d’un robot industriel et de service doit être particulièrement attentif aux clauses contractuelles rela- tives à la garantie, à la propriété intellectuelle, à la con dentialité, à la responsabilité et à la conformité aux directives techniques. Les spéci cités liées au robot, telles que les éléments relatifs à l’intelligence arti cielle, pourront être intégrées dans des annexes spéci ques. Intelligence arti cielle L’algorithme d’intelligence arti cielle dont est équipé un robot industriel et de service peut, dans certaines condi- tions, béné cier d’une protection grâce au droit d’auteur, à la protection du savoir-faire et au brevet. Aucun régime spécial n’existe à ce jour protégeant les œuvres conçues par le robot intelligent. Mobilité Les véhicules et drones autonomes utilisés au sein même de l’usine sont considérés comme des machines. Etant don- né les risques existants, il convient de xer de règles internes d’utilisation. Les véhicules autonomes ne peuvent à ce jour quitter l’espace privé. En revanche, les drones peuvent circuler dans l’espace aérien en respectant strictement le cadre réglementaire. Douanes Le taux de perception des droits de douanes d’un robot industriel et de service est conditionné par la connaissance de l’origine, préférentielle ou non préférentielle, du robot qui est déterminée par la position tarifaire de ce dernier. Le robot industriel et de service entre dans le chapitre 84, qui concerne notamment les machines, de la nomenclature du système harmonisé établi par l’Organisation mondiale de douanes. Sécurité En application de la « directive machines », le robot peut recevoir la quali cation de machine ou de quasi-machine. En vertu de cette directive, mais également au titre du Code du travail, de nombreuses obligations en matière de santé et de sécurité doivent être respectées pour la commercialisation et l’utilisation des robots. Conformité Le Code du travail, en transposant la « directive machines », a prévu de nombreuses obligations et procédures, appli- cables aux robots industriels et de service, permettant ainsi de s’assurer que ces derniers respectent les exigences de conformité nécessaires en matière de santé et de sécurité. Maintenance Dans le cadre de la maintenance, le fournisseur d’un robot industriel et de service est soumis à plusieurs obligations législatives aux titres de la disponibilité des pièces détachées et de la location. Les dispositions contractuelles de- vront prendre en considération les spéci cités propres au robot et ne pas ignorer la maintenance prédictive. Quali cation juridique Dans le cadre de la conception, de la fabrication et de l’utilisation du robot, il convient de porter une attention par- ticulière à quatre textes spéciaux qui peuvent être applicables aux robots industriels et de service : le règlement 428/2009 sur les biens à double usage, la directive 2014/35/UE applicable au matériel électrique basse tension, la directive 2014/53/UE applicable aux équipements radioélectriques et la directive 2014/30/UE sur la compatibilité électromagnétique. Responsabilité Bien que les régimes de responsabilité, civile et pénale, ne sont pas adaptés aux robots autonomes, la responsabilité civile de droit commun, la responsabilité du fait des choses, la responsabilité du fait des produits défectueux et la responsabilité des commettants du fait de leurs préposés peuvent s’appliquer en cas de fait dommageable causé par le robot tout comme la responsabilité pénale en cas d’infraction commise dans le cadre de l’utilisation du robot. Assurance La police d’assurance relative aux robots doit permettre de protéger le robot contre les risques auxquels ils sont confrontés mais également d’assurer la responsabilité pour les dommages qu’ils pourraient causer, on peut alors parler de « dommages robotiques ». Données et bases de données Les bases de données contenues dans un robot industriel et de service doivent respecter les droits dont dispose l’auteur sur la structure de la base de données et/ou les droits du producteur des bases de données dans lesquelles gurent les données utilisées. La réglementation Informatique et libertés est également applicable au robot lorsque celui-ci collecte et/ou traite des données personnelles. Droit de la robotique dans le monde Aucun Etat ne s’est à ce jour doté d’un régime juridique détaillé et spéci que à la robotique. Des dispositions juri- diques relatives aux robots peuvent tout de même se retrouver de façon éparse dans certains droits étrangers concer- nant notamment les drones et les véhicules terrestres autonomes. (shrink)

On the basis of the distinction between logical and factual probability, epistemic justification is distinguished from logical justification of induction. It is argued that, contrary to the accepted interpretation of Hume, Hume believes that inductive inferences are epistemically legitimate and justifiable. Hence the beliefs arrived at via (correct) inductive inferences are rational beliefs. According to this interpretation, Hume is not a radical skeptic about induction.

La falsifiabilité de Popper a été critiquée à la fois pour avoir exclu la science légitime et pour avoir accordé un statut scientifique aux pseudo-sciences. Selon Larry Laudan, « cela a la conséquence fâcheuse de considérer comme « scientifique » toute demande faisant de fausses allégations de manière concluante ». Certains reprochent à Popper en disant que sa théorie ne constitue pas une alternative légitime aux propositions inductives qu’il critique. Jeffrey soutient que le bayésianisme, qui insiste sur le point de (...) savoir dans quelle mesure les preuves empiriques appuient une hypothèse, est beaucoup plus proche de la pratique scientifique que la falsifiabilité de Popper. DOI: 10.13140/RG.2.2.21235.27680. (shrink)

In this article, I contend that the three Cuban philosophers/pedagogues of the nineteenth century – Félix Varela y Morales, José de la Luz y Caballero, and Enrique José Varona were responsible for overcoming the teaching of late scholastic at the Royal and Pontifical University of St. Jerome of Havana. Against late scholastic philosophers and pedagogues who preferred syllogistic logic and the authority of tradition over induction, they argued in favor of the latter over the first. Since they defended liberal and (...) republican ideas, they also argued against those who appeal to the authority of tradition rather than to our ordinary experiences. Of course, their liberal spirit challenged not only the tyrannical regime imposed by Spain at the time but any other regime whose authority depends on force rather than on the will of the people. (shrink)

This text provides a brief portrait of teacher induction programs in place in the school boards in Quebec and an analysis of three major support systems used. The analysis is based on both the descriptive documents integration programs posted on the website of the Carrefour national de l’insertion professionnelle en enseignement (CNIPE) as well as a review of research. Ce texte présente un bref portrait des programmes d’insertion professionnelle mis en place dans les commissions scolaires québécoises ainsi qu’une analyse de (...) trois des principaux dispositifs de soutien utilisés. L’analyse se base à la fois sur les documents descriptifs des programmes d’insertion mis en ligne sur le site web du Carrefour national de l’insertion professionnelle en enseignement (CNIPE) ainsi que sur une recension des recherches. (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)

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)

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)

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.

The de nition of qualia — a contribution to logical philosophy In my article, I propose an abstract de nition of a quale, which (generally speaking) identi es qualia with sets belonging to certain relational structures. I maintain that my de nition, by not taking advantage of psychological terms, makes the notion of a quale more understandable and the existence of qualia themselves less disputable than is commonly supposed. In addition, I brie y discuss the traditional concept of a quale.

In a first part I present the results of the philosophy of scientific explanation with an attempt to apply them to the case of the theory of evolution. Then I observe that the requirements of modelization of phenomena with the help of inductive logic do not capture efficiently the pertinent factors and fail just as much to exclude those which end up being neutral as explanatory premises. I then query in the direction of confirmation theory, and show that probabilistic (...) reasoning does not possess the syntactic means of testing evolutionary hypotheses in a way that would rely on a valid mode of inference. In a second part, I try to show how biology has oscillated between two privileged modes of explanation, the first one being through form of which I suggest here that it has never been replaced and that it has known a forgotten vitality in the middle and latter part of the 19th Century, and the second one being through function here evaluated critically alongside that of tinkering. Finally, some limits are seen to hold against the pretence to epistemological exclusivism of those two outlooks on the biological object. (shrink)

Grounding is claimed to offer a promising characterization of the fundamental as thatwhich is ungrounded. Detractors of this view argue that there can be fundamental and yet mutuallygrounded entities. Such a possibility undermines the denition of the fundamental as theungrounded. I aim to show, however, that the possibility of fundamental mutually grounded entitiesdoes not force us to renounce the prospects of characterizing fundamentality in terms of ground-ing. To accomplish this aim, I defend a grounding-based view that accommodates fundamentalmutually grounded entities (...) straightforwardly. My denition of fundamentality is similar to, butimportantly different from, one that Karen Bennett discusses. I conclude by resisting two objec-tions raised by Jessica Wilson against the Bennettian framework that also target theproposed view. (shrink)

Knowledge is still an enigma, with its ability to inductively bring out a pattern without restricting itself to an empirical count of situations experienced. Instead of seeing the concept as a weakened object representing an external reality, it is suggested to view knowledge as the bridging of a distance with an ability for the knower to stay connected with outward reality. Attempts at defining an external and quantitative criterion of truth are questioned, as many human performances are not likely to (...) be solved or even properly grasped by the project of artificial intelligence. The positive side of the cognitive constructivist project is finally assessed and it is argued that one of its unexpected results could be to reinsert the human knowing power in the sub-human realm. (shrink)

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the (...) S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

The article is aimed to identify the influence of style of leadership onto the characteristic features of the organizational culture of tourism enterprises. A detailed analysis of the scientific literature about leadership styles has been conducted, wherein some peculiarities of their implementation in the tourism enterprises of Ukraine has been disclosed. The integrated definition of leadership has been updated in view of the current socio-economic conditions. Role of style of leadership as a determinant for type of organizational culture has been (...) proven. Particular attention is paid to the devastating (neurotic) style and the style of non-intervention, which are still not covered by Ukrainian researchers, however, they are relevant for understanding peculiarities of formation and management of the organizational culture related to the tourism and hospitality enterprises. In course of the study the following methods of scientific research have been used: ideographic; formal; content analysis; analysis and synthesis; correlation analysis. The results obtained can be used by practicing managers for selection of a management style, suitable for the established or emerging organizational culture at the enterprise. (shrink)

In the chapter “Information and Content” of their Impossible Worlds, Berto and Jago provide us with a semantic account of information in deductive reasoning such that we have an explanation for why some, but not all, logical deductions are informative. The framework Berto and Jago choose to make sense of the above-mentioned idea is a semantic interpretation of Sequent Calculus rules of inference for classical logic. I shall argue that although Berto and Jago’s idea and framework are hopeful, their (...) class='Hi'>definitions do not capture what is intended. This is so because the definitions are solely based on the logical complexity of an argument and they fail to capture the richness of the non- logical content of that argument. Then I will suggest some amendments to address this problem. Finally, I will extend the application of the definitions to first-order logic. It shall be observed that in some classical deductions, applying contraction may lead to hiding some epistemic impossibilities. This happens when formulae which contribute different propositions to the proof get contracted at the quantified level. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...) not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)

The precautionary principle in public decision making concerns situations where following an assessment of the available scientific information, there are reasonable grounds for concern for the possibility of adverse effects on the environment or human health, but scientific uncertainty persists. In such cases provisional risk management measures may be adopted, without having to wait until the reality and seriousness of those adverse effects become fully apparent. This is the definition of the precautionary principle as operationalized under EU law. The precautionary (...) principle is a deliberative principle. Its application involves deliberation on a range of normative dimensions which need to be taken into account while making the principle operational in the public policy context. Under EU law, any risk management measures to be adopted while implementing the precautionary principle, have to be proportionate to ensure the chosen high level of protection in the European Community. This articlewill illustrate the established practice concerning the release of genetically modified organisms into the environment and how the principle is implemented under hard law. The article also provides an outlook on what this may imply for the relative new case of nanotechnology and the use of precautionary principle within the context of soft law (use of codes of conduct). (shrink)

It is common practice in formal semantics to assume that the context specifies an assignment of values to variables and that the same variables that receive contextually salient values when they occur free may also be bound by quantifiers and λs. These assumptions are at work to provide a unified account of free and bound uses of third person pronouns, namely one by which the same lexical item is involved in both uses. One way to pursue this account is to (...) treat quantifiers and λs as monsters in Kaplan’s sense. We argue that this move should be avoided and explore an alternative route based on the idea that there is a variable assignment coordinate in the context and a variable assignment coordinate in the circumstance of evaluation, with the definition of truth in context identifying them. One fundamental challenge that arises in pursuing a unified account is to explain the difference in the way the gender presuppositions of bound and free pronouns project. The proposal that emerges from the attempt to meet this challenge is a non-indexical account of free third person pronouns and a new conception of the role and structure of assignment functions. (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)

SNePS, the Semantic Network Processing System 45, 54], has been designed to be a system for representing the beliefs of a natural-language-using intelligent system (a \cognitive agent"). It has always been the intention that a SNePS-based \knowledge base" would ultimatelybe built, not by a programmeror knowledge engineer entering representations of knowledge in some formallanguage or data entry system, but by a human informing it using a natural language (NL) (generally supposed to be English), or by the system reading books or (...) articles that had been prepared for human readers. Because of this motivation, the criteria for the development of SNePS have included: it should be able to represent anything and everything expressible in NL; it should be able to represent generic, as well as speci c information; it should be able to use the generic and the speci c information to reason and infer information implied by what it has been told; it cannot count on any particular order among the pieces of information it is given; it must continue to act reasonably even if the information it is given includes circular de nitions, recursive rules, and inconsistent information. (shrink)

Relevant logics provide an alternative to classical implication that is capable of accounting for the relationship between the antecedent and the consequence of a valid implication. Relevant implication is usually explained in terms of information required to assess a proposition. By doing so, relevant implication introduces a number of cognitively relevant aspects in the de nition of logical operators. In this paper, we aim to take a closer look at the cognitive feature of relevant implication. For this purpose, we develop (...) a cognitively-oriented interpretation of the semantics of relevant logics. In particular, we provide an interpretation of Routley-Meyer semantics in terms of conceptual spaces and we show that it meets the constraints of the algebraic semantics of relevant logic. (shrink)

In recent years, in the era of multiple crises, there are many political parties and leaders that use conspiracy theories in their discourse, trying to explain facts and figures on politics, economy, society, environment and space. There is an ongoing debate in populism studies on the possible connection between the populist phenomenon and conspiracy theories, thus creating two main theoretical camps. On the one hand, there are many scholars who recognize a strong correlation between the two phenomena, with some of (...) them believing that they are directly equated. On the other hand, there are several researchers who consider populism as a phenomenon with its own unique essence without predetermined characteristics. Hence, the question that arises here is: Is conspiracism endogenous to populism, or not? In this article, I first look at the definitions of conspiracy theories/conspiracism and populism, attempting to avoid stereotypical readings. After that, I highlight the discussion that takes place in academia around the internal features of the populist phenomenon and its possible connection with conspiracism, with the aim of showing that populism presents a unique logic, without a necessary connection to conspiracism. Finally, I focus on the Greek case of recent years, describing an example where the concept of conspiracy theory became a polemical tool against political rivals, negatively affecting politics and society. My analysis is based on post-structuralist theory and methodological tools of the Essex School of Discourse Analysis, taking into account aspects of other approaches to populism. (shrink)

I take some initial steps toward a theory of real definition, drawing upon recent developments in higher-order logic. The resulting account allows for extremely fine- grained distinctions (i.e., it can distinguish between any relata that differ in their syntactic structure, while avoiding the Russell-Myhill problem). It is the first account that can consistently embrace three desirable logical principles that initially appear to be incompatible: the Identification Hypothesis (if F is, by definition, G then F is the same as G), Irreflexivity (...) (there are no reflexive definitions) and Leibniz’s Law. Additionally, it possesses the resources to resolve the paradox of analysis. (shrink)

Contextual vocabulary acquisition (CVA) is the deliberate acquisition of a meaning for a word in a text by reasoning from context, where “context” includes: (1) the reader’s “internalization” of the surrounding text, i.e., the reader’s “mental model” of the word’s “textual context” (hereafter, “co-text” [3]) integrated with (2) the reader’s prior knowledge (PK), but it excludes (3) external sources such as dictionaries or people. CVA is what you do when you come across an unfamiliar word in your reading, realize that (...) you don’t know what it means, decide that you need to know what it means in order to understand the passage, but there is no one around to ask, and it is not in the dictionary (or you are too lazy to look it up). In such a case, you can try to figure out its meaning “from context”, i.e., from clues in the co-text together with your prior knowledge. Our computational theory of CVA—implemented in a the SNePS knowledge representation and reasoning system [28]—begins with a stored knowledge base containing SNePS representations of relevant PK, inputs SNePS representations of a passage containing an unfamiliar word, and draws inferences from these two (integrated) information sources. When asked to define the word, definition algorithms deductively search the resulting network for information of the sort that might be found in a dictionary definition, outputting a definition frame whose slots are the kinds of features that a definition might contain (e.g., class membership, properties, actions, spatio-temporal information, etc.) and whose slot-fillers contain information gleaned from the network [6–8,20,23,24]. We are investigating ways to make our system more robust, to embed it in a naturallanguage-processing system, and to incorporate morphological information. Our research group, including reading educators, is also applying our methods to the develop-. (shrink)

The two-fold ontological character of linguistic objects revealed due to the distinction between “type” and “token” introduced by Ch. S. Peirce can be a base of the two-fold, both theoretical and axiomatic, approach to the language. Referring to some ideas included in A. A. Markov’s work [1954] (in Russian) on Theory of Algorithms and in some earlier papers of the author, the problem of formalization of the concrete and abstract words theories raised by J. Słupecki was solved. The construction of (...) the theories presented here has two levels. The axiomatic theory of label-tokens: material, physical linguistic objects, constitutes the first one. Label-types, according to the literature of the subject, are defined on the other level as equivalence classes of equiform label-tokens. Assuming the opposite point of view, one can accept that theory of label-types: abstract labels, formalized on the first level, in which it is possible to define the notion of label-token as well as the derivative notions on the second level, should become the basis of formalization of the theory of linguistic expressions and the theory of language in general. The axioms and definitions of both theories of labels: T k and T p representing the other approach to the ontology of language are included in the sequel of the abstract. The foundations of the theory of labels T k in which the primary assumption as to the label-types existence is superfluous have been referred on the basis of the author's monography "Teorie Języków Syntaktycznie Kategorialnych" ( "The Theories of Syntactically Categorial Languages"), PWN, Warszawa-Wrocław 1985. The basis of the theory of labels T p which takes into account the other position has to be presented here for the first time. Some extended ideas of the paper will also be presented in author's paper "Logiczne podstawy ontologii składni Języka" ("Logical foundations of language syntax ontology), Studia Filozoficzne 6-7 (271-272), (1988), pp. 263-284. (shrink)

This article aims to elucidate, albeit in a preliminary way, the concept of liquidity in Zygmunt Bauman and its effects onsociety. The deductive-inductive method will be used. As for the methodology, this will be of a bibliographic nature. This study is in line with what the sociologist Zygmunt Bauman (1925-2017), in his texts, postulates that Modernity can be divided into two phases: Solid Modernity and Liquid Modernity. The first began in the 15th century and lasted until the 19th century; (...) the second began in the 20th century and continues to the present time. To describe modern society from the end of the 20th century, Bauman uses the metaphor of 'liquidity', aiming to point out that the contemporary world is going through a period of uncertainty, ephemerality and instabilities. According to Bauman, the modern ideal coined between the 15th and 19th centuries postulated the primacy of reason and the autonomy of capitalist man and such assumptions led society to liquid modernity. In this liquid “contemporaneity”, nothing is lasting, everything is volatile, ephemeral; consumption is the social parameter, whether of the individual, the family, the State or religion. (shrink)

This paper argues for a reinterpretation of Aristotle's concept of an enthymeme and also his wider informal logic in terms of arguments that are defeasible. They are represented by forms of argument that are called argumentation schemes, considered to be similar to forms of argument found in deductive logic, but different from the foregoing in virtue of their being defeasible. Indeed, the most interesting schemes have been put forward as a helpful way of characterizing structures of human reasoning that have (...) proved troublesome to model deductively. The paper sheds new light on Aristotle's topics and how to dene `enthymeme'. If the traditional denition of an enthymeme in logic accepted for over two thousand years is a misnomer, the question is raised whether we ought to redene it as a defeasible argumentations scheme or leave things as they are. (shrink)

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)

the purpose of this paper is to o er a logico‐philosophical critical overview of the theory of multiple realities (tWr). the paper is divided into three sections. In the rst section I present a brief history of the development of some ideas, which combined together form the conceptual amework of the theory in question, whose main thesis is that there is more than one reality. In the second part I present (and try to address) some interpretations of tWr, which can (...) be described as: ontological; epistemological; esthetical; logical ad mixed interpretations. When do‐ ing so, a special emphasis is laid on the presentation of an explication of tWr based on theory of models, an explication authored by teresa Kostyrko. this explication rests on a conditional recognition of the particular ‘realities’ of Chwistek’s theory as proper models (i.e. those, which ful ll the condition of the identity of meaning of theory’s fundamental notions) of the theories of reality, with the provision that such models are indeed constructible. In the last section of my paper I propose a preliminary appraisal of the tWr as well as a way to reengineer this theory in order to avoid some of its di culties. By appealing to Kostyrko’s idea on one hand and the spirit Quinean ontological relativism on the other, I wish to argue as follows: ‘reality’ is the name of the set comprising all meanings of the term ‘reality’; under particular conditions these meanings can be arranged in a theory, which posseses a proper model (scienti c discourse, some forms of the common talk); model proper designate by de nition classes of objects, which we regard as existent on the grounds of a given theory. the above set of theses forms the core of a concept, which I propose to call the ‘manifold reality’ in order to di erentiate it om tWr, the development of which theory it is, as well as its modi cation towards a new kind of ontology. (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)

The central topic of this article is (the possibility of) de re knowledge about natural numbers and its relation with names for numbers. It is held by several prominent philosophers that (Peano) numerals are eligible for existential quantification in epistemic contexts (‘canonical’), whereas other names for natural numbers are not. In other words, (Peano) numerals are intimately linked with de re knowledge about natural numbers, whereas the other names for natural numbers are not. In this article I am looking for (...) an explanation of this phenomenon. It is argued that the standard induction scheme plays a key role. (shrink)

For years, the European world saw millions of swans, and all of them without exception were white. If inductive reasoning is valid, one may conclude that all swans are white. However, this would be incorrect: in 1667 Dutch explorer Willem de Vlamingh observed black swans in Australia, falsifying the hypothesis that all swans are white. While often used as a cautionary tale for the use of induction, such as with Popper’s falsification principle, I want to explore a slightly different (...) idea: does the existence of fabricated or otherwise failed accounts of Black swans give me a reason to ignore future arguments or doubt their existence? I argue that while faulty or fabricated reports do not give us a logical reason to reject a claim, they can give us a practical one for refusing to consider future arguments. This practical vs logical distinction gives an inductive reason for believing that future arguments will be invalid, but keeps one from being able to necessarily deny the claim in question without further argumentation. (shrink)

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)

Normatively inappropriate scientific dissent prevents warranted closure of scientific controversies and confuses the public about the state of policy-relevant science, such as anthropogenic climate change. Against recent criticism by de Melo-Martín and Intemann of the viability of any conception of normatively inappropriate dissent, I identify three conditions for normatively inappropriate dissent: its generation process is politically illegitimate, it imposes an unjust distribution of inductive risks, and it adopts evidential thresholds outside an accepted range. I supplement these conditions with an (...) inference-to-the-best-explanation account of knowledge-based consensus and dissent to allow policy makers to reliably identify unreliable scientific dissent. (shrink)

In this essay we collect and put together a number of ideas relevant to the under- standing of the phenomenon of creativity, confining our considerations mostly to the domain of cognitive psychology while we will, on a few occasions, hint at neuropsy- chological underpinnings as well. In this, we will mostly focus on creativity in science, since creativity in other domains of human endeavor have common links with scientific creativity while differing in numerous other specific respects. We begin by briefly (...) introducing a few basic notions relating to cognition, among which the notion of ‘concepts’ is of basic relevance. The myriads of concepts lodged in our mind constitute a ‘conceptual space’ of an enormously complex structure, where con- cepts are correlated by beliefs that are themselves made up of concepts and are as- sociated with emotions. The conceptual space, moreover, is perpetually in a state of dynamic evolution that is once again of a complex nature. A major component of the dynamic evolution is made up of incessant acts of inference, where an inference occurs essentially by means of a succession of correlations among concepts set up with beliefs and heuristics, the latter being beliefs of a special kind, namely, ones relatively free of emotional associations and possessed of a relatively greater degree of justification. Beliefs, along with heuristics, have been described as the ‘mind’s software’, and con- stitute important cognitive components of the self-linked psychological resources of an individual. The self is the psychological engine driving all our mental and physical activity, and is in a state of ceaseless dynamics resulting from one’s most intimate ex- periences of the world accumulating in the course of one’s journey through life. Many of our psychological resources are of a dual character, having both a self-linked and a shared character, the latter being held in common with larger groups of people and imbibed from cultural inputs. We focus on the privately held self-linked beliefs of an individual, since these are presumably of central relevance in making possible inductive inferences – ones in which there arises a fundamental need of adopting a choice or making a decision. Beliefs, decisions, and inferences, all have the common link to the self of an individual and, in this, are fundamentally analogous to free will, where all of these have an aspect of non-determinism inherent in them. Creativity involves a major restructuring of the conceptual space where a sustained inferential process eventually links remote conceptual domains, thereby opening up the possibility of a large number of new correlations between remote concepts by a cascading process. Since the process of inductive inference depends crucially on de- cisions at critical junctures of the inferential chain, it becomes necessary to examine the basic mechanism underlying the making of decisions. In the framework that we attempt to build up for the understanding of scientific creativity, this role of decision making in the inferential process assumes central relevance. With this background in place, we briefly sketch the affect theory of decisions. Affect is an innate system of response to perceptual inputs received either from the exter- nal world or from the internal physiological and psychological environment whereby a positive or negative valence gets associated with a perceptual input. Almost every sit- uation faced by an individual, even one experienced tacitly, i.e., without overt aware-ness, elicits an affective response from him, carrying a positive or negative valence that underlies all sorts of decision making, including ones carried out unconsciously in inferential processes. Referring to the process of inferential exploration of the conceptual space that gener- ates the possibility of correlations being established between remote conceptual do- mains, such exploration is guided and steered at every stage by the affect system, analogous to the way a complex computer program proceeds through junctures where the program ascertains whether specified conditions are met with by way of generating appropriate numerical values – for instance, the program takes different routes, depending on whether some particular numerical value turns out to be positive or negative. The valence generated by the affect system in the process of adoption of a choice plays a similar role which therefore is of crucial relevance in inferential processes, especially in the exploration of the conceptual space where remote domains need to be linked up – the affect system produces a response along a single value dimension, resembling a number with a sign and a magnitude. While the affect system plays a guiding role in the exploration of the conceptual space, the process of exploration itself consists of the establishment of correlations between concepts by means of beliefs and heuristics, the self-linked ones among the latter having a special role in making possible the inferential journey along alternative routes whenever the shared rules of inference become inadequate. A successful access to a remote conceptual domain, necessary for the creative solution of a standing problem or anomaly – one that could not be solved within the limited domain hitherto accessed – requires a phase of relatively slow cumulative search and then, at some stage, a rapid cascading process when a solution is in sight. Representing the conceptual space in the form of a complex network, the overall process can be likened to one of self-organized criticality commonly observed in the dynamical evolution of complex systems. In order that inferential access to remote domains may actually be possible, it is necessary that restrictions on the exploration process – necessary for setting the context in ordinary instances of inductive inference – be relaxed and a relatively free exploration in a larger conceptual terrain be made possible. This is achieved by the mind going into the default mode, where external constraints – ones imposed by shared beliefs and modes of exploration – are made inoperative. While explaining all these various aspects of the creative process, we underline the supremely important role that analogy plays in it. Broadly speaking, analogy is in the nature of a heuristic, establishing correlations between concepts. However, analo- gies are very special in that these are particularly effective in establishing correlations among remote concepts, since analogy works without regard to the contiguity of the concepts in the conceptual space. In establishing links between concepts, analogies have the power to light up entire terrains in the conceptual space when a rapid cas- cading of fresh correlations becomes possible. The creative process occurs within the mind of a single individual or of a few closely collaborating individuals, but is then continued by an entire epistemic community, eventually resulting in a conceptual revolution. Such conceptual revolutions make pos- sible the radical revision of scientific theories whereby the scope of an extant theory is broadened and a new theoretical framework makes its appearance. The emerging theory is characterized by a certain degree of incommensurability when compared with the earlier one – a feature that may appear strange at first sight. But incommen- surability does not mean incompatibility and the apparently contrary features of the relation between the successive theories may be traced to the multi-layered structureof the conceptual space where concepts are correlated not by means of single links but by multiple ones, thereby generating multiple layers of correlation, among which some are retained and some created afresh in a conceptual restructuring. We conclude with the observation that creativity occurs on all scales. Analogous to correlations being set up across domains in the conceptual space and new domains being generated, processes with similar features can occur within the confines of a domain where a new layer of inferential links may be generated, connecting up sub- domains. In this context, insight can be looked upon as an instance of creativity within the confines of a domain of a relatively limited extent. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses to truth. Then (...) I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)

De Ray argues that relying on inference to the best explanation (IBE) requires the metaphysical belief that most phenomena have explanations. I object that instead the metaphysical belief requires the use of IBE. De Ray uses IBE himself to establish theism that God is the cause of the metaphysical belief, and thus he has the burden of establishing the metaphysical belief independently of using IBE. Naturalism that the world is the cause of the metaphysical belief is preferable to theism, contrary (...) to what de Ray thinks. (shrink)

Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intra-mathematical explanation and the second is dedicated to extra-mathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intra-mathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...) mathematical induction are addressed. Regarding the extra-mathematical explanation, modal, abstract and deductive models are addressed. (shrink)