Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s methods. Several (...) possible solutions are explored and rejected. (shrink)

It has been argued that an advantage of the safety account over the sensitivity account is that the safety account preserves epistemic closure, while the sensitivity account implies epistemic closure failure. However, the argument fails to take the method-relativity of the modal conditions on knowledge, viz., sensitivity and safety, into account. In this paper, I argue that the sensitivity account and the safety account are on a par with respect to epistemic closure once the method-relativity of the modal conditions is (...) taken into account. Therefore, epistemic closure is no longer an arbiter in the debate. (shrink)

El artículo tiene como objetivo describir las competencias informacionales a desarrollar durante la formación profesional. Se presenta los referentes teóricos a partir del empleo de un enfoque de sistema que supone el análisis y la síntesis, la inducción y la deducción como métodos de investigación, con el propósito de dar conocer los hitos en las universidades y organizaciones internacionales relacionadas. La modelación fue empleada para la construcción de un nuevo proyecto de desarrollo de competencias informacionales desde la perspectiva de la (...) formación profesional universitaria ajustada a las necesidades de la educación superior en Cuba. El nuevo proyecto se configura en tres unidades básicas (acceso, procesamiento y comunicación), con sus respectivos elementos de competencia, saberes esenciales e indicadores para la evaluación del desempeño. El artículo fundamenta la tesis de que el desarrollo de competencias informacionales debe ser sistemáticamente estructurado, planificado y ejecutado como parte integral de la formación curricular en interacción con los contenidos de las disciplinas docentes, bajo la dirección del profesor y la participación protagónica de los profesionales en formación. -/- ABSTRACT -/- The article aims at describing the competence to be developed during professional training. It presents the theoretical referents by means of an approach system that includes synthesis and analysis, induction and deduction as research methods in order to reveal the milestones of information skills development in universities and related international organizations. Modeling was used for the construction of a new skills development project from the perspective of university professional training according to the needs of Higher Education in Cuba. The new project is composed of three basic units (access, processing and communication), with their respective competence elements, essential knowledge and indicators for the evaluation of the performance. The article supports the theory that information development skills must be systematically structured, planned and implemented as an integral part of the curricular training in interaction with the contents of subjects, under the teacher´s guidance and the active participation of profesionals in training. -/- . (shrink)

It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that single-premise closure succumbs to (...) risk aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...) are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

The vision of natural kinds that is most common in the modern philosophy of biology, particularly with respect to the question whether species and other taxa are natural kinds, is based on a revision of the notion by Mill in A System of Logic. However, there was another conception that Whewell had previously captured well, which taxonomists have always employed, of kinds as being types that need not have necessary and sufficient characters and properties, or essences. These competing views employ (...) different approaches to scientific methodologies: Mill’s class-kinds are not formed by induction but by deduction, while Whewell’s type-kinds are inductive. More recently, phylogenetic kinds (clades, or monophyletic-kinds) are inductively projectible, and escape Mill’s strictures. Mill’s version represents a shift in the notions of kinds from the biological to the physical sciences. (shrink)

Theorists of the legal process in common law countries have, in recent years, been preoccupied with hard cases. A hard case occurs where a legal rule or legal rules cannot determine a uniquely correct result when applied to given facts. This paper examines what theorists and law practitioners alike have believed to be a very different kind of case: the clear case. Practising lawyers assure us that clear cases occupy a large percentage of their case load. Professional law teachers design (...) teaching materials and often conduct themselves in the classroom with apparent assurance that most cases in the 'real world' of a law practice are clear cases. The lawyer is presented with material facts and rules which are rid of the difficulties giving rise to hard cases. The facts have been ascertained and proved. The lawyer has been able to sort out the material from the immaterial facts with a much-envied ability to determine the criteria of materiality. He has also discovered the rules and somehow has rejected some and accepted others as legally relevant. The lawyer need only deduce a conclusion by applying the relevant rule to the material facts. Choice, uncertainty, or human frailty enter the picture only when the lawyer makes that final deduction. Consequently, clear cases are supposed to be relatively easy. This Paper questions whether there is more to the competent lawyer's job in clear cases than carrying on the deductive process of applying the relevant rule to the material facts. The primary objective of this essay is to make an argument concerning the issue as to whether there is more to the competent lawyer's job in clear cases than carrying on the deductive process of applying the relevant rule to the material facts. My argument hinges upon what constitutes a properly decided judicial decision. And this, in turn, depends upon the differing conceptions about justice which underlie the activities of courts and legislatures in a democratic state. The Paper then connects those differing conceptions to such concepts as formal justice, substantive justice, liberty, guidance to lawyers, and accountability in the context of clear cases. (shrink)

In this article, I propose a formal criterion that distinguishes between deductively valid arguments that do and do not beg the question. I define the concept of a Never-failing Minimally Competent Knower (NMCK) and suggest that an argument begs the question just in case it cannot possibly assist an NMCK in extending his or her knowledge.

In Ancient Greece, when philosophy began, it included all the theoretical knowledge. But later, in the time of Aristotle, specialized sciences started to emerge and the scope of philosophy grew smaller and smaller. The question is what to do when philosophy has lost its competence to deal with any relevant topic. The paper discusses three possible views of the relation between philosophy and science: anti-scientism, conceptual analysis and naturalism. All these approaches deal with various disadvantages. For anti-scientism it is mainly (...) the inability to explain the unprecedented success of modern science. Proponents of conceptual analysis are confronted with Quine’s attack on analytic statements and its consequences for a priori truths. Finally, naturalistic philosophers might be threatened by hegemony of science and its universal application of hypothetico-deductive method. The worst scenario for naturalistic philosophers is not as bad as some worry. Philosophers can solve their traditional problems using the knowledge of well-established special sciences, even though they might play the role of high-end science journalists. (shrink)

In my review I shall look upon the theology of the Incarnation. The “mystery of Christ”, in the words of Polycarp, that created the centre and “stood at the very heart of the St. Maximus’ synthesis.” Maximus’ stands within the Cyrillian-Chalcedonian situation.’ This situation is eminent by three main properties. First is the acceptance of the Theopaschite form of St. Cyril. Second is that there was no contradiction into St. Cyril and the Council of Chalcedon. Third and finally is the (...) term of a consistent terminology into Triadology and Christology that is relevant to both. We shall see later in this paper, the Chalcedonian theme of “precision” and “tautology,” with respect to Christ’s natures, similarly role in Maximus’ vision of the divine incarnation of the logoi or power with respect to each other and the divine essence. It is within this deduction that Maximum “was competent of establishing the orthodox solution of the Monothelite question.” I will outline the metaphysics of Monenergism, its three folds dialectic, Maximum break up of this dialectic, and conclude with Maximu’s overall matrix for a coherent doctrine of predestination absorb under Christology and Eschatology. (shrink)

(1) In the first part of this paper, I review Chomsky's meandering journey from the formalism/mentalism of Syntactic Structures, through several methodological positions, to the minimalist theory of his latest work. Infected with mentalism from first to last, each and every position vitiates Chomsky's repeated claims that his theories will provide useful guidance to later theories in such fields as cognitive psychology and cognitive neuroscience. With the guidance of his insights, he claims, psychologists and neuroscientists will be able to avoid (...) costly dead-end lines of research. -/- (2) This never happened. As I have shown, this never could have happened. (See Johnston, 2018). What has happened, instead, is that current neurolinguistic research (with the arguable exception of the now-dated Lemma Model of Willem Levelt) proceeds without reference to Chomsky. It also wholeheartedly rejects the mentalism of the associated Language of Thought theory of Jerry Fodor. (See Johnston, 2018). -/- (3) I make this argument in the first part of this paper. I would also like to point out that most of my argument was developed in 1972, when I was a graduate student. I know of no other sustained criticisms of Chomsky at that time, and certainly none along the lines I had developed back then. -/- (4) In the second part of this paper, I present my own account of the methodology of science. When I was a graduate student, philosophy of science was dominated by an attempt to describe a methodology common to all the specific sciences, i.e. Hempel’s deductive-nomological model. These days, Hempel’s emphasis on the methodological unity of science has been rejected by such “dis-unity” philosophers of science as Ian Hacking, Patrick Suppes and Nancy Cartwright (see Cat, 2021). -/- (5) I view this change as the swing of a pendulum or, to change the metaphor, a journey from one end point of a continuum to another. As the level of abstraction at which one tries to describe scientific method is raised, the descriptions become increasingly general. Whether or not unity-of-science theories become so general as to be vacuous, is ultimately a subjective judgment. And so I expect that philosophers will eventually become tired of increasingly specific “close to the workbench” descriptions of how scientists work, and begin to turn back to methodological “big pictures”, finding in them powerful abstractions rather than empty irrelevancies. -/- (6) In the second part of this paper, I present my own account of the methodology of science, which I would situate somewhere between the “unity” and “dis-unity” accounts. However, I am not a scientist. My own views about scientific method have three origins: -/- (6a) my work as a graduate student from 1966 until I passed my comprehensive exams in 1973 (at a different university); -/- (6b) reading every issue of Scientific American from 1972 until nearly 2000, (at which point I continued to read it only sporadically, since I concluded that, around that time, it had evolved from a serious science magazine to a popular science magazine); and -/- (6c) my three-year immersion in the cognitive neuroscience of language after I retired, based on repeated study of and note-taking for (Banesh & Compton, 2018), (Kemmerer, 2015), several other books and, finally, numerous articles not hidden behind a paywall. -/- So, as always with my writings: caveat emptor. (shrink)

If a conclusion was reached that creatures without a language capability exhibit some form of a capability for logic, this would shed a new light on the relationship between logic, language, and thought. Recent experimental attempts to test whether some animals, as well as pre-linguistic human infants, are capable of exclusionary reasoning are taken to support exactly that conclusion. The paper discusses the analyses and conclusions of two such studies: Call’s (2004) two cups task, and Mody and Carey’s (2016) four (...) cups task. My paper exposes hidden assumptions within these analyses, which enable the authors to settle on the explanation which assigns logical capabilities to the participants of the studies, as opposed to the explanations which do not. The paper then demonstrates that the competing explanations of the experimental results are theoretically underdeveloped, rendering them unclear in their predictions concerning the behavior of cognitive subjects, and thus difficult to distinguish by use of experiments. Additionally, it is questioned whether the explanations are rivals at all, i.e. whether they compete to explain the cognitive processes of the same level. The contribution of the paper is conceptual. Its aim is to clear up the concepts involved in these analyses, in order to avoid oversimplified or premature conclusions about the cognitive abilities of pre- and non-linguistic creatures. It is also meant to show that the theoretical space surrounding the issues involved might be much more diverse and unknown than many of these studies imply. (shrink)

Knowledge representation (KR) is actually more than representation: It involves also inference, namely inference of “new” knowledge, i.e. new facts. Logic programming is a suitable KR medium, but more often than not discussions on this programming paradigm focus on aspects other than KR. In this paper, I elaborate on the general theory of logic programming and give the essentials of two of its main implementations, to wit, Prolog and Datalog, from the viewpoint of deductive computing over knowledge bases, which includes (...) deductive programming. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...) number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both with (...) one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values. (shrink)

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some (...) point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

From the second half of the last century, there has been a widespread view in the Anglophone world that Kant’s transcendental deduction (aka TD) aims to vindicate our common-sense view of the world as composed of public and objective particulars against some unqualified forms of skepticism. This widespread assumption has raised serious doubt not only about the success of TD but also about the very nature of its argument in both editions of the Critique. Yet, if there is a (...) connection between TD and global skepticism, the intriguing question is: Who is this skeptic? According to Strawson, “the skeptic” is a hypothesis of a purely sense-datum experience. In contrast, the fact that TD turns on the key notion of self-consciousness has induced several other scholars to assume that the skeptic is no none but a Cartesian external-world skeptic. None of those readings find textual support or are compatible with the very structure of the first Critique. The question is: Does this mean that TD aims only to undermine empiricism, as Guyer suggests? I do not believe so. I am pretty convinced that TD addresses a peculiar form of global skepticism, namely “Hume’s challenge to reason.” Assuming that we cognize (erkennen) and experience (erfahren) appearances as objects as a requirement of Newtonian physics, TD aims to provide a justification of the principle that nature is uniform that is superior to Hume’s justification. (shrink)

In Education Sciences, the notion of ‘competence’ is widely used, both as an aim to be reached with students and as performance in teachers’ education. This article advances a type of competence that is highly relevant for teachers’ work, namely the ‘ethical competence.’ Ethical competence enables teachers to responsibly deal with the daily challenges arising from their professional roles. In this study, I put forward a definition of ethical competence and I propose a conceptual structure, both meant to support the (...) illustration, description, and development of ethical competence for teachers. (shrink)

Because corporate social responsibility can be beneficial to both companies and its stakeholders, interest in factors that support CSR performance has grown in recent years. A thorough integration of CSR in core business processes is particularly important for achieving effective long-term CSR practices. Here, we explored the individual CSR-related competencies that support CSR implementation in a corporate context. First, a systematic literature review was performed in which relevant scientific articles were identified and analyzed. Next, 28 CSR directors and managers were (...) interviewed. The literature review complemented with interview data resulted in the following eight distinct CSR-related competencies: Anticipating CSR challenges; Understanding CSR-relevant systems and subsystems; Understanding CSR-relevant standards; CSR management competencies, including Leading CSR programs, Managing CSR programs, and Identifying and realizing CSR-related business opportunities; Realizing CSR-supportive interpersonal processes; Employing CSR-supportive personal characteristics and attitudes; Personal value-driven competencies, including Ethical normative competencies, Balancing personal ethical values and business objectives, and Realizing self-regulated CSR-related behaviors and active involvement; and Reflecting on personal CSR views and experiences. Based on these results, implications for further research on this topic, as well as implications for practitioners, are discussed. (shrink)

Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. (...) I prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions (...) of the connectives in question. (shrink)

In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...) the paper, I then argue, on the basis of epistemic communism, for a view about rationality itself. I set up the argument in section 2 by saying what a theory of rational deduction is supposed to do. I claim that such a theory would provide a necessary, sufficient, and explanatorily unifying condition for being a rational rule for inferring deductive consequences. I argue in section 3 that, given epistemic communism and the conventionality that it entails, there is no such theory. Nothing explains why certain rules for deductive reasoning are rational. (shrink)

The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.

The definitions of ‘deduction’ found in virtually every introductory logic textbook would encourage us to believe that the inductive/deductive distinction is a distinction among kinds of arguments and that the extension of ‘deduction’ is a determinate class of arguments. In this paper, we argue that that this approach is mistaken. Specifically, we defend the claim that typical definitions of ‘deduction’ operative in attempts to get at the induction/deduction distinction are either too narrow or insufficiently precise. We (...) conclude by presenting a deflationary understanding of the inductive/deductive distinction; in our view, its content is nothing over and above the answers to two fundamental sorts of questions central to critical thinking. (shrink)

Looking at every sense this article proves through deduction; that your mind needs a source to dream. Dreams are old experienced essences of platonic forms. You can only experience new forms essences when you are awake because of initial experiences. If dreams are old, experienced essences (what this article proves) therefore you know you are awake when you initially sense new experienced essences.

ABSTRACTAchievements are among the things that make a life good. Assessing the plausibility of this intuitive claim requires an account of the nature of achievements. One necessary condition for achievement appears to be that the achieving agent acted competently, i.e. was not just lucky. I begin by critically assessing existing accounts of anti-luck conditions for achievements in both the ethics and epistemology literature. My own proposal is that a goal is reached competently, only if the actions of the would-be-achiever make (...) success likely, and that this is the reason why she acts that way. (shrink)

This chapter investigates different ways that pro tanto reasons bearing on our options can compete with one another in order to determine the overall normative status of those options. It argues for two key claims: (i) any theory of this competition must include a distinct role for reasons against, in addition to reasons for, and (ii) any theory must allow for comparative verdicts about how strongly supported the options are by the reasons, rather than simply which options are permissible or (...) required. A simple balancing account and an account based on a distinction between requiring and justifying reasons are rejected, and a new account giving a distinct role for reasons against is introduced. (shrink)

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and that it (...) is in good epistemic standing. (shrink)

This article examines how deduction preserves certainty and how much certainty it can preserve according to Descartes’s Rules for the Direction of the Mind. I argue that the certainty of a deduction is a matter of four conditions for Descartes. First, certainty depends on whether the conjunction of simple propositions is composed with necessity or contingency. Second, a deduction approaches the certainty of an intuition depending on how many “acts of conceiving” it requires and—third—the complexity or difficulty (...) of the acts of thinking, which is determined by the content of the thoughts and on external factors. Fourth, certainty depends on the intellectual aptitude of the person using the deduction. A deduction lacks certainty when it relies on memory such that it is not apprehended with immediacy. However, the mental capacity and speed of a mind can be increased by training the special mental faculties of perspicacity and discernment. Increasing one’s intellectual aptitude allows for more steps of a deduction to be inferred in fewer acts of conceiving, thereby helping preserve the certainty of a deduction. (shrink)

The deduction of categories in the 1781 edition of the Critique of the Pure Reason (A Deduction) has “two sides”—the “objective deduction” and the “subjective deduction”. Kant seems ambivalent about the latter deduction. I treat it as a significant episode of Kant’s thinking about categories that extended from the early 1770s to around 1790. It contains his most detailed answer to the question about the origin of categories that he formulated in the 1772 letter to (...) Marcus Herz. The answer is that categories are generated a priori through a kind of intellectual “epigenesis”. This account leaves unexplained why precisely such and such categories should be generated. While this observation caused Kant to worry about the hypothetical status of the subjective deduction in 1781, he would come to acquiesce in the recognition that the ground of the possibility of categories is itself inscrutable. I call this his “methodological skepticism”. (shrink)

In relation to inferences, there is a tendency to conflate alethic with epistemic modalities. Concerning deductive inferences, necessity is conflated with certainty, but deductive inferences can be just likely based on the available evidence. Non-deductive inferences are defined by their uncertainty, but their epistemic status is insufficient to distinguish them from deductive inferences.

The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids inference to (...) the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated. (shrink)

In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s proof (...) of the validity of the categories in the objective deduction. I challenge this standard reading of the subjective deduction, arguing, first, that there is little textual evidence for it, and, second, that it encourages a problematic conception of how the deduction works. In its place, I present a new reading of the subjective deduction. Rather than being a broad investigation of our cognitive faculties, it should be seen as addressing a specific worry that arises in the course of the objective deduction. The latter establishes the need for a necessary connection between our capacities for thinking and being given objects, but Kant acknowledges that his readers might struggle to comprehend how these seemingly independent capacities are coordinated. Even worse, they might well believe that in asserting this necessary connection, Kant’s position amounts to an implausible subjective idealism. The subjective deduction ismeant to allay these concerns by showing that they rest on a misunderstanding of the relation between these faculties. This new reading of the subjective deduction offers a better fit with Kant’s text. It also has broader implications, for it reveals the more philosophically plausible account of our relation to the world as thinkers that Kant is defending – an account that is largely obscured by the standard reading of the subjective deduction. (shrink)

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Duncan Pritchard recently proposed a Wittgensteinian solution to closure-based skepticism. According to Wittgenstein, all epistemic systems assume certain truths. The notions that we are not disembodied brains, that the Earth has existed for a long time and that one’s name is such-and-such all function as “hinge commitments.” Pritchard views a hinge commitment as a positive propositional attitude that is not a belief. Because closure principles concern only knowledge-apt beliefs, they do not apply to hinge commitments. Thus, from the fact that (...) a subject knows that he is sitting in a room, and the fact that the subject’s sitting in a room entails his bodily existence, it does not follow that the subject also knows that he is not an envatted brain. This paper rejects Pritchard’s non-belief reading of hinge commitments. I start by showing that the non-belief reading fails to solve the skeptical paradox because the reasons that Pritchard uses to support the non-belief reading do not exempt hinge propositions from closure principles. I then proceed to argue that the non-belief reading is false as it claims that hinge commitments, unlike ordinary beliefs, are rationally unresponsive—with the help of a scenario in which a subject’s experience is internally chaotic, we can safely conclude that the hinge commitment that one is not systematically mistaken about the world is equally responsive to one’s evidential situations. (shrink)

The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive (...) stage of a single conclusion mentioned above. The concept of “transcendental invariance” meaning ontologically and physically interpreting the mathematical equivalence of the axiom of choice and the well-ordering “theorem” is utilized again. Then, time arrow is a corollary from that transcendental invariance, and in turn, it implies quantum information conservation as the Noether correlate of the linear “increase of time” after time arrow. Quantum information conservation implies a few fundamental corollaries such as the “conservation of energy conservation” in quantum mechanics from reasons quite different from those in classical mechanics and physics as well as the “absence of hidden variables” (versus Einstein’s conjecture) in it. However, the paper is concentrated only into the inference of another corollary from quantum information conservation, namely, dark matter and dark energy being due to entanglement, and thus and in the final analysis, to the conservation of quantum information, however observed experimentally only on the “cognitive screen” of “Mach’s principle” in Einstein’s general relativity. therefore excluding any other source of gravitational field than mass and gravity. Then, if quantum information by itself would generate a certain nonzero gravitational field, it will be depicted on the same screen as certain masses and energies distributed in space-time, and most presumably, observable as those dark energy and dark matter predominating in the universe as about 96% of its energy and matter quite unexpectedly for physics and the scientific worldview nowadays. Besides on the cognitive screen of general relativity, entanglement is available necessarily on still one “cognitive screen” (namely, that of quantum mechanics), being furthermore “flat”. Most probably, that projection is confinement, a mysterious and ad hoc added interaction along with the fundamental tree ones of the Standard model being even inconsistent to them conceptually, as far as it need differ the local space from the global space being definable only as a relation between them (similar to entanglement). So, entanglement is able to link the gravity of general relativity to the confinement of the Standard model as its projections of the “cognitive screens” of those two fundamental physical theories. (shrink)

What does it mean to know how to do something? This book develops a comprehensive account of know-how, a crucial epistemic goal for all who care about getting things right, not only with respect to the facts, but also with respect to practice. It proposes a novel interpretation of the seminal work of Gilbert Ryle, according to which know-how is a competence, a complex ability to do well in an activity in virtue of guidance by an understanding of what it (...) takes to do so. This idea is developed into a full-fledged account, Rylean responsibilism, which understands know-how in terms of the normative guidance and responsible control of one's acts. Within the complex current debate about know-how, this view occupies a middle ground position between the intellectualist claim that know-how just is propositional or objectual knowledge and the anti-intellectualist claim that know-how just is ability. In genuine know-how, practical ability and guiding intellect are both necessary, but essentially intertwined. (shrink)

In this paper, I examine the connections between bipolar disorder and consent. I defend the view that many (although far from all) individuals with bipolar disorder are competent to consent to a wide variety of things when they are in a manic state.

Recent increases in the rates of parental refusal of routine childhood vaccination have eroded many countries’ “herd immunity” to communicable diseases. Some parents who refuse routine childhood vaccines do so because they deny the mainstream medical consensus that vaccines are safe and effective. I argue that one reason these vaccine denialists disagree with vaccine proponents about the reasons in favor of vaccination is because they also disagree about the sorts of practices that are conducive to good reasoning about healthcare choices. (...) Vaccine denialists allocate epistemic authority more democratically than do mainstream medical professionals. They also sometimes make truth ascriptions for nonepistemic reasons, fail to recognize legitimate differences in expertiseand competence, and seek uncritical affirmation of their existing beliefs. By focusing on the different epistemic values and practices of vaccine denialists and mainstream medical professionals, I locate my discussion of vaccine denialism within broader debates about rationality. Furthermore, I argue that gender inequality and gendered conceptions of reason are important parts of the explanation of vaccine denialism. Accordingly, I draw upon feminist work—primarily feminist social epistemology—to help explain and evaluate this form of vaccine refusal. (shrink)

This study's focus was to determine students' English competency level after exposure to video lessons as supplemental materials. The respondents of the study were 139 Grade 9 students of Mahaplag National High School coming from four sections enrolled for School Year 2022-2023. Quasi-experimental method of research particularly the pretest-posttest design was utilized in the study. Frequency counts, mean percentage score, weighted mean, standard deviation, and paired samples T-test were utilized in data analysis. Results of the study revealed that the competency (...) level of the students on all three learning competencies before the exposure to video lessons is in the poor category. On the other hand, it was revealed in the study that after exposure to video lessons and through the administered post-test, students’ competency levels improved, which now belongs to the fair category. As to the student’s acceptance level of video lessons as supplemental materials, it was found that students positively accept video lessons as supplemental materials for selected English 9 competencies. It was also ascertained that there was a statistically significant increase in the scores of the students on all three competencies after exposure to video lessons. Furthermore, there was a significant increase in students' overall scores on the three competencies. From the results of the study, it can be concluded that video lessons can be a great supplemental material in teaching English 9 competencies. (shrink)

The study identified the level of competencies and the extent of professional development needs of kindergarten teachers in the Sultan Kudarat Division, during the school year 2019 - 2020. The study employed a descriptive method. The study involved 54 kindergarten teachers in the division in accomplishing the 12-item self-assessment instrument. Data were analyzed using descriptive statistics. The results revealed that kindergarten teachers have a high level of competencies in content knowledge and pedagogy, learning environment and diversity of learners, curriculum and (...) planning, and assessment and reporting. These indicate that they possess almost all of the competencies of efficient teachers. Results further revealed a very high extent of professional needs in content knowledge and pedagogy and the learning environment and diversity of learners, while they had a high extent of professional needs in the remaining domains. Since they reported very high priorities in content knowledge and pedagogy and the learning environment and diversity of learners, these areas would be the main considerations in the crafting of a professional development plan. (shrink)

James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, (...) and it suggests an interesting reason why the rewriting might have been thought necessary. (shrink)

What is an inference and when is an inference deductive rather than inductive, abductive, etc. The goal of this paper is precisely to determine what is that we, humans, do when we engage in deduction, i.e., whether there is something that satisfies both our pre-theoretical intuitions and theoretical presuppositions about deduction, as a cognitive process. The paper is structured in two parts: the first one deals with the issue of what is an inference. There, I will defend the (...) hypothesis that an inference is a causal process where an initial cognitive state causes another in such a way that the causal translation depends essentially on the content of the involved states. In other words, in an inference, a mental state A causes another B, partially because they have the content they have. Based on the conclusion from the first part, I will develop an account of deductive inference in the second part of the article. In order to achieve this, I will start by setting the stage and developing four constraints that an adequate account of deductive inference ought to satisfy. Then, I will present six different hypotheses that one might propose to characterize inferences of this kind. I have divided the proposals in two groups, the first one – which I will call the “logical proposals” – assume that whether an inference is a deduction or not depends exclusively on the content of the mental states involved in the inference, while the second – which I will call the “cognitive proposals” – reject the aforementioned assumption and instead recognize that extra cognitive information is required to determine whether an inference is a deduction or not. I will evaluate each proposal in turn, according to whether they satisfy the constraints introduced at the beginning of this second part. As a result of such evaluation, I will conclude that only one of the cognitive proposals actually satisfies the four constraints and therefore should be considered to give an adequate characterization of deductive inference. (shrink)

How is moral knowledge possible? This paper defends the anti-Humean thesis that we can acquire moral knowledge by deduction from wholly non-moral premises. According to Hume’s Law, as it has become known, we cannot deduce an ‘ought’ from an ‘is’, since it is “altogether inconceivable how this new relation can be a deduction from others, which are entirely different from it” (Hume, 1739, 3.1.1). This paper explores the prospects for a deductive theory of moral knowledge that rejects Hume’s (...) Law. (shrink)

Dogmatism holds that an experience or seeming that p can provide prima facie immediate justification for believing p in virtue of its phenomenology. Dogmatism about perceptual justification has appealed primarily to proponents of representational theories of perceptual experience. Call dogmatism that takes perceptual experience to be representational "representational phenomenal dogmatism." As we show, phenomenal seemings play a crucial role in dogmatism of this kind. Despite its conventional appeal to representational theorists, dogmatism is not by definition committed to any particular view (...) of perceptual experience. Naive realists and disjunctivists who hold that perceptual experience is a perceptual relation of direct acquaintance can also endorse dogmatism. Indeed, we argue that they ought to do so. Otherwise, they cannot maintain that relationalism about perceptual experience has an epistemic advantage compared to the representational view. We then show that even if we grant that relationalism has this advantage, only dogmatism that takes perceptual experience to be representational can be extended to account for non-deductive inferential justification. As an account of the latter is required to avoid succumbing to skepticism, relationalism, we argue, does not have the epistemic advantage its defenders claim it has. (shrink)