Experiences of embodied remembering are familiar and diverse. We settle bodily into familiar chairs or find our way easily round familiar rooms. We inhabit our own kitchens or cars or workspaces effectively and comfortably, and feel disrupted when our habitual and accustomed objects or technologies change or break or are not available. Hearing a particular song can viscerally bring back either one conversation long ago, or just the urge to dance. Some people explicitly use their bodies to record, store, or (...) cue memories. Others can move skilfully, without stopping to think, in complex and changing environments thanks to the cumulative expertise accrued in their history of fighting fires, or dancing, or playing hockey. The forms of memory involved in these cases may be distinct, operating at different timescales and levels, and by way of different mechanisms and media, but they often cooperate in the many contexts of our practices of remembering. (shrink)

A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced so far seem amenable to a more complicated contextualist theory. We argue, however, that no contextualist theory can capture the evaluations speakers naturally make of sentences containing epistemic modals. If (...) we want to respect these evaluations, our best option is a relativist theory of epistemic modals. On a relativist theory, an utterance of a might be F can be true relative to one context of evaluation and false relative to another. We argue that such a theory does better than any rival approach at capturing all the behaviour of epistemic modals. (shrink)

Philosophers have often noted a contrast between practical and theoretical reasons when it comes to cases involving equally balanced reasons. When there are strong practical reasons for A-ing, and equally strong practical reasons for some incompatible option, B-ing, the agent is permitted to make an arbitrary choice between them, having sufficient reason to A and sufficient reason to B. But when there is strong evidence for P and equally strong evidence for ~ P, one isn’t permitted to simply believe one (...) or the other. Instead, one must withhold belief, neither believing that P nor believing that ~ P. This paper examines what explains this contrast, focusing in particular on a proposal recently developed by Mark Schroeder across several papers. Schroeder aims to explain the contrast by an appeal to non-evidential, epistemic reasons against belief. But, I argue, it’s not clear exactly what those reasons are, nor how those reasons are to be weighed against evidential reasons. Despite these challenges, I argue that there are grounds for optimism that the contrast can be explained within the broad framework Schroeder provides, and I aim to provide resources to meet the aforementioned challenges. (shrink)

In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...) by means of a formal deduction in the system. Review of the system makes the first point obvious. The purpose of the present article is to prove the second. Strong completeness is demonstrated for the Aristotelian system. (shrink)

Researchers recently demonstrated a strong direct relationship between judgments about what a person knows and judgments about how a person should act. But it remains unknown whether actionability judgments cause knowledge judgments, or knowledge judgments cause actionability judgments. This paper uses causal modeling to help answer this question. Across two experiments, we found evidence that actionability judgments cause knowledge judgments.

The paper begins by reviewing two problems for fallibilism: the lottery problem, or the problem of explaining why fallible evidence, though otherwise excellent, is not enough to know that one will lose the lottery, and Gettier problems. It is then argued that both problems can be resolved if we note an important illocutionary force of knowledge attributions: namely, that when we attribute knowledge to someone we mean to give the person credit for getting things right. Alternatively, to say that a (...) person knows is to say that she got things right due to her own abilities, efforts and actions, rather than due to dumb luck, or blind chance, or something else. (shrink)

For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...) is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories. (shrink)

It is commonly thought that one is irrationally akratic when one believes one ought to F but does not intend to F. However, some philosophers, following Robert Audi, have argued that it is sometimes rational to have this combination of attitudes. I here consider the question of whether rational akrasia is possible. I argue that those arguments for the possibility of rational akrasia advanced by Audi and others do not succeed. Specifically, I argue that cases in which an akratic agent (...) acts as he has most reason to act, and cases in which an akratic agent achieves a kind of global coherence he wouldn’t have achieved had he instead formed intentions in line with his best judgment, do not establish the possibility of rational akrasia. However, I do think that rational akrasia is possible, and I present two arguments for this thesis. The first argument involves a case in which one is incapable of revising one’s belief about what one ought to do, where one also acknowledges this belief to be insufficiently supported by the evidence. The second argument involves a case in which one rationally believes that one ought to have an akratic combination of attitudes. (shrink)

Many philosophers claim that interesting forms of epistemic evaluation are insensitive to truth in a very specific way. Suppose that two possible agents believe the same proposition based on the same evidence. Either both are justified or neither is; either both have good evidence for holding the belief or neither does. This does not change if, on this particular occasion, it turns out that only one of the two agents has a true belief. Epitomizing this line of thought are thought (...) experiments about radically deceived “brains in vats.” It is widely and uncritically assumed that such a brain is equally justified as its normally embodied human “twin.” This “parity” intuition is the heart of truth-insensitive theories of core epistemological properties such as justification and rationality. Rejecting the parity intuition is considered radical and revisionist. In this paper, I show that exactly the opposite is true. The parity intuition is idiosyncratic and widely rejected. A brain in a vat is not justified and has worse evidence than its normally embodied counterpart. On nearly every ordinary way of evaluating beliefs, a false belief is significantly inferior to a true belief. Of all the evaluations studied here, only blamelessness is truth-insensitive. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

If the contents of our thoughts are partly determined by facts outside our heads, can we still know those contents directly, without investigating our environment? What if we were surreptitiously switched to Twin-Earth? Would we know the contents of our thoughts under these unusual circumstances? By looking carefully at what determines the content of a second-order thought, a candidate for self-knowledge, the paper argues that we can know the contents of our thoughts directly, even after being switched. Learning about the (...) switch, however, does raise some interesting difficulties. (shrink)

This paper considers the formulation of the moral requirement against hypocrisy, paying particular attention to the logical scope of ‘requires’ in that formulation. The paper argues (i) that we should prefer a wide-scope formulation to a narrow-scope formulation, and (ii) this result has some advantages for our normative theorizing about hypocrisy – in particular, it allows us to resist several of Daniela Dover’s (2019) recent arguments against the anti-hypocrisy requirement.

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

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...) machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently "potent" to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident "yes" has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

[If you find this article interesting, let me mention another of my articles, “On Deducing Ethical Egoism from Psychological Egoism” (Theoria, 2023), which in many ways is a more thorough treatment of the topic. But it’s not an expanded version of this one. For instance, each article addresses arguments not addressed in the other.] Philosophers generally reject the view that psychological egoism (suitably supplemented with further premises) entails ethical egoism. Their rejections are generally unsatisfying. Some are too brief to win (...) confidence; others employ an uncharitable statement of psychological egoism. This is unfortunate, for the view that psychological egoism entails ethical egoism is philosophically significant (and not without proponents). Although it ultimately deserves rejection, it warrants better treatment than it typically receives. I thus examine it in some detail. Among other things, I carefully consider some original, sophisticated attempts to establish it, having first taken care to produce proper formulations of ethical and psychological egoism. (shrink)

The A-theory and the B-theory advance competing claims about how time is grounded. The A-theory says that A-facts are more fundamental in grounding time than are B-facts, and the B-theory says the reverse. We argue that whichever theory is true of the actual world is also true of all possible worlds containing time. We do this by arguing that time is uniquely groundable: however time is actually grounded, it is necessarily grounded in that way. It follows that if either the (...) A-theory or the B-theory is actually false, then it is necessarily false. (shrink)

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...) better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

Teaching while managing instructional workload is causal to the teaching-learning process. The study determined the teachers' instructional workload management to the teachers' teaching efficacy. It was conducted in a community college in Tangub City, Misamis Occidental. The descriptive-correlational design was used in the study. There were 15 program heads and 361 students who served as the respondents selected through a stratified random sampling technique. The researcher-made Teachers' Instructional Workload Management and Teachers' Teaching Efficacy Questionnaires were used as research instruments. Mean, (...) Standard Deviation, and Pearson Product-Moment Correlation Coefficient were used as statistical tools to analyze the data gathered. Results revealed that the teachers were very good in their instructional workload management. The teachers' teaching efficacy was very high. Some aspects of the teachers' instructional workload management like the preparation of instructional materials influenced the teachers' administration of assessment tasks and classroom management. Their conduct of consultation also influenced the administration of assessment tasks. Moreover, their submission of academic reports influenced the administration of assessment tasks and school resource utilization. The workload management of teachers play a crucial role in shaping teachers' teaching efficacy. It is recommended for teachers to manage their workload proactively since it can impact their teaching efficacy. (shrink)

There is little question as to whether there is good boring art, though its existence raises a number of questions for both the philosophy of art and the philosophy of emotions. How can boredom ever be a desideratum of art? How can our standing commitments concerning the nature of aesthetic experience and artistic value accommodate the existence of boring art? How can being bored constitute an appropriate mode of engagement with a work of art as a work of art? More (...) broadly, how can there be works of art whose very success requires the experience of boredom? Our goal in this paper is threefold. After offering a brief survey of kinds of boring art, we: i) derive a set of questions that we argue constitutes the philosophical problem of boring art; ii) elaborate an empirically informed theory of boredom that furnishes the philosophical problem with a deeper sense of the affect at the heart of the phenomenon; and iii) conclude by offering and defending a solution to the problem that explains why and how artworks might wish to make the experience of boredom key to their aesthetic and artistic success. (shrink)

In this paper I refute the chief arguments for cultural relativism, meaning the moral (not the descriptive) theory that goes by that name. In doing this I walk some oft-trodden paths, but I also break new ones. For instance, I take unusual pains to produce an adequate formulation of cultural relativism, and I distinguish that thesis from the relativism of present-day anthropologists, with which it is often conflated. In addition, I address not one or two, but eleven arguments for cultural (...) relativism, many of which contribute to its popularity but receive scant attention from its critics. To elicit the failings of these arguments I deploy a host of pertinent but often neglected distinctions. (shrink)

This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical (...) consequence. Adequacy criteria for systems of the first two types include: effectiveness, soundness, completeness, Post completeness, "strong soundness" and strong completeness. Consideration of a logical system as a theory of deduction leads us to attempt to formulate two adequacy criteria for systems of proofs. The first deals with the concept of rigor or "gaplessness" in proofs. The second is a completeness condition for a system of proofs. An historical note at the end of the paper suggests a remarkable parallel between the above hierarchy of systems and the actual historical development of this area of logic. (shrink)

To what extent are the answers to theological questions knowable? And if the relevant answers are knowable, which sorts of inquirers are in a position to know them? In this chapter we shall not answer these questions directly but instead supply a range of tools that may help us make progress here. The tools consist of plausible structural constraints on knowledge. After articulating them, we shall go on to indicate some ways in which they interact with theological scepticism. In some (...) cases the structural constraints bear directly on whether one can know answers to theological questions. But the structural considerations are related to theological scepticism in other interesting ways as well; for instance we will also be using them to explore the significance of scepticism, by addressing questions such as ‘To what extent does it matter whether or not we can know the answer to theological questions?’. (shrink)

Supervision of teachers is essential for ensuring effective educational practices, fostering professional development, and achieving student success. The study determined the relationship of program heads' supervisory practices to the teachers’ teaching efficacy. It was conducted in a community college in Tangub City, Misamis Occidental. The descriptive-correlational design was used in the study. There were 146 faculty and 361 students who served as the respondents selected through a stratified random sampling technique. The adapted Program Heads’ Supervisory Practices and researcher-made Teachers’ Teaching (...) Efficacy Questionnaires were used as research instruments. Mean, Standard Deviation, and Pearson Product-Moment Correlation Coefficient were used as statistical tools to analyze the data gathered. Results revealed that the program heads were good in their supervisory practices. The teachers’ teaching efficacy was very high. The program heads’ supervisory practices did not influence the teacher’s teaching efficacy. The strategies employed by program heads in their supervisory roles do not always translate into improved teaching efficiency. The study's findings indicate that program heads need to adopt more responsive and tailored supervisory practices that directly address the specific needs of teachers to enhance teaching efficacy. This may involve integrating targeted professional development focused on practical classroom strategies and fostering peer collaboration to share best practices. Program heads may prioritize open communication and continuous feedback mechanisms to better align their supervisory approaches with the realities of classroom instruction, ensuring that support translates into improved teaching efficiency. (shrink)

The supervision of teachers is essential for ensuring effective teaching methods, ongoing professional growth, and student success. This study explored the experiences of program heads in supervising teachers. It was conducted in a local college in Tangub City, Misamis Occidental. The phenomenological design was used in the study. Eleven program heads served as the participants selected through the purposive sampling technique. The Interview Guide was used as the research instrument. Moustakas' transcendental phenomenology of data analysis was utilized to analyze the (...) data gathered. Results revealed the following main themes: the critical role of supervision in advancing teacher development and educational excellence, mutual learning and growth, the role of program heads in teacher supervision, overcoming challenges in teacher supervision, and effective communication strategies. Supervision improves teaching and learning quality, which supports professional development. The complex nature of supervisory roles requires adaptive strategies and strong support networks. It is recommended for program heads and teachers to establish open communication to help address the challenges encountered during supervision. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...) Q is one whose existentialization, ∃ x Q, is logically true; otherwise, Q is existential-import-free or simply import-free.How abundant or widespread is existential import? How abundant or widespread are existential-import predicates in themselves or in comparison to import-free predicates? We show that existential-import predicates are quite abundant, and no less so than import-free predicates. Existential.. (shrink)

A familiar question is whether psychological egoism (suitably supplemented with plausible further premises) entails ethical egoism. This paper considers this question, treating it much more thoroughly than do any previous treatments. For instance, it discusses all of the most common understandings of ethical and psychological egoism. It further discusses many strategies and arguments relevant to the question addressed. Although this procedure creates complexity, it has value. It forestalls the suspicion, aroused by so many treatments of this subject, that the results (...) stem largely from leaving stones unturned – for instance, from ignoring many natural argumentative strategies and many familiar understandings of the views discussed. The paper’s conclusion is that psychological egoism (suitably supplemented …) does not entail ethical egoism. (shrink)

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...) of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...) that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless without rigor and objectivity. The logician urging us to be dispassionate is in resonance and harmony with the ethicist urging us to be compassionate.

We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...) contextualism, and pluralism. Besides the new spirit there have been quiet developments in logic and its history and philosophy that could radically improve logic teaching. This lecture expands points which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

The ‘managed-metabolism’ hypothesis suggests that a ‘cooperation barrier’ must be overcome if self-producing chemical organizations are to undergo the transition from non-life to life. This dynamical barrier prevents un-managed autocatalytic networks of molecular species from individuating into complex, cooperative organizations. The barrier arises because molecular species that could otherwise make significant cooperative contributions to the success of an organization will often not be supported within the organization, and because side reactions and other ‘free-riding’ processes will undermine cooperation. As a result, (...) the barrier seriously impedes the emergence of individuality, complex functionality and the transition to life. This barrier is analogous to the cooperation barrier that also impedes the emergence of complex cooperation at all levels of living organization. As has been shown at other levels of organization, the barrier can be overcome comprehensively by appropriate ‘management’. Management implements a system of evolvable constraints that can overcome the cooperation barrier by ensuring that beneficial co-operators are supported within the organization and by suppressing free-riders. In this way, management can control and manipulate the chemical processes of a collectively autocatalytic organization, producing novel processes that serve the interests of the organization as a whole and that could not arise and persist in an un-managed chemical organization. Management self-organizes because it is able to capture some of the benefits that are produced when its interventions promote cooperation, thereby enhancing productivity. Selection will therefore favour the emergence of managers that take over and manage chemical organizations so as to overcome the cooperation barrier. The managed-metabolism hypothesis demonstrates that if management is to overcome the cooperation barrier comprehensively, its interventions must be digitally coded. In this way, the hypothesis accounts for the two-tiered structure of all living cells in which a digitally-coded genetic apparatus manages an analogically-informed metabolism.GraphicalOpen image in new window. (shrink)

In this paper, I explore a possible convergence between two great twentieth century thinkers, Nishida Kitarō of Japan and Martin Heidegger of Germany. The focus is on the quasi-religious language they employ in discussing the grounding of human existence in terms of an encompassing Wherein for our being. Heidegger speaks of “the sacred” and “the passing of the last god” that mark an empty clearing wherein all metaphysical absolutes or gods have withdrawn but are simultaneously indicative of an opening wherein (...) beings are given. Nishida speaks of “the religious” dimension in the depths of one's being, that he calls “place,” and that somehow envelops the world through its kenotic self-negation. In both we find reference to a kind of originary space—the open or place—associated with quasireligious themes. I also point to their distinct approaches to metaphysical language in their attempts to give voice to that abysmal thought. (shrink)

A psychological study of thought and language which takes an exposition of scientific linquistics as a point of departure.

This accessible essay treats knowledge and belief in a usable and applicable way. Many of its basic ideas have been developed recently in Corcoran-Hamid 2014: Investigating knowledge and opinion. The Road to Universal Logic. Vol. I. Arthur Buchsbaum and Arnold Koslow, Editors. Springer. Pp. 95-126. http://www.springer.com/birkhauser/mathematics/book/978-3-319-10192-7 .

We show that someone who believes in both gunk and the possibility of supertasks has to give up either a plausible principle about where gunk can be located, or plausible conservation principles.

This paper raises obvious questions undermining any residual confidence in Mates work and revealing our embarrassing ignorance of true nature of Stoic deduction. It was inspired by the challenging exploratory work of JOSIAH GOULD.

In his contribution to the first issue of Memory Studies, Jeffrey Olick notes that despite “the mutual affirmations of psychologists who want more emphasis on the social and sociologists who want more emphasis on the cognitive”, in fact “actual crossdisciplinary research … has been much rarer than affirmations about its necessity and desirability” (2008: 27). The peculiar, contingent disciplinary divisions which structure our academic institutions create and enable many powerful intellectual cultures: but memory researchers are unusually aware that uneasy faultlines (...) and glaring gulfs lie in the uncertain zones between them. The processes of memory are simultaneously natural and cultural. But our difficulties in imagining even fragments of a genuinely integrated framework for understanding diverse memory-related phenomena do not arise from a simple ‘two-cultures’ problem: it’s not as if there are substantially unified visions of memory within either ‘the sciences’ or ‘the humanities’. (shrink)

This paper questions the idea that theism can function as an explanatory hypothesis to account for the nature and origins of the cosmos. Invoking God cannot dissolve the mystery of existence, and the characteristic religious response here is one of awe and humility. I then address David E. Cooper’s challenge of showing how a ”doctrine of mystery’ can have any discursible content. It is argued that certain aspects of our human experience afford us glimpses of the divine nature -- intimations (...) of the transcendent, which shine through from the ineffable source of our being to the human world we inhabit. (shrink)

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...) many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

Computation and Metacognitive skills are essential sub-skills under the domain of Critical Thinking which is a 21 st Century Skill. Having acquired these skills can greatly help students to have a better performance in the Mathematics course. The purpose of this study was to determine whether computation and metacognitive skills are significant predictors of students' performance in Mathematics. Students from four sections of the course Mathematics in the Modern World which was offered during the first semester of the academic year (...) 2018-2019 were selected as the participants of this study which was conducted at Gov. Alfonso D. Tan College, Tangub City, Misamis Occidental, Philippines. The results of this study showed that students' scores in computation and metacognitive test of skills significantly correlate with the students' performance in Mathematics in terms of Grade Point Average (GPA) and a positive direct relationship has been established. Using the Regression Analysis, the result revealed that both computation and metacognitive skills of the students were significant predictors of their performance in Mathematics. These research outcomes affirm that if students acquire these skills, they tend to perform better in Mathematics. This suggests that teachers are encouraged to be more strategic in training the students to acquire and develop computation and metacognitive skills by administering various mathematical problems that encourage students to think critically. (shrink)

This entry considers the question of whether rationality is normative; that is, the question of whether one always ought (or, more weakly, has a reason) to be rational. It first distinguishes substantive from structural rationality, noting how structural rationality presents a more serious challenge to the thesis that rationality is normative. It then considers the plausibility of skepticism about structural rationality, and notes some problems facing such skepticism. However, if we are not skeptics about structural requirements, we face the task (...) of formulating those requirements. But both narrow-scope and wide-scope formulations seem incompatible with the idea that we always ought to be rational. This suggests that we have good reason to think that rationality is not strongly normative. (shrink)

A Inseparabilidade entre Lógica e a Ética. Philósophos. 18 (2013) 245–259. Portuguese translation by Décio Krause and Pedro Merlussi: The Inseparability of Logic and Ethics, Free Inquiry, Spring 1989, 37–40. This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science of justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless (...) without rigor and objectivity. The logician’s advice to be dispassionate is in resonance and harmony with the ethicist’s advice to be compassionate. (shrink)

The Evolutionary Manifesto shows that evolution is directional and demonstrates that this has major implications for humanity. The Manifesto shows that humanity must align its social systems and behaviour with the trajectory of evolution if we are to survive and thrive into the future. The Manifesto goes on to demonstrate that humanity has an essential role to play in the future evolution of life on this planet. It demonstrates that life on Earth has reached a critical stage in evolution’s trajectory. (...) Up to now evolution has moved along its trajectory blindly and unconsciously. But if evolution on Earth is to continue to advance successfully in the future, the process will have to be driven intentionally and consciously by humanity. In this way, a proper understanding of evolution shows us how we can live a life that matters in a larger scheme of things. An evolutionary worldview answers the fundamental existential question that faces us all: “What should I do with my life?” The Manifesto outlines in broad terms what humanity must do to advance the evolutionary process—how we will intentionally have to re-make our political, social and economic systems, and how we will need to develop our cognition and consciousness. As such, the Manifesto presents a detailed case for evolutionary activism--coordinated action directed at advancing the evolutionary process intentionally. (shrink)