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)

Time in electromagnetism shares many features with time in other physical theories. But there is one aspect of electromagnetism's relationship with time that has always been controversial, yet has not always attracted the limelight it deserves: the electromagnetic arrow of time. Beginning with a re-analysis of a famous argument between Ritz and Einstein over the origins of the radiation arrow, this chapter frames the debate between modern Einsteinians and neo-Ritzians. It tries to find a clean statement of what the arrow (...) is and then explains how it relates to the cosmological and thermodynamic arrows, representing the most developed and sophisticated attack yet, in either the physics or philosophy literature, on the electromagnetic arrow of time. (shrink)

Positive review of John Earman's *Bangs, Crunches, Shrieks, Whispers*.

In this paper, I try to make sense of the growing block view using Kit Fine’s three-fold classification of A-theoretic views of time. I begin by motivating the endeavor of making sense of the growing block view by examining John Earman’s project in ‘Reassessing the prospects for a growing block model of the universe’. Next, I review Fine’s reconstruction of McTaggart’s argument and its accompanying three-fold classification of A-theoretic views. I then consider three interpretations of Earman’s growing (...) block model: the hybrid growing block, the purely tensed growing block, and Michael Tooley’s growing block. I argue for three claims. First, Finean ‘standard’ versions of these views are less congenial to the growing blocker than ‘non-standard’ ones. Second, the hybrid view is problematic on either version. And third, ‘non-standard’ versions are not fully intelligible. I provide further support for the first and third of these claims and explain why I take them to support a minimal account of passage as succession, which undercuts some of the motivation for Earman’s project. Lastly, I answer three objections. (shrink)

Review of John Earman's _Hume's Abject Failure_.

This paper defends David Hume's "Of Miracles" from John Earman's (2000) Bayesian attack by showing that Earman misrepresents Hume's argument against believing in miracles and misunderstands Hume's epistemology of probable belief. It argues, moreover, that Hume's account of evidence is fundamentally non-mathematical and thus cannot be properly represented in a Bayesian framework. Hume's account of probability is show to be consistent with a long and laudable tradition of evidential reasoning going back to ancient Roman law.

Newton had a fivefold argument that true motion must be motion in absolute space, not relative to matter. Like Newton, Kant holds that bodies have true motions. Unlike him, though, Kant takes all motion to be relative to matter, not to space itself. Thus, he must respond to Newton’s argument above. I reconstruct here Kant’s answer in detail. I prove that Kant addresses just one part of Newton’s case, namely, his “argument from the effects” of rotation. And, to show that (...) rotation is relative to matter, Kant changes the meaning of ‘relative motion.’ However, that change puts Kant’s doctrine in deep tension with Newton’s science. Based on my construal, I correct earlier readings of Kant by John Earman and Martin Carrier. And, I argue that we need to revise Michael Friedman’s influential view of Kant. Kant’s struggle, I conclude, illustrate the difficulties that early modern relationists faced as they turned down Newtonian absolute space ; and it typifies their selective engagement with Newton’s case for it. (shrink)

There is a virtual consensus in contemporary epistemology that knowledge must be reliably produced. Everyone, it seems, is a reliabilist about knowledge in that sense. I present and defend two arguments that unreliable knowledge is possible. My first argument proceeds from an observation about the nature of achievements, namely, that achievements can proceed from unreliable abilities. My second argument proceeds from an observation about the epistemic efficacy of explanatory inference, namely, that inference to the best explanation seems to produce knowledge, (...) even if it isn't reliable. I also propose a successor to standard versions of reliabilism, which I call ‘ecumenical reliabilism’. Ecumenical reliabilism is consistent with unreliably produced knowledge and helps explain why unreliably produced knowledge is possible. (shrink)

According to the Self-Location Thesis, one’s own location can be among the things that visual experience represents, even when one’s body is entirely out of view. By contrast, the Minimal View denies this, and says that visual experience represents things only as "to the right", etc., and never as "to the right of me". But the Minimal View is phenomenologically inadequate: it cannot explain the difference between a visual experience of self-motion and one of an oppositely moving world. To show (...) this, I argue (i) that these experiences are different in an important respect, (ii) that this difference is genuinely experiential, (iii) that it is visual, (iv) that it is not purely phenomenal, and (v) that it cannot be identified with anything other than the apparent motion of the self. So the Self-Location Thesis is upheld: reports of one’s own motion can correspond to aspects of visual experiences every bit as basic to their contents as the apparent motion or rest of the things one has in view. (shrink)

In all probability, future generations will outnumber us by thousands or millions to one. In the aggregate, their interests therefore matter enormously, and anything we can do to steer the future of civilization onto a better trajectory is of tremendous moral importance. This is the guiding thought that defines the philosophy of longtermism. Political science tells us that the practices of most governments are at stark odds with longtermism. But the problems of political short-termism are neither necessary nor inevitable. In (...) principle, the state could serve as a powerful tool for positively shaping the long-term future. In this chapter, we make some suggestions about how to align government incentives with the interests of future generations. First, in Section II, we explain the root causes of political short-termism. Then, in Section III, we propose and defend four institutional reforms that we think would be promising ways to increase the time horizons of governments: 1) government research institutions and archivists; 2) posterity impact assessments; 3) futures assemblies; and 4) legislative houses for future generations. Section IV concludes with five additional reforms that are promising but require further research: to fully resolve the problem of political short-termism we must develop a comprehensive research program on effective longtermist political institutions. (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)

One widely used method for allocating health care resources involves the use of cost-effectiveness analysis (CEA) to rank treatments in terms of quality-adjusted life-years (QALYs) gained. CEA has been criticized for discriminating against people with disabilities by valuing their lives less than those of non-disabled people. Avoiding discrimination seems to lead to the ’QALY trap’: we cannot value saving lives equally and still value raising quality of life. This paper reviews existing responses to the QALY trap and argues that all (...) are problematic. Instead, we argue that adopting a moderate form of prioritarianism avoids the QALY trap and disability discrimination. (shrink)

The foundations of research ethics are riven with fault lines emanating from a fear that if research is too closely connected to weighty social purposes an imperative to advance the common good through research will justify abrogating the rights and welfare of study participants. The result is an impoverished conception of the nature of research, an incomplete focus on actors who bear important moral responsibilities, and a system of ethics and oversight highly attuned to the dangers of research but largely (...) silent about threats of ineffective, inefficient, and inequitable medical practices and health systems. -/- In For the Common Good: Philosophical Foundations of Research Ethics, Alex John London defends a conception of the common good that grounds a moral imperative with two requirements. The first is to promote research that generates the information necessary to enable key social institutions to effectively, efficiently, and equitably safeguard the basic interests of individuals. The second is to ensure that research is organized as a voluntary scheme of social cooperation that respects its various contributors' moral claims to be treated as free and equal. Connecting research to the goals of a just social order grounds a framework for assessing and managing research risk that reconciles these requirements and justifies key oversight practices in non-paternalistic terms. Reconceiving research ethics as resolving coordination problems and providing credible assurance that these requirements are being met expands the issues and actors that fall within the purview of the field and provides the foundation for a more unified and coherent approach to domestic and international research. -/- This is an open access title available under the terms of a CC BY-NC-ND 4.0 license. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations. (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)

After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...) involving the distinction between characterizing a system and axiomatizing the truths of a system. (shrink)

Embodied human minds operate in and spread across a vast and uneven world of things—artifacts, technologies, and institutions which they have collectively constructed and maintained through cultural and individual history. This chapter seeks to add a historical dimension to the enthusiastically future-oriented study of “natural-born cyborgs” in the philosophy of cognitive science,3 and a cognitive dimension to recent work on material memories and symbol systems in early modern England, bringing humoral psychophysiology together with material culture studies. The aim is to (...) sketch an integrative framework which spans early modern ideas and practices relating to brains, bodies, memory, and objects. Embodiment and environment, I’ll argue, were not (always) merely external influences on feeling, thinking, and remembering, but (in certain circumstances) partly constitutive of these activities. (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)

Many real-world agents recognise that they impose harms by choosing to emit carbon, e.g., by flying. Yet many do so anyway, and then attempt to make things right by offsetting those harms. Such offsetters typically believe that, by offsetting, they change the deontic status of their behaviour, making an otherwise impermissible action permissible. Do they succeed in practice? Some philosophers have argued that they do, since their offsets appear to reverse the adverse effects of their emissions. But we show that (...) they do not. In practice, standard carbon offsetting does not reverse the harms of the original action, nor does it even benefit the same group as was harmed. Standard moral theories hence deny that such offsetting succeeds. Indeed, we show that any moral theory that allows offsetting in this setting faces a dilemma between allowing any wrong to be offset, no matter how grievous, and recognising an implausibly sharp discontinuity between offsettable actions and non-offsettable actions. The most plausible response is to accept that carbon offsetting fails to right our climate wrongs. (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)

I start with a brief assessment of the implications of Sterelny’s anti-individualist, anti-internalist apprentice learning model for a more historical and interdisciplinary cognitive science. In a selective response I then focus on two core features of his constructive account: collaboration and skill. While affirming the centrality of joint action and decision making, I raise some concerns about the fragility of the conditions under which collaborative cognition brings benefits. I then assess Sterelny’s view of skill acquisition and performance, which runs counter (...) to dominant theories that stress the automaticity of skill. I suggest that it may still overestimate the need for and ability of experts to decompose and represent the elements of their own practical knowledge. (shrink)

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...) by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...) attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

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

Everyone will agree that education ought to prepare young people to lead a meaningful life, but there are different ways in which this notion can be understood. A religious interpretation has to be distinguished from the secular one on which this paper focuses. Meaningfulness in this non-religious sense is a necessary condition of a life of well-being, having to do with the nesting of one’s reasons for action within increasingly pervasive structures of activity and attachment. Sometimes a life can seem (...) meaningless when it is not so in fact. In more extreme cases it may in fact be to some extent meaningless. Equipping young people for a meaningful life is a worthwhile, but not all-important educational aim. Educators should help them not only to see their lives as meaningful but also to lead lives that <are> meaningful. This involves continuous engagement in the nesting of reasons mentioned above. Where autonomy is also an aim, temperamental attunement to possible options – rather than exposure to all possible options – and time to explore them are important considerations. Questions arise here both about social justice and about whether current school curriculum and timetabling arrangements help or hinder pupils in living a meaningful life. (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)

In England and Wales we have had a National Curriculum since 1988. How can it have survived so long without aims to guide it? This IMPACT pamphlet argues that curriculum planning should begin not with a boxed set of academic subjects of a familiar sort, but with wider considerations of what schools should be for. We first work out a defensible set of wider aims backed by a well-argued rationale. From these we develop sub-aims constituting an aims-based curriculum. Further detail (...) is provided here on one of the most central educational aims, to do with equipping each child to live a flourishing personal and civic life. [A later, more detailed account of an aims-based curriculum is available in Reiss, M and White J <An Aims-based Curriculum: the significance of human flourishing for schools> Institute of Education Press 2013]. (shrink)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (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)

I am going to argue that it is a cost of libertarianism that it holds our status as agents hostage to theoretical physics, but that claim has met with disagreement. Some libertarians regard it as the cost of doing business, not a philosophical liability. By contrast, Peter van Inwagen has addressed the worry head on. He says that if he were to become convinced that causal determinism were true, he would not change his view that humans are free and morally (...) responsible. Rather, he would give up at least one of the formerly-thought-to-be a priori truths that are elements in his argument for the incompatibility of causal determinism and the relevant sort of freedom. Thus, according to van Inwagen, our status as free and morally responsible agents would not be held hostage to the physicists or hang on a thread I think that van Inwagen’s strategy for securing our freedom and responsibility is unattractive. Somewhat tendentiously, I have called the rejection of an a priori ingredient in the incompatibilist’s argument, contingent upon learning that causal determinism is true, ‘metaphysical fip-flopping.’ -/- And it does seem that van Inwagen’s approach is implausible insofar as he is open to such metaphysical fip-fopping. That he is open to it—that he would fip-fop if he became convinced of the truth of causal determinism—is a problem for his actual philosophical position. Or so I will argue. (shrink)

There are two different ways of understanding alienation: as a condition and as a struggle. On this distinction turns the whole theory and practice of Marxism.

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

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)

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)

Scholars of ideology in social-scientific disciplines, including psychology, sociology, and political science, stand to benefit from taking seriously the philosophical contributions of Professor Peter Railton. This is because Railton provides much-needed conceptual precision—and a rare sense of epistemological and moral clarity—to a topic that is notoriously slippery and prone to relativistic musing and the drawing of false equivalences. In an essay entitled “Morality, Ideology, and Reflection: Or, the Duck Sits Yet,” Railton (2000/2003) aptly identified the purpose of ideological analysis as (...) the unmasking of “nonepistemic” interests—that is, interests other than truth-seeking, accuracy, or warrant —that contribute to the development, adoption, and dissemination of political and religious belief systems. (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)

Given demonstrated global knowledge inequality, this article attempts to draw out the connection between tertiary education and research (TER), economic development and infrastructure, and human development. We first explore the connection between knowledge and economic development by tracing a short history of the emergence of knowledge in economic analysis and by introducing the concept of a ‘knowledge economy’. The World Bank’s ‘Knowledge Assessment Methodology’ (2000) attempted to evaluate such ‘knowledge economies’ through a number of proposed variables. We describe relationships between (...) such TER-variables, economic development, and infrastructure building, especially in the shift towards digital economies. We will show that there is a tangible, negative human impact from disparities in knowledge production, and significant improvement in human welfare when knowledge production capacities improve. Finally, we will illustrate how these relationships play out in two case studies, in Montenegro and Bangladesh. (shrink)

This paper is concerned with the problem of speaking past one another due to an asymmetry of the interlocutors' backgrounds. When individuals with different levels of relative privilege interact, the party with relative privilege may fail to engage with what is being communicated. I take up critical Gadamerian hermeneutics to ask how we, as individuals with relative privilege, can 'unstop' our ears so that the burden of explanation does not (unfairly) remain on those we hurt by our mishearing/non-hearing. I offer (...) two methods to achieve this 'unstopping': 'critical self-knowledge' through Quassim Cassam's 'Vice Epistemology' framework and 'critical world-knowledge' through the Frankfurt School of Critical Theory (Max Horkheimer and Jürgen Habermas, specifically). I then take up contemporary critical hermeneutics (Lorenzo Simpson) to show how, through the application of the critical methods, one might be able to achieve a useful, cross-cultural dialogue. This is imperative given our inexorably multi-cultural world today. (shrink)

The representation of propositional attitudes (beliefs, desires, etc.) and the analysis of natural-language, propositional-attitude reports presents difficult problems for cognitive science and artificial intelligence. In particular, various representational approaches to attitudes involve the incorrect “imputation,” to cognitive agents, of the use of artificial theory-laden notions. Interesting cases of this problem are shown to occur in several approaches to attitudes. The imputation problem is shown to arise from the way that representational approaches explicate properties and relationships, and in particular from the (...) way they explicate propositional attitudes themselves. Another factor contributing to imputation is the compositional nature of typical semantic approaches to propositional-attitude reports. Some strategies for avoiding undesirable imputation are examined. One of the main conclusions is that the importance of imputations that arise in a representation scheme depends strongly on the use to which the scheme is put -- on whether, for instance, the scheme is used as part of a formal, objective account of natural language, or is used rather as a representational tool within an agent. (shrink)

A counterfactual is a conditional statement in the subjunctive mood. For example: If Suzy hadn’t thrown the rock, then the bottle wouldn’t have shattered. The philosophical importance of counterfactuals stems from the fact that they seem to be closely connected to the concept of causation. Thus it seems that the truth of the above conditional is just what is required for Suzy’s throw to count as a cause of the bottle’s shattering. If philosophers were reluctant to exploit this idea prior (...) to 1970, it was because of a widespread feeling that the truth-conditions of the counterfactual conditional were not sufficiently well understood. The development of a formal semantics for counterfactuals by Robert Stalnaker [1968] and David Lewis [1973b] stands as a major recent achievement in philosophical logic. (shrink)

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 .

Misinformation can have significant societal consequences. For example, misinformation about climate change has confused the public and stalled support for mitigation policies. When people lack the expertise and skill to evaluate the science behind a claim, they typically rely on heuristics such as substituting judgment about something complex (i.e. climate science) with judgment about something simple (i.e. the character of people who speak about climate science) and are therefore vulnerable to misleading information. Inoculation theory offers one approach to effectively neutralize (...) the influence of misinformation. Typically, inoculations convey resistance by providing people with information that counters misinformation. In contrast, we propose inoculating against misinformation by explaining the fallacious reasoning within misleading denialist claims. We offer a strategy based on critical thinking methods to analyse and detect poor reasoning within denialist claims. This strategy includes detailing argument structure, determining the truth of the premises, and checking for validity, hidden premises, or ambiguous language. Focusing on argument structure also facilitates the identification of reasoning fallacies by locating them in the reasoning process. Because this reason-based form of inoculation is based on general critical thinking methods, it offers the distinct advantage of being accessible to those who lack expertise in climate science. We applied this approach to 42 common denialist claims and find that they all demonstrate fallacious reasoning and fail to refute the scientific consensus regarding anthropogenic global warming. This comprehensive deconstruction and refutation of the most common denialist claims about climate change is designed to act as a resource for communicators and educators who teach climate science and/or critical thinking. (shrink)

A brief account of educational aims, focussing on preparation for a life of autonomous well-being.

Knowledge entails the truth of the proposition known; that which is merely believed may be false. If I have beliefs about your beliefs, then I may believe that some of your beliefs are false. I may believe, for example, that you mistakenly believe that it is now raining outside. This is a coherent belief for me, though not for you. You cannot coherently believe that you believe falsely that it is raining, and this despite the fact that your having that (...) false belief is clearly a logical possibility. The proposition is, for you, a kind of doxastic blindspot. (shrink)

Political short-termism costs the global economy hundreds of billions to trillions of dollars annually, and leads to many millions of deaths from disasters and suboptimal spending. In this paper, I propose a futures assembly explicitly incentivised to promote the interests of future generations as a promising strategy to ameliorate short-termism. The assembly I propose is governed by citizens randomly selected from among the populace, who are rewarded in the future to the extent that they successfully promote the welfare of future (...) generations. The most initially promising such retrospective accountability mechanism is an iterated mechanism, in which each generation of policymakers rewards the previous generation for their policy choices and for their own evaluation of the previous generation. Such an assembly, supplemented with the duties, powers, and tools that I describe, and with appropriate support from archivists and experts, may manage to represent generations many years into the future. (shrink)

An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...) algorithmic methods for certain classes of such problems. The results are then applied to classical number theory, in particular, to questions concerning possible refinements of the 1931 Gödel Axiom Set, e.g. whether any of its axioms can be analyzed into “informational atoms”. Two propositions are “informationally unconnected” [with each other] if no informative (nontautological) consequence of one also follows from the other. A proposition is an “informational atom” if it is informative but no information can be dropped from it without rendering it uninformative (tautological). Presentation, employment, and investigation of these two new concepts are prominent features of this paper. (shrink)