Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...) virtually everything written by Tarski concerns logic more or less directly. There is no doubt that Tarski wrote more on logic than any other author; he started publishing on logic in 1921 at the age of 20 and continued until his death at the age of 82. Two of his works appeared posthumously [Hist. Philos. Logic 7 (1986), no. 2, 143--154; MR0868748 (88b:03010); Tarski and Givant, A formalization of set theory without variables, Amer. Math. Soc., Providence, RI, 1987; MR0920815 (89g:03012)]. Tarski's voluminous writings were widely scattered in numerous journals, some quite rare. It has been extremely difficult to study the development of Tarski's thought and to trace the interconnections and interdependence of his various papers. Thanks to the present collection all this has changed, and it is likely that the increased accessibility of Tarski's papers will have the effect of increasing Tarski's already enormous influence. (shrink)

Conceptualism is the thesis that, for any perceptual experience E, (i) E has a Fregean proposition as its content and (ii) a subject of E must possess a concept for each item represented by E. We advance a framework within which conceptualism may be defended against its most serious objections (e.g., Richard Heck's argument from nonveridical experience). The framework is of independent interest for the philosophy of mind and epistemology given its implications for debates regarding transparency, relationalism and representationalism, demonstrative (...) thought, phenomenal character, and the speckled hen objection to modest foundationalism. (shrink)

One fairly common view about practical reason has it that whether you have a reason to act is not determined by what you know, or believe, or are justified in believing. Your reasons are determined by the facts. Perhaps there are two kinds of reasons, and however it goes with motivating reasons, normative reasons are determined by the facts, not your take on the facts. One fairly common version of this view has it that what's reasonable for you to do (...) is determined by what you know or believe. Any view that drives this kind of wedge between reasons and rationality is inherently unstable. I argue against this view, criticize the arguments typically presented in its favor, and sketch an alternative. (shrink)

I consider a serious objection to the knowledge account of assertion and develop a response. In the process I introduce important new data on prompting assertion, which all theorists working in the area should take note of.

Plato is associated with the idea that the body holds us back from knowing ultimate reality and so we should try to distance ourselves from its influence. This sentiment appears is several of his dialogues including Theaetetus where the flight from the physical world is compared to becoming like God. In some major dialogues of Plato's later career such as Philebus and Laws, however, the idea of becoming like God takes a different turn. God is an intelligent force that tries (...) to create order in the physical world. I argue that likeness to God in these dialogues involves imitating God's effort by trying to order our bodies, souls, and societies as intelligence directs. Becoming like Plato's God is not to abandon the world. It is to improve it. (shrink)

Human obsolescence is imminent. We are living through an era in which our activity is becoming less and less relevant to our well-being and to the fate of our planet. This trend toward increased obsolescence is likely to continue in the future, and we must do our best to prepare ourselves and our societies for this reality. Far from being a cause for despair, this is in fact an opportunity for optimism. Harnessed in the right way, the technology that hastens (...) our obsolescence can open us up to new utopian possibilities and enable heightened forms of human flourishing. (shrink)

We are living through an era of increased robotisation. Some authors have already begun to explore the impact of this robotisation on legal rules and practice. In doing so, many highlight potential liability gaps that might arise through robot misbehaviour. Although these gaps are interesting and socially significant, they do not exhaust the possible gaps that might be created by increased robotisation. In this article, I make the case for one of those alternative gaps: the retribution gap. This gap arises (...) from a mismatch between the human desire for retribution and the absence of appropriate subjects of retributive blame. I argue for the potential existence of this gap in an era of increased robotisation; suggest that it is much harder to plug this gap than it is to plug those thus far explored in the literature; and then highlight three important social implications of this gap. (shrink)

The most cursory examination of the history of artificial intelligence highlights numerous egregious claims of its researchers, especially in relation to a populist form of ‘strong’ computationalism which holds that any suitably programmed computer instantiates genuine conscious mental states purely in virtue of carrying out a specific series of computations. The argument presented herein is a simple development of that originally presented in Putnam’s (Representation & Reality, Bradford Books, Cambridge in 1988 ) monograph, “Representation & Reality”, which if correct, has (...) important implications for turing machine functionalism and the prospect of ‘conscious’ machines. In the paper, instead of seeking to develop Putnam’s claim that, “everything implements every finite state automata”, I will try to establish the weaker result that, “everything implements the specific machine Q on a particular input set ( x )”. Then, equating Q ( x ) to any putative AI program, I will show that conceding the ‘strong AI’ thesis for Q (crediting it with mental states and consciousness) opens the door to a vicious form of panpsychism whereby all open systems, (e.g. grass, rocks etc.), must instantiate conscious experience and hence that disembodied minds lurk everywhere. (shrink)

What is the relation between works of fiction and the acquisition of knowledge?

If a robot sends a deceptive signal to a human user, is this always and everywhere an unethical act, or might it sometimes be ethically desirable? Building upon previous work in robot ethics, this article tries to clarify and refine our understanding of the ethics of robotic deception. It does so by making three arguments. First, it argues that we need to distinguish between three main forms of robotic deception (external state deception; superficial state deception; and hidden state deception) in (...) order to think clearly about its ethics. Second, it argues that the second type of deception – superficial state deception – is not best thought of as a form of deception, even though it is frequently criticised as such. And third, it argues that the third type of deception is best understood as a form of betrayal because doing so captures the unique ethical harm to which it gives rise, and justifies special ethical protections against its use. (shrink)

Rapid advances in AI-based automation have led to a number of existential and economic concerns. In particular, as automating technologies develop enhanced competency they seem to threaten the values associated with meaningful work. In this article, we focus on one such value: the value of achievement. We argue that achievement is a key part of what makes work meaningful and that advances in AI and automation give rise to a number achievement gaps in the workplace. This could limit people’s ability (...) to participate in meaningful forms of work. Achievement gaps are interesting, in part, because they are the inverse of the (negative) responsibility gaps already widely discussed in the literature on AI ethics. Having described and explained the problem of achievement gaps, the article concludes by identifying four possible policy responses to the problem. (shrink)

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and validates (...) the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

This article argues that access to meaningful sexual experience should be included within the set of the goods that are subject to principles of distributive justice. It argues that some people are currently unjustly excluded from meaningful sexual experience and it is not implausible to suggest that they might thereby have certain claim rights to sexual inclusion. This does not entail that anyone has a right to sex with another person, but it does entail that duties may be imposed on (...) society to foster greater sexual inclusion. This is a controversial thesis and this article addresses this controversy by engaging with four major objections to it: the misogyny objection; the impossibility objection; the stigmatisation objection; and the unjust social engineering objection. (shrink)

Human values seem to vary across time and space. What implications does this have for the future of human value? Will our human and (perhaps) post-human offspring have very different values from our own? Can we study the future of human values in an insightful and systematic way? This article makes three contributions to the debate about the future of human values. First, it argues that the systematic study of future values is both necessary in and of itself and an (...) important complement to other future-oriented inquiries. Second, it sets out a methodology and a set of methods for undertaking this study. Third, it gives a practical illustration of what this ‘axiological futurism’ might look like by developing a model of the axiological possibility space that humans are likely to navigate over the coming decades. (shrink)

There is a problem regarding God and perception right at the heart of Berkeley ’s metaphysics. With respect to this problem, I will argue for : It is intractable. Berkeley has no solution to this problem, and neither can we hope to offer one on his behalf. However, I will also argue for : The truth of need not be seen as threatening the viability of Berkeley ’s metaphysics. In fact, it may even be seen as speaking in its favor.

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)

In a recent very interesting and important challenge to tracking theories of knowledge, Williams & Sinhababu claim to have devised a counter-example to tracking theories of knowledge of a sort that escapes the defense of those theories by Adams & Clarke. In this paper we will explain why this is not true. Tracking theories are not undermined by the example of the backward clock, as interesting as the case is.

In July 2014, the roboticist Ronald Arkin suggested that child sex robots could be used to treat those with paedophilic predilections in the same way that methadone is used to treat heroin addicts. Taking this onboard, it would seem that there is reason to experiment with the regulation of this technology. But most people seem to disagree with this idea, with legal authorities in both the UK and US taking steps to outlaw such devices. In this paper, I subject these (...) different regulatory attitudes to critical scrutiny. In doing so, I make three main contributions to the debate. First, I present a framework for thinking about the regulatory options that we confront when dealing with child sex robots. Second, I argue that there is a prima facie case for restrictive regulation, but that this is contingent on whether Arkin’s hypothesis has a reasonable prospect of being successfully tested. Third, I argue that Arkin’s hypothesis probably does not have a reasonable prospect of being successfully tested. Consequently, we should proceed with utmost caution when it comes to this technology. (shrink)

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.

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)

Few problems in the philosophy of evolutionary biology are more widely disseminated and discussed than the charge of Darwinian evolution being a tautology. The history is long and complex, and the issues are many, and despite the problem routinely being dismissed as an introductory-level issue, based on misunderstandings of evolution, it seems that few agree on what exactly these misunderstandings consist of. In this paper, I will try to comprehensively review the history and the issues. Then, I will try to (...) present the following “solution”, or, one might say, “dissolution”, of the problem, and consider the wider implications of formal, or schematic, explanations in science: yes, the principle of natural selection is a tautology, and so what? It is a promissory note for actual, physical, explanations in particular cases, and is none the worse for that. This is not a new argument, of course, but it does point up the importance of formal schematic models in science. (shrink)

This paper investigates the meaning of the neo-Confucian concept of 'li'. From early on, it has the sense of a pattern designating how things are and ought to be. But it takes on the appearance of something transcendent to the world only at a certain point in history, when it becomes juxtaposed to 'qi'. Zhu Xi has been criticized for this 'li-qi' dichotomization and the transcendentalization of 'li'. The paper re-examines this putative dualism and transcendentalism, looking into both Zhu's discussions (...) and pre- and post-Zhu discussions of 'li', and concludes it to be an inter-connective threading immanent to the world. (shrink)

Stephen Law developed a challenge to theism, known as the evil-god challenge (Law (2010) ). The evil-god challenge to theism is to explain why the theist’s responses to the problem of evil are any better than the diabolist’s – who believes in a supremely evil god – rejoinders to the problem of good, when all the theist’s ploys (theodicy, sceptical theism, etc.) can be parodied by the diabolist. In the first part of this article, I extend the evil-god challenge by (...) showing that additional theist replies to the problem of evil (more theodicies, the privation view of evil, and others) also may be appropriated, with just as much plausibility, in support of the diabolist position. In the second part of the article, I defend the evil-god challenge against several objections. (shrink)

My job has been made easier tonight, given that Larry Hickman has already done most of the ‘heavy lifting’ for me. I think his paper is an excellent and convincing intervention into this debate, and one of the problems for me in constructing my talk has been that our discussions have forced me to rethink what I wanted to say. Given my Continental biases, I had expected to come out on Rorty’s side; in writing this paper, however, things have become (...) more complicated. So let me here thank Larry for both at once making my job tonight easier, and much to my chagrin, surprisingly difficult. What I want to suggest, in contrast to what you’ve just heard, is that the neopragmatism of Richard Rorty is not wholly inconsistent with Dewey’s pragmatism – or, at least, with a ‘thin’ version of Deweyian pragmatism. As we shall see, while the differences between Dewey and Rorty on the status of metaphysics are in all probability irreconcilable, Rorty’s reclamation of a ‘thin’ Dewey can be read as consistent with at least the spirit of Dewey’s work. I will try to make the stronger case that this reconciliation is possible according to the letter of Dewey’s philosophy as well, and the interrelated issues of method and social hope will serve as the avenues for this investigation. Given my audience, I imagine that what I’m about to say will be fodder for some interesting conversation, and so, in the spirit of Rorty’s thought, let me get on with my paper. (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)

How should we react to the development of sexbot technology? Taking their cue from anti-porn feminism, several academic critics lament the development of sexbot technology, arguing that it objectifies and subordinates women, is likely to promote misogynistic attitudes toward sex, and may need to be banned or restricted. In this chapter I argue for an alternative response. Taking my cue from the sex positive ‘feminist porn’ movement, I argue that the best response to the development of ‘bad’ sexbots is to (...) make better ones. This will require changes to the content, process and context of sexbot development. Doing so will acknowledge the valuable role that technology can play in human sexuality, and allow us to challenge gendered norms and assumptions about male and female sexual desire. This will not be a panacea to the social problems that could arise from sexbot development, but it offers a more realistic and hopeful vision for the future of this technology in a pluralistic and progressive society. (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)

It is widely believed that a conservative moral outlook is opposed to biomedical forms of human enhancement. In this paper, I argue that this widespread belief is incorrect. Using Cohen’s evaluative conservatism as my starting point, I argue that there are strong conservative reasons to prioritise the development of biomedical enhancements. In particular, I suggest that biomedical enhancement may be essential if we are to maintain our current evaluative equilibrium (i.e. the set of values that undergird and permeate our current (...) political, economic, and personal lives) against the threats to that equilibrium posed by external, non-biomedical forms of enhancement. I defend this view against modest conservatives who insist that biomedical enhancements pose a greater risk to our current evaluative equilibrium, and against those who see no principled distinction between the forms of human enhancement. (shrink)

Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department in (...) 1969 when I was appointed. Soon after, he became Chair. As his Associate Chair from 1971to 1975, I spent many hours with him in Buffalo and on professional trips .. (shrink)

While I strongly agree with Patrick Grim that abstract relationships are real, and that it is possible to get them right, the danger that we will get them wrong is just as real. The use of visual representation of abstract phenomena, precisely because of our predilection to see patterns in everything and because we don't have to think so hard about visible representations generally, may lead us to see things that aren't there.

Which risks are bad? This is not an easy question to answer in any non-circular way. Not only are risks sought out for various reasons, but risks are plainly discounted in many situations. What may seem "risky" when examined all by itself, may not seem risky when encountered in a real lived situation. Thus risks that are imposed by others, in particular, might seem horrendous when considered in abstraction, but quite acceptable when encountered in life. What we need to do, (...) among other things, is to examine this "seeming." Are people being deluded or distracted when they fail to take seriously the riskiness of activities undertaken by others, or does this make some rational sense? There can be no doubt that people sometimes are deluded, of course. We are all fallible. But risks are not unalloyed evils. They are typically taken because of their association with something positive. So questions about whether people are making wise judgments when they don’t care about certain risks that they take, or, on the other side of the coin, when they become absolutely hysterical when confronted with a risk that appears to others to be insignificant, hinge on a web of further factors. (shrink)

Historical Cognitive Science I am lucky to strike three reviewers who extract so clearly my book's spirit as well as its substance. They all both accept and act on my central methodological assumption; that detailed historical research, and consideration of difficult contemporary questions about cognition and culture, can be mutually illuminating. It's gratifying to find many themes which recur in different contexts throughout _Philosophy and Memory_ _Traces_ so well articulated here. The reviews catch my desires to interweave discussion of cognitive (...) theories of memory with moral questions of psychological control and self-mastery, to evoke the virtues and the pleasures of strange, baroque beliefs about fickle 'animal spirits' coursing through the nerves and the brain, to demonstrate that mechanistic explanation (even in its blunt old Cartesian form) can acknowledge complexity, and to develop scientific conceptions of dynamic memory traces and representations which can survive uncharitable philosophical criticism. The book's insistent interdisciplinarity is just an inchoate quest to acknowledge the daunting variety of the phenomena: remembering is both natural and cultural, and is studied by narrative theorists as well as neurobiologists, by physicists as well as psychologists. By fusing the rangy detail of a history of early modern neurophysiology with the committed, even gullible fervor of a defence of 'new connectionist' cognitive science, I wanted to pull out the carpet from all those who are happy to let 'scientific' and 'cultural' approaches to the mind run along independently. Once this general project is given space, as it is by all three reviewers, we can get down to specifics. (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)

Artificial intelligence (AI) is increasingly expected to disrupt the ordinary functioning of society. From how we fight wars or govern society, to how we work and play, and from how we create to how we teach and learn, there is almost no field of human activity which is believed to be entirely immune from the impact of this emerging technology. This poses a multifaceted problem when it comes to designing and understanding regulatory responses to AI. This article aims to: (i) (...) defend the need for a novel conceptual model for understanding the systemic legal disruption caused by new technologies such as AI; (ii) to situate this model in relation to preceding debates about the interaction of regulation with new technologies (particularly the ‘cyberlaw’ and ‘robolaw’ debates); and (iii) to set out a detailed model for understanding the legal disruption precipitated by AI, examining both pathways stemming from new affordances that can give rise to a regulatory ‘disruptive moment’, as well as the Legal Development, Displacement or Destruction that can ensue. The article proposes that this model of legal disruption can be broadly generalisable to understanding the legal effects and challenges of other emerging technologies. (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)

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)

“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)

Drawing on recent scholarship and delving systematically into Iamblichean texts, these ten papers establish Iamblichus as the great innovator of Neoplatonic philosophy who broadened its appeal for future generations of philosophers.

Populations in developed societies are rapidly aging: fertility rates are at all-time lows while life expectancy creeps ever higher. This is triggering a social crisis in which shrinking youth populations are required to pay for the care and retirements of an aging majority. Some people argue that by investing in the right kinds of lifespan extension technology – the kind that extends the healthy and productive phases of life – we can avoid this crisis (thereby securing a ‘longevity dividend’). This (...) chapter argues that this longevity dividend is unlikely to be paid if lifespan extension coincides with rampant technological unemployment. This does not mean that we should not pursue lifespan extension, but it does mean that the argument in its favor needs to rest on other grounds. After articulating these grounds, the chapter proceeds to consider the implications this has for our vision of the extended life, postwork utopia. It argues that this vision may need to be reconceived and suggests that one plausible reconception involves prioritizing the role of games in the well-lived life. (shrink)

This work treats the correlative concepts knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowledge is truth. Some but not all opinion is truth. Every proposition known to be true is believed to be true. Some but (...) not every proposition believed to be true is known to be true. Our focus is thus on propositional belief (“belief-that”): the combination of propositional knowledge (“knowledge-that”) and propositional opinion (“opinion-that”). Each of a person’s beliefs, whether knowledge or opinion, is the end result of a particular thought process that continued during a particular time interval and ended at a particular time with a conclusive act—a judgment that something is the case. This work is mainly about beliefs in substantive informative propositions—not empty tautologies. We also treat objectual knowledge (knowledge of objects in the broadest sense, or “knowledge-of”), operational knowledge (abilities and skills, “knowledge-how-to”, or “know-how”), and expert knowledge (expertise). Most points made in this work have been made by previous writers, but to the best of our knowledge, they have never before been collected into a coherent work accessible to a wide audience. -/- Key words: belief, knowledge/opinion, propositional, operational, objectual, cognition, . (shrink)

ABSTRACT: In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. This principle, its history, (...) and its relevance to some of Oswaldo Chateaubriand's work are discussed in my 2004 paper "The Principle of Wholistic Reference" in Essays on Chateaubriand's "Logical Forms". In Chateaubriand's réplica (reply), which is printed with my paper, he raised several important additional issues including the three I focus on in this tréplica (reply to his reply): truth-values, universes of discourse, and formal ontology. This paper is self-contained: it is not necessary to have read the above-mentioned works. The principle of wholistic reference (PWR) was first put forth by George Boole in 1847 when he espoused a monistic fixed-universe viewpoint similar to the one Frege and Russell espoused throughout their careers. Later, Boole elaborated PWR in 1854 from the pluralistic multiple-universes perspective. (shrink)

Present progress in mind science is racing away in the direction of denying the existence of human freewill and animal and human sentience. This brief paper attempts to summarise a few brief reasons why areas of present work by prominent authors have departed from fact to the realms of folk psychology and summarises some of the ways in which present work can be put right. An experiment is described and carried out in an attempt to breach a little more of (...) the present gap between experimental fact and the outmoded theory which others have tried to apply blindly.<br>. (shrink)

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and 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; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; 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 analyze 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)

Memory Detection Tests (MDTs) are a general class of psychophysiological tests that can be used to determine whether someone remembers a particular fact or datum. The P300 MDT is a type of MDT that relies on a presumed correlation between the presence of a detectable neural signal (the P300 “brainwave”) in a test subject, and the recognition of those facts in the subject’s mind. As such, the P300 MDT belongs to a class of brain-based forensic technologies which have proved popular (...) and controversial in recent years. With such tests increasingly being proffered for use in the courtroom — to either support or call into question testimony — it would behoove the legal system to have some systematic framework for ensuring that they are used responsibly. In this paper, I defend one such framework for ensuring that this is the case: the legitimacy enhancing test. According to this test, it is appropriate to make use of technologies such as the P300 MDT whenever doing so would (probably) enhance the legitimacy of the trial. I argue that this test addresses tensions between scientific and legal norms of evidence, and exhibits a number of additional virtues including unification, simplicity and flexibility. Although the test is defended by considering the example of the P300 MDT, its significance is much broader than that. If it has the virtues I claim for it, it should provide a general framework for the responsible use of technologies, and the responsible innovation of social epistemic systems. (shrink)

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

Our modern egalitarian and individualistic age is suspicious of authority, and in recent times there have been almost daily reports in the press of cases where trust in various authorities, including financial, governmental, political and religious, has been found to have been abused or misplaced. Such disappointments seem to bolster the case for withholding trust in external authority and falling back on one’s own resources. But if the lessons from Linda Zagzebski’s groundbreaking work are accepted, 1 self- reliance turns out (...) to be a confused and probably incoherent ideal ; and the rational and self-reflective person is committed to believing and acting on authority. In the second half of this short discussion paper I shall raise some possible concerns about Zagzebski’s positive case for reliance on authority, focussing on the moral and religious spheres. First however, let me say something about the negative part of Zagzebski’s work, her critique of self-reliance. Since I find this wholly convincing, I shall confine myself to some supplementary observations, mainly to do with the historical context in which her critique is located. (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...) weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself. (shrink)

2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and Sriram (...) Nambiar, I have written several publications trying to set the record straight—but so far to little avail. This encyclopedia entry is one more attempt to set the record straight in a way that can be appreciated by non-experts.Also see https://www.academia.edu/10161999/Booles_criteria_of_validity_and_invalidity . (shrink)