Discerning the decisionmaking of Kim Jong-Un and the North Korean regime on issues of peaceful engagement and warlike actions endures as a mighty challenge for U.S. intelligence analysts and policymakers. In this report, we seek to inform analysis of Democratic People’s Republic of Korea (DPRK) leadership decisionmaking. To do so, we use three discussion papers that were written to facilitate discussion of an interagency working group. The three papers are assembled here in a single report. The first discussion paper describes (...) decisionmaking among different authoritarian regimes, including North Korea, and the opening up of those economies to outside engagement. The second paper outlines two different scenarios that might occur when conventional deterrence on the Korean Peninsula breaks down and the resulting decisions that North Korea’s leadership could face. The third paper assesses DPRK decisionmaking about nuclear weapon use. The report concludes with some observations, drawn from the issues covered in these three discussion papers, about DPRK decisionmaking and stability on the Korean Peninsula. (shrink)

JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised (...) to find out that in normal first-order logic existential import is quite common: some universals “Everything that is S is P” —actually quite a few—imply their corresponding existentials “Something that is S is P”. Anyway, perhaps contrary to its title, this paper is not a cataloging of surprises in logic but rather about the mistakes that did or might have or might still lead people to think that there are no surprises in logic. The paper cataloging of surprises in logic is on our “to-do” list. -/- ► JOHN CORCORAN AND WILIAM FRANK, Surprises in logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: [email protected] There are many surprises in logic. Peirce gave us a few. Russell gave Frege one. Löwenheim gave Zermelo one. Gödel gave some to Hilbert. Tarski gave us several. When we get a surprise, we are often delighted, puzzled, or skeptical. Sometimes we feel or say “Nice!”, “Wow, I didn’t know that!”, “Is that so?”, or the like. Every surprise belongs to someone. There are no disembodied surprises. Saying there are surprises in logic means that logicians experience surprises doing logic—not that among logical propositions some are intrinsically or objectively “surprising”. The expression “That isn’t surprising” often denigrates logical results. Logicians often aim for surprises. In fact, [1] argues that logic’s potential for surprises helps motivate its study and, indeed, helps justify logic’s existence as a discipline. Besides big surprises that change logicians’ perspectives, the logician’s daily life brings little surprises, e.g. that Gödel’s induction axiom alone implies Robinson’s axiom. Sometimes wild guesses succeed. Sometimes promising ideas fail. Perhaps one of the least surprising things about logic is that it is full of surprises. Against the above is Wittgenstein’s surprising conclusion : “Hence there can never be surprises in logic”. This paper unearths basic mistakes in [2] that might help to explain how Wittgenstein arrived at his false conclusion and why he never caught it. The mistakes include: unawareness that surprise is personal, confusing logicians having certainty with propositions having logical necessity, confusing definitions with criteria, and thinking that facts demonstrate truths. People demonstrate truths using their deductive know-how and their knowledge of facts: facts per se are epistemically inert. [1] JOHN CORCORAN, Hidden consequence and hidden independence. This Bulletin, vol.16, p. 443. [2] LUDWIG WITTGENSTEIN, Tractatus Logico-Philosophicus, Kegan Paul, London, 1921. -/-. (shrink)

Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08. -/- Constance Reid was an insider of the Berkeley-Stanford logic circle. Her San Francisco home was in Ashbury Heights near the homes of logicians such as Dana Scott and John Corcoran. Her sister Julia Robinson was one of the top mathematical logicians of her generation, as was Julia’s husband Raphael Robinson for whom Robinson Arithmetic was named. Julia was a Tarski PhD (...) and, in recognition of a distinguished career, was elected President of the American Mathematics Society. https://en.wikipedia.org/wiki/Julia_Robinson http://www.awm-math.org/noetherbrochure/Robinson82.html. (shrink)

What’s wrong with begging the question? Some philosophers believe that question-begging arguments are inevitably fallacious and that their fallaciousness stems from a shared “formal” deficiency. In contrast, some philosophers, like Robinson deny that begging the question is fallacious at all. And others characterize begging the question as an “informal” fallacy of reasoning that can only be understood with the aid of epistemic notions. Sorensen joins this last camp by offering a powerful argument against both Robinson’s skepticism and fully (...) formal approaches to the phenomenon. According to Sorensen’s view, question-begging is fallacious because it compromises the rationality of the question-beggar’s position. Though his argument forces Robinson into a peculiar dialectical position, it does little to elucidate the reasons why Robinson’s position is unstable and it fails to embody Sorensen’s own conception of rationally persuasive argumentation. I utilize this conception to show how Robinson is left with no easily identifiable grounds on which to deny the fallaciousness of begging the question. By advancing the dialectic between Sorensen and Robinson, I aim to show that our argumentative practices must take the perspectives of others seriously, whether or not those perspectives are rational. (shrink)

What’s so good about John Ames? The narrator of Marilynne Robinson’s Gilead has been much admired, but it’s far from obvious why. His life is quiet and unassuming, and has for the most part been uneventful in the extreme. In this chapter I draw on Iris Murdoch’s moral philosophy to explain the moral arc of the novel, and suggest that the novel in turn can shed light on Murdoch’s key ethical ideas. What is so notable about John (...) Ames, I suggest, is his commitment to seeing the world justly and lovingly—a commitment which for Murdoch is at the heart of virtuous agency. (shrink)

In 1937 Joan Robinson proposed that “when capitalism is rightly understood, the rate of interest will be set at zero and the major evils of capitalism will disappear”. A permanent zero rate would abolish capitalist profit except in limited cases, leaving nearly all output to be claimed by labour as wages. It would allow capital to be allocated on the basis of prospective social benefit rather than short-term profitability and a collateral basis that favours the wealthy. It would remove (...) some of the economic pressure to use resources unsustainably. So why not do this? I argue that the few available philosophical arguments for positive interest rates are unsatisfactory. Those who want a just and sustainable form of capitalism should target net zero for the interest rate. (shrink)

Epiphenomenalism is the view that phenomenal properties – which characterize what it is like, or how it feels, for a subject to be in conscious states – have no physical effects. One of the earliest arguments against epiphenomenalism is the evolutionary argument (James 1890/1981; Eccles and Popper 1977; Popper 1978), which starts from the following problem: why is pain correlated with stimuli detrimental to survival and reproduction – such as suffocation, hunger and burning? And why is pleasure correlated with stimuli (...) beneficial to survival and reproduction – such as eating and breathing? According to the argument, the fact that we have these particular correlations and not other ones must have an evolutionary explanation. But given epiphenomenalism, differences in phenomenal properties could not cause differences in fitness, so natural selection would not be expected to favor these correlations over any other ones. Epiphenomenalism thus renders these correlations an inexplicable coincidence, and should therefore be rejected. The evolutionary argument has been widely criticized and few have deemed it cogent (Broad 1925; Jackson 1982; Robinson 2007; Corabi 2014). In this paper, I will consider previous and potential criticisms and conclude some of them are indeed fatal to the argument if it is understood, as it traditionally has been, as an argument for any standard version of non-epiphenomenalism such as physicalism and interactionism. I will then offer a new and improved version of the argument, as an argument for a particular non-epiphenomenalist view, which I will call the phenomenal powers view. This is the view that phenomenal properties produce and thereby (metaphysically) necessitate their effects in virtue of how they feel, or in virtue of their intrinsic, phenomenal character alone – along the lines of C. B. Martin and John Heil’s powerful qualities view (Martin and Heil 1999; Heil 2003). I will argue that the phenomenal powers view explains the correlations given natural selection far better than any other view. It follows that if (and only if) understood as an argument for the phenomenal powers view, the evolutionary argument is far stronger than it is usually thought to be. (shrink)

Berkeley doesn't use the Time-Gap Argument, as Leibniz does, to prove either that we immediately see only ideas or that we see physical objects mediately. It may be doubted whether he was even aware of the time-gap problem that gives rise to the argument. But certain passages in the Three Dialogues and elsewhere suggest that Berkeley would have had cogent answers to anyone who claimed that this argument, construed as being in aid of the conclusion that we only perceive ideas, (...) is unsound. Discussing points made by Bertil Belfrage, Len Carrier, John Foster, A. C. Grayling, Howard Robinson, A. D. Smith, Tom Stoneham, and Colin Turbayne, I try to show that the Time-Gap Argument can be expanded into a strong argument for Berkeleian Idealism. I also idnicate how the latter provides a solution to J. J. Valberg's "puzzle of experience" and disarms James Cornman's argument in Perception, Common Sense, and Science that Berkeley, too, faces a time-gap problem. (shrink)

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.

Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how such (...) an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber. (shrink)

Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.

Nossa seleção de verbetes parte do interesse de cada pesquisador e os dispomos de maneira histórico-cronológica e, ao mesmo tempo, temática. O verbete de Melissa Lane, “Filosofia Política Antiga” vai da abrangência da política entre os gregos até a república e o império, às portas da cristianização. A “Filosofia Política Medieval”, de John Kilcullen e Jonathan Robinson, é o tópico que mais demanda espaço na nossa seleção em virtude das disputas intrínsecas ao período, da recepção de Aristóteles pelo (...) medievo e da tensão entre poder Papal e Civil. No verbete “Liberalismo”, de Gerald Gaus, Shane Courtland e David Schmidtz, vemos as fontes fundantes da Filosofia Política da modernidade. As ideias de liberdade negativa e positiva se coadunam com a Ética Liberal e sua influência sobre a abrangência do valor fundamental da liberdade individual diante das políticas públicas. O texto de Ian Carter, “Liberdade Positiva e Liberdade Negativa”, expõe o paradoxo da liberdade em suas concepções valorativas e neutra, muito úteis para compreender os problemas políticos que enfrentamos hoje. Por fim, Bas Van Der Vossen no texto “Libertarianismo” trata das noções tensas entre Estado e indivíduos. A concepção de “liberdade de si”, genuinamente negativa, ganha destaque justificatório. Jackie Scully, no verbete Bioética Feminista, exemplifica o valor da influência dessas correntes no âmago de todos os contemporâneos. Sua escrita homenageia postumamente Anne Donchin com um apanhado histórico da luta de inserção de políticas feministas na pesquisa acadêmica global. No verbete “Democracia”, os professores brasileiros Gustavo Dalaqua e Alberto Ribeiro Barros acrescentaram tópicos importantes ao tema geral, respectivamente: “Construtivismo Representativo vs. Representação Descritiva” e “Democracia Contestatória de Philip Pettit”. O texto de Thomas Christiano perpassa os principais argumentos de justificação política contra e a favor da democracia ocidental, com foco central nas concepções de liberdade e igualdade. Os verbetes dispostos nessa seleção de textos são tendenciosos na medida que expressam o interesse genuíno de cada pesquisador com os assuntos relevantes em suas pesquisas. Em virtude disso, a escolha “adota um lado” em detrimento de outros – mais especificamente: de outro que poderia ser mais “progressista”. Por si só, o livro já nasce reclamando um segundo volume, que será providenciado. Colocamos de lado qualquer exigência de “imparcialidade”, algo que não existe na Filosofia, muito menos na Filosofia Política. Sobressai, nesse aspecto, o caráter reflexivo que o assunto exige e a importância do assunto, sem o qual não teríamos a modernas concepções de representatividade, as teorias da justiça ou mesmo as ciências sociais. Um outro volume, portanto, se faz imperativo, por conta da abrangência da própria SEP e do respeito a seu projeto inicial, genuinamente um plano plural. (shrink)

Providing the most thorough coverage available in one volume, this comprehensive, broadly based collection offers a wide variety of selections in four major genres, and also includes a section on film. Each of the five sections contains a detailed critical introduction to each form, brief biographies of the authors, and a clear, concise editorial apparatus. Updated and revised throughout, the new Fourth Edition adds essays by Margaret Mead, Russell Baker, Joan Didion, Annie Dillard, and Alice Walker; fiction by Nathaniel Hawthorne, (...) Ursula K. LeGuin, Anton Chekov, James Joyce, Katherine Mansfield, F. Scott Fitzgerald, William Faulkner, Alice Walker, Louise Erdrich, Donald Barthelme, and James McPherson; poems by John Donne, Robert Browning, Walt Whitman, Edwin Arlington Robinson, e.e. cummings, Langston Hughes, W.H. Auden, Philip Levine, and Louise Gluck; and plays by August Wilson, Marsha Norman, Wendy Wasserstein, and Vaclav Havel. The chapter devoted to film examines the relation of film to literature and gives the complete screenplay for Citizen Kane plus close analysis of a scene from the film. With its innovative structure, comprehensive coverage, and insightful and stimulating presentation of all kinds of literature, this is an anthology readers will turn to again and again. (shrink)

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

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)

This paper examines some recent arguments for internalism that (i) appeal to an analogy between practical and theoretical reasons, (ii) look toward our practices of reasoning with others, or (iii) tie reasons to good deliberation. The conclusion of this paper is a skeptical one: none of these new arguments gives us sufficient reason to think that internalism is true.

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

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)

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)

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)

Can the best arguments for a privation theory of evil be parodied, with equal plausibility, as arguments for a privation theory of good? The privation theory of evil claims that evil has no positive existence, and it is but a privation of good. The privation theory of good claims the opposite. I approach this topic as one element in the so-called evil-God Challenge. Stephen Law has argued that the epistemic support for belief in an omniscient, omnipotent, and morally perfect God (...) (theism) is on a par with the epistemic support for belief in an omniscient, omnipotent, but completely evil-God (maltheism). In fact, he concludes, the arguments for an evil God are symmetrical with, and isomorphic to, those for a good God. The privation theory of evil has often been used to defend theism against the argument from evil. Thus, part of the evil-God Challenge is to evaluate arguments for the privation theory of evil for their vulnerability to maltheist parody. I consider a broad range of arguments for the privation theory of evil, and I argue that most of them are vulnerable to parodic neutralization. Furthermore, I argue that although the thesis of the convertibility of being and goodness is often held to entail the privation theory of evil, or to be entailed by it (or to be equivalent to it), it is independent of the privation theory. I do find that David Oderberg’s recent argument for the privation theory of evil resists any easy maltheist parody, but I argue that it has a defect. I sketch an argument according to which his good-as-fulfillment account is compatible with a perfectly evil god. My tentative conclusion is that the privation theory of evil enjoys little more plausibility than does the privation theory of good. (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 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)

According to the Aristotelian Thesis, the conclusion of practical reasoning is an action. Critics argue against it by pointing to cases in which some interference or inability prevents the production of action, yet in which that interference or inability doesn’t impugn the success of an agent’s reasoning. Some of those critics suggest instead that practical reasoning concludes in an intention, while others suggest it concludes in a belief with normative content, such as a belief about what one has conclusive, or (...) sufficient, reason to do. In this paper, I argue that we should allow that practical reasoning could conclude in either an intention or a belief with normative content. I begin by developing an objection to the Aristotelian Thesis, showing how the objection will not also undermine the possibility of practical reasoning concluding in an intention or a belief. I then respond to an argument from Joseph Raz designed to exclude the possibility of intentions as conclusions of practical reasoning. Lastly, I show how the worry that belief isn’t sufficiently “practical” to qualify as a conclusion of practical reasoning is misplaced. (shrink)

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

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

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

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

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

Economists can value things for cost-benefit analysis using either a structured or an unstructured approach. The first imposes some theoretical structure on the valuation; the second does not. This paper explains the difference between the approaches and examines the relative merits of each. Cost-benefit analysis may be aimed at finding what would be the best action, or alternatively at finding which action should be done in a democracy. The paper explains the difference, and argues that the appropriate aim is the (...) first. Given that, it comes down in favour of the structured approach to valuation. As an example, it discusses different approaches to valuing life in economics. (shrink)

The purpose of this paper is to review and discuss Luciano Floridi’s 2019 book The Logic of Information: A Theory of Philosophy as Conceptual Design, the latest instalment in his philosophy of information (PI) tetralogy, particularly with respect to its implications for library and information studies (LIS) .

In Rational Powers in Action, Sergio Tenenbaum sets out a new theory of instrumental rationality that departs from standard discussions of means-ends coherence in the literature on structural rationality in at least two interesting ways: it takes intentional action (as opposed to intention) to be what puts in place the relevant instrumental requirements, and it applies to both necessary and non-necessary means. I consider these two developments in more detail. On the first, I argue that Tenenbaum’s theory is too narrow (...) since there could be instrumental irrationality with respect to an intention to X even if one is not yet engaged in any relevant intentional action. On the second, I argue against Tenenbaum’s claim that “an agent is instrumentally irrational if she knowingly fails to pursue some sufficient means to an end she is pursuing.”. (shrink)

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

This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...) numbers satisfying “not odd but not not-prime”. The mistake is thinking that every two logically-equivalent false universal propositions have the same counterexamples. Only false universal propositions have counterexamples. A counterexample for “every two logically-equivalent false universal propositions have the same counterexamples” is two logically-equivalent false universal propositions not having the same counterexamples. The following counterexample arose naturally in my sophomore deductive logic course in a discussion of inner and outer converses. “Every even number precedes every odd number” is counterexemplified only by even numbers, whereas its equivalent “Every odd number is preceded by every even number” is counterexemplified only by odd numbers. Please let me know if you see this mistake in print. Also let me know if you have seen these points discussed before. I learned them in my own course: talk about learning by teaching! (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)

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)

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)

I argue that the dispute between two leading theories of interpretation of legal texts, textual originalism and textual evolutionism, depends on the false presupposition that changes in the way a word is used necessarily require a change in the word’s meaning. Semantic externalism goes a long way towards reconciling these views by showing how a word’s semantic properties can be stable over time, even through vicissitudes of usage. I argue that temporal externalism can account for even more semantic stability, however. (...) Temporal externalism is the theory that the content of an utterance at time t may be determined by developments in linguistic usage subsequent to t. If this semantic theory is correct, then the originalist and evolutionist positions effectively collapse. Originalism is correct in that the original meaning of the text is the meaning that is binding on jurists, but evolutionism is vindicated, as it is the current practices and standards that determine the meaning the text now has, and has always had. Objections to temporal externalism, and to its application to the interpretation of legal texts, are considered and addressed. (shrink)

This paper has as its topic two recent philosophical disputes. One of these disputes is internal to the project known as decision theory, and while by now familiar to many, may well seem to be of pressing concern only to specialists. It has been carried on over the last twenty years or so, but by now the two opposing camps are pretty well entrenched in their respective positions, and the situation appears to many observers (as well as to some of (...) the parties involved) to have reached a sort of stalemate. The second of these two disputes is, on the other hand, very much alive. While it has been framed in decision theoretic terms, it is definitely not a dispute internal to that enterprise. It is, rather, a debate about the very coherence of the notion of objective value, and as such touches on issues of central importance to, for example, meta–ethics and moral psychology. (shrink)

Excerpts and paraphrases of this memoir appeared in 2008 and 2009. I posted it in full here in happy memory of Peter Hare and my joyful years with him. -/- 2008. Remembering Peter Hare 1935–2008. Philosophy Now. Co-authors: T. Madigan and A. Razin. Issue 66 March/April 2008. Pages 50–2. PDF -/- 2009. Remembering My Life with Peter Hare. Remembering Peter Hare 1935–2008. Ed. J. Campbell. Society for the Advancement of American Philosophy. pp. 9–16. http://american-philosophy.org/documents/RememberingPeterHare_final.pdf -/- Peter H. Hare, Distinguished Professor (...) Emeritus of Philosophy at the University of Buffalo (SUNY at Buffalo), died peacefully in his sleep on Thursday, January 3, 2008. I would like to share my memories of my life with him. Others have eulogized him, enumerated his virtues and accomplishments, and written his obituaries. I am revisiting my personal relationship with him. These memories are as much about me as about him. (shrink)

Newcomb’s problem is a decision puzzle whose difficulty and interest stem from the fact that the possible outcomes are probabilistically dependent on, yet causally independent of, the agent’s options. The problem is named for its inventor, the physicist William Newcomb, but first appeared in print in a 1969 paper by Robert Nozick [12]. Closely related to, though less well-known than, the Prisoners’ Dilemma, it has been the subject of intense debate in the philosophical literature. After three decades, the issues remain (...) unresolved. Newcomb’s problem is of genuine importance because it poses a challenge to the theoretical adequacy of orthodox Bayesian decision theory. It has led both to the development of causal decision theory and to efforts aimed at defending the adequacy of the orthodox theory. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Contrary to dictionaries, a non sequitur isn’t “any statement that doesn’t follow logically from previous statements”. Otherwise, every opening statement would be a non sequitur: a non sequitur is a statement claimed to follow from previous statements but that doesn’t follow. If the sentence making a given statement doesn’t contain ‘thus’, ‘so’, ‘hence’, ‘therefore’, or something else indicating an implication claim, the statement isn’t a non sequitur in this sense. But this is only one of several senses of that expression, (...) which, contrary to appearances, is a unitary common noun more properly written as one word: non-sequitur or nonsequitur. Above a nonsequitur was, roughly speaking, a conclusion of an invalid premise- conclusion argument, but not every such, only those that were stated to follow from premises that had been stated. Every informative proposition is the conclusion of an invalid argument. Anyway, nonsequiturs were not arguments. However, the expression ‘nonsequitur’ also means “invalid premise- conclusion argument”. It also means something like “fallacious reasoning” as in ‘Abe’s proof of the big-bang hypothesis is a nonsequitur’. The English noun is also used for an irrelevancy, an abrupt change of topic, or for any of many other expressions that are gratuitous, inappropriate, incongruous, or in some other way out of place. The English noun is derived from the Latin expression ‘non sequitur’, which is not a common noun but a sentence variously meaning “it isn’t in sequence ”, “it doesn’t follow”, “it is out of order”, etc. A statement that begins ‘in the second place’ is a nonsequitur if the previous sentence lacked implication of something like ‘in the first place’ or if it contained something similar to ‘in the third place’. In fact, a true implication claim can be a nonsequitur if there is no reason for making it. If Ben says ‘Hence, Abe swims and Abe swims’ in reply to Carl’s statement ‘Abe swims‘, then Ben may well be committing a nonsequitur. Many conversation stoppers are nonsequiturs. This lecture surveys and analyses a wide selection of uses of ‘nonsequitur’ in logic and logic-related literature. -/- END OF DRAFT 4 -/- NOTE 091215: When Rick Perry was discussing possible withdrawal from the race—unfortunately not the human race but the Republican race—a reporter reminded him that just last week Donald Trump predicted the Perry withdrawal. Perry interrupted with “A broken clock is right once a day”. -/- If you did not know Perry you might think his reply was a brilliant diversionary nonsequitur. If you know Perry you might think his reply was a stupid nonsequitur. -/- For the record, he did say ‘once a day’, not ‘twice a day’. BTW, my interjection ‘unfortunately not the human race but the Republican race’ was also a nonsequitur. (shrink)

The expressions ‘form’, ‘structure’, ‘schema’, ‘shape’, ‘pattern’, ‘figure’, ‘mold’, and related locutions are used in logic both as technical terms and in metaphors. This paper juxtaposes, distinguishes, and analyses uses of [FOR these PUT such] expressions by logicians. No [FOR such PUT similar] project has been attempted previously. After establishing general terminology, we present a variant of traditional usage of the expression ‘logical form’ followed by a discussion of the usage found in the two-volume Chateaubriand book Logical Forms (2001 and (...) 2005)—the most comprehensive work on the subject ever written and in many ways the focus of this paper. Key Words: morphology, character, sense, sentence, proposition, form, structure, schema, alternative constituent, type, token . (shrink)

The primary sense of the word ‘hypothesis’ in modern colloquial English includes “proposition not yet settled” or “open question”. Its opposite is ‘fact’ in the sense of “proposition widely known to be true”. People are amazed that Plato [1, p. 1684] and Aristotle [Post. An. I.2 72a14–24, quoted below] used the Greek form of the word for indemonstrable first principles [sc. axioms] in general or for certain kinds of axioms. These two facts create the paradoxical situation that in many cases (...) it is impossible to translate the Greek form of the word using the English form: the primary sense of the word ‘hypothesis’ in modern colloquial English is diametrically opposed to one sense used by Plato and by his most accomplished student Given current colloquial English usage it is impossible to get the word hypothesis to carry the connotation of “settled truth” much less “axiomatic truth”. The ‘hypo-’ [under] in the Plato-Aristotle use of ‘hypothesis’ might carry the sense of “basis” or “foundational” as opposed to “less than usual or normal”. This paradox parallels the one pointed out by Robin Smith: it is impossible for the English word ‘syllogism’ to carry the meaning of its Greek form Aristotle intended. There are other cases as well: it is impossible for the English biological term ‘genus’ to carry the meaning of its Greek form the Greek genos refers to family as in our ‘genealogy’, not to “higher species” as in our ‘generic’. (shrink)