In this paper, I critique arguments made by philosopher David Buller against central evolutionary-psychological explanations of human mating. Specifically, I aim to rebut his criticisms of Evolutionary Psychology regarding (1) women's long-term mating preferences for high-status men; (2) the evolutionary rationale behind men's provisioning of women; (3) men's mating preferences for young women; (4) women's adaptation for extra-pair sex; (5) the sex-differentiated evolutionary theory of human jealousy; and (6) the notion of mate value. In sum, I aim to demonstrate that (...) Buller's arguments contra Evolutionary Psychologists are left wanting. (shrink)

The cognitive scientist Donald Hoffman argues that we don't perceive reality: spacetime, objects, colors, sounds, tastes, and so forth, are all merely an interface that we evolved to track evolutionary fitness rather than to perceive truths about external reality. In this paper, I expound on his argument, then I extend it, primarily, by looking at key ideas in physics that are quite germane to it. Among the topics in physics that I discuss are black holes, the holographic principle, string theory, (...) duality, quantum gravity, and special relativity. I discuss these ideas from physics with an eye to their relevance for Hoffman's view. (shrink)

The evolutionary psychologist Geoffrey Miller has argued that various features of human psychology have been sculpted, at least in part, by the evolutionary process of sexual selection via mate choice. This paper specifically examines the central claim of Miller’s account, namely that certain cognitive traits have evolved to function as good genes fitness indicators. First, I expound on and clarify key foundational concepts comprising the focal hypothesis, especially condition-dependence, mutation target size, and mutation-selection balance. Second, I proceed to highlight some (...) subtle distinctions with respect to the concepts of exaptation and adaptation, as well as Fisherian runaway selection and good genes sexual selection, all of which in turn bear importantly on the overall framework of cognitive traits as fitness indicators. Third and finally, I close out the paper by examining various conceptual and methodological criteria which are integral to identifying sexually selected adaptations, then briefly examine some empirical work that has aimed to test the hypothesis that traits such as humor and creativity function as sexually attractive fitness indicators. (shrink)

Can robots have significant moral status? This is an emerging topic of debate among roboticists and ethicists. This paper makes three contributions to this debate. First, it presents a theory – ‘ethical behaviourism’ – which holds that robots can have significant moral status if they are roughly performatively equivalent to other entities that have significant moral status. This theory is then defended from seven objections. Second, taking this theoretical position onboard, it is argued that the performative threshold that robots need (...) to cross in order to be afforded significant moral status may not be that high and that they may soon cross it (if they haven’t done so already). Finally, the implications of this for our procreative duties to robots are considered, and it is argued that we may need to take seriously a duty of ‘procreative beneficence’ towards robots. (shrink)

One of the most noticeable trends in recent years has been the increasing reliance of public decision-making processes on algorithms, i.e. computer-programmed step-by-step instructions for taking a given set of inputs and producing an output. The question raised by this article is whether the rise of such algorithmic governance creates problems for the moral or political legitimacy of our public decision-making processes. Ignoring common concerns with data protection and privacy, it is argued that algorithmic governance does pose a significant threat (...) to the legitimacy of such processes. Modelling my argument on Estlund’s threat of epistocracy, I call this the ‘threat of algocracy’. The article clarifies the nature of this threat and addresses two possible solutions. It is argued that neither solution is likely to be successful, at least not without risking many other things we value about social decision-making. The result is a somewhat pessimistic conclusion in which we confront the possibility that we are creating decision-making processes that constrain and limit opportunities for human participation. (shrink)

Friendship is an important part of the good life. While many roboticists are eager to create friend-like robots, many philosophers and ethicists are concerned. They argue that robots cannot really be our friends. Robots can only fake the emotional and behavioural cues we associate with friendship. Consequently, we should resist the drive to create robot friends. In this article, I argue that the philosophical critics are wrong. Using the classic virtue-ideal of friendship, I argue that robots can plausibly be considered (...) our virtue friends - that to do so is philosophically reasonable. Furthermore, I argue that even if you do not think that robots can be our virtue friends, they can fulfil other important friendship roles, and can complement and enhance the virtue friendships between human beings. (shrink)

This paper adds another argument to the rising tide of panic about robots and AI. The argument is intended to have broad civilization-level significance, but to involve less fanciful speculation about the likely future intelligence of machines than is common among many AI-doomsayers. The argument claims that the rise of the robots will create a crisis of moral patiency. That is to say, it will reduce the ability and willingness of humans to act in the world as responsible moral agents, (...) and thereby reduce them to moral patients. Since that ability and willingness is central to the value system in modern liberal democratic states, the crisis of moral patiency has a broad civilization-level significance: it threatens something that is foundational to and presupposed in much contemporary moral and political discourse. I defend this argument in three parts. I start with a brief analysis of an analogous argument made in pop culture. Though those arguments turn out to be hyperbolic and satirical, they do prove instructive as they illustrates a way in which the rise of robots could impact upon civilization, even when the robots themselves are neither malicious nor powerful enough to bring about our doom. I then introduce the argument from the crisis of moral patiency, defend its main premises and address objections. (shrink)

Suppose we are about to enter an era of increasing technological unemployment. What implications does this have for society? Two distinct ethical/social issues would seem to arise. The first is one of distributive justice: how will the efficiency gains from automated labour be distributed through society? The second is one of personal fulfillment and meaning: if people no longer have to work, what will they do with their lives? In this article, I set aside the first issue and focus on (...) the second. In doing so, I make three arguments. First, I argue that there are good reasons to embrace non-work and that these reasons become more compelling in an era of technological unemployment. Second, I argue that the technological advances that make widespread technological unemployment possible could still threaten or undermine human flourishing and meaning, especially if they do not remain confined to the economic sphere. And third, I argue that this threat could be contained if we adopt an integrative approach to our relationship with technology. In advancing these arguments, I draw on three distinct literatures: the literature on technological unemployment and workplace automation; the antiwork critique—which I argue gives reasons to embrace technological unemployment; and the philosophical debate about the conditions for meaning in life—which I argue gives reasons for concern. (shrink)

This chapter examines a common objection to sex robots: the symbolic-consequences argument. According to this argument sex robots are problematic because they symbolise something disturbing about our attitude to sex-related norms such as consent and the status of our sex partners, and because of the potential consequences of this symbolism. After formalising this objection and considering several real-world uses of it, the chapter subjects it to critical scrutiny. It argues that while there are grounds for thinking that sex robots could (...) symbolically represent a troubling attitude toward women (and maybe children) and the norms of interpersonal sexual relationships, the troubling symbolism is going to be removable in many instances and reformable in others. What will ultimately matter are the consequences of the symbolism but these consequences are likely to be difficult to ascertain. This may warrant an explicitly experimental approach to the development of this technology. (shrink)

The growth of self-tracking and personal surveillance has given rise to the Quantified Self movement. Members of this movement seek to enhance their personal well-being, productivity, and self-actualization through the tracking and gamification of personal data. The technologies that make this possible can also track and gamify aspects of our interpersonal, romantic relationships. Several authors have begun to challenge the ethical and normative implications of this development. In this article, we build upon this work to provide a detailed ethical analysis (...) of the Quantified Relationship. We identify eight core objections to the QR and subject them to critical scrutiny. We argue that although critics raise legitimate concerns, there are ways in which tracking technologies can be used to support and facilitate good relationships. We thus adopt a stance of cautious openness toward this technology and advocate the development of a research agenda for the positive use of QR technologies. (shrink)

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

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

Humans have long wondered whether they can survive the death of their physical bodies. Some people now look to technology as a means by which this might occur, using terms such 'whole brain emulation', 'mind uploading', and 'substrate independent minds' to describe a set of hypothetical procedures for transferring or emulating the functioning of a human mind on a synthetic substrate. There has been much debate about the philosophical implications of such procedures for personal survival. Most participants to that debate (...) assume that the continuation of identity is an objective fact that can be revealed by scientific enquiry or rational debate. We bring into this debate a perspective that has so far been neglected: that personal identities are in large part social constructs. Consequently, to enable a particular identity to survive the transference process, it is not sufficient to settle age-old philosophical questions about the nature of identity. It is also necessary to maintain certain networks of interaction between the synthetic person and its social environment, and sustain a collective belief in the persistence of identity. We defend this position by using the example of the Dalai Lama in Tibetan Buddhist tradition and identify technological procedures that could increase the credibility of personal continuity between biological and artificial substrates. (shrink)

Technology could be used to improve morality but it could do so in different ways. Some technologies could augment and enhance moral behaviour externally by using external cues and signals to push and pull us towards morally appropriate behaviours. Other technologies could enhance moral behaviour internally by directly altering the way in which the brain captures and processes morally salient information or initiates moral action. The question is whether there is any reason to prefer one method over the other? In (...) this article, I argue that there is. Specifically, I argue that internal moral enhancement is likely to be preferable to external moral enhancement, when it comes to the legitimacy of political decision-making processes. In fact, I go further than this and argue that the increasingly dominant forms of external moral enhancement may already be posing a significant threat to political legitimacy, one that we should try to address. Consequently, research and development of internal moral enhancements should be prioritised as a political project. (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 article argues that the word ψυχαγωγία and its cognates which are found in the writings of Philodemus retain a semantic connection to the domain of magic and are best translated in terms of ‘enchantment’ rather than the more generic sense of ‘entertainment’.

This article argues that the creation of artificial offspring could make our lives more meaningful. By ‘artificial offspring’ I mean beings that we construct, with a mix of human and non-human-like qualities. Robotic artificial intelligences are paradigmatic examples of the form. There are two reasons for thinking that the creation of such beings could make our lives more meaningful and valuable. The first is that the existence of a collective afterlife—i.e. a set of human-like lives that continue after we die—is (...) likely to be an important source and sustainer of meaning in our present lives. The second is that the creation of artificial offspring provides a plausible and potentially better pathway to a collective afterlife than the traditional biological pathway. Both of these arguments are defended from a variety of objections and misunderstandings. (shrink)

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

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

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

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

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

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

The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until recently, however, nothing has been known about how much negativity is necessary in a quasiprobability representation. Zhu :120404, 2016) proved that the upper and lower bounds with respect to one type of negativity measure are saturated by quasiprobability representations which are in one-to-one correspondence with the (...) elusive symmetric informationally complete quantum measurements. We define a family of negativity measures which includes Zhu’s as a special case and consider another member of the family which we call “sum negativity.” We prove a sufficient condition for local maxima in sum negativity and find exact global maxima in dimensions 3 and 4. Notably, we find that Zhu’s result on the SICs does not generally extend to sum negativity, although the analogous result does hold in dimension 4. Finally, the Hoggar lines in dimension 8 make an appearance in a conjecture on sum negativity. (shrink)

Some moral disagreements are so persistent that we suspect they are deep : we would disagree even when we have all relevant information and no one makes any mistakes. The possibility of deep disagreement is thought to drive cognitivists toward relativism, but most cognitivists reject relativism. There is an alternative. According to divergentism, cognitivists can reject relativism while allowing for deep disagreement. This view has rarely been defended at length, but many philosophers have implicitly endorsed its elements. I will defend (...) it. (shrink)

This is a response to Earp and colleagues' target article "If I could just stop loving you: Anti-love biotechnology and the ethics of a chemical break-up". I argue that the authors may indulge in the vice of in-principlism when presenting their ethical framework for dealing with anti-love biotechnology, and that they mis-apply the concept of harm.

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

The debate over the merits of originalism has advanced considerably in recent years, both in terms of its intellectual sophistication and its practical significance. In the process, some prominent originalists—Lawrence Solum and Jeffrey Goldsworthy being the two discussed here—have been at pains to separate out the linguistic and normative components of the theory. For these authors, while it is true that judges and other legal decision-makers ought to be originalists, it is also true that the communicated content of the constitution (...) is its original meaning. That is to say: the meaning is what it is, not what it should be. Accordingly, there is no sense in which the communicated content of the constitution is determined by reference to moral desiderata; linguistic desiderata do all the work. In this article, I beg to differ. In advancing their arguments for linguistic originalism, both authors rely upon the notion of successful communications conditions. In doing so they implicitly open up the door for moral desiderata to play a role in determining the original communicated content. This undercuts their claim and changes considerably the dialectical role of linguistic originalism in the debate over constitutional interpretation. (shrink)

Lengthy critical notice of J. B. Kennedy, The Musical Structure of Plato's Dialogues (Acumen, 2011). -/- We approached the prospect of reviewing Kennedy’s book with excitement and optimism, but we’ve left rather disappointed. The case doesn’t hang together, we think, because it requires us to suppose that Plato composed to a pattern that his readers wouldn’t be looking for. They wouldn’t be looking for it musically, because it is not musically significant. Moreover, if he expected them to be looking for (...) such a pattern in the stichometry, then the evidence available to us suggests that his expectations went wholly unfulfilled. Plato may have been a perverse writer in many ways – for instance, by disparaging philosophical writing in a philosophical text – but we think Kennedy’s hypothesis requires us to attribute a touch too much perversity to one of our favourite authors. (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)

Critical thinking involves deliberate application of tests and standards to beliefs per se and to methods used to arrive at beliefs. Pedagogical license is authorization accorded to teachers permitting them to use otherwise illicit means in order to achieve pedagogical goals. Pedagogical license is thus analogous to poetic license or, more generally, to artistic license. Pedagogical license will be found to be pervasive in college teaching. This presentation suggests that critical thinking courses emphasize two topics: first, the nature and usefulness (...) of critical thinking; second, the nature and pervasiveness of pedagogical license. Awareness of pedagogical license alerts the student to the need for critical thinking. Indoctrination is done to students; education is done by students. (shrink)

God seemingly had a duty to create minds each of infinite worth through possessing God-like knowledge. People might object that God’s own infinite worth was all that was needed, or that no mind that God created could have truly infinite worth; however, such objections fail. Yet this does not generate an unsolvable Problem of Evil. We could exist inside an infinite mind that was one among endlessly many, perhaps all created by Platonic Necessity. “God” might be our name for this (...) Necessity, or for the infinite mind inside which we existed, or for an infinite ocean of infinite minds. (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 am saying farewell after more than forty happy years of teaching logic at the University of Buffalo. But this is only a partial farewell. I will no longer be at UB to teach classroom courses or seminars. But nothing else will change. I will continue to be available for independent study. I will continue to write abstracts and articles with people who have taken courses or seminars with me. And I will continue to honor the LogicLifetimeGuarantee™, which is earned (...) by taking one of my logic courses or seminars. As you know, according to the terms of the LogicLifetimeGuarantee™, I stand behind everything I teach. If you find anything to be unsatisfactory, I am committed to fixing it. If you forget anything, I will remind you. If you have questions, I will answer them or ask more questions. And if you need more detail on any topic we discussed, I will help you to broaden and deepen your knowledge—and maybe write an abstract or article. Stay in touch. (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)

English translation of an entry on pages 137–42 of the Spanish-language dictionary of logic: Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta. -/- DEDICATION: To my friend and collaborator Kevin Tracy. -/- This short essay—containing careful definitions of ‘counterargument’ and ‘counterexample’—is not an easy read but it is one you’ll be glad you struggled through. It contains some carefully chosen examples suitable for classroom discussion. -/- Using the word ‘counterexample’ instead of ‘counterargument’ in connection with Aristotle’s invalidity (...) proofs leads to a misinterpretation of Aristotle’s intentions. The two relations expressed by these two words are drastically different—as explained in this essay. There is however a subtle overlap: Every argument that is a counterargument for a given argument is a counterexample to the universal proposition that every argument in the same form as the given argument is valid. The word ‘counterexample’ was coined in the 1800s. The word ‘counterargument’ was given this sense in the 1960s. Saying that one argument is a counterexample for another argument is bad English—taking the word ‘counterexample’ in its Standard English sense. The word ‘counterinstance’ is an exact synonym for ‘counterexample’. Which logic books define ‘counterinstance’ or ‘counterexample’? Who started using ‘counterinstance’ or ‘counterexample’ in the sense of ‘counterargument’? Did they note that they were not using the word in the Standard sense? Why did it catch on? -/- Also see: https://www.academia.edu/8840909/Argumentations_and_logic_1989_ . (shrink)

It is widely agreed by philosophers that the so-called “Frege-Russell definition of natural number” is actually an assertion concerning the nature of the numbers and that it cannot be regarded as a definition in the ordinary mathematical sense. On the basis of the reasoning in this paper it is clear that the Frege-Russell definition contradicts the following three principles (taken together): (1) each number is the same entity in each possible world, (2) each number exists in each possible world, (3) (...) some entities existing in the actual world do not exist in every possible world. Since these principles seem to be true, the paper is a refutation of the Frege-Russell definition. The paper does more. It shows that the contradictory of the Frege-Russell definition follows even when principles 2 and 3 are replaced by one considerably weaker principle. The ideas contained in the paper are related to two earlier objections to the definition. The first, sometimes attributed to the mathematician, C. S. Keyser, is that existence of the numbers as defined implies the existence of infinitely many particulars in each possible world. The second is, in effect, an idea which is said to have led Whitehead to reject the definition of number to which he had subscribed in Principia Mathematica. Whitehead is supposed to have said that he could not believe that the number two changes every “time twins are born”. The mathematician H. Jeffreys expressed similar ideas [Philos. of Sci. 5 (1938), 434–451]. One of the merits of the author’s work is that it refutes the Frege-Russell definition without the need to take sides on controversial points presupposed by the Keyser and Whitehead objections. The objections made by the author are therefore not to be identified with the Keyser and Whitehead objections. Even if the author’s work is to be regarded as a refinement and integration of previous ideas, it is nevertheless a contribution—not only because the basic points are well worth repeating but also because the refinements are logically significant improvements and because the author has stated them clearly and concisely in the idiom of contemporary philosophy. (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)

CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI’S COLLECTED PAPERS 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. (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)

This 4-page review-essay—which is entirely reportorial and philosophically neutral as are my other contributions to MATHEMATICAL REVIEWS—starts with a short introduction to the philosophy known as mathematical structuralism. The history of structuralism traces back to George Boole (1815–1864). By reference to a recent article various feature of structuralism are discussed with special attention to ambiguity and other terminological issues. The review-essay includes a description of the recent article. The article’s 4-sentence summary is quoted in full and then analyzed. The point (...) of the quotation is to make clear how murky, incompetent, and badly written the paper is. There is no way to determine from the article whether the editor or referees suggests improvements. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .

PUTNAM has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) is largely correct as far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary (...) science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers, scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. The book can be recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the literature of the 1950’s and before, when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. QUINE’S book is not easy to read, partly because the level of sophistication fluctuates at high frequency between remote extremes and partly because of convoluted English prose style and devilish terminology. Almost all of the minor but troublesome technical errata in the first printing have been corrected [see reviews, e.g., the reviewer, Philos. Sci. 39 (1972), no. 1, 97–99]. In the opinion of the reviewer the book is not suitable for undergraduate instruction, and without external motivation few mathematicians are likely to have the patience to appreciate it. Nevertheless, a careful study of the book will more than repay the effort and one should expect to find frequent references to this book in coming years. (shrink)

This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does (...) not follow from its premises? This result does nothing to vitiate the theories of distribution developed over the period beginning in medieval times. What it does vitiate is many if not all attempts to use distribution in tests of invalidity outside of the standard two-premise categorical arguments—where they were verified on a case-by-case basis without further theoretical grounding. In addition it shows that there was no theoretical basis for many if not all claims of fundamental status of rules of distribution. These results are further support for approaching historical texts using mathematical archeology. (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.Em sua forma mais forte e geral, o princípio da referência universalista afirma que toda proposição refere-se ao universo completo do discurso propriamente dito, independentemente de quão limitados sejam os referentes de seus termos não-lógicos ou com conteúdo. Embora Boole mudasse de um modelo monístico de universo-fixo nos seus trabalhos iniciais de 1847 e 1848 para um modelo pluralista de universo-múltiplo no seu tratado maduro de 1854, ele nunca hesitou em sua aceitação franca do princípio da referência universalista, possivelmente em uma forma ligeiramente mais fraca. De fato, ele considerou este princípio como um acompanhamento essencial para a sua teoria de formação de conceitos e de proposições. Visões semelhantes são encontradas em lógicos posteriores, e algumas das mais recentes formulações da lógica clássica de primeira ordem parecem estar de acordo com uma forma deste, se é que elas não implicam, de fato, o próprio princípio. (shrink)

Down through the ages, logic has adopted many strange and awkward technical terms: assertoric, prove, proof, model, constant, variable, particular, major, minor, and so on. But truth-value is a not a typical example. Every proposition, even if false, no matter how worthless, has a truth-value:even “one plus two equals four” and “one is not one”. In fact, every two false propositions have the same truth-value—no matter how different they might be, even if one is self-contradictory and one is consistent. It (...) is not such a big surprise that every true proposition, no matter how worthless, has a truth-value. Every proposition, whether valuable or worthless, has a truth-value.But it is a little strange that every two true propositions, no matter how different they might be, have the same truth-value. The Pythagorean Theorem has the same truth-value as the proposition that one is one. It is a stretch to think of truth-values as values in any of the normal senses of the word ‘value’. (shrink)