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: corcoran@buffalo.edu 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)

Many philosophical debates take for granted that there is such a thing as ‘the’ common-sense conception of the phenomenon of interest. Debates about the nature of perception tend to take for granted that there is a single, coherent common-sense conception of vision, consistent with Direct Realism. This conception is often accorded an epistemic default status. We draw on philosophical and psychological literature on naïve theories and belief fragmentation to motivate the hypothesis that untutored common sense encompasses conflicting Direct Realist and (...) Indirect Realist conceptions: there is no such thing as ‘the’ common-sense conception of vision that could enjoy epistemic default status. To examine this hypothesis, a survey administered an agreement rating task with verbal and pictorial stimuli to lay participants. We found many laypeople simultaneously hold conflicting Direct Realist and Indirect Realist beliefs about vision. Against common assumptions, Direct Realist beliefs are not clearly dominant, and consistent adherence to Direct Realism is not the norm, but the exception. These findings are consistent with recent accounts of belief fragmentation. They forcefully challenge common methodology in philosophical debates about the nature of perception and beyond. (shrink)

Some ‘naturalist’ accounts of disease employ a biostatistical account of dysfunction, whilst others use a ‘selected effect’ account. Several recent authors have argued that the biostatistical account offers the best hope for a naturalist account of disease. We show that the selected effect account survives the criticisms levelled by these authors relatively unscathed, and has significant advantages over the BST. Moreover, unlike the BST, it has a strong theoretical rationale and can provide substantive reasons to decide difficult cases. This is (...) illustrated by showing how life-history theory clarifies the status of so-called diseases of old age. The selected effect account of function deserves a more prominent place in the philosophy of medicine than it currently occupies. _1_ Introduction _2_ Biostatistical and Selected Effect Accounts of Function _3_ Objections to the Selected Effect Account _3.1_ Boorse _3.2_ Kingma _3.3_ Hausman _3.4_ Murphy and Woolfolk _4_ Problems for the Biostatistical Account _4.1_ Schwartz _5_ Analysis versus Explication _6_ Explicating Dysfunction: Life History Theory and Senescence _7_ Conclusion. (shrink)

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary logic (...) of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if <em>x</em> doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it. (shrink)

Ever since Darwin people have worried about the sceptical implications of evolution. If our minds are products of evolution like those of other animals, why suppose that the beliefs they produce are true, rather than merely useful? In this chapter we apply this argument to beliefs in three different domains: morality, religion, and science. We identify replies to evolutionary scepticism that work in some domains but not in others. The simplest reply to evolutionary scepticism is that the truth of beliefs (...) in a certain domain is, in fact, connected to evolutionary success, so that evolution can be expected to design systems that produce true beliefs in that domain. We call a connection between truth and evolutionary success a ‘Milvian bridge’, after the tradition which ascribes the triumph of Christianity at the battle of the Milvian bridge to the truth of Christianity. We argue that a Milvian bridge can be constructed for commonsense beliefs, and extended to scientific beliefs, but not to moral and religious beliefs. An alternative reply to evolutionary scepticism, which has been used defend moral beliefs, is to argue that their truth does not depend on their tracking some external state of affairs. We ask if this reply could be used to defend religious beliefs. (shrink)

Ever since Darwin people have worried about the sceptical implications of evolution. If our minds are products of evolution like those of other animals, why suppose that the beliefs they produce are true, rather than merely useful? We consider this problem for beliefs in three different domains: religion, morality, and commonsense and scientific claims about matters of empirical fact. We identify replies to evolutionary scepticism that work in some domains but not in others. One reply is that evolution can be (...) expected to design systems that produce true beliefs in some domain. This reply works for commonsense beliefs and can be extended to scientific beliefs. But it does not work for moral or religious beliefs. An alternative reply which has been used defend moral beliefs is that their truth does not consist in their tracking some external state of affairs. Whether or not it is successful in the case of moral beliefs, this reply is less plausible for religious beliefs. So religious beliefs emerge as particularly vulnerable to evolutionary debunking. (shrink)

Biological sexes (male, female, hermaphrodite) are defined by different gametic strategies for reproduction. Sexes are regions of phenotypic space which implement those gametic reproductive strategies. Individual organisms pass in and out of these regions – sexes - one or more times during their lives. Importantly, sexes are life-history stages rather than applying to organisms over their entire lifespan. This fact has been obscured by concentrating on humans, and ignoring species which regularly change sex, as well as those with non-genetic or (...) facultatively genetic sex determination systems. But the general point applies equally to humans. Assigning sexes to pre-reproductive life history stages involves ‘prospective narration’ – classifying the present in terms of its anticipated future. Assigning sexes to adult stages of non-reproductive castes or non-reproductive individuals is a complex matter whose biological meaning differs from case to case. The chromosomal and phenotypic ‘definitions’ of biological sex that are contested in philosophical discussions of sex are actually operational definitions which track gametic sex more or less effectively in some species or group of species. Neither ‘definition’ can be stated for species in general except by defining them in terms of gametic sex. The gametic definition of sex also features in widely accepted models which explain why two biological sexes – either in separate individuals or combined in hermaphroditic individuals - are almost universal in multicellular species. Finally, the fact that a species has only two biological sexes does not imply that every member of the species is either male, female or hermaphroditic, or that the sex of every individual organism is clear and determinate. The idea of biological sex is critical for understanding the diversity of life, but ill-suited to the job of determining the social or legal status of human beings as men or women. (shrink)

At the end of the nineteenth century, Ludwig Edinger completed the first comparative survey of the microscopic anatomy of vertebrate brains. He is regarded as the founder of the field of comparative neuroanatomy. Modern commentators have misunderstood him to have espoused an anti-Darwinian linear view of brain evolution, harkening to the metaphysics of the scala naturae. This understanding arises, in part, from an increasingly contested view of nineteenth-century morphology in Germany. Edinger did espouse a progressionist, though not strictly linear, view (...) of forebrain evolution, but his work also provided carefully documented evidence that brain stem structures vary in complexity independently from one another and across species in a manner that is not compatible with linear progress. This led Edinger to reject progressionism for all brain structures other than the forebrain roof, based on reasoning not too dissimilar from those his successors used to dismiss it for the forebrain roof. (shrink)

The only subtype of epistemic agent currently recognized within scientonomy is community. The place of both individuals and epistemic tools in the scientonomic ontology is yet to be clarified. This paper extends the scientonomic ontology to include epistemic agents and epistemic tools as well as their relationship to one another. Epistemic agent is defined as an agent capable of taking epistemic stances towards epistemic elements. These stances must be taken intentionally, that is, based on a semantic understanding of the epistemic (...) element in question and its available alternatives, with reason, and for the purpose of acquiring knowledge. I argue that there can be both communal and individual epistemic agents. Epistemic agents are linked by relationships of authority delegation based on their differing areas of expertise. Having established the role of epistemic agents in the process of scientific change, I then turn to the role of epistemic tools, such as a thermometer, a text, or a particle accelerator in epistemic activities. I argue that epistemic tools play a different role in scientific change than do epistemic agents. This role is specified by an agent’s employed method. A physical object or system is an epistemic tool for some epistemic agent if there is a procedure by which the tool can provide an acceptable source of knowledge for answering some question under the employed method of the agent. An agent is said to rely on such a tool. (shrink)

Intuitive judgments elicited by verbal case-descriptions play key roles in philosophical problem-setting and argument. Experimental philosophy's ‘sources project’ seeks to develop psychological explanations of philosophically relevant intuitions which help us assess our warrant for accepting them. This article develops a psycholinguistic explanation of intuitions prompted by philosophical case-descriptions. For proof of concept, we target intuitions underlying a classic paradox about perception, trace them to stereotype-driven inferences automatically executed in verb comprehension, and employ a forced-choice plausibility-ranking task to elicit the relevant (...) stereotypical associations of perception- and appearance-verbs. We obtain a debunking explanation that resolves the philosophical paradox. (shrink)

In Nicomachean Ethics 2.1, Aristotle draws a now familiar analogy between aretai ('virtues') and technai ('skills'). The apparent basis of this comparison is that both virtue and skill are developed through practice and repetition, specifically by the learner performing the same kinds of actions as the expert: in other words, we become virtuous by performing virtuous actions. Aristotle’s claim that “like states arise from like activities” has led some philosophers to challenge the virtue-skill analogy. In particular, Aristotle’s skill analogy is (...) sometimes dismissed because of the role that practical wisdom or phronesis purportedly plays in character virtue. In this paper, I argue that a proper understanding of character virtue, phantasia-based emotions, and Aristotle’s implicit distinction between habituated and strict or full virtue (aretè kuria) grounds his virtue-skill analogy. Character virtue stems from the non-rational orektikon and is developed through the habituation of passionate elements, primarily phantasia and pathé. Pathé are pleasurable or affective perceptions, not judgments or beliefs. Thus, pathé are subject to non-rational habituation. Practical wisdom, on the other hand, is an intellectual virtue stemming from the rational part of the soul. Though practical wisdom is necessary for full virtue (aretè kuria), it is not necessary for the habituated character virtue that Aristotle refers in Book II. Once we understand the phantastic basis of emotions and the distinction between habituated and full virtue, the virtue-skill analogy is apt. I conclude by briefly mentioning two contemporary forms of emotion regulation—cognitive reappraisal and cognitive behavioral therapy—that lend support from empirical psychology to Aristotle’s claim that emotions (pathé) can be habituated. Character virtue is indeed a skill; it is—at least in part—the skill of emotion regulation. (shrink)

Teaching at a private, conservative religious institution poses unique challenges for equality, diversity, and inclusivity education (EDI). Given the realities of the student population in the Honors College of a private, religious institution, it is necessary to first introduce students to the contemporary realities of inequality and oppression and thus the need for EDI. This chapter proposes a conceptual framework and pedagogical suggestions for teaching basic concepts of social justice in a team-taught, interdisciplinary social science course. The course integrates four (...) different approaches to justice: theoretical, social scientific, narratological, and experiential. The discussion of the experiential dimension of the course references practical pedagogical strategies for making social justice and inequality real for our students. Understanding the realities of social inequality and its roots can foster a better understanding of the social forces and structures that perpetuate inequality. Furthermore, this approach can plant the intellectual and empathic seeds to challenge in-group bias and hopefully germinate into fruitful interaction with diverse others. Finally, this rich, interdisciplinary encounter with social inequality and justice can prepare students to work for just social structures that will lead to a more inclusive world. (shrink)

The sociotechnical domain is the realm of scientists, the communities and institutions they form, and the tools and instruments they use to create, disseminate, and preserve knowledge. This paper reviews current scientonomic theory concerning this domain. A core scientonomic concept is that of an epistemic agent. Generally, an agent is an entity capable of intentional action—action that has content or meaning due to its purposeful direction towards a goal. An epistemic agent is one whose actions are the taking of epistemic (...) stances, such as acceptance or rejection, towards epistemic elements, like theories or questions. An epistemic agent must semantically understand the propositions in question, and their alternatives, and choose among them with reason, with the motive of acquiring knowledge. The most obvious example of an epistemic agent is an individual human being. Rejecting the network of practitioners view, current scientonomic theory argues that appropriately organized communities of scientists can also function as epistemic agents. Communal epistemic agents are of particular scientonomic importance. Whereas the methods of theory assessment of individual scientists can be idiosyncratic, scientonomic theory contends that the taking of epistemic stances by scientific communities is a lawful, rule-governed process. A second concept of central importance is that of an epistemic tool. A physical object or system is an epistemic tool for some epistemic agent if there is a procedure by which the tool can provide an acceptable source of knowledge under the method employed by that agent. The agent is then said to rely on the tool. (shrink)

The sociotechnical domain is the realm of scientists, the communities and institutions they form, and the tools and instruments they use to create, disseminate, and preserve knowledge. This paper reviews current scientonomic theory concerning this domain. A core scientonomic concept is that of an epistemic agent. Generally, an agent is an entity capable of intentional action—action that has content or meaning due to its purposeful direction towards a goal. An epistemic agent is one whose actions are the taking of epistemic (...) stances, such as acceptance or rejection, towards epistemic elements, like theories or questions. An epistemic agent must semantically understand the propositions in question, and their alternatives, and choose among them with reason, with the motive of acquiring knowledge. The most obvious example of an epistemic agent is an individual human being. Rejecting the network of practitioners view, current scientonomic theory argues that appropriately organized communities of scientists can also function as epistemic agents. Communal epistemic agents are of particular scientonomic importance. Whereas the methods of theory assessment of individual scientists can be idiosyncratic, scientonomic theory contends that the taking of epistemic stances by scientific communities is a lawful, rule governed process. A second concept of central importance is that of an epistemic tool. A physical object or system is an epistemic tool for some epistemic agent if there is a procedure by which the tool can provide an acceptable source of knowledge under the method employed by that agent. (shrink)

Recent work by Brian Skyrms offers a very general way to think about how information flows and evolves in biological networks — from the way monkeys in a troop communicate, to the way cells in a body coordinate their actions. A central feature of his account is a way to formally measure the quantity of information contained in the signals in these networks. In this paper, we argue there is a tension between how Skyrms talks of signalling networks and his (...) formal measure of information. Although Skyrms refers to both how information flows through networks and that signals carry information, we show that his formal measure only captures the latter. We then suggest that to capture the notion of flow in signalling networks, we need to treat them as causal networks. This provides the formal tools to define a measure that does capture flow, and we do so by drawing on recent work defining causal specificity. Finally, we suggest that this new measure is crucial if we wish to explain how evolution creates information. For signals to play a role in explaining their own origins and stability, they can’t just carry information about acts: they must be difference-makers for acts. (shrink)

Stereotypes shape inferences in philosophical thought, political discourse, and everyday life. These inferences are routinely made when thinkers engage in language comprehension or production: We make them whenever we hear, read, or formulate stories, reports, philosophical case-descriptions, or premises of arguments – on virtually any topic. These inferences are largely automatic: largely unconscious, non-intentional, and effortless. Accordingly, they shape our thought in ways we can properly understand only by complementing traditional forms of philosophical analysis with experimental methods from psycholinguistics. This (...) paper seeks, first, to bring out the wider philosophical relevance of stereotypical inference, well beyond familiar topics like gender and race. Second, we wish to provide philosophers with a toolkit to experimentally study these ubiquitous inferences and what intuitions they may generate. This paper explains what stereotypes are, and why they matter to current and traditional concerns in philosophy – experimental, analytic, and applied. It then assembles a psycholinguistic toolkit and demonstrates through two studies how potentially questionnaire-based measures can be combined with process measures to garner evidence for specific stereotypical inferences and study when they ‘go through’ and influence our thinking. (shrink)

In this chapter we examine the relationship between biological information, the key biological concept of specificity, and recent philosophical work on causation. We begin by showing how talk of information in the molecular biosciences grew out of efforts to understand the sources of biological specificity. We then introduce the idea of ‘causal specificity’ from recent work on causation in philosophy, and our own, information theoretic measure of causal specificity. Biological specificity, we argue, is simple the causal specificity of certain biological (...) processes. This, we suggest, means that causal relationships in biology are ‘informational’ relationships simply when they are highly specific relationships. Biological information can be identified with the storage, transmission and exercise of biological specificity. It has been argued that causal relationships should not be regarded as informational relationship unless they are ‘arbitrary’. We argue that, whilst arbitrariness is an important feature of many causal relationships in living systems, it should not be used in this way to delimit biological information. Finally, we argue that biological specificity, and hence biological information, is not confined to nucleic acids but distributed among a wide range of entities and processes. (shrink)

This paper provides new tools for philosophical argument analysis and fresh empirical foundations for ‘critical’ ordinary language philosophy. Language comprehension routinely involves stereotypical inferences with contextual defeaters. J.L. Austin’s Sense and Sensibilia first mooted the idea that contextually inappropriate stereotypical inferences from verbal case-descriptions drive some philosophical paradoxes; these engender philosophical problems that can be resolved by exposing the underlying fallacies. We build on psycholinguistic research on salience effects to explain when and why even perfectly competent speakers cannot help making (...) stereotypical inferences which are contextually inappropriate. We analyse a classical paradox about perception, suggest it relies on contextually inappropriate stereotypical inferences from appearance-verbs, and show that the conditions we identified as leading to contextually inappropriate stereotypical inferences are met in formulations of the paradox. Three experiments use a forced-choice plausibility-ranking task to document the predicted inappropriate inferences, in English, German, and Japanese. The cross-linguistic study allows us to assess the wider relevance of the proposed analysis. Our findings open up new perspectives for ‘evidential’ experimental philosophy. (shrink)

Experimental philosophy’s much-discussed ‘restrictionist’ program seeks to delineate the extent to which philosophers may legitimately rely on intuitions about possible cases. The present paper shows that this program can be (i) put to the service of diagnostic problem-resolution (in the wake of J.L. Austin) and (ii) pursued by constructing and experimentally testing psycholinguistic explanations of intuitions which expose their lack of evidentiary value: The paper develops a psycholinguistic explanation of paradoxical intuitions that are prompted by verbal case-descriptions, and presents two (...) experiments that support the explanation. This debunking explanation helps resolve philosophical paradoxes about perception (known as ‘arguments from hallucination’). (shrink)

This article explores the notion of pedagogical authority as exercised in the Community of Inquiry, the method for facilitating Philosophy for Children (P4C). It argues that the teachers’ pedagogical authority in a Community of Inquiry is not predicated on their intellectual superiority or status. Rather it finds its legitimacy in their role as instigators of students’ thinking skills, which are assumed to be already possessed by the learners. This thesis is discussed in relation to Rancière’s concept of the dissociation of (...) the will and the intellect, which is treated here as conceptual complement to the existing interpretation of pedagogical authority as understood and practiced by scholars in the field of P4C. (shrink)

This new study of the “First” Crusade argues that “apocalyptic fervor” (p. 305) was the driving force of the expedition, as well as the Crusade movement. Previous studies, the author contends, have failed “to capture how precisely apocalyptic the First Crusade was” (p. xii). The remedy Rubenstein offers is a relentless focus on apocalypticism that ignores any weaknesses inherent in this approach and overlooks alternative explanations.

This essay proposes that Socrates practiced various spiritual exercises, including meditation, and that this Socratic practice of meditation was habitual, aimed at cultivating emotional self-control and existential preparedness. Contemporary research in neurobiology supports the view that intentional mental actions, including meditation, have a profound impact on brain activity, neuroplasticity, and help engender emotional self-control. This impact on brain activity is confirmed via technological developments, a prime example of how technology benefits humanity. Socrates attains the balanced emotional self-control that Alcibiades describes (...) in the Symposium because of the sustained mental effort he exerts that directly impacts his brain and his emotional and philosophical life. The essay concludes that Socratic meditative practices aimed at manifesting true dignity as human beings within the complexities of a technological world offer a promising model of self-care worthy of embracing today. (shrink)

Philosophers are often credited with particularly well-developed conceptual skills. The ‘expertise objection’ to experimental philosophy builds on this assumption to challenge inferences from findings about laypeople to conclusions about philosophers. We draw on psycholinguistics to develop and assess this objection. We examine whether philosophers are less or differently susceptible than laypersons to cognitive biases that affect how people understand verbal case descriptions and judge the cases described. We examine two possible sources of difference: Philosophers could be better at deploying concepts, (...) and this could make them less susceptible to comprehension biases (‘linguistic expertise objection’). Alternatively, exposure to different patterns of linguistic usage could render philosophers vulnerable to a fundamental comprehension bias, the linguistic salience bias, at different points (‘linguistic usage objection’). Together, these objections mount a novel ‘master argument’ against experimental philosophy. To develop and empirically assess this argument, we employ corpus analysis and distributional semantic analysis and elicit plausibility ratings from academic philosophers and psychology undergraduates. Our findings suggest philosophers are better at deploying concepts than laypeople but are susceptible to the linguistic salience bias to a similar extent and at similar points. We identify methodological consequences for experimental philosophy and for philosophical thought experiments. (shrink)

In this article, I intend to underscore the importance of critical thinking in rendering invaluable positive contributions and impact within professional organizations in the developing world. I argue that critical thinking treated as a normative principle and balanced with a pragmatic orientation provides a rational framework for resolving conflicts that oftentimes ensue from the incoherence between Western-based organizational theories and the actual circumstances of a developing country. In order to optimize the benefits of critical thinking, I also argue that it (...) should not be expected only among leaders and managers, but also and more importantly, among organizational members and associates. It is for this reason that I introduce Matthew Lipman’s Community of Inquiry as a model for cultivating critical thinking within professional environments. (shrink)

This essay is titled "Critique the Postulation of the Historical Law Theory and relate it to African Law. The postulation of the historical law school that law emanates from customs through an ordered pattern of systematized progress into a codified system in relation to African law forms the crust of this essay. To achieve this task, this essay adopts a critical method in exposing c postulation of the historical law school and the African Law (keeping in mind the Ukelle communal (...) Law System). This essay questions whether there can be an independent law made or promulgated without targeting a given people or that there can be a people-free law? This essay claims that like the historical law school, laws emanate from their ground norms but insists that unlike the historical law school, laws in Ukelle Traditional System do not necessarily have to submit to through the rigor of systematic and strict evolutionary pattern of progress. Like Herder, this essay avers that there is a unique character with each culture, and as such Ukelle Traditional Law does not have to submit to any universal character of law. (shrink)

Animal ethicists have recently debated the ethical questions raised by disenhancing animals to improve their welfare. Here, we focus on the particular case of breeding hens for commercial egg-laying systems to become blind, in order to benefit their welfare. Many people find breeding blind hens intuitively repellent, yet ‘welfare-only’ positions appear to be committed to endorsing this possibility if it produces welfare gains. We call this the ‘Blind Hens’ Challenge’. In this paper, we argue that there are both empirical and (...) theoretical reasons why even those adopting ‘welfare-only’ views should be concerned about breeding blind hens. But we also argue that alternative views, which (for example) claim that it is important to respect the telos or rights of an animal, do not offer a more convincing solution to questions raised by the possibility of disenhancing animals for their own benefit. (shrink)

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

The task of this chapter is to investigate and assess Grossmann’s view of the ontological status of categories. It has two dimensions. Because Grossmann does not offer a full discussion of the ontology of categories, we first need to present an interpretation of his view. Our point of departure is Grossmann’s claim that a category is a fundamental property of being (which implies that he holds view 3 above). Our second task is to assess the adequacy of his view. We (...) do this by raising some problems with Grossmann’s account, offering as an alternative view a version of 4 above, and defending it against what we construe as Grossmann’s possible counter-arguments. We argue that the best way to view categories themselves is as ontologically neutral insofar as this opens the way for particular categories to be linguistic entities, mental acts, or properties of extra-mental things. This requires, in turn, a qualified defense of two views rejected by Grossmann—common natures and modes of being. (shrink)

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 essay offers a reconstruction of Aristotle’s account of the voluntary in the Nicomachean Ethics, arguing that the voluntary grounds one notion of responsibility with two levels, and therefore both rational and non-rational animals are responsible for voluntary actions. Aristotle makes no distinction between causal and moral responsibility in the NE; rather, voluntariness and prohairesis form different bases for responsibility and make possible different levels of responsibility, but both levels of responsibility fall within the ethical sphere and are aptly appraised. (...) Important differences between the two levels remain. Animals and children are aptly appraised for direct voluntary actions. Conversely, only adults capable of prohairesis or rational choice are appraised for indirect voluntary actions—psychologically compelled actions that stem from character. Furthermore, while children and animals are responsible for actions, only adults casually contribute to the formation of their characters and thus are aptly appraised for character traits. (shrink)

Psycholinguistic methods hold great promise for experimental philosophy. Many philosophical thought experiments and arguments proceed from verbal descriptions of possible cases. Many relevant intuitions and conclusions are driven by spontaneous inferences about what else must also be true in the cases described. Such inferences are continually made in language comprehension and production. This chapter explains how methods from psycholinguistics can be employed to study such routine automatic inferences, with a view to assessing intuitions and reconstructing arguments. We demonstrate how plausibility (...) ratings, pupillometry, and reading time measurements can be used to examine hypotheses about automatic inferences in speech and text comprehension. Two experiments on inferences from polysemous (perception-)verbs provide evidence of a potentially consequential ‘salience bias’. Findings help assess intuitions about unusual cases and analyse a philosophical paradox (‘argument from hallucination’). The paper thus illustrates how we can adapt psycholinguistic methods for philosophical purposes and demonstrates the methods’ philosophical usefulness. (shrink)

What are the freedom-relevant conditions necessary for someone to be a morally responsible person? I examine several key authors beginning with Harry Frankfurt that have contributed to this debate in recent years, and then look back to the writings or Søren Kierkegaard to provide a solution to the debate. In this project I investigate the claims of semi-compatibilism and argue that while its proponents have identified a fundamental question concerning free will and moral responsibility—namely, that the agential properties necessary for (...) moral responsibility ascriptions are found in scenarios where the agent acts on her own as opposed to her action resulting from freedom undermining external causes such as manipulation, phobias, etc.—they have failed to show that the freedom-relevant agential properties identified in those actual-sequence scenarios are compatible with causal determinism. My argument is that only a voluntarist-libertarian theory can adequately account for the kinds of cases that the semicompatibilist identify. I argue that there are three freedom-relevant conditions necessary for someone to be a morally responsible person: a hierarchical understanding of human desires [specifically and mental states generally], an incompatibilist (non-deterministic) understanding of human action, and a historical understanding of character development. The ability to reflect critically about one’s own desires and emotions, and thus to have a kind of self-knowledge and understanding with regard to the springs of one’s own actions, is required to make it possible for the agent to be the “source” of her own actions and character. The non-deterministic understanding of human action is needed for a similar reason: if determinism is true, then every action a person performs can be ultimately traced to and exhaustively explained in terms of factors outside the agent’s control, thus making the agent’s responsibility for his actions an illusion. And finally,human nature must be such that, over time, one’s choices leave a dispositional residue self-understanding and motivation in the person’s self, out of which, in mature understanding and motivation, the person acts as a fully responsible agent. (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)

The study focused on the persistent poverty status in Nigeria in spite of all the actions and activities directly and indirectly put in place to reduce it. Nigerian poverty statistics and government actions in tackling poverty were examined. Few countries that have succeeded in reducing poverty position were briefly examined. Specifically, we highlighted how Malaysia, China and South Korea aspired and attained high level poverty alleviation. The lessons of their success stories were the basis for recommendations for Nigeria as a (...) panacea for poverty reduction which has persevere in spite of every efforts over the years. Among the recommendations made include designing of poverty line for the entire geopolitical zone, stating target of poverty reduction within a time frame, and sincerely implementing and monitoring of strategies, programmes and policies. Kalu E. Uma | Paul C.Obidike | Frank O. Ozoh "Poverty and it's Alleviation: Lessons for Nigeria" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-4 , June 2017. (shrink)

JOHN CORCORAN AND WAGNER SANZ, Disbelief Logic Complements Belief Logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 USA E-mail: corcoran@buffalo.edu Filosofia, Universidade Federal de Goiás, Goiás, GO 74001-970 Brazil E-mail: [email protected] -/- Consider two doxastic states belief and disbelief. Belief is taking a proposition to be true and disbelief taking it to be false. Judging also dichotomizes: accepting a proposition results in belief and rejecting in disbelief. Stating follows suit: asserting a proposition conveys belief and denying conveys disbelief. (...) Traditional logic implicitly focused on logical relations and processes needed in expanding and organizing systems of beliefs. Deducing a conclusion from beliefs results in belief of the conclusion. Deduction presupposes consequence: one proposition is a consequence of a set of a propositions if the latter logically implies the former. The role of consequence depends on its being truth-preserving: every consequence of a set of truths is true. This paper, which builds on previous work by the second author, explores roles of logic in expanding and organizing systems of disbeliefs. Aducing a conclusion from disbeliefs results in disbelief of the conclusion. Aduction presupposes contrequence: one proposition is a contrequence of a set of propositions if the set of negations or contradictory opposites of the latter logically implies that of the former. The role of contrequence depends on its being falsity-preserving: every contrequence of a set of falsehoods is false. A system of aductions that includes, for every contrequence of a given set, an aduction of the contrequence from the set is said to be complete. Historical and philosophical discussion is illustrated and enriched by presenting complete systems of aductions constructed by the second author. One such, a natural aduction system for Aristotelian categorical propositions, is based on a natural deduction system attributed to Aristotle by the first author and others. ADDED NOTE: Wagner Sanz reconstructed Aristotle’s logic the way it would have been had Aristole focused on constructing “anti-sciences” instead of sciences: more generally, on systems of disbeliefs. (shrink)

Many philosophical thought experiments and arguments involve unusual cases. We present empirical reasons to doubt the reliability of intuitive judgments and conclusions about such cases. Inferences and intuitions prompted by verbal case descriptions are influenced by routine comprehension processes which invoke stereotypes. We build on psycholinguistic findings to determine conditions under which the stereotype associated with the most salient sense of a word predictably supports inappropriate inferences from descriptions of unusual (stereotype-divergent) cases. We conduct an experiment that combines plausibility ratings (...) with pupillometry to document this “salience bias.” We find that under certain conditions, competent speakers automatically make stereotypical inferences they know to be inappropriate. (shrink)

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

Corcoran, J. 2005. Counterexamples and proexamples. Bulletin of Symbolic Logic 11(2005) 460. -/- John Corcoran, Counterexamples and Proexamples. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: corcoran@buffalo.edu Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even. Conversely, every counterexample for the proposition “every perfect number is even” is a perfect number that is not even. Every perfect number that is odd is a proexample for the existential (...) proposition that some perfect number is odd. Conversely, every proexample for the proposition “some perfect number is odd” is a perfect number that is odd. As trivial these remarks may seem, they can not be taken for granted, even in mathematical and logical texts designed to introduce their respective subjects. One well-reviewed book on counterexamples in analysis says that in order to demonstrate that a universal proposition is false it is necessary and sufficient to construct a counterexample. It is easy to see that it is not necessary to construct a counterexample to demonstrate that the proposition “every true proposition is known to be true” is false–necessity fails. Moreover the mere construction of an object that happens to be a counterexample does not by itself demonstrate that it is a counterexample–sufficiency fails. In order to demonstrate that a universal proposition is false it is neither necessary nor sufficient to construct a counterexample. Likewise, of course, in order to demonstrate that an existential proposition is true it is neither necessary nor sufficient to construct a proexample. This article defines the above relational concepts of counterexample and of proexample, it discusses their surprising history and philosophy, it gives many examples of uses of these and related concepts in the literature and it discusses some of the many errors that have been made as a result of overlooking the challenging subtlety of the proper use of these two basic and indispensable concepts. (shrink)

John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development (...) of algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. -/- It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems). (shrink)

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. One rather conspicuous example is that the process of refining logical terminology has been productive. Future logic students will no longer be burdened by obscure terminology and they will be able to read, think, talk, and write about logic in a more careful and more rewarding manner. Closely related is increased use and study of variable-enhanced natural language as in “Every proposition x that implies some proposition y that is false also implies some proposition z that is true”. Another welcome development is the culmination of the slow demise of logicism. No longer is the teacher blocked from using examples from arithmetic and algebra fearing that the students had been indoctrinated into thinking that every mathematical truth was a tautology and that every mathematical falsehood was a contradiction. A fifth welcome development is the separation of laws of logic from so-called logical truths, i.e., tautologies. Now we can teach the logical independence of the laws of excluded middle and non-contradiction without fear that students had been indoctrinated into thinking that every logical law was a tautology and that every falsehood of logic was a contradiction. This separation permits the logic teacher to apply logic in the clarification of laws of logic. This lecture expands the above points, which apply equally well in first, second, and third courses, i.e. in “critical thinking”, “deductive logic”, and “symbolic logic”. (shrink)

The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact fallacy if (...) they think that a proposition has different consequences were it true than it would have if false. C. I. Lewis said that confusing logical consequence with material consequence leads to this fallacy. See Corcoran’s 1973 “Meanings of implication” [available on Academia. edu]. -/- The premise-fact confusion occurs in a written passage that implies the premise-fact fallacy or that suggests that the writer isn’t clear about the issues involved in the premise-fact fallacy. Here are some examples. -/- E1: If Abe is Ben and Ben swims, then it would follow that Abe swims. -/- Comment: The truth is that from “Abe is Ben and Ben swims”, the proposition “Abe swims” follows. Whether in fact Abe is Ben and Ben swims is irrelevant to whether “Abe swims” follows from “Abe is Ben and Ben swims”. -/- E1 suggests that maybe “Abe swims” wouldn’t follow from “Abe is Ben and Ben swims” if the latter were false. -/- E2: The truth of “Abe is Ben and Ben swims” implies that Abe swims. -/- E3: Indirect deduction requires assuming something false. -/- Comment: If the premises of an indirect deduction are true the conclusion is true and thus the “reductio” assumption is false. But deduction, whether direct or indirect, does not require true premises. In fact, indirect deduction is often used to determine that the premises are not all true. -/- Anyway, the one-page paper accompanying this abstract reports one of dozens of premise-fact errors in PRIOR ANALYTICS. In the session, people can add their own examples and comment on them. For example, is the one at 25b32 the first? What is the next premise-fact error after 25b32? Which translators or commentators discuss this? -/- . (shrink)

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...) many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology. (shrink)

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

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, NY (...) 14260-4150 E-mail: corcoran@buffalo.edu The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

►JOHN CORCORAN AND IDRIS SAMAWI HAMID, Two-method errors: having it both ways. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu Philosophy, Colorado State University, Fort Collins, CO 80523-1781 USA E-mail: [email protected] Where two methods produce similar results, mixing the two sometimes creates errors we call two-method errors, TMEs: in style, syntax, semantics, pragmatics, implicature, logic, or action. This lecture analyzes examples found in technical and in non-technical contexts. One can say “Abe knows whether Ben draws” in (...) two other ways: ‘Abe knows whether or not Ben draws’ or ‘Abe knows whether Ben draws or not’. But a stylistic TME occurs in ‘Abe knows whether or not Ben draws or not’. One can say “Abe knows how Ben looks” using ‘Abe knows what Ben looks like’. But syntactical TMEs are in ‘Abe knows what Ben looks’ and in ‘Abe knows how Ben looks like’. One can deny that Abe knows Ben by prefixing ‘It isn’t that’ or by interpolating ‘doesn’t’. But a pragmatic TME occurs in trying to deny that Abe knows Ben by using ‘It isn’t that Abe doesn’t know Ben’. There are several standard ways of defining truth using sequences. Quine’s discussions in the 1970 first printing of Philosophy of logic [3] and in previous lectures were vitiated by mixing two [1, p. 98]. The logical TME in [3], which eluded Quine’s colleagues, was corrected in the 1978 sixth printing [2]. But Quine never explicitly acknowledged, described, or even mentioned the error. This lecture presents and analyses two-method errors in the logic literature. [1] JOHN CORCORAN, Review of Quine’s 1970 Philosophy of Logic. In Philosophy of Science, vol. 39 (1972), pp. 97–99. [2] JOHN CORCORAN, Review of sixth printing of Quine’s 1970 Philosophy of Logic. In Mathematical Reviews MR0469684 (1979): 57 #9465. [3] WILLARD VAN ORMAN QUINE, Philosophy of logic, Harvard, 1970/1986. (shrink)

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

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)

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)