Several scholars, including Martin Hengel, R. Alan Culpepper, and Richard Bauckham, have argued that Papias had knowledge of the Gospel of John on the grounds that Papias’s prologue lists six of Jesus’s disciples in the same order that they are named in the Gospel of John: Andrew, Peter, Philip, Thomas, James, and John. In “A Note on Papias’s Knowledge of the Fourth Gospel” (JBL 129 [2010]: 793–794), Jake H. O’Connell presents a statistical analysis of this argument, (...) according to which the probability of this correspondence occurring by chance is lower than 1%. O’Connell concludes that it is more than 99% probable that this correspondence is the result of Papias copying John, rather than chance. I show that O’Connell’s analysis contains multiple mistakes, both substantive and mathematical: it ignores relevant evidence, overstates the correspondence between John and Papias, wrongly assumes that if Papias did not know John he ordered the disciples randomly, and conflates the probability of A given B with the probability of B given A. In discussing these errors, I aim to inform both Johannine scholarship and the use of probabilistic methods in historical reasoning. (shrink)

Synthesizing the domains of investigation highlighted in current research in distributed cognition and related fields, this paper offers an initial taxonomy of the overlapping types of resources which typically contribute to distributed or extended cognitive systems. It then outlines a number of key dimensions on which to analyse both the resulting integrated systems and the components which coalesce into more or less tightly coupled interaction over the course of their formation and renegotiation.

This paper introduces a new, expanded range of relevant cognitive psychological research on collaborative recall and social memory to the philosophical debate on extended and distributed cognition. We start by examining the case for extended cognition based on the complementarity of inner and outer resources, by which neural, bodily, social, and environmental resources with disparate but complementary properties are integrated into hybrid cognitive systems, transforming or augmenting the nature of remembering or decision-making. Adams and Aizawa, noting this distinctive complementarity argument, (...) say that they agree with it completely: but they describe it as “a non-revolutionary approach” which leaves “the cognitive psychology of memory as the study of processes that take place, essentially without exception, within nervous systems.” In response, we carve out, on distinct conceptual and empirical grounds, a rich middle ground between internalist forms of cognitivism and radical anti-cognitivism. Drawing both on extended cognition literature and on Sterelny’s account of the “scaffolded mind” (this issue), we develop a multidimensional framework for understanding varying relations between agents and external resources, both technological and social. On this basis we argue that, independent of any more “revolutionary” metaphysical claims about the partial constitution of cognitive processes by external resources, a thesis of scaffolded or distributed cognition can substantially influence or transform explanatory practice in cognitive science. Critics also cite various empirical results as evidence against the idea that remembering can extend beyond skull and skin. We respond with a more principled, representative survey of the scientific psychology of memory, focussing in particular on robust recent empirical traditions for the study of collaborative recall and transactive social memory. We describe our own empirical research on socially distributed remembering, aimed at identifying conditions for mnemonic emergence in collaborative groups. Philosophical debates about extended, embedded, and distributed cognition can thus make richer, mutually beneficial contact with independently motivated research programs in the cognitive psychology of memory. (shrink)

Many philosophers favour the simple knowledge account of assertion, which says you may assert something only if you know it. The simple account is true but importantly incomplete. I defend a more informative thesis, namely, that you may assert something only if your assertion expresses knowledge. I call this 'the express knowledge account of assertion', which I argue better handles a wider range of cases while at the same time explaining the simple knowledge account's appeal. §1 introduces some new data (...) that a knowledge account of assertion well explains. §2 explains the simple knowledge account's advantage over two of its main competitors. §3 presents a problem for the simple account and offers a solution, which is to adopt the express knowledge account. §4 encapsulates the case for the express knowledge account, and offers a unifying vision for the epistemology of belief and assertion. §5 answers an objection. §6 briefly sums up. Even those who ultimately reject my conclusion can still benefit from the new data presented in §1, and learn an important lesson from the problem discussed in §3, which demonstrates a general constraint on an acceptable account of the norm of assertion. (shrink)

‘There is no place in the phenomenology of fully absorbed coping’, writes Hubert Dreyfus, ‘for mindfulness. In flow, as Sartre sees, there are only attractive and repulsive forces drawing appropriate activity out of an active body’1. Among the many ways in which history animates dynamical systems at a range of distinctive timescales, the phenomena of embodied human habit, skilful movement, and absorbed coping are among the most pervasive and mundane, and the most philosophically puzzling. In this essay we examine both (...) habitual and skilled movement, sketching the outlines of a multidimensional framework within which the many differences across distinctive cases and domains might be fruitfully understood. Both the range of movement phenomena which can plausibly be seen as instances of habit or skill, and the space of possible theories of such phenomena are richer and more disparate than philosophy easily encompasses. We seek to bring phenomenology into contact with relevant movements in psychological theories of skilful action, in the belief that phenomenological philosophy and cognitive science can be allies rather than antagonists. (shrink)

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

Mitochondrial DNA (mtDNA) diseases are a group of neuromuscular diseases that often cause suffering and premature death. New mitochondrial replacement techniques (MRTs) may offer women with mtDNA diseases the opportunity to have healthy offspring to whom they are genetically related. MRTs will likely be ready to license for clinical use in the near future and a discussion of the ethics of the clinical introduction ofMRTs is needed. This paper begins by evaluating three concerns about the safety of MRTs for clinical (...) use on humans: (1) Is it ethical to use MRTs if safe alternatives exist? (2) Would persons with three genetic contributors be at risk of suffering? and (3) Can society trust that MRTs will be made available for humans only once adequate safety testing has taken place, and that MRTs will only be licensed for clinical use in a way that minimises risks? It is then argued that the ethics debate about MRTs should be reoriented towards recommendingways to reduce the possible risks of MRT use on humans. Two recommendations are made: (1) licensed clinical access to MRTs should only be granted to prospective parents if they intend to tell their children about their MRT conception by adulthood; and (2) sex selection should be used in conjunction with the clinical use ofMRTs, in order to reduce transgenerational health risks. (shrink)

The paper begins by reviewing two problems for fallibilism: the lottery problem, or the problem of explaining why fallible evidence, though otherwise excellent, is not enough to know that one will lose the lottery, and Gettier problems. It is then argued that both problems can be resolved if we note an important illocutionary force of knowledge attributions: namely, that when we attribute knowledge to someone we mean to give the person credit for getting things right. Alternatively, to say that a (...) person knows is to say that she got things right due to her own abilities, efforts and actions, rather than due to dumb luck, or blind chance, or something else. (shrink)

This paper addresses the foundations of Teleological Individualism, the view that organisms, even non-sentient organisms, are goal-oriented systems while biological collectives, such as ecosystems or conspecific groups, are mere assemblages of organisms. Typical defenses of Teleological Individualism ground the teleological organization of organisms in the workings of natural selection. This paper shows that grounding teleological organization in natural selection is antithetical to Teleological Individualism because such views assume a view about the units of selection on which it is only individual (...) organisms that are units of selection. However, none of the Conventionalist, Reductionist, or Multi-Level Realist theories serve to justify such an assumption. Thus, Teleological Individualism cannot be grounded in natural selection. (shrink)

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

This article accomplishes two closely connected things. First, it refutes an influential view about the relationship between perception and knowledge. In particular, it demonstrates that perceiving does not entail knowing. Second, it leverages that refutation to demonstrate that knowledge is not the most general factive propositional attitude.

Our environmental wrongdoings result in a moral debt that requires restitution. One component of restitution is reparative and another is remediative. The remediative component requires that we remediate our characters in ways that alter or eliminate the character traits that tend to lead, in their expression, to environmental wrongdoing. Restitutive restoration is a way of engaging in ecological restoration that helps to meet the remediative requirement that accompanies environmental wrongdoing. This account of restoration provides a new motivation and justification for (...) engaging in restorative practices in addition to the standard pragmatist justification and motivations. (shrink)

We think we have lots of substantial knowledge about the future. But contemporary wisdom has it that indeterminism prevails in such a way that just about any proposition about the future has a non-zero objective chance of being false.2, 3 What should one do about this? One, pessimistic, reaction is scepticism about knowledge of the future. We think this should be something of a last resort, especially since this scepticism is likely to infect alleged knowledge of the present and past. (...) One anti-sceptical strategy is to pin our hopes on determinism, conceding that knowledge of the future is unavailable in an indeterministic world. This is not satisfying either: we would rather not be hostage to empirical fortune in the way that this strategy recommends. A final strategy, one that we shall explore in this paper, is one of reconciliation: knowledge of a proposition is compatible with a subject’s belief having a non-zero objective chance of error.4 Following Williamson, we are interested in tying knowledge to the presence or absence of error in close cases, and so we shall explore the connections between knowledge and objective chance within such a framework. We don’t want to get tangled up here in complications involved in attempting to formulate a necessary and sufficient condition for knowledge in terms of safety. Instead, we will assume the following rough and ready necessary condition: a subject knows P only if she could not easily have falsely believed P.5 Assuming that easiness is to be spelt.. (shrink)

A philosopher once wrote the following words:If I examine the PTOLOMAIC and COPERNICAN systems, I endeavour only, by my enquiries, to know the real situation of the planets; that is, in other words, I endeavour to give them, in my conception, the same relations, that they bear towards each other in the heavens. To this operation of the mind, therefore, there seems to be always a real, though often an unknown standard, in the nature of things; nor is truth or (...) falsehood variable by the various apprehensions of mankind. Though all human race should for ever conclude, that the sun moves, and the earth remains at rest, the sun stirs not an inch from his place for all these reasonings; and such conclusions are eternally false and erroneous. (shrink)

The Knowledge Account of Assertion (KAA) says that knowledge is the norm of assertion: you may assert a proposition only if you know that it’s true. The primary support for KAA is an explanatory inference from a broad range of linguistic data. The more data that KAA well explains, the stronger the case for it, and the more difficult it is for the competition to keep pace. In this paper we critically assess a purported new linguistic datum, which, it has (...) been argued, KAA well explains. We argue that KAA does not well explain it. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

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

In this paper I refute the chief arguments for cultural relativism, meaning the moral (not the descriptive) theory that goes by that name. In doing this I walk some oft-trodden paths, but I also break new ones. For instance, I take unusual pains to produce an adequate formulation of cultural relativism, and I distinguish that thesis from the relativism of present-day anthropologists, with which it is often conflated. In addition, I address not one or two, but eleven arguments for cultural (...) relativism, many of which contribute to its popularity but receive scant attention from its critics. To elicit the failings of these arguments I deploy a host of pertinent but often neglected distinctions. (shrink)

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

The essay is framed by conflict between Christianity and Darwinian science over the history of the world and the nature of human personhood. Evolutionary science narrates a long prehuman geological and biological history filled with vast amounts, kinds, and distributions of apparently random brutal and pointless suffering. It also strongly suggests that the first modern humans were morally primitive. This science seems to discredit Christianity's common meta-narrative of the Fall, understood as a story of Paradise Lost. The author contends that (...) this Augustinian story and its character of Adam as endowed with superhuman gifts, and yet as so fragile as to fall, as claimed, is implausible, at any rate, even apart from science. He proposes that Christians consider adopting a Supralapsarian metaphysics of divine purpose supported by the intuitions of Irenaeus, who depicted the first human beings as comparable to innocent, but morally undeveloped children. In this approach the existence of evils is part of the divine plan to "defeat" them in and through the Incarnation, Atonement, and Resurrection of Christ. Putting an "Irenaean Adam" in place of the "Augustinian" counterpart may not remove conflict with science completely, but at least reduces it, and leads to a Christian narrative that is more plausible, in the light of science. (shrink)

RÉSUMÉ : Dans son récent recueil d’articles Language, Truth and History, Donald Davidson semble pencher en faveur d’une philosophie du langage mettant l’accent sur la notion de l’intention communicative du sujet parlant; en quoi il se rapproche du point de vue de Paul Grice. Si cela est juste, la pensée de Davidson se serait dégagée de l’approche sémantique formelle qu’il soutenait dans ses Inquiries into Truth and Interpretation. Dans cet article, je soutiens que, bien qu’il y ait beaucoup de similitudes (...) entre ces deux penseurs, Davidson n’a pas abandonné ses précédentes vues sur le langage. (shrink)

This is an English translation of Waldenfels' German essay: Equality and inequality are basic elements of law, justice and politics. Equality integrates each of us into a common sphere by distributing rights, duties and chances among us. Equality turns into mere indifference as far as we get overintegrated into social orders. When differences are fading away experience loses its relief and individuals lose their face. Our critical reflections start from the inevitable paradox of making equal what is not equal. In (...) various ways they refer to Nietzsche’s concept of order, to Marx’s analysis of money, to Lévinas’s ethics of the Other, and to novelists like Dostoevsky and Musil. Our critique turns against two extremes, on the one hand against any sort of normalism fixed on functioning orders, on the other hand against any sort of anomalism dreaming of mere events and permanent ruptures. Responsive phenomenology shows how we are confronted with extraordinary events. Those deviate from the ordinary and transgress its borders, without leaving the normality of our everyday world behind. The process of equalizing moves between the ordinary and the extraordinary. What makes the difference and resists mere indifference are creative responses which are to be invented again and again. (shrink)

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

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)

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

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)

It is sometimes asked whether virtue ethics can be assimilated by Kantianism or utilitarianism, or if it is a distinct position. A look atAristotle’s ethics shows that it certanly can be distinct. In particular, Aristotle presents us with an ethics of aesthetics in contrast to themore standard ethics of cognition: A virtuous agent identifies the right actions by their aesthetic qualities. Moreover, the agent’s concernwith her own aesthetic character gives us a key to the important role the emotions play for (...) Aristotle, which further distinguishes him from the other two theories we have mentioned. (shrink)

In this paper, I explore a possible convergence between two great twentieth century thinkers, Nishida Kitarō of Japan and Martin Heidegger of Germany. The focus is on the quasi-religious language they employ in discussing the grounding of human existence in terms of an encompassing Wherein for our being. Heidegger speaks of “the sacred” and “the passing of the last god” that mark an empty clearing wherein all metaphysical absolutes or gods have withdrawn but are simultaneously indicative of an opening wherein (...) beings are given. Nishida speaks of “the religious” dimension in the depths of one's being, that he calls “place,” and that somehow envelops the world through its kenotic self-negation. In both we find reference to a kind of originary space—the open or place—associated with quasireligious themes. I also point to their distinct approaches to metaphysical language in their attempts to give voice to that abysmal thought. (shrink)

It is generally accepted that Mill’s classification of names as nonconnotative terms is incompatible with Frege’s thesis that names have senses. However, Milldescribed the senses of nonconnotative terms—without being aware that he was doing so. These are the senses for names that were sought in vain by Frege. When Mill’s and Frege’s doctrines are understood as complementary, they constitute a fully satisfactory theory of names.

Recovering from its obsession with the computer in the 1990's psychology realised that minds come with bodies, something that Whitehead had pointed out in the 1920's. However, the problem of how the mind and body are linked remained. Bisemiotics solves it.

1. The restless mind[1] Like us, early modern philosophers, both natural and moral, didn’t always understand the springs of their own actions. They didn’t want to feel everything they felt, and couldn’t trace the sources of all their thoughts and imaginings. Events from past experience come to mind again unwilled: abstract thought is interrupted by fantastical images, like the ‘winged horses, fiery dragons, and monstrous giants’ by which Hume exemplified ‘the liberty of the imagination’[2]. Then, as now, a failure to (...) keep a train of thought on track could be blamed for both personal and social ills, for wasted lives and erratic policies. The ongoing struggle to distinguish the deliverances of reason from what Hume called ‘the loose and indolent reveries of a castle-builder’ (1739/ 1978, p.624) thus required scrutiny of daydream and fancy as much as belief and knowledge (see also Tierney- Hynes 2007 on the ‘castle-builder’). The mind’s tendencies to float and to roam were of great interest to early modern philosophers as well as to others concerned with medicine, mental health, morals, education, and taste. This paper sketches one local line of thinking and theorizing about ‘mind-wandering’ and its bodily causes in British philosophy over the first decades of the 18th century, as a small exemplar of a form of cognitive history intended to illuminate independent historical and contemporary concerns about our understanding of mental life. The dual aim is to see problems in our historical material that we might otherwise miss, and to use history to explore phenomena more or less marginalized by modern psychology[3]. (shrink)

HMI and Ofsted modes of school inpection are described and compared. The links between these modes are stressed. The information gathering capacity of Ofsted enables it to formulate specific and authoritative advice on good curriculum and pedagogic practice and thus to influence the direction of education policy and steer the system generally.

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement of (...) mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (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)

The key problem for normative (or moral) cultural relativism arises as soon as we try to formulate it. It resists formulations that are (1) clear, precise, and intelligible; (2) plausible enough to warrant serious attention; and (3) faithful to the aims of leading cultural relativists, one such aim being to produce an important alternative to moral universalism. Meeting one or two of these conditions is easy; meeting all three is not. I discuss twenty-four candidates for the label "cultural relativism," showing (...) that not one meets all three conditions. In the end I conclude that cultural relativists have produced nothing that threatens universalism. (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more commonly, (...) from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

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

Ideas about soul and body – about thinking or remembering, mind and life, brain and self – remain both diverse and controversial in our neurocentric age. The history of these ideas is significant both in its own right and to aid our understanding of the complex sources and nature of our concepts of mind, cognition, and psychology, which are all terms with puzzling, difficult histories. These topics are not the domain of specialists alone, and studies of emotion, perception, or reasoning (...) have never been isolated theoretical endeavours. As Francis Bacon described human philosophy or ‘the knowledge of ourselves’, within which he located the study of body, soul, and mind, it ‘deserveth the more accurate handling, by how much it toucheth us more nearly’ (1605/ 2000: 93). The history of ideas in these domains is particularly challenging given the practical dimensions and implications of theories of mind. Because theories of human nature and debates about body and mind do ‘touch us’ so ‘nearly’, they attract and can thus reveal, in specific historical contexts, interconnected discourses or associations which may be quite unlike our own. So there are no neat boundaries around a historical category of ‘seventeenth-century British philosophy of the soul’. The central topic of this chapter can be thought of either as pneumatology, the doctrine or science of spirits and souls, or as continuous with the ‘psychologia’ or psychology of Aristotelian traditions (Park and Kessler 1988; Hatfield 1995: 184-6). In neither case, however, should we expect any deep unity to be provided by history, geography, discipline, or subject-matter. (shrink)

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

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

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

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

Issues about the nature and ontology of works of art play a central part in contemporary aesthetics. But such issues are complicated by the fact that there seem to be two fundamentally different kinds of artworks. First, a visual artwork such as a picture or drawing seems to be closely identified with a particular physical object, in that even an exact copy of it does not count as being genuinely the same work of art. Nelson Goodman describes such works as (...) being “autographic.” Second, other artworks such as musical or literary works seem to be copyable without any such limitations: for example, two identical copies of a novel could each equally be a genuine instance of that novel; such works are “allographic,” in Goodman’s terminology. Nevertheless, it seems clear enough that a deeper understanding of both kinds of artworks requires the pursuit of analogies or similarities between them, in spite of their differences. Any such analogies that may be found will provide critical tests for more general theories about the nature of artworks. I show how to resolve such analogies for the orientational concept of inversion. (shrink)

This article further explains and develops a recent, comprehensive semantic naturalization theory, namely the interactive indexing (II) theory as described in my 2008 Minds and Machines article Semantic Naturalization via Interactive Perceptual Causality (Vol. 18, pp. 527–546). Folk views postulate a concrete intentional relation between cognitive states and the worldly states they are about. The II theory eliminates any such concrete intentionality, replacing it with purely causal relations based on the interactive theory of perception. But intentionality is preserved via purely (...) abstract propositions about the world that index, or correlate with, appropriate cognitive states. Further reasons as to why intentionality must be abstract are provided, along with more details of an II-style account of representation, language use and propositional attitudes. All cognitive representation is explained in terms of classification or sorting dispositions indexed by appropriate propositions. The theory is also related to Fodor’s representational theory of mind, with some surprisingly close parallels being found in spite of the purely dispositional basis of the II theory. In particular, Fodor’s insistence that thinking about an item cannot be reduced to sorting dispositions is supported via a novel two-level account of cognition—upper level propositional attitudes involve significant intermediate processing of a broadly normative epistemic kind prior to the formation of sorting dispositions. To conclude, the weak intentional realism of the II theory—which makes intentional descriptions of the world dispensable—is related to Dennett’s ‘intentional stance’ view, and distinguished from strong (indispensable) intentional realist views. II-style dispositions are also defended. (shrink)

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

This paper discusses the idea of "pure experience" within the context of the Buddhist tradition and in connection with the notions of emptiness and dependent origination via a reading of Dale Wright's reading of 'Huangbo' in his 'Philosophical Meditations on Zen Buddhism'. The purpose is to appropriate Wright's text in order to engender a response to Steven Katz's contextualist-constructivist thesis that there are no "pure" (i.e., unmediated) experiences. In light of the Mahayana claim that everything is empty of substance, i.e., (...) originates dependently through conditions, contingencies, and contexts, what does the "purity" of the Enlightenment experience mean for Chan/Zen Buddhism? (shrink)

A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an IQ (...) of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided. (shrink)