Experiences of embodied remembering are familiar and diverse. We settle bodily into familiar chairs or find our way easily round familiar rooms. We inhabit our own kitchens or cars or workspaces effectively and comfortably, and feel disrupted when our habitual and accustomed objects or technologies change or break or are not available. Hearing a particular song can viscerally bring back either one conversation long ago, or just the urge to dance. Some people explicitly use their bodies to record, store, or (...) cue memories. Others can move skilfully, without stopping to think, in complex and changing environments thanks to the cumulative expertise accrued in their history of fighting fires, or dancing, or playing hockey. The forms of memory involved in these cases may be distinct, operating at different timescales and levels, and by way of different mechanisms and media, but they often cooperate in the many contexts of our practices of remembering. (shrink)

Martin and Deutscher’s remarkable 1966 paper ‘Remembering’ still offers great riches to memory researchers across distinctive traditions, both in its methodological ambition (successfully marrying phenomenological and causal discourses) and in its content. In this short discussion, after briefly setting the paper in its context, we hone in on two live and under-explored issues which have gained attention recently under new labels – the extended mind hypothesis, and the constructive nature of memory. We suggest that Martin and Deutscher’s causal analysis of (...) memory is compatible with the idea that activities of remembering may be distributed across heterogeneous social and external resources, focussing in on their neglected example of creatures who ‘remember as we do’ as long as they carry round metal boxes which are given to them at birth. We then argue that the causal analysis is in some tension with the extent to which remembering is a constructive activity, because there may be no clear way to determine the appropriate ‘limits of accuracy’ within which a past event or experience must be represented. (shrink)

Remembering is one of the most characteristic and most puzzling of human activities. Personal memory, in particular – the ability mentally to travel back into the past, as leading psychologist Endel Tulving puts it – often has intense emotional or moral significance: it is perhaps the most striking manifestation of the peculiar way human beings are embedded in time, and of our limited but genuine freedom from our present environment and our immediate needs. Memory has been significant in the history (...) of philosophy as much in relation to ethics and to epistemology as in theories of psyche, mind, and self. (shrink)

I argue against the orthodox view of the relationship between propositional and doxastic justification. The view under criticism is: if p is propositionally justified for S in virtue of S's having reason R, and S believes p on the basis of R, then S's belief that p is doxastically justified. I then propose and evaluate alternative accounts of the relationship between propositional and doxastic justification, and conclude that we should explain propositional justification in terms of doxastic justification. If correct, this (...) proposal would constitute a significant advance in our understanding of the sources of epistemic justification. (shrink)

Epistemic reasons are mental states. They are not propositions or non-mental facts. The discussion proceeds as follows. Section 1 introduces the topic. Section 2 gives two concrete examples of how our topic directly affects the internalism/externalism debate in normative epistemology. Section 3 responds to an argument against the view that reasons are mental states. Section 4 presents two problems for the view that reasons are propositions. Section 5 presents two problems for the view that reasons are non-mental facts. Section 6 (...) argues that reasons are mental states. Section 7 responds to objections. (shrink)

This paper addresses relations between memory and imagery in expert sport in relation to visual or visuospatial perspective. Imagining, remembering, and moving potentially interact via related forms of episodic simulation, whether future- or past-directed. Sometimes I see myself engaged in action: many experts report switching between such external visual perspectives and an internal, 'own-eyes', or field perspective on their past or possible performance. Perspective in retrieval and in imagery may be flexible and multiple. I raise a range of topics for (...) empirical research on perspective and visualization. (shrink)

In this essay I show how to reconcile epistemic invariantism with the knowledge account of assertion. My basic proposal is that we can comfortably combine invariantism with the knowledge account of assertion by endorsing contextualism about speech acts. My demonstration takes place against the backdrop of recent contextualist attempts to usurp the knowledge account of assertion, most notably Keith DeRose's influential argument that the knowledge account of assertion spells doom for invariantism and enables contextualism's ascendancy.

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)

This paper is a tentative step towards a historical cognitive science, in the domain of memory and personal identity. I treat theoretical models of memory in history as specimens of the way cultural norms and artifacts can permeate ('proto')scientific views of inner processes. I apply this analysis to the topic of psychological control over one's own body, brain, and mind. Some metaphors and models for memory and mental representation signal the projection inside of external aids. Overtly at least, medieval and (...) Renaissance theorists agreed that such models had to allow for, or even guarantee, some conception of cognitive order and discipline. Individual memory traces had to be independent, not mixed up or interfering with others. The long tradition of improving or bypassing 'natural memory' by deliberately internalizing artefactual models was part of an arduous process of self-fashioning. Moral panic about confusion and mixture features centrally in the imposition of cognitive discipline in local memory traditions. (shrink)

Early modern critics of materialism (and of associated doctrines like determinism and mechanism) sometimes employed a transcendental argument form. If materialism were true, then some valuable feature of reality could not exist; but that feature does exist; therefore materialism is false. Depending on current context and concerns, the valuable 'X' in question might be God, the soul, hell, objective morality, free will, conscience, truth, knowledge, social order, or justice and the law: all, in the critics' eyes, obvious and unchallengeable realities (...) which materialism would, impossibly, extinguish.1 As David Hawkes notes in his delightfully provocative essay, it is because Hell is so manifestly real, in both the play and its world, that Faustus manifestly refutes himself in telling Mephistopheles that it is a fable. The success of such transcendental arguments relies on the truth of both their premises: Hell really must exist, and Faustus's materialism must really be incompatible with its existence. Hawkes celebrates early modern moralists who focussed on the alleged worldly and carnal roots and consequences of 'philosophical materialism', who attacked its proponents as villainous, self-interested, and depraved. (shrink)

Lloyd Jones’s *The Book of Fame*, a novel about the stunningly successful 1905 British tour of the New Zealand rugby team, represents both skilled group action and the difficulty of capturing it in words. The novel’s form is as fluid and deceptive, as adaptable and integrated, as the sweetly shaped play of the team that became known during this tour for the first time as the All Blacks. It treats sport on its own terms as a rich world, a set (...) of bodily skills, and an honest profession in itself. A reading of *The Book of Fame* can contribute to the interdisciplinary study of literature and cognition, exemplifying two-way ‘exchange values’. On the one hand, we gain insights into the nature of skilful group agency, of distinct forms and at distinct timescales, by focussing on the precise forms taken by the All Blacks’ creation of space. Here, we treat The Book of Fame as a brilliant evocation of features of collective thought, movement, and emotion that both everyday and scientific inquiry can easily miss. On the other hand, we also read back into the novel a subtle, fascinated interrogation of the mechanisms by which small groups form, evolve, and act. In this more ambitious mode of analysis, we use independently motivated theoretical concerns to help us see real features of the literary work that might otherwise remain invisible. We focus on the relationship between skilful performance and collective action. These topics fall outside the ambit of much current work by literary theorists using cognitive research, who tend to focus on theory of mind and modularity, metaphor and blending, emotion and empathy, consciousness and concepts, representation and so on. But skilled performance and collective action comprise surprisingly lively research fields across the sciences, from neuropsychology to philosophy of mind and cognitive anthropology. These areas of inquiry may provide even more productive avenues for future work in the interfield of literary and cultural theory and the cognitive sciences. (shrink)

I argue that you can have a priori knowledge of propositions that neither are nor appear necessarily true. You can know a priori contingent propositions that you recognize as such. This overturns a standard view in contemporary epistemology and the traditional view of the a priori, which restrict a priori knowledge to necessary truths, or at least to truths that appear necessary.

Some natural philosophers in the 17th century believed that they could control their own innards, specifically the animal spirits coursing incessantly through brain and nerves, in order to discipline or harness passion, cognition and action under rational guidance. This chapter addresses the mechanisms thought necessary after Eden for controlling the physiology of passion. The tragedy of human embedding in the body, with its cognitive and moral limitations, was paired with a sense of our confinement in sequential time. I use two (...) strands of 17th-century natural philosophy to exemplify forms of the perceived connection between physiology, memory, and the passions. I deal at length with Cartesian mechanism, and more briefly with Restoration natural philosophy in England. These are fruitful historical domains for connecting cognition and culture, since relations of domination, disruption, or accommodation between present and past are in play for both selves and societies. Despite the difficulty of integrating affect with cognition in theories of brain and mind, the capacity to treat passion and memory together is crucial for future cognitive science to address issues which outsiders care about. (shrink)

Mistakes can be made in both personal and official accounts of past events: lies can be told. Stories about the past have many functions besides truth-telling: but we still care deeply that our sense of what happened should be accurate. The possibility of error in memory and in history implies a commonsense realism about the past. Truth in memory is a problem because, coupled with our desires to find out what really happened, we recognize that our individual and collective access (...) to past events may be indirect. This chapter sketches some approaches, from across the disciplines, to such problems about authority over the past. I open up recent lines of research on autobiographical memory which should be more accessible in the humanities and social sciences. Psychological work on constructive remembering should not be seen as sceptically challenging the very possibility of everyday authority over our own past, but as identifying specific forms of fallibility. I argue that the study of historical and social processes is an integral part of the cognitive sciences of memory, not a humanistic curiosity. (shrink)

This was a class handout that I turned into a publication. As its title indicates, it's about the relation (or non-relation) of (ethical) cultural relativism to tolerance. Core elements of the paper were later absorbed into sections 5K, 6M, and 7K of my paper "Cultural Relativism" (2000), which is listed (and downloadable) on my PhilPapers page.

The study of remembering is both compelling and challenging, in part, because of the multiplicity and the complexity of influences on memory. Whatever their interests, memory researchers are always aware of the many different factors that can drive the processes they care about. A search for the phrase ‘influences on memory’ confirms this daunting and exhilarating array of influences, of many different kinds, operating at many different timescales, and presumably often interacting in ways that we can’t yet imagine, let alone (...) model. There are hormonal and neuromodulatory, genetic and pharmacological, developmental and age-related influences; there are influences of arousal, stress, gender, mood, emotion, sleep and personality; there are unconscious, schematic or semantic influences, and there are influences of context, situation, task and environment. There are many aspects of ‘media influence on memory’ (Loftus and Banaji, 1989; Strange and Garry, 2007), and, of course, there are both ‘social influences on memory’ (Echterhoff and Hirst, 2009) and ‘cultural influences on memory’ (Gutchess and Indeck, 2009). Notoriously, there are numerous ‘suggestive influences’ on memory (Loftus, 2003): influences of misinformation (Seifert, 2002; Wright and Loftus, 1998), or of ‘memory conformity’ (Gabbert et al., 2006) and ‘memory contagion’ (Roediger et al., 2002). People who know each other well, such as intimate couples, ‘may be well practised in yielding to each other’s influence and incorporating their partner’s information into their own memories of the past’ (French et al., 2008: 264). (shrink)

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper concludes with a (...) modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (shrink)

'Io trace a path from Pico della Mirandola's Renaissance man to the Jacobean malcontents of Marston or Webster is to document not an inflation of hopes for dominion over the natural world, but rather a loss of confidence in the possibility of control over even human affairs. 'For I am going into a wilderness, /Where I shall find nor path, nor friendly clew/To be my guide'.2 The bleak consequences of this lack of direction, leaving traces through into the Restoration period (...) in England, are particularly evident in the free will debate: of Milton's angels,. (shrink)

In 2002, a remake of the 1975 film Rollerball was released in theaters. It flopped at the box-office, disappearing quickly from movie screens and reappearing shortly thereafter on home video. While aesthetically horrendous, the remake of Rollerball is instructive, as it provides a point of contrast to the original film, highlighting a change in our culture’s manner of engagement with the difficult philosophical problem of nihilism. Both films share a roughly similar plot, yet in the differing manners that they explore (...) and develop that plot, we can glimpse two separate ways in which nihilism may be discovered, confronted and dealt with. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent (...) scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (shrink)

Upon its release in 1968, George Romero's Night of the Living Dead was attacked by many critics as an exploitative low budget film of questionable moral value. I argue in this paper that Night of the Living Dead is indeed nihilistic, but in a deeper philosophical sense than the critics had in mind.

Projects in memory studies are best driven by topic not tradition, because the phenomena under investigation are usually interactive, not neatly compartmentalized. This imposes open-endedness not only in tracing diverse activities of remembering across the spread of relevant disciplines, but also in looking beyond memory altogether in order better to understand its diverse manifestations.

The three papers in this special section of Cognitive Processing continue and extend the December 2005 issue, which was devoted in its entirety to reviews, research reports, and laboratory reports on the theme of ‘Memory and the Extended Mind: embodiment, cognition, and culture’ (Sutton 2005). Like the papers in that issue, these are revised versions of papers first presented at two workshops on ‘Memory, Mind, and Media’ in Sydney on November 29–30 and December 2–3, 2004. Where that issue focussed specifically (...) on memory, these three papers deal with more general issues in the foundations of cognitive science. (shrink)

Recent work in the methodology of connectionist explanation has I'ocrrsccl on the notion of levels of explanation. Specific issucs in conncctionisrn hcrc intersect with rvider areas of debate in the philosophy of psychology and thc philosophy of science generally. The issues I raise in this chapter, then, are not unique to cognitive science; but they arise in new and important contexts when connectionism is taken seriously as a model of cognition. The general questions are the relation between levels and the (...) status of levels which have no obvious relation to others. In speaking of levels, what is the connection, if there is one, between explanation and ontology? Which, if any, conccpt of reduction is applicable to connectionist systems? What kind of legitinrtcy can the constructs of common sense psychology, or of that vclsion ol intentional realism represented by classical symbol-systems n I, hirvc irr ir full-scale connectionist theory of mind? (shrink)

Sutton's review of Renaissance Magic and the Return of the Golden Age.

This paper is a commentary on the target article by Lokendra Shastri & Venkat Ajjanagadde [S&A]: “From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony” in same issue of the journal, pp.417–451. -/- It puts S&A's temporal-synchrony binding method in a broader context, comments on notions of pointing and other ways of associating information - in both computers and connectionist systems - and mentions types of reasoning that are a challenge to (...) S&A's system (amongst many other connectionist systems, recognizing that S&A's is much more capable as regards reasoning than most other contemporary systems). (shrink)

Descartes, the textbooks say, divided human beings, or at least their minds, from the natural world. This is not just the consequence of metaphysical dualism, but of the concomitant indirect ‘ideas’ theory of perception. On the standard view, the soul must dimly infer the nature of the external world from the meagre, fragmentary, and often misleading input which is causally transmitted from objects through the nervous system to the brain and, ultimately, to the pineal gland. The metaphysical solipsism of the (...) cogito, on this picture, has its psychophysiological counterpart in the way Descartes sets all goings-on in nature at such a distance from the knowing subject who is temporarily and imperfectly united with a physical body. We cannot be sure, after all, that there are human beings rather than mere automata under the hats and cloaks we see from our window. (shrink)

This paper is a commentary on the target article by Michael Arbib, “Levels of modeling of mechanisms of visually guided behavior”, in the same issue of the journal, pp. 407–465. -/- I focus on the importance of the inclusion of an ability of a system to entertain, at a given time, multiple instantiations of a given schema (situation template, frame, script, action plan, etc.), and complications introduced into neural/connectionist network systems by such inclusion.

English instrument-maker, experimentalist, and natural philosopher who made key contributions in a wide range of areas including physiology, geology, and mechanics. Born on the Isle of Wight, Hooke showed early aptitude with the design of mechanical toys. At Westminster School he learnt mathematics and geometry, and at Christ Church, Oxford, he joined a remarkable group of natural philosophers working before the Restoration on physiological and physical topics (Frank 1980). Much of Hooke’s career was driven by financial uncertainty. As an employee, (...) working firstly with Robert Boyle and then as curator of experiments at the new Royal Society from 1662 to 1677, Hooke’s status as a professional in a society of gentlemen natural philosophers was problematic. He was continually concerned to establish his credibility, and his defences of ownership of his ideas were often vitriolic. (shrink)

Francis Bacon was the youngest son of Nicholas Bacon, lord keeper of the great seal under Elizabeth I. He left Cambridge in 1575, studied law, and entered Parliament in 1581. Though roughly contemporary with Kepler, Galileo, and Harvey, Bacon’s grand schemes for the advancement of knowledge were not driven by their discoveries: he resisted the Copernican hypothesis, and did not give mathematics a central place in his vision of natural philosophy. His active public life, under both Elizabeth and James I, (...) was taken up with political business and legal reform. Bacon achieved high office as Lord Chancellor in 1618, until disgraced by corruption charges. His final years saw a furious spate of writing on natural philosophy, politics, and history. (shrink)

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

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

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)

While there are numerous differences between the approaches taken by Maurice Merleau-Ponty and James J. Gibson, the basic motivation of the two thinkers, as well as the internal logic of their respective views, is extraordinarily close. Both were guided throughout their lives by an attempt to overcome the dualism of subject and object, and both devoted considerable attention to their "Gestaltist" predecessors. There can be no doubt but that it is largely because of this common cause that the subsequent development (...) of their ideas is so similar. It is not my objective in what follows merely to demonstrate a similarity between two lines of thought. Instead, I will try to show that each approach gains considerably from attention to the other. There are numerous ways to begin such a project, each about as arbitrary as the next. For present purposes, I shall take as of central importance the question of the character of the perceived world, both in relation to the traditionally opposed mental and material "substances", and in relation to its identification and individuation of things vis a vis one another and vis a vis ourselves. This will implicate especially Gibson's "affordances" and Merleau-Ponty's thesis concerning the "materiality of meaning.". (shrink)

Infinitists argue that their view outshines foundationalism because infinitism can, whereas foundationalism cannot, explain two of epistemic justification’s crucial features: it comes in degrees and it can be complete. I present four different ways that foundationalists could make sense of those two features of justification, thereby undermining the case for infinitism.

The move from good to ought, a premise form found in many justifications of environmental ethics, is itself in need of justification. Of the potential moves from good to ought surveyed, some have considerable promise and others less or none. Those without much promise include extrapolations of obligations based on human goods to nonsentient natural entities, appeals to educated judgment, precautionary arguments, humanistic consequentialist arguments, and justifications that assert that our obligations to natural entities are neither directly to those entities (...) nor derived from our obligations to humans. Some arguments that extrapolate obligations based on goods involving sentience from humans to sentient animals are promising, but whether they are sufficient is controversial. Gandhian andAristotlian arguments are also promising, provided we can justify their ought premises. (shrink)

Any satisfactory epistemology must account for the distinction between propositional and doxastic justification. Can infinitism account for it? Proposals to date have been unsatisfactory. This paper advances a new infinitist account of the distinction. The discussion proceeds as follows. Section 1 sets the stage. Section 2 presents Peter Klein's account. Section 3 raises a problem for Klein's account and suggests an improvement. Section 4 raises a further challenge. Sections 5 to 7 consider several unsuccessful attempts to meet the challenge. Section (...) 8 presents my new proposal, which can meet the challenge. Section 9 concludes the discussion. (shrink)

I objected that the defeasibility theory of knowledge prohibits you from knowing that you know that p if your knowledge that p is a posteriori. Rodrigo Borges claims that Peter Klein has already satisfactorily answered a version of my objection. He attempts to defend Klein’s reply and argues that my objection fails because a principle on which it is based is false.I will show that my objection is not a version of the old one that Klein attempts (unsuccessfully) to address, (...) that Borges’ defence of Klein’s reply fails and that his argument against my new objection leaves it untouched. (shrink)

An encyclopedic article on epistemic supervenience in Blackwell companion to epistemology, 2 ed.

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)

This paper clarifies and evaluates a premise of William Alston’s argument in Perceiving God. The premise in question: if it is practically rational to engage in a doxastic practice, then it is epistemically rational to suppose that said practice is reliable. I first provide the background needed to understand how this premise fits into Alston’s main argument. I then present Alston’s main argument, and proceed to clarify, criticize, modify, and ultimately reject Alston’s argument for the premise in question. Without this (...) premise, Alston’s main argument fails. (shrink)

This is an encyclopedia article about epistemic closure principles. The article explains what they are, their various philosophical uses, how they are argued for or against, and provides an overview of the related literature.

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

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)

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...) for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical. This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that in 1831, De Morgan was still in the grips of the allegedly Aristotelian paradigm. (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)

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)

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

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".