Many strands are woven into the ideas and work of Jeffrey Gray. From a background of classical languages and a spell in military intelligence spent honing skills in languages and typing, he took two BA degrees (in modern languages and psychology) at Oxford University. He then trained as a clinical psychologist at the Institute of Psychiatry (IOP), London, capping this with a PhD on the sources of emotional behaviour.

During the last forty or so years it has become popular to offer explanations of logical notions in terms of games. There is no doubt that many people find games helpful for understanding various logical phenomena. But we ask whether anything is really 'explained' by these accounts, and we analyse Paul Lorenzen's dialogue foundations for constructive logic as an example. The conclusion is that the value of games lies in their ability to provide helpful metaphors and representations, rather than (...) in any true conceptual analysis. In fact some of the standard explanations of logical notions in terms of competitive games simply don't work. /// [Erik C. W. Krabbe] In an attempt to redeem the Lorenzen-type dialogues from their detractors, it is perhaps best first to provide a survey of the various benefits these dialogues have been supposed to yield. This will be done in Section I. It will not be possible, within the confines of this paper, to scrutinize them all, but in Section II we shall delve deeper into the capacity of this type of dialogue to yield a model for the immanent criticism of philosophical positions. Section III will extend the concept of a dialogue in such a way as to conform better with our intuitive conceptions of what a rational discussion of a position should contain. This will be followed up by a concept of 'winning a dialogue' that takes position midway between the old conception of 'winning one play' and that of the full-fledged presentation of a winning strategy . Concepts of 'rational discussion' are thus shown to be, plausibly, more fundamental than those of proof. In Section IV, I shall discuss the specific problems about dialogical foundations put forward by Wilfrid Hodges. (shrink)

In two studies, we explored the frequency and phenomenology of musical imagery. Study 1 used retrospective reports of musical imagery to assess the contribution of individual differences to imagery characteristics. Study 2 used an experience sampling design to assess the phenomenology of musical imagery over the course of one week in a sample of musicians and non-musicians. Both studies found episodes of musical imagery to be common and positive: people rarely wanted such experiences to end and often heard music that (...) was personally meaningful. Several variables predicted musical imagery, including personality, musical preferences, and positive mood. Musicians tended to hear musical imagery more often, but they reported less frequent episodes of deliberately-generated imagery. Taken together, the present research provides new insights into individual differences in musical imagery, and it supports the emerging view that such experiences are common, positive, and more voluntary than previously recognized. (shrink)

[Wilfrid Hodges] During the last forty or so years it has become popular to offer explanations of logical notions in terms of games. There is no doubt that many people find games helpful for understanding various logical phenomena. But we ask whether anything is really 'explained' by these accounts, and we analyse Paul Lorenzen's dialogue foundations for constructive logic as an example. The conclusion is that the value of games lies in their ability to provide helpful metaphors and (...) representations, rather than in any true conceptual analysis. In fact some of the standard explanations of logical notions in terms of competitive games simply don't work. /// [ Erik C. W. Krabbe] In an attempt to redeem the Lorenzen-type dialogues from their detractors, it is perhaps best first to provide a survey of the various benefits these dialogues have been supposed to yield. This will be done in Section I. It will not be possible, within the confines of this paper, to scrutinize them all, but in Section II we shall delve deeper into the capacity of this type of dialogue to yield a model for the immanent criticism of philosophical positions. Section III will extend the concept of a dialogue in such a way as to conform better with our intuitive conceptions of what a rational discussion of a position should contain. This will be followed up by a concept of 'winning a dialogue' that takes position midway between the old conception of 'winning one play' and that of the full-fledged presentation of a winning strategy. Concepts of 'rational discussion' are thus shown to be, plausibly, more fundamental than those of proof. In Section IV, I shall discuss the specific problems about dialogical foundations put forward by Wilfrid Hodges. (shrink)

[Wilfrid Hodges] During the last forty or so years it has become popular to offer explanations of logical notions in terms of games. There is no doubt that many people find games helpful for understanding various logical phenomena. But we ask whether anything is really 'explained' by these accounts, and we analyse Paul Lorenzen's dialogue foundations for constructive logic as an example. The conclusion is that the value of games lies in their ability to provide helpful metaphors and (...) representations, rather than in any true conceptual analysis. In fact some of the standard explanations of logical notions in terms of competitive games simply don't work. /// [Erik C. W. Krabbe] In an attempt to redeem the Lorenzen-type dialogues from their detractors, it is perhaps best first to provide a survey of the various benefits these dialogues have been supposed to yield. This will be done in Section I. It will not be possible, within the confines of this paper, to scrutinize them all, but in Section II we shall delve deeper into the capacity of this type of dialogue to yield a model for the immanent criticism of philosophical positions. Section III will extend the concept of a dialogue in such a way as to conform better with our intuitive conceptions of what a rational discussion of a position should contain. This will be followed up by a concept of 'winning a dialogue' that takes position midway between the old conception of 'winning one play' and that of the full-fledged presentation of a winning strategy. Concepts of 'rational discussion' are thus shown to be, plausibly, more fundamental than those of proof. In Section IV, I shall discuss the specific problems about dialogical foundations put forward by Wilfrid Hodges. (shrink)

Introduction -- Media and representation. On the one medium / Eric Gans -- The scapegoat mechanism and the media: beyond the folk devil paradigm / John O'Carroll -- The apocalypse will not be televised / Chris Fleming -- Film. Mirrors of nature: artificial agents in real life and virtual worlds / Paul Dumouchel -- Superheroes, scapegoats, and saviors: the problem of evil and the need for redemption / Joel Hodge -- Sanctified victimage on page and screen: The hunger games (...) as prophetic media / Debra E. Macdonald -- The mimetic e-motion: from The matrix to Avatar / Nidesh Lawtoo -- Apocalypse of the therapeutic: The cabin in the woods and the death of mimetic desire / Peter Y. Paik -- Eyes wide shut: mimesis and historical memory in Stanley Kubrick's The shining / David Humbert -- Against romantic love: mimeticism and satire in Woody Allen's Vicky, Cristina, Barcelona; you will meet a tall dark stranger; and To Rome with love / Scott Cowdell -- A beautiful crisis: Ang Lee's film adaptation of The ice storm / Carly Osborn -- Cowboy metaphysics, the virtuous-enough cowboy, and mimetic desire in Stephen Fears' The hi-lo country / Thomas Ryba -- Television. The self in crisis: watching Mad men and Homeland with Girard and Hegel / Paolo Diego Bubbio -- Media, murder, and memoir: Girardian baroque in Robert Drewe's The shark net / Rosamund Dalziell -- Conversion in Dexter / Matthew John Paul Tan and Joel Hodge. (shrink)

We trace two logical ideas further back than they have previously been traced. One is the idea of using diagrams to prove that certain logical premises do—or don’t—have certain logical consequences. This idea is usually credited to Venn, and before him Euler, and before him Leibniz. We find the idea correctly and vigorously used by Abū al-Barakāt in 12th century Baghdad. The second is the idea that in formal logic, P logically entails Q if and only if every model of (...) P is a model of Q. This idea is usually credited to Tarski, and before him Bolzano. But again we find Abū al-Barakāt already exploiting the idea for logical calculations. Abū al-Barakāt’s work follows on from related but inchoate research of Ibn Sīnā in eleventh century Persia. We briefly trace the notion of model-theoretical consequence back through Paul the Persian and in some form back to Aristotle himself. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"The Fittest Man in the Kingdom":Thomas Reid and the Glasgow Chair of Moral PhilosophyPaul Wood (bio)Paul Wood Paul Wood is at the Department of History, University of Victoria, PO Box 3045, MS 7381, Victoria BC V8W 3P4 Canada. email: [email protected] August 1996Revised January 1997Notes. An earlier version of this paper was delivered at a plenary session of the 23rd International Hume Conference held at the University of (...) Nottingham. For comments and/or references, the author wishes to thank Roger Emerson, Carol Gibson-Wood, Knud Haakonssen, Ian Simpson Ross, Stephen Snobelen, M. A. Stewart, and the anonymous Hume Studies referees. For permission to cite and quote from manuscripts, he is grateful to the Keeper of the Manuscripts of Scotland as well as to the Librarians of Aberdeen University Library, Edinburgh University Library, Glasgow University Archives and Business Records Centre, Glasgow University Library (Department of Special Collections), the Mitchell Library Glasgow, and Dr. Williams' Library.1. Although little information survives regarding Law's teaching, we do know that he discussed Pufendorf in his classes; see Christine Mary King [Shepherd], "Philosophy and Science in the Arts Curriculum of the Scottish Universities in the Seventeenth Century," (Unpublished Ph.D. Dissertation, University of Edinburgh, 1974), 177. Carmichael's edition of Pufendorf first appeared in Glasgow in 1718, and a second edition was published in Edinburgh in 1724 while Hume was still a student there.2. The surviving correspondence between the two men from this period is to be found in The Letters of David Hume, ed. J.Y.T. Greig, 2 vols. (Oxford: Clarendon Press, 1932), I 32-35; 36-40; 45-48 (hereafter abbreviated as HL).3. The first detailed discussion of the 1745 election appeared in the introduction to David Hume, A Letter from a Gentleman to His Friend in Edinburgh, edited by Ernest C. Mossner and John V. Price (Edinburgh: Edinburgh University Press, 1967). This account has recently been challenged in Roger L. Emerson, "The 'Affair' at Edinburgh and the 'Project' at Glasgow: The Politics of Hume's Attempts to become a Professor," in Hume and Hume's Connexions, edited by M. A. Stewart and John P. Wright (Edinburgh: Edinburgh University Press, 1994), 1-22; and M. A. Stewart, The Kirk and the Infidel (Lancaster: Lancaster University Publications Office, 1995). For historically sensitive contextual analysis of Hume's philosophical relations with Hutcheson, see inter alia James Moore, "Hume and Hutcheson," in Stewart and Wright, 23-57, and M. A. Stewart, Warmth in the Cause of Virtue (Edinburgh: Edinburgh University Press, forthcoming).4. In January 1752, "Mr. Smith read an Account of some of Mr. David Hume's Essays on Commerce" to the Society, and Hume was elected a member in 1753; see Notices and Documents Illustrative of the Literary History of Glasgow, During the Greater Part of Last Century, edited by W. J. Duncan (Glasgow: T. D. Morison, 1886), 132-133. Hume's failed candidacy is discussed in Emerson, "The 'Affair' at Edinburgh," 14-16, and Ian Simpson Ross, The Life of Adam Smith (Oxford: Clarendon Press, 1995), 112-113. Smith's Glasgow colleague from 1751 to 1755, William Cullen, was also sympathetic to Hume's philosophy, as was John Millar, who was elected Professor of Law in 1761. On Cullen and Hume see J.R.R. Christie, "Ether and the Science of Chemistry: 1740-1790," in Conceptions of Ether: Studies in the History of Ether Theories 1740-1900, edited by G. N. Cantor and M.J.S. Hodge (Cambridge: Cambridge University Press, 1981), 90-96.5. David Hume to William Strahan, 26 October 1775, HL II 301.6. See, for example, The Works of Thomas Reid, D.D., edited by Sir William Hamilton, 4th ed. (Edinburgh: Maclachlan and Stewart, 1854), 30n; James McCosh, The Scottish Philosophy, Biographical, Expository, Critical, from Hutcheson to Hamilton (London: Macmillan, 1875), 36; James Veitch, "Philosophy in the Scottish Universities," Mind 2 (1877): 207-234 (209).7. John Rae, Life of Adam Smith (London and New York: Macmillan, 1895); William Robert Scott, Francis Hutcheson: His Life, Teaching and Position in the History of Philosophy (Cambridge: Cambridge University Press, 1900); idem., Adam Smith as Student and Professor (Glasgow: Jackson... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"The Fittest Man in the Kingdom":Thomas Reid and the Glasgow Chair of Moral PhilosophyPaul Wood (bio)Paul Wood Paul Wood is at the Department of History, University of Victoria, PO Box 3045, MS 7381, Victoria BC V8W 3P4 Canada. email: [email protected] August 1996Revised January 1997Notes. An earlier version of this paper was delivered at a plenary session of the 23rd International Hume Conference held at the University of (...) Nottingham. For comments and/or references, the author wishes to thank Roger Emerson, Carol Gibson-Wood, Knud Haakonssen, Ian Simpson Ross, Stephen Snobelen, M. A. Stewart, and the anonymous Hume Studies referees. For permission to cite and quote from manuscripts, he is grateful to the Keeper of the Manuscripts of Scotland as well as to the Librarians of Aberdeen University Library, Edinburgh University Library, Glasgow University Archives and Business Records Centre, Glasgow University Library (Department of Special Collections), the Mitchell Library Glasgow, and Dr. Williams' Library.1. Although little information survives regarding Law's teaching, we do know that he discussed Pufendorf in his classes; see Christine Mary King [Shepherd], "Philosophy and Science in the Arts Curriculum of the Scottish Universities in the Seventeenth Century," (Unpublished Ph.D. Dissertation, University of Edinburgh, 1974), 177. Carmichael's edition of Pufendorf first appeared in Glasgow in 1718, and a second edition was published in Edinburgh in 1724 while Hume was still a student there.2. The surviving correspondence between the two men from this period is to be found in The Letters of David Hume, ed. J.Y.T. Greig, 2 vols. (Oxford: Clarendon Press, 1932), I 32-35; 36-40; 45-48 (hereafter abbreviated as HL).3. The first detailed discussion of the 1745 election appeared in the introduction to David Hume, A Letter from a Gentleman to His Friend in Edinburgh, edited by Ernest C. Mossner and John V. Price (Edinburgh: Edinburgh University Press, 1967). This account has recently been challenged in Roger L. Emerson, "The 'Affair' at Edinburgh and the 'Project' at Glasgow: The Politics of Hume's Attempts to become a Professor," in Hume and Hume's Connexions, edited by M. A. Stewart and John P. Wright (Edinburgh: Edinburgh University Press, 1994), 1-22; and M. A. Stewart, The Kirk and the Infidel (Lancaster: Lancaster University Publications Office, 1995). For historically sensitive contextual analysis of Hume's philosophical relations with Hutcheson, see inter alia James Moore, "Hume and Hutcheson," in Stewart and Wright, 23-57, and M. A. Stewart, Warmth in the Cause of Virtue (Edinburgh: Edinburgh University Press, forthcoming).4. In January 1752, "Mr. Smith read an Account of some of Mr. David Hume's Essays on Commerce" to the Society, and Hume was elected a member in 1753; see Notices and Documents Illustrative of the Literary History of Glasgow, During the Greater Part of Last Century, edited by W. J. Duncan (Glasgow: T. D. Morison, 1886), 132-133. Hume's failed candidacy is discussed in Emerson, "The 'Affair' at Edinburgh," 14-16, and Ian Simpson Ross, The Life of Adam Smith (Oxford: Clarendon Press, 1995), 112-113. Smith's Glasgow colleague from 1751 to 1755, William Cullen, was also sympathetic to Hume's philosophy, as was John Millar, who was elected Professor of Law in 1761. On Cullen and Hume see J.R.R. Christie, "Ether and the Science of Chemistry: 1740-1790," in Conceptions of Ether: Studies in the History of Ether Theories 1740-1900, edited by G. N. Cantor and M.J.S. Hodge (Cambridge: Cambridge University Press, 1981), 90-96.5. David Hume to William Strahan, 26 October 1775, HL II 301.6. See, for example, The Works of Thomas Reid, D.D., edited by Sir William Hamilton, 4th ed. (Edinburgh: Maclachlan and Stewart, 1854), 30n; James McCosh, The Scottish Philosophy, Biographical, Expository, Critical, from Hutcheson to Hamilton (London: Macmillan, 1875), 36; James Veitch, "Philosophy in the Scottish Universities," Mind 2 (1877): 207-234 (209).7. John Rae, Life of Adam Smith (London and New York: Macmillan, 1895); William Robert Scott, Francis Hutcheson: His Life, Teaching and Position in the History of Philosophy (Cambridge: Cambridge University Press, 1900); idem., Adam Smith as Student and Professor (Glasgow: Jackson... (shrink)

In September 2010 at the Johns Hopkins Hospital, one of the nation's elite academic hospitals located in East Baltimore, Maryland, Paul Warren Pardus entered the facility to visit his mother, a patient. During a discussion with her doctor in a hospital hallway, Pardus became “overwhelmed” about the care and condition of his mother, pulled a handgun from his waistband, and shot the doctor in the chest. Pardus then locked himself and his mother in her room, shot and killed her, (...) and committed suicide.Dr. Gabe Kelen, a national expert on emergency preparedness and director of the Johns Hopkins emergency department, admitted several years later that this tragic event “really got us thinking in a very serious way.” Together with colleagues at the Johns Hopkins Office of Critical Event Preparedness and Response, Kelen conducted research on the threat and impact of “active shooters” in health care settings. (shrink)

On the 27th of October, 1949, the Department of Philosophy at the University of Manchester organized a symposium "Mind and Machine", as Michael Polanyi noted in his Personal Knowledge (1974, p. 261). This event is known, especially among scholars of Alan Turing, but it is scarcely documented. Wolfe Mays (2000) reported about the debate, which he personally had attended, and paraphrased a mimeographed document that is preserved at the Manchester University archive. He forwarded a copy to Andrew Hodges and (...) B. Jack Copeland, who in then published it on their respective websites. The basis of this interpretation here is the copy preserved in the Regenstein Library of the University of Chicago, Special Collections, Polanyi Collection (abbreviated RPC, box 22, folder 19). The same collection holds the mimeographed statement that Polanyi prepared for this symposium: "Can the mind be represented by a machine?" This text has not been studied by Polanyi scholars. (shrink)

We describe a logic which is the same as first-order logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gives a compositional meaning to formulas of the 'information-friendly' language of Hintikka and Sandu. For first-order formulas the semantics reduces to Tarski's semantics for first-order logic. We prove that two formulas have the same (...) interpretation in all structures if and only if replacing an occurrence of one by an occurrence of the other in a sentence never alters the truth-value of the sentence in any structure. (shrink)

Little appears to have changed in the western imagining of the Pacific region since ancient times. While metaphors of redemption and condemnation, paradise and paradise lost, utopia and dystopia persist, Australia's place in the Pacific will remain elusive and insecure. The essay is in two parts. The first half discusses the metaphors implicit in the names given to the region, the South Seas, the Pacific and Oceania, and relates their imagining in the early European expeditions of Balboa and Magellan, in (...) Hodges' paintings done on Cook's second voyage in the 18th century, and in conceptualizations of Australian identity from the colonial period to the mid-20th century writing of historians such as Hancock, Barnard and Manning Clark. The second half of the essay traces the repetition of the same metaphors in the theories of de Certeau and Baudrillard, and in the writings of contemporary Australian critics, including McKenzie Wark, Ross Gibson and Paul Carter. (shrink)

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

BackgroundMoral distress (MD) is an emotional and psychological response to morally challenging dilemmas. Moral distress is experienced frequently by nurses in the intensive care unit (ICU) and can result in emotional anguish, work dissatisfaction, poor patient outcomes, and high levels of nurse turnover. Opportunities to discuss ethically challenging situations may lessen MD and its associated sequela.ObjectiveThe purpose of this project was to develop, implement, and evaluate the impact of nursing ethics huddles on participants’ MD, clinical ethics knowledge, work satisfaction, and (...) patient care among ICU nurses.Sample and SettingThe sample, 32 nurses from three ICU settings in an 800-bed tertiary academic medical center, participated in six nursing ethics huddles over a two-month period.MethodsAlvita K. Nathaniel’s Theory of Moral Reckoning guided development of the nursing ethics huddle process.1 The Moral Distress Thermometer was administered at three data points: baseline level of MD, and pre- and post-huddle to determine changes in the subjects’ level of MD.2 Focused content analysis was used to analyze qualitative responses from questionnaires about the subjects’ perception of the effect of the huddles on work satisfaction and patient care. Knowledge attainment was evaluated via open-ended short-answer questions.ResultsOverall, use of nurse-ethicist-led nursing ethics huddles was associated with improved quality of work life, patient care, and clinical ethics knowledge. The change in pre- and post-nursing ethics huddles MD scores was statistically significant (p < 0.0001). (shrink)

The paper analyses what is said and what is presupposed by thePrinciple of Compositionality for semantics, as it is commonly stated. ThePrinciple of Compositionality is an axiom which some semantics satisfy andsome don’t. It says essentially that if two expressions have the same meaning then they make the same contribution to the meanings of expressionscontaining them. This is a sensible axiom only if one combines it with aconverse, that if two expressions make the same contribution to the meanings of sentences (...) containing them, then they have the same meaning;and some assumption that two expressions which can’t meaningfully besubstituted for each other have different meanings. as a full abstraction principle, and as ‘Husserl’s principle’.) Moreoverthe Principle of Compositionality speaks only about when two expressionshave the same meaning; it adds nothing whatever about what that meaningmight be . Some recent discussions by writers in linguistics and logic are assessed. The paper finishes by reviewing thehistory of the notion of compositionality. (shrink)

Paul Snowdon; XI*—Perception, Vision and Causation, Proceedings of the Aristotelian Society, Volume 81, Issue 1, 1 June 1981, Pages 175–192, https://doi.org/10.

At the bottom of all human activities are “values,” the conviction that some things “ought to be” and others not. Science, however, with its immense interest in mere facts seems to lack all understanding of such‘requiredness.’… A science … which would seriously admit nothing but indifferent facts … could not fail to destroy itself.

In Baghdad in the mid twelfth century Abū al-Barakāt proposes a radical new procedure for finding the conclusions of premise-pairs in syllogistic logic, and for identifying those premise-pairs that have no conclusions. The procedure makes no use of features of the standard Aristotelian apparatus, such as conversions or syllogistic figures. In place of these al-Barakāt writes out pages of diagrams consisting of labelled horizontal lines. He gives no instructions and no proof that the procedure will yield correct results. So the (...) reader has to work out what his procedure is and whether it is correct. The procedure turns out to be insightful and entirely correct, but this paper may be the first study to give a full description of the procedure and a rigorous proof of its correctness. (shrink)

§1. Introduction. I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument—what had it done to make them (...) angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge.These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all.In 1995 an engineer named William Dilworth, who had published a refutation of Cantor's argument in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, sued for libel a mathematician named Underwood Dudley who had called him a crank. (shrink)

Ibn Sīnā proposed an analysis of arguments by reductio ad absurdum. His analysis contains, perhaps for the first time, a workable method for handling the making and discharging of assumptions in a formal proof. We translate the relevant text of Ibn Sīnā and put his analysis into the context of his general approach to logic.

Paul Abela presents a powerful, experience-sensitive form of realism about the relation between mind and world, based on an innovative interpretation of Kant. Abela breaks with tradition in taking seriously Kant's claim that his Transcendental Idealism yields a form of empirical realism, and giving a realist analysis of major themes of the Critique of Pure Reason. Abela's blending of Kantian scholarship with contemporary epistemology offers a new way of resolving philosophical debates about realism.

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately (...) for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. (shrink)

This chapter surveys set theory, model theory, and computability theory: how they first emerged from the foundations of mathematics, and how they have developed since. There are any amounts of mathematical technicalities in the background, but the chapter highlights those themes that have some philosophical resonance.