The first British New Left formed in response to a crisis in international and British socialism. Although never a formal movement, its associated members set themselves the tasks of, first, confronting the rapid change transforming social life at both global and national scales, and second, articulating a new political culture able to accommodate the good and resist the bad of it. As part of this process, a series of intense debates took place on the role of the socialist intellectual in (...) stimulating such a culture. In this article, I consider three of the NL’s main protagonists, EP Thompson, Stuart Hall, and Raphael Samuel, and the different positions they took on this issue. I argue here that while all made important contributions to the argument, Samuel’s practice as an intellectual, currently the least well known of the three, is worth closer attention for its relevance to contemporary educational debates. (shrink)

ABSTRACT The First British New Left formed around two journals, The New Reasoner edited by E.P.Thompson and John Saville, and the Universities and Left Review edited by Stuart Hall, Gabriel Pearson, Raphael Samuel and Charles Taylor. Both sought a ‘new’ socialism which, based on a loose concept of socialist humanism, restored the role of the individual and revitalised a popular left movement. Early commentators critiqued its lack of robust theory and organisational structure. More recently, others have proposed that, particularly (...) amongst the ULR cohort, with this ‘new’ socialism emerged a ‘new’ activist politics. Building on this, I examine the ULR’s activism as a performative politics which stressed active participation over theory and dissolved any distinction between means and ends. Whilst Thompson and Hall have tended to be considered the main protagonists in shaping this, I argue that it was Samuel, an experienced organiser, who was most responsible for shaping their early agenda. His role has been neglected because he wrote no ‘position piece’ but, appropriately for an activist politics, expressed his ideas through his actions. ‘Reading’ his performances, then, illuminates more fully both the scope and the limits of this activist politics. (shrink)

The Philosophy of Adam Smith contains essays by some of the most prominent philosophers and scholars working on Adam Smith today. It is a special issue of The Adam Smith Review, commemorating the 250th anniversary of Smith's Theory of Moral Sentiments. Introduction Part 1: Moral phenomenology 1. The virtue of TMS 1759 D.D. Raphael 2. The Theory of Moral Sentiments and the inner life Emma Rothschild 3. The standpoint of morality in Adam Smith and Hegel Angelica Nuzzo Part 2: (...) Sympathy and moral judgment 4. Smith and Rousseau in dialogue: sympathy, pitié, spectatorship and narrative Charles L. Griswold 5. Adam Smith’s concept of sympathy and its contemporary interpretations Bence Nanay 6. Smith’s ambivalence about honour Stephen Darwall 7. Sentiments and spectators: Adam Smith’s theory of moral judgment Geoffrey Sayre-McCord 8. Smith’s anti-cosmopolitanism Fonna Forman-Barzilai 9. Resentment and moral judgment in Smith and Butler Alice MacLachlan Part 3: Economics, religion, aesthetics and value theory 10. Adam Smith’s problems: individuality and the paradox of sympathy Robert Urquhart 11. Scepticism and naturalism in Adam Smith Ryan Patrick Hanley 12. Adam Smith’s solution to the paradox of tragedy Arby Ted Siraki 13. Smithian intrinsic value Patrick Frierson Memoir on Adam Smith’s life 14. Adam Smith’s smile: his years at Balliol College, 1740–6, in retrospect Ian Simpson Ross. (shrink)

Using various meanings of ?visit? and ?friend? this essay freely explores connections between Milton's cultivation of fame in Europe, leading to reports in the early lives of visits of scholarly foreigners to his door, and the extraordinary concentration on scenarios of human and divine visitation in the late poems. Social, political and religious strands are followed, from humanist self-presentation in the sonnets through to prophetic isolation in the late poems. Codes of friendship are rehearsed concerning confidentiality and betrayal, and attention (...) is paid to the effect of blindness on the activities of the humanist writer, the need for supporting visits, and an increasing interiority and preoccupation with the responsibilities of those engaged with God's special causes. The proto-humanist visit of Raphael to Adam in Paradise Lost and the many guiding visitations in that poem are contrasted with the situation in Samson Agonistes, where divine guidance is presented as clearer in the past than the present, and the reader is invited to share difficulties of discernment in the Restoration world, prefigured in Judges. The essay ends with the simultaneous publication of Milton's humanist legacy and sale of many of his foreign-language books. (shrink)

About a month after his 83rd birthday Raphael Robinson was almost wholly incapacitated by a massive stroke, and 8 weeks later, on January 27, 1995, he died of ensuing complications. Mathematics was his life. He was always working on problems—those brought to him in journals or by colleagues, and others that he invented. Just three days before his death he received word that a paper of his, originating in a published problem, was accepted for publication. His 64 publications spanned (...) a full 6 decades, and included significant papers on number theory, combinatorics, complex analysis, and geometry, in addition to logic and set theory.Robinson was born on November 2, 1911, in National City, California. He came to Berkeley to study mathematics, obtaining an A.B. in 1932, an M.A. in 1933, and his Ph.D. in December, 1934. His dissertation was in complex analysis. He took 12 graduate courses in a variety of fields, but not one was close to logic or set theory—which was later the setting of about a quarter of his publications.After completing his studies Robinson served as Instructor for two years at Brown University, then returned for good to Berkeley in 1937, reaching the rank of full Professor in 1949. He taught a great variety of courses and was known as an excellent teacher, but was most interested in problemsolving and research and in 1972, at age 61, he elected early retirement, at considerable financial sacrifice, in order to concentrate on these pursuits. (shrink)

Decision theory and folk psychology both purport to represent the same phenomena: our belief-like and desire- and preference-like states. They also purport to do the same work with these representations: explain and predict our actions. But they do so with different sets of concepts. There's much at stake in whether one of these two sets of concepts can be accounted for with the other. Without such an account, we'd have two competing representations and systems of prediction and explanation, a dubious (...) dualism. Folk psychology structures our daily lives and has proven fruitful in the study of mind and ethics, while decision theory is pervasive in various disciplines, including the quantitative social sciences, especially economics, and philosophy. My interest is in accounting for folk psychology with decision theory -- in particular, for believe and wanting, which decision theory omits. Many have attempted this task for belief. (The Lockean Thesis says that there is such an account.) I take up the parallel task for wanting, which has received far less attention. I propose necessary and sufficient conditions, stated in terms of decision theory, for when you're truly said to want; I give an analogue of the Lockean Thesis for wanting. My account is an alternative to orthodox accounts that link wanting to preference (e.g. Stalnaker (1984), Lewis (1986)), which I argue are false. I argue further that want ascriptions are context-sensitive. My account explains this context-sensitivity, makes sense of conflicting desires, and accommodates phenomena that motivate traditional theses on which 'want' has multiple senses (e.g. all-things-considered vs. pro tanto). (shrink)

According to the Desiderative Lockean Thesis, there are necessary and sufficient conditions, stated in the terms of decision theory, for when one is truly said to want. What one is truly said to want, it turns out, varies remarkably by context—and to an underappreciated degree. To explain this context-sensitivity, and closure properties of wanting, I advance a Desiderative Lockean view that is distinctive in having two context-sensitive parameters.

Where exactly should we place Adam Smith in the cannon of classical liberalism? Smith's advocacy of free market economics and defence of religious liberty in The Wealth of Nations suffice for including him somewhere in that tradition.1 The nature and extent of Smith's liberalism, however, remain up for debate. One recent trend has been to characterise Smith as a proponent of social liberalism. This includes those like Stephen Darwall, Samuel Fleischacker and Charles Griswold, who have drawn attention to a kind (...) of descriptive moral egalitarianism in Smith.2 Humans, Smith seems to hold, are naturally disposed to valuing one another under a conception of equality. But that is not all these scholars suggest. They have also hinted at something more contentious ? the idea that, according to Smith, we value one another in a way resonant with contemporary notions of human dignity, conceived as the inherent value of persons grounding certain rights to, or restrictions on, treatment by others.3 In saying so, these scholars have hit upon something remarkable. However, I also think their arguments in this respect are both indirect and incomplete. Consequently, the full import of Smith's view remains obscure. This essay aims to bring some clarity. 1I intend this historically. I grant there are good reasons to be sceptical about the ultimate fate of liberty in capitalist society (e.g. Marxist reasons and reasons based on various postmodern critiques of enlightenment ideology). Also, the designation ?free market? should be understood loosely, as most scholars now agree it is a mistake to identify Smith with thoroughgoing laissez-faire economics. 2Darwall, S., ?Sympathetic Liberalism: Recent Work on Adam Smith?, Philosophy Fleischacker, S., A Third Concept of Liberty (Princeton: Princeton University Press, 1999) and On Adam Smith's Wealth of Nations (Princeton: Princeton University Press, 2004); and Griswold, C., Adam Smith and the Virtues of Enlightenment (New York: Cambridge University Press, 1999). Other major commentators holding some version of this view might include Raphael, D. D. The Impartial Spectator (New York: Oxford University Press, 2007) and Vivienne Brown, Adam Smith's Discourse: Canonicity, Commerce and Conscience (London: Routledge, 1994). 3See e.g. Fleischacker (2004), 205; Darwall at 142, 156 and Griswold at 235?239. However, one must read Fleischacker carefully, for he also uses the adjectival ?dignified? to express Smith's concern with what is ?honourable? or ?respectable? about persons, which use does not obviously match up with the notion of inherent value (see e.g. p. 207). Darwall's argument includes by far the most explicit discussion of ?dignity? as I've defined it. But as Darwall's article is ostensibly a book review (albeit a substantive one that addresses three books at once, including Griswold's), it cannot be called a direct inquiry. Griswold never explicitly puts his interpretation in terms of ?dignity?, but that is clearly what he is after. Thus Darwall also reads him that way. (shrink)

You want to see the concert, but don’t want to take a long drive (even though the concert is far away). Such *strongly conflicting desire ascriptions* are, I show, wrongly predicted incompatible by standard semantics. I then object to possible solutions, and give my own, based on *some-things-considered desire*. Considering the fun of the concert, but ignoring the drive, you want to see the concert; considering the boredom of the drive, but ignoring the concert, you don’t want to take the (...) drive. (shrink)

Algorithms wield increasing control over our lives—over the jobs we get, the loans we're granted, the information we see online. Algorithms can and often do wield their power in a biased way, and much work has been devoted to algorithmic bias. In contrast, algorithmic neutrality has been largely neglected. I investigate algorithmic neutrality, tackling three questions: What is algorithmic neutrality? Is it possible? And when we have it in mind, what can we learn about algorithmic bias?

Painted in 1656 by Diego Velasquez (1599-1660), Las Meninas has engendered countless philosophical commentaries. Artists, too, have explored the painting's puzzles and paradoxes. All of the responses to this masterpiece, now over 350 years old, show that Las Meninas continues to live with us on several levels. Indeed, Las Meninas is one of the most controversial paintings of our time (Brown and Garrido, 1998, p. 181); no small feat given that cutting-edge art today is often media-based and/or media-driven. The (...) wealth of controversy has generated so much material since the work's conception that James Elkins, in his book Why Are Our Pictures Puzzles, characterized Las Meninas as an artwork that has become monstrous. According to Elkins, it has effectively outgrown the discipline of art history. Like the frescos in the Brancacci Chapel, the Mona Lisa, Raphael's School of Athens and the Oath of Horatio by David, the scholarship surrounding Las Meninas is so vast that no single thinker or volume can present it fully; it is not even possible to teach these works in a yearlong seminar (Elkins, 1999). While I am among those captivated by the painting, I am also aware of how little a short essay can accomplish. Nevertheless, I do hope to convey why this immense canvas continues to inspire people creatively, intellectually, and passionately. In terms of consciousness, my comments are intended to weave the physicality of the work with epistemological interpretations and empirical investigations so that its mutability is more present in our consciousness discourse. (shrink)

“Artworks are not being but a process of becoming” —Theodor W. Adorno, Aesthetic Theory In the everyday use of the concept, saying that something is grotesque rarely implies anything other than saying that something is a bit outside of the normal structure of language or meaning – that something is a peculiarity. But in its historical use the concept has often had more far reaching connotations. In different phases of history the grotesque has manifested its forms as a means of (...) subversive resistance against society’s prevailing notions of form and power. What aids this impact and distinguishes two of its basic stylistic features is the grotesque’s dissolution of form and its hyperbole. Such grotesqueries, however, soon solidify into new forms, new structures of meaning, hierarchy and practice, and in this sense the history of the grotesque is, on one hand, a continual opposition and transgression of the prevailing notions of art as well as of God and humanity, while on the other hand it offers continual resistance to its own solidifying process. As such the grotesque will not and cannot be contained in form without it losing the very thing that makes it grotesque. Even though it is somewhat easy to point out certain stylistic features of the grotesque, the sum of those features tell us very little about what is at play within it. Definitions concerned with the grotesque’s content rather than its form faces similar difficulties. Throughout history, expressions relating to the grotesque have been used in defense of a whole host of different social and cultural discourse including, for instance, Catholicism (See Erhard Schön’s Der Teufel mit der Sackpfeife , 1536), Protestantism (See Lucas Cranach’s Der Papstesel , 1523), a material folk culture (see Mikhail Bakhtin’s Rabelais and his World , 1984) and an idealistic romantic structure of meaning (see Wolfgang Kayser’s The Grotesque in Art and Literature , 1957). Thus though the grotesque cannot be reduced to the expression of certain forms or meanings, in order to examine what the grotesque is about one has to try to see how it’s relationship to flow and process and how, by maintaining this relationship, it attempts to avoid solidifying into form and meaning. The process of the grotesque alluded to here revolves around a play between periphery and center, the marginalized and the dominant. Most often this is expressed as a direct negation of the center of power. In the medieval grotesque tradition of the carnival, for example, it is expressed by its emphasis on the nether regions of the body as the center of creation of meaning. Spirit does not come from above, but from the belly, buttocks and genitals, and there is, expressed in this manner, a mockery of the predominant Christian notion of truth and meaning. Such inversions of the sites of meaning most often explicitly express an increased interest in materiality instead of ideal content which comes to the fore through the play between periphery and center. Even in early grotesque Renaissance art (for example in the works of Raphael) the depiction of the mythological or ideal reveals an exploration of the possibilities of the material. The works of art thus explore their own boundaries rather than act as vessels of the divine and in this way the grotesque explores the limits of form and materiality. This in turn brings to the fore a metaphysical dimension in the workings of the grotesque: It is an immanent exploration of its own boundaries. Materiality and metaphysics are joined together, because it is through the awareness of itself as a structuring (dis)order that it places itself in opposition to the prevailing notions of form and power. This way the grotesque expresses an awareness of the division of sign and reality and a search for this reality. It implicitly expresses the awareness that meaning is not something God-given and static, but fluctuating and man-made. In modern explorations of the history of the grotesque it is commonly seen as a form of realism that manifests a shift from the ideal towards the material, freeing art from representing some hidden higher order and instead making the work of art the very site of creation and meaning. Going even further, the grotesque actively opposes the notions of the ideal by marking a shift from an ahistorical view of the world towards the historical. However, this also makes clear why the grotesque has a tendency to solidify into new static forms of meaning, for by establishing itself as a subversive counterforce there is an idea of transgression and emancipation. That is why the grotesque often historicizes and relativizes only to repeat the mistakes of that which it negates: putting itself in the king’s chair. The exploration of the material seems to create new forms and notions of the ideal. The representation of an otherness outside the prevailing notions of meaning and truth becomes a positive manifestation of this otherness as truth itself. Thus the historical “truths” of the grotesque are superseded by history itself. When the expressions of the grotesque solidify into static form and meaning, they become mere objects like anything else in the world. Instead of being this elusive thing of process and flow, it becomes tangible to the existing hierarchy of power as well as history itself. In this way the grotesque can be expunged, included or simply revealed as yet another false notion of truth, which is precisely what has happened with the grotesque throughout the course of history. If from the beginning the expression of the grotesque has not already been in the service of some structure of meaning and truth, it has quickly been included or has quickly included itself in such a structure. But by doing so it rejects its own basis: the tension between periphery and center is replaced by the attempt to create a new center, a new structure of meaning and truth. The doubleness, ambiguity and flow of the grotesque are then rejected by the grotesque itself. THE NON-FORM OF FORM In the critical thinking of Theodor W. Adorno (1903-69) the problem of art, caught between a reductive and prevalent notion of truth and meaning and a peripheral and alienated otherness, is reexamined and reformulated. For Adorno, the instrumental rationality of Enlightenment itself reverts into a new form of mythology which is every bit as static and exclusive as the hierarchies of religion it supersedes. All is excluded that is non-identical to the instrumental mastery of the objects of the world, "For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry." 1 As such the non-identical has been banished from the realm of thought and action, and banished specifically to the realm of art. But the realm of art is not able to provide a decent home for it because even modern art is not something entirely autonomous. While it is excluded from the notions of truth and meaning provided by instrumental rationality, it still originates from society. Just like instrumental rationality art is about mastery, structuring and exclusion. Therefore, the problem for art is that it cannot directly provide a space for the non-identical because its mode of operation is similar to that of instrumental rationality. Even worse, art has very few possibilities to free itself from this. If it becomes l’art pour l’art it is at the same time reduced to the very thing instrumental rationality claims it to be: a subjective judgment of taste.expressionism also stands as an example of this. Conversely, art cannot work within the framework of the identity-thinking of society, because any notion of freedom or emancipation would reproduce the exclusive practices of instrumental rationality. For example: Explicit socialist literature may establish itself in opposition to instrumental rationality while at the same time reproducing it. Its language may seem different, but in reality it merely provides a different set of reductive schematics for human life and experience. The problem for the art of the grotesque was, as I mentioned earlier, that far too often it was merely a symbolic manifestation of a notion of otherness—not otherness itself. Because of this the subversive character of the grotesque ends up shaping and containing otherness instead of providing a space for it. According to Adorno the only way to avoid this is to radicalize the grotesque. In order to avoid solidifying into form the work of art has to be an object which cannot be contained in thought or form—a non-form of form. The work of art has to work in a way that it strives for autonomy but without entirely leaving a discernible reality. In other words, it has to pull in two directions at once. Thus the work of art is a paradox. It is autonomous in the sense that it closes itself off from everything outside of the work of art, trying to shy away from the contaminating influence of the identity thinking of instrumental rationality. At the same time though the work of art is heteronomous in the sense that it originates from a specific historical context and is bound to be what society is not. Autonomy and heteronomy are inseparably intertwined. Unable to display otherness itself, but still trying to be a refuge for it, there is only one option for art: It has to turn against itself and destroy its own logic of form, thereby demonstrating how any representation of otherness is impossible. Art becomes a lamentation of the victims of the identity thinking of instrumental rationality and shows the traces of the otherness that is unable to appear. Adorno’s pessimistic theory of art and history stages art as a negative dialectical process where the work of art closes itself off and rejects everything outside, while the individual elements in the work of art destroys its very own logic of form from within: Artworks synthetize ununifiable, nonidentical elements that grind away at each other; they truly seek the identity of the identical and nonidentical processually because even their unity is only an element and not the magical formula of the whole […]. The resistance to them of otherness, on which they are nevertheless dependent compels them to articulate their own formal language, to leave not the smallest unformed particle as remnant. This reciprocity constitutes art’s dynamic; it is an irresolvable antithesis that is never brought to rest in the state of being. 2 Relative to a traditional understanding of the grotesque, Adorno radicalizes the tension between center and periphery, autonomy and heteronomy. In the traditional understanding of the grotesque, as we find it for example in the writings of Mikhail Bakhtin, the grotesque establishes the display of otherness as a new center of meaning and truth. However Adorno rejects such notions and argues instead for a modernism of the grotesque in which both center and periphery are included in a negative dialectical process and continually synthesizing and destabilizing each other’s positions. A modernism of the grotesque works on the inside of the sign or the artwork, continually outlining and questioning the boundaries between materiality and form. This moves the focus away from the relation between the sign or work of art as a conceptual manifestation on one side and the object it refers to on the other side. Instead it implicitly points to the amorphous mass from which the signs and thereby meaning have been carved, the remnants that have been left behind. Modernism of the grotesque does not imply that it is emancipatory or that it reconciles man with nature, and does not represent a new position or a new ideology. It merely remembers and insists on the double nature of man and art: to write or paint yourself or an artwork whole by inscribing meaning in life or by applying form on a canvas is at the same time both creation and destruction. The very signs we use to center meaning in our lives carry its own alienation in them. Meaning surfaces only when process and flow comes to a halt—solidifying, but at the same time excluding parts that do not fit into that particular structure of meaning. NOTHING DONE AND NOTHING UNDONE It has always been difficult for art historians to find a suitable category for the works of the Danish artist Leif Lage (b. 1933). In his paintings the sensitive figuration seems so fragile that it is on the verge of turning into abstraction. Or conversely: the figurative emerges cautiously and hesitantly out of abstraction. As an art critic once wrote, he can almost paint things away. 3 Working in some undefinable space between abstraction and figuration, the Lage’s works shy away from the realm of words, and as a result few critics have been able to write anything meaningful about his works. In fact even fewer have been able to write more than one or two pages. The Danish author and art critic Leif Hjernøe is one of those few, but even he starts off by saying how impossible it is to write about Lage, confessing that his works exist both as process and in a field of in-between which words cannot reach. He writes: Always you find yourself in a place where nothing is done and nothing left undone, and where the elements of the work of art rest in a continuous motion. Always there is the open wound, where infection rather than surgical intervention is considered as an opportunity. And the conflict between matter and antimatter makes all diagnoses uncertain and allows conditions of uncertainty to spread in a place of raw presence. 4 The art works against the diagnosis and the certainty. Words are being eaten up by what is outside the realm of words: tension, process and doubleness. An approach to an understanding of the work of Lage could be to follow his connection to Samuel Beckett (1906-89). One can note, therefore, that Lage has illustrated several of the Danish translations of Beckett’s works. Though one is an author and the other a painter both seek a place where figuration, where the word, erodes. For both this entails an attempt to question and examine and so move in behind the façade of the surface in an exploration of that something or nothing that may be behind representation. At the same time even in the vanishing point of figuration or words, the meaningless words or the disjointed lines still stand as signs of human activity—signs of movement in emptiness. With very few exceptions Lage’s artworks revolve around one motif: Man—most often “en face.” But unlike traditional portraitures Lage’s people are found within. The artworks do not sense the reality of appearances, but rather the existential dimensions within man. As a seismograph they are sensitive to the utmost subjectivity in order to display an objective, sensuous depiction of the very problem of subjectivity. Instead of a static façade of a man, Lage’s “en face” shows the process-character of man. The people in Lage’s paintings are always in process—in the midst of becoming or dissolving. I will take a closer look in the following at the ways in which Lage establishes this sense of being in constant process, of being in-between modes or categories. THE DOUBLENESS OF THE STROKE Lage’s etchings attract attention in particular for the tension conveyed there between the material and the form. The material physically opposes the violence of the needle. But instead of embracing the violence of the needle and the victory over matter—instead of making the artistic creation and figuration express a heroic mastery of the background it is made out of—Lage uses the stroke to express the very tension between stroke and material, figuration and background. In the drypoint etching Untitled from 1983, which illustrated the Danish translation of Beckett’s Ill Seen, Ill Said , the needle tears up the material in long rough lines: Together, the primarily horizontal and vertical lines form a face. Thus the force needed to etch a line in the metal-plate draws attention to itself: It is there in the absence of curves and nuances. Man emerges on the metal-plate after great exertion and in a very simplistic form. This way Lage enhances the nature of the material, as the material’s resistance is not something to overcome. On the contrary the figuration is smitten by its very resistance and as such expresses the violence of its own becoming. Even more pronounced is the fact that the lines do not just show the violence of creation—it actively erases figuration in the same process that creates it. For example the mouth consists of 8-10 horizontal strokes, of which some seem to be connected to each other as if the mouth has been quickly scratched out. The mouth speaks of the inability to speak. In the same way, the eyes are black holes due to a large amount of criss-cross cuts, which together form a dark middle. Those lines, at the same time, form the eyes of the figuration and scratch out the eyes of the figuration. The extroverted aspects of the face—connected to speech and sight—are portrayed as introverted as well. Just as the etchings down into the metal-plate makes something appear. Leif Lage, Untitled , 1983 (etching) The figuration of the etching is connected to creation. It expresses that something is wrought into existence out of nothing by sheer artistic force. However, this force is at the same time presented as a violence of creation, which makes it impossible for form to truly emerge. Herein lies one of the basic principles of Lage’s art, namely that art cannot be that nothing or something behind the realm of words or signs. Without form, art would lose its ability to express anything at all. Form is a necessity if art is to avoid becoming as devoid of expression as the reality is that we cannot reach behind the appearance of things. On the other hand, art cannot raise itself above its own material in joyous celebration of the beauty of form. This would use the material in the manner of an instrument and thus would suppress the otherness it attempts to rescue. When art becomes mere form, any traces of otherness will have dissolved. Then art would be a question of technique, in no way different from the instrumental rationality of society. Therefore art works in a particular space between form and non-form. As Hjernøe says of the works of Lage, it is in the center of the event, in the in-between where things neither are nor are not, "And everything takes place just before it changes character. As the blood just before it coagulates, as the milk just before it separates, as fried egg just before it turns white […]." 5 The precise emphasis on the in-between of Lage’s art points in particular to the work of art as both outside of and in time. The work of art is a singular point in time, but at the same time it is continually in process. In the borderland between form and non-form, between creation and destruction, it shimmers like a fata morgana . The work is done but at the same time undone. It is only there as a cry in response to the inability to come into being. Akin to the etching is the drawing, but while both, of course, use the stroke or line as their main instrument, the paper does not resist the line in the same sense as the metal-plate of the etching. As a result in Lage’s drawings the stroke frolics in a space with almost no tension at all. There is nothing there to keep the pencil stroke at bay, but at the same time this means that there is nothing there to keep it together. One of the more expressive examples of this is found in an untitled drawing from Tegninger og Text ( Drawings and Text ) from 1999. The drawing consists of one unbroken pencil stroke. It is as if the stroke is confused—it darts around on the paper making doodles on the way or gathers itself in more straight lines in the center of the paper. It is in this manner that the semblance of a body is established. A couple of small circles serve as eyes and are the reason that the rest can be read as both face and body instead of pure abstraction. In fact the unbroken stroke serves as both abstraction and figuration as on the one hand it is the stroke that seemingly outlines the shape of a figure, while on the other hand the unbroken stroke dissolves any truly recognizable figuration by continuously, without end or aim, overflowing the boundaries of the figure. Seen again here is a doubleness to the stroke and the act of creation. In the etching it was all about the tension between the resistance of the material which created the doubleness. Here it is the opposite. It is the lack of tension. The stroke is free to do anything, but has no aim: without some kind of resistance, there is nothing to hold figuration together. It threatens to dissolve into nothingness. Conversely, the drawing can also be seen as a process of becoming. Like a form of automatic writing, the pencil darts around until it finds a point of densification. But even in such an interpretation of the drawing, the figuration appears artificial—it points to itself as the result of the artistic act of creation. The stroke is primarily stroke and only secondarily figuration. With its wild movement it calls attention to itself as stroke. Thus the figuration never becomes something in its own right. It points to the basic principle of creation: Someone has drawn me, I am the result of artistic endeavors, and therefore I am not for myself but always overflowing the boundaries that contain me. It is the stroke that in the very same movement creates figuration and dissolves it. Leif Lage, Untitled , 1999 (drawing) THE LIGHTNESS OF COLOR, THE DENSITY OF PAPER Often the watercolor is used as a precursor for larger paintings, because it has an immediacy in which one can quickly paint the main lines of a composition. However, Lage’s watercolors are not temporary points in a process leading to another final painting. They are not sketches, later to be filled with details in another material. For him watercolor is an end in itself. This also implies that he doesn’t try to work against the paper’s absorption of the water color and its tendency to absorb detail. On the contrary, he examines the possibilities inherent in this blurring of the line and absorption of color. As in the previous examples, there are of course recognizable shapes in Lage’s water colors. But these shapes are rarely separable from color, line or even paper. In other words: the figurative and the abstract more or less become one. One of the reasons for this is that Lage often works on wetted paper which means that the paper hungrily absorbs color into its fabric instead of it being on top of the paper. The paper becomes line because it is the absorption of the color which, together with the brush stroke itself, separates the colors from each other. The line is also color and the color is also line, because there is no separation between the different colors other than the colors themselves. At times this results in almost complete abstraction. In such cases Lage add lines with a pencil as if he wants to hold some sort of figuration together. At other times it is the other way around: the strokes of the pencil are a being dissolved by the water color blurring out the figuration. Untitled 1 from 1999 displays various tones of green. The contour of the colors appears unusually rough. Most of all it is reminiscent of a shoreline which has found its form through the work of thousands of years between water and land. Pockets of resistance surface as islands not yet drowned in color—as paper or color not yet consumed by the dominant color. The shape of the colors does not seem created by the hand of the artist, but rather by the inner workings of the watercolor: color against color over time has resulted in this very image, as if it is all a part of a natural process of change and decay. Despite the fact that there are no strong differences in color there seems to be a struggle taking place in the watercolor. For example, inexplicable holes in the dark color, which cover most of the right side of the watercolor, appear as if the underlying color is eating away the dark color, or that the dark color is in the process of covering up the underlying color. The small pockets of resistance demonstrate a process and development that, almost as a happy accident, evokes a couple of small eyes and a large mouth. Behind the colors a few slanted lines can be discerned, but the hand of the artist has long ago disappeared behind the life of the colors. Thus the watercolor seems to be held at precisely the point in time where figuration randomly appears. The small eyes and wide mouth seemingly express the realization of the figuration’s temporality. It is just a moment in time, soon to be consumed again in the life of the colors. The nature, the background it stems from and is part of, moves on undeterred, continuing its everlasting process of creation and decay. In this sense, the watercolor provides an experience of how neither artist nor man is able to transcend the materiality they consist of. The colors of man, the materials man consists of are “becoming” and “progress” but also “decay” and “disappearance”. The artist’s pencil strokes have been eaten up long ago, and the figuration is living on borrowed time. Human or artistic activity is about creating form, transcending mere matter by shaping and applying meaning to it. But Untitled 1 shows the doubleness of such creation: the transience and fragility of human life. Should the figuration come into being, should it rise and transcend the material, which binds it to its temporal existence, it would become nothing because its very existence is conditioned by the life and work of the colors. In the same sense man cannot escape his own temporality. He too, for better or worse, must accept a life in the volatility of sensation. Leif Lage, Untitled 1 , 1999 (watercolor) In most of Lage’s watercolors there seem to be a stronger artistic control than in Untitled 1 . Most often both the arrangement of colors and the technique in which they are painted express the hand of the artist. An example of this is Untitled 2 from 1999. While figuration in Untitled 1 seemed to appear as a happy accident, the figuration is much more “created” in Untitled 2 . Here the most important parts of the figuration, the eyes, the mouth and part of the skull, are colored black and painted on top of the background’s play of colors. The background primarily consists of blue and yellow tones. Only parts of the paper are covered in color, however, which yet again stresses the act of painting: There is a surface which is being filled by color by an artist. The blue tones are concentrated in the figuration, while the yellow tones surround it. All this means that the figuration stands out more clearly in this watercolor. This is also underlined by the fact that the blue and dark tones cover part of the yellow tones as spots here and there. Thus it is not a background which is in the process of consuming figuration, but rather the emerging figuration which blots out the background. Such an understanding is even suggested by how the mouth and eyes are placed in the larger blue color field. The eyes and mouth are in the center of the watercolor, while the blue color field is placed from center out towards the left side. This gives the impression of a face turned slightly to the right and slightly upwards, which again makes the mouth appear to emerge from the paper. It also helps that the mouth cuts the center axis of the watercolor. In other words, the arrangement of the blue and black colors create some depth and perspective which gives the illusion of a figuration, seen partially in profile, emerging from the background. Seen in profile, the eyes and mouth seem extroverted—they almost seem as if they are put on top of the face. But at the same time they are painted as black holes, sucking in the gaze of the onlooker. The watercolor is even more challenging if one follows what may be the faint outline of the skull, which, on the right side of the watercolor, no longer works together with the blue color, but rather alone postulates the outline of the skull. If not the blue color field, but this line, is the outline of the skull, then all of a sudden the face is not in profile but “en face”—staring directly towards the onlooker. Outline and color seemingly work against each other and establish two different expressions. Without the slightly upward tilted expression of the profile, the eyes and mouth do not seem to emerge from the paper. On the contrary, seen “en face,” the eyes and mouth are really gaping pits of darkness. In this sense Untitled 2 is at the same time surface and depth of perspective. The line gives form but at the same time it dissolves the form created by the colors, and vice versa. Leif Lage, Untitled 2 , 1999 (watercolor) As the last example of Lage’s artistic method, I have chosen another untitled work (as indeed nearly all of Lage’s artworks are)—this time from 2000. This is perhaps one of the most figurative watercolors Lage has created, though that doesn’t tell us too much. The painting depicts a human face in blue and green tones on a yellow toned background. The colors create a clear demarcation between the figure and the background, which compensate for the watercolor’s lack of outline. Beneath the face darker tones imply the beginning of the torso, and nuances of color even hint at something which could be a collar. The hair is in even darker tones and its structure is emphasized using pencil strokes on top of the water color. One eye is marked by a brown spot with a darker spot in the middle, while the other eye is added by pencil. The mouth is a round, red dot. In Untitled from 2000 the work between abstraction and figuration is much less pronounced than in the previous examples cited here. Nonetheless the watercolor has a delicacy to it which almost makes the figuration disappear, even as it appears. This has something to do with the fact that all the individual brush strokes have dissolved. The only outlines are those created by the clash of colors. Even the red mouth seems to be more paint than mouth—unable to be formed truly as anything other than a speck of color with some small semblance to a mouth. In contrast to the other watercolors, there is no movement, no progress or decay, just a vibrating standstill. The figure is not emerging or disappearing but embedded in and as surface, and as such it makes the figure seem stuck in its condition rather than freed by the act of giving form: mouth open as a wound. Pencil strokes add detail and life to the hair as an attempt to help the figure emerge. But all this does is create two levels in the watercolor: The pencil strokes are put on top of the figuration rather than being part of it. Thus they end up highlighting the endless distance between the movement and form-giving of the pencil strokes and the static and stuck figure behind these strokes. Leif Lage, Untitled , 2000 (watercolor) MAN AND THE VIEW OF THE ONLOOKER Lage’s works seem at the same time to be an examination of tensions between form and material in art and a display of an image of man full of the same tensions. This is because the people who are emerging in Lage’s images are not just in his works, They are his works. This means that man is not something emerging from a background but is part of this background and vice versa. The art of Lage inscribes man in its surroundings and background. Man is not the ruler of nature. Man does not rise above matter; there is no truly transcendent position for man to occupy in the art of Lage. Instead man is a part of the very matter, it, at the same time, tries to distance itself from in order to distinguish itself from its surroundings. Man emerges in an attempt not to be line, stroke, color. In an attempt to free itself of matter. Should it succeed in this, however, it would turn into nothing. On the other hand, if man fully accepted itself as mere matter it would disappear in it—in instincts, urges and lack of reflection. The appearance of man is thus subject to a state of being in-between. Only in the tension between material and its negation can the outlines of man be traced. However this also means that in the art of Lage man is never something in itself but always in process—on the way to its freedom and its loss. However, Lage’s art is not just about showing the tensions inherent in man but also about showing such tension on the verge of breaking point. In the moment before everything is done, or when nothing yet has been done, the delicate tension between form and material has been stretched to its utmost in such a way that man’s character of process emerges and is contained on the paper or canvas. Therefore, Lage’s art contain traces of human life. Not only is it an autonomous unity of tensions where man is stretched out between its singularity and the surroundings it is a part of. It is also this pulsation between figuration and material which brings about the traces of human endeavor and activity. Even when man almost seems to have disappeared into the material, strokes and lines are still there as a reminder of human activity and potential creative power—as a reminder that hope is still possible and that man is still there. The view of the onlooker seeks out forms and meaning. It seeks outlines and edges. But first and foremost it is the eyes in Lage’s works of art that allow the onlooker to decode the figuration at play. This creates a distinctive relationship between the onlooker and the artwork. The onlooker tries to wrest the enigma from the artwork, tries to reduce it to solid, meaningful form. But the very same moment that hints at such a possibility sees the view of the onlooker confronted with a gaze of its own. The eyes of the figure in the work of art are most often dark pits, as if they were an illustration of the violence committed against the eyes of the onlookers and their search for meaning. Or as if they were a dark reflection of the onlooker’s failed attempts to delineate the traces of life in the artwork to a solid meaningful form. Therefore, the gaze of the figuration speaks not only of its own powerlessness but also of the powerlessness of the onlooker. When the view or sight has trouble finding solid meaningful forms, it has something to do with the fact that the precondition for sight, light, no longer stems from something transcendent. In Lage’s art there is nothing outside the works of art, nothing outside of human life, and as such nothing to shed light on the works of art or human life and reveal solid meaningful forms. All light comes from within. In a western context, light as a medium for sight is central to the understanding of meaning. People speak of the clarity of thought, while knowledge is tied together with enlightenment, and so forth. But the light no longer originates from a divine point of view. It originates from man, who has created himself in the image of God. The problem with this is that light always covers up its own base. Light illuminates something but at the same time it hides itself. 6 While it was previously God who was unknowable, now it is man. It is also problematic that sight and the medium of sight stem from the same place. Following this thought one can posit two final problems. Firstly, the immediacy and presence established by light by making forms and objects accessible to sight is fake. Light is not some independent entity which present things in a neutral manner for the onlooker. It is inextricably tied together with the gaze’s desire after meaning. In other words: Light perverts the appearance of things because it doesn’t originate from some objective entity which allows them to appear as they are. Instead light is based upon and originates from the subject and its conquering gaze, seeking out meaning and form constantly. Secondly, the joining of sight and light makes introspection within human life impossible. Everything can be illuminated by its use value for the subject but only as long as it is separated from the subject, as long as it is an object. But the subject itself cannot be illuminated. Lage’s art tears down such a dividing line between subject and matter, but it does so without reestablishing a divine position from where the light emanates. Therefore, the light in Lage’s art may not illuminate very well. It may not have the certainty presented by modern science or the religions of yesterday. But it does show what such light tries to hide, namely, the subject as it is in its material reality—inscribed in time and death, which are the basic conditions of materiality, but at the same time also full of life in its joy and will to create. For the onlooker the meeting of the gaze in Lage’s works of art is thus also a destruction of the view of the onlooker. The ability to see is challenged in a radical way. Those outlines will not solidify into static form, as if the light was too dim to see. Just as in Lage’s figurations, the view of the onlooker turns to black: turns towards the onlooker in recognition and becoming—or disappearance. NOTES Max Horkheimer and Theodor W. Adorno. Dialectic of Enlightenment . (Palo Alto: Stanford University Press, 2002): 4-5. Theodor W. Adorno. Aesthetic Theory . (London & New York, 2002): 176. Carsten Bach-Nielsen. “Mere glæde end gru.” Kristeligt Dagblad . September 24, 2002. Leif Hjernøe. “Den yderliggående inderlighed.” LEIF LAGE—Retrospektiv udstilling 1983 . (Copenhagen: Brøndum, 1983): 18. Ibid. Maurice Blanchot. The Infinite Conversation . (Minneapolis: University of Minnesota Press, 1993): 162-163. (shrink)

This paper puts forward a new account of rigorous mathematical proof and its epistemology. One novel feature is a focus on how the skill of reading and writing valid proofs is learnt, as a way of understanding what validity itself amounts to. The account is used to address two current questions in the literature: that of how mathematicians are so good at resolving disputes about validity, and that of whether rigorous proofs are necessarily formalizable.

1. Hobbes-Gay.--2. Hume-Bentham and Index.

Meet Tega. Blue, fluffy, and AI-enabled, Tega is a relational robot: a robot designed to form relationships with humans. Created to aid in early childhood education, Tega talks with children, plays educational games with them, solves puzzles, and helps in creative activities like making up stories and drawing. Children are drawn to Tega, describing him as a friend, and attributing thoughts and feelings to him ("he's kind," "if you just left him here and nobody came to play with him, he (...) might be sad"). Scholars and members of the public alike have raised the alarm about relational robots, worrying that the relationships that people, and especially children, form with such robots are objectionably inauthentic. We, members of an interdisciplinary team that developed and studies Tega, make this inauthenticity worry precise and offer practical recommendations for addressing it. We distinguish two kinds of (in)authenticity -- inauthenticity as unreality, and inauthenticity as deception -- arguing that neither is just what others have thought it is. With our distinction in hand, we argue that the authenticity concern can be met only through co-design methods -- methods that give stakeholders of all kinds (e.g. parents, educators, and children themselves) a genuine say in how relational robots are built. (shrink)

Advocates anthropology as a science focused on social structure.

The practice of a priori conceptual analysis requires that the concept being analyzed be available in the analyst's mind. The difficulties of analysis and the existence of disagreements among analysts are explained by distinguishing the implicit knowledge we have of these concepts from the explicit knowledge we seek. This view of disagreement assumes that those who disagree are typically attempting to analyze a single shared concept. In this paper, reasons are developed for replacing this guiding assumption with the alternative assumption (...) that members of a conceptual community often have similar, but not identical, concepts. Adopting this alternative requires that we rethink the nature and aims of conceptual analysis. (shrink)

This book is both expository and critical and concentres on Hobbes' ethical and political theory, but also considering the effect on these of his metaphysics.

What darkness was the ‘Enlightenment’ supposed to have removed? The answer is irrational forms of religion. Most of the ‘enlightened’ took the view that revealed religion was irrational and that natural religion could be rational; but some were sceptical about natural religion too. Hume was the most honest and the most penetrating thinker of the latter group. His biographer, Professor E. C. Mossner, is not alone in believing that the Dialogues concerning Natural Religion is ‘his philosophical testament’.

: This paper is a response to Siegel 2004. I take Siegel's remarks as a basis for clarifying, defending, and further developing my account of the role of judgment in a theory of rationality.

Despite its preeminent position in the just war tradition, the concept of proportionality is not well understood by military leaders. Especially lacking is a realization that there are four distinct types of proportionality. In determining whether a particular resort to war is just, national leaders must consider the proportionality of the conflict, i.e., balance the expected gain or just redress against the total harm likely to be inflicted by the impending armed action. This proportionality consideration is called jus ad bellum (...) proportionality. The second type of proportionality discussed is a continuing re-evaluation of the proportionality, taking into account the changing situation. The last true proportionality discussed is a consideration of hostile action taking during a conflict, or jus in bello proportionality. This consideration weighs the expected military gain of a particular action against the collateral damage and injuries that are expected from the act. Finally, the fourth category addressed is ‘political proportionality’, which is not a true proportionality consideration, but is rather self-interested deliberation on the possible political and military outcomes of actions. In some instances, it could be referred to as a measured response. A better understanding of proportionality in all its forms will help military leaders to give appropriate and moral advice on the potential resort to war, as well as on the conduct of military actions in war. The recent US war with Iraq in the spring of 2003 in defiance of the wishes of the majority of the UN Security Council, and especially with the potential for high noncombatant casualties in Baghdad, makes a discussion of the proper conduct of war even more poignant. (shrink)

Environmental actions require a willingness to act, which, in turn, is stimulated partially by the belief that an action will yield the desired consequences. In determining whether an actor was justified in exerting the will to act, therefore, it is essential to examine the nature of evidence offered by the actor in support of any beliefs about the environment. In this paper we explore the points in environmental risk analyses at which evidence is brought to bear in support of inferences (...) conceming environmental effects of regulatory actions. The intent is to provide a framework for discussing the manner in which evidence may provide a sufficient basis for ethically sound decisions for environmental actions. (shrink)

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.

In recent years empiricism has been under persistent attack, and serious questions have been raised about the ability of empiricism to provide the basis for a viable philosophy of science. The attack has been sufficiently vigorous, and in some quarters sufficiently successful, that many now maintain that empiricism is dead. My aim in this paper is to argue that, rather than being ready for embalmment and emplacement in the museum of philosophic oddities, empiricism is very much alive, and the central (...) thesis of empiricism remains the cornerstone for any viable philosophy of science. This is not to say that the recent attacks on empiricism have been without a point, rather, they have put anyone who would defend empiricism in the position of having to rethink many datails of the empiricist viewpoint. But it is the details, the way in which empiricism has been elaborated by its proponents, not the central empiricist insight, that must be reconsidered. (shrink)

Philosophy of science is still, in the minds of many, identified with positivism. This is understandable since twentieth century philosophy of science originates with the work of the Vienna Circle. Positivism is most famous for the verification theory of meaning, the doctrine that the meaning of any proposition is the method by which it is verified, and that any nonanalytic locution which cannot be proven or disproven by some empirical test has no cognitive significance. Positivism is an attempt to construct (...) a “scientific philosophy” in the worst sense: it is maintained that (with the exception of propositions which are analytic and thus vacuous) only those propositions which occur in the sciences are meaningful, all other discourse having at best some emotive value, but no cognitive content, and all of this is maintained within the confines of an exceedingly narrow notion of scientific knowledge. This notion is so narrow that its advocates found themselves in danger of having to relegate most of physics to the realm of nonsense since physics contains many statements which are strictly universal and thus cannot be conclusively verified. (shrink)

ABSTRACT The article constitutes an attempt to answer the question contained in the title, by reference to three example topics: individual privacy, ownership of software, and computer ‘hacking’. The ethical question is approached via the legal one of whether special, computer–specific legislation is appropriate. The conclusion is in the affirmative, and rests on the claim that computer technology has brought with it, not so much the potential for committing totally new kinds of crimes, as a distinctive set of linguistic and (...) conceptual apparatus which makes it necessary to describe computer–related activity in special ways. (shrink)

The novel has always provided a vehicle for commenting on various aspects of human existence. We are familiar with the political novel, the historical novel, or the metaphysical novel, and in this sense Sorrentino's Mulligan Stew, with its running commentary on novels, novelists, critics and publishers, may be viewed as a critical novel. A critical novel, however, has a striking feature which it does not share with the other sorts of novels mentioned above in that a critical novel is itself (...) a novel, and a member of the class of objects on which it is commenting. This is a structure that logicians call “self-reference” and the phenomenon of self-reference has provided a central theme in twentieth century logic and philosophy. (shrink)

For the case of statistical theories, the criteria of explanation, prediction, and testability can all be viewed as particular instances of a more general evaluation scheme. Using the ideas of a gain matrix and expected gain from statistical decision theory, these three criteria can be compared in terms of the elements in their associated gain matrices. This analysis leads to (1) further understanding of the interrelationship between the current criteria, (2) the proposal of an ordering for the criteria, and (3) (...) the suggestion of a new criterion. (shrink)

Aim: To assess, against a checklist of specific areas of required information and using standard published criteria, to what extent leaflets given before cataract surgery provided patients with enough information to give adequately informed consent.Method: Twelve ophthalmology departments in the West Midlands region were asked to submit the cataract information leaflets given to their patients at the preoperative assessment for analysis. Using criteria published by the General Medical Council, British Medical Association, and Medical Defence Union the leaflets were assessed for (...) their contribution to informed consent for patients considering cataract surgery. Leaflets were scored according to the information they provided on: diagnosis, prognosis, treatment options, costs to the patient, details about the procedure, its purpose, likely benefits, how to prepare for it, what to expect during and after the operation, and the common as well as serious complications that may occur. The readability of the information was also assessed.Results: All the units’ leaflets provided information on diagnosis, the lifestyle changes required postoperatively, and cost involved to the patient. Only five units had leaflets that mentioned the risks involved in cataract surgery. The other areas of information were covered by 50–75% of the leaflets. Fifty per cent of the leaflets included a diagram. The average SMOG readability score was high.Conclusion: Although present cataract information leaflets make some contribution to the process of informed consent, most do not address important areas outlined by the General Medical Council. Many of the areas of information that are required for informed consent could easily be covered, and should be borne in mind when designing patient information leaflets. Resources are available on the internet including toolkits, guides, and means of assessment for the production of patient information leaflets. (shrink)

The Chronicle of Jerome states that Gaius Lucilius was born in 148 B.C. and died in 103 B.C. in his forty-sixth year. The Oxford Classical Dictionary says that Gaius Lucilius was probably born in 180 B.C. and died in 102/1 B.C.

“There is, in addition, a second reason for doubting that scientists reject paradigms because confronted with anomalies or counterinstances. In developing it my argument will itself foreshadow another of this essay's main theses. The reasons for doubt sketched above were purely factual; they were, that is, themselves counterinstances to a prevalent epistemological theory. As such, if my present point is correct, they can at best help to create a crisis or, more accurately, to reinforce one that is already very much (...) in existence. By themselves they cannot and will not falsify that philosophical theory, for its defenders will do what we have already seen scientists doing when confronted by anomaly. They will devise numerous articulations and ad hoc modifications of their theory in order to eliminate any apparent conflict. Many of the relevant modifications and qualifications are, in fact, already in the literature. If, therefore, these epistemological counterinstances are to constitute more than a minor irritant, that will be because they help to permit the emergence of a new and different analysis of science within which they are no longer a source of trouble. Furthermore, if a typical pattern, which we shall later observe in scientific revolutions, is applicable here, these anomalies will then no longer seem to be simply facts. From within a new theory of scientific knowledge, they may instead seem very much like tautologies, statements of situations that could not conceivably have been otherwise.”. (shrink)

Neo-Fregeanism aims to provide a possible route to knowledge of arithmetic via Hume’s principle, but this is of only limited significance if it cannot account for how the vast majority of arithmetic knowledge, accrued by ordinary people, is obtained. I argue that Hume’s principle does not capture what is ordinarily meant by numerical identity, but that we can do much better by buttressing plural logic with plural versions of the ancestral operator, obtaining natural and plausible characterizations of various key arithmetic (...) concepts, including finiteness, equinumerosity and addition and multiplication of cardinality—revealing these to be logical concepts, and obtaining much of ordinary arithmetic knowledge as logical knowledge. Supplementing this with an abstraction principle and a simple axiom of infinity (known either empirically or modally) we obtain a full interpretation of arithmetic. (shrink)

The initial motivating question for this thesis is what the standard of rigour in modern mathematics amounts to: what makes a proof rigorous, or fail to be rigorous? How is this judged? A new account of rigour is put forward, aiming to go some way to answering these questions. Some benefits of the norm of rigour on this account are discussed. The account is contrasted with other remarks that have been made about mathematical proof and its workings, and is tested (...) and illustrated by considering a case study discussed in the literature. On the view put forward here one can obtain a manner of informal, rigorous mathematics founded on any of a variety of proof systems. The latter part of the thesis is concerned with the question of how we should decide which of these competing proof systems we should base our mathematics on: i.e., the question of which proof system we should take as a foundation for our mathematics. A novel answer to this question is proposed, in which the key property we should require of a proof system is that for as many different kinds of structures as possible, when the proof system allows a generalization about that kind of structure to be proved, the generalization actually holds of all real examples of that kind of structure which exist. This is the requirement of soundness of the proof system. It is argued that the best way to establish the soundness of a proof system may be by giving an interpretation of its axioms on which they are established as true. As preparation for this discussion, the thesis first investigates the logical and conceptual basis of various arithmetic concepts, with the results obtained used in the final discussion of soundness. (shrink)

This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.