We present a game semantics in the style of Lorenzen for Girard's linear logic . Lorenzen suggested that the meaning of a proposition should be specified by telling how to conduct a debate between a proponent P who asserts and an opponent O who denies . Thus propositions are interpreted as games, connectives as operations on games, and validity as existence of a winning strategy for P. We propose that the connectives of linear logic can be naturally interpreted as the (...) operations on games introduced for entirely different purposes by Blass . We show that affine logic, i.e., linear logic plus the rule of weakening, is sound for this interpretation. We also obtain a completeness theorem for the additive fragment of affine logic, but we show that completeness fails for the multiplicative fragment. On the other hand, for the multiplicative fragment, we obtain a simple characterization of game-semantical validity in terms of classical tautologies. An analysis of the failure of completeness for the multiplicative fragment leads to the conclusion that the game interpretation of the connective is weaker than the interpretation implicit in Girard's proof rules; we discuss the differences between the two interpretations and their relative advantages and disadvantages. Finally, we discuss how Gödel's Dialectica interpretation , which was connected to linear logic by de Paiva , fits with game semantics. (shrink)

By a model of set theory we mean a Boolean-valued model of Zermelo-Fraenkel set theory allowing atoms (ZFA), which contains a copy of the ordinary universe of (two-valued,pure) sets as a transitive subclass; examples include Scott-Solovay Boolean-valued models and their symmetric submodels, as well as Fraenkel-Mostowski permutation models. Any such model M can be regarded as a topos. A logical subtopos E of M is said to represent M if it is complete and its cumulative hierarchy, as defined by Fourman (...) and Hayashi, coincides with the usual cumulative hierarchy of M. We show that, although M need not be a complete topos, it has a smallest complete representing subtopos, and we describe this subtopos in terms of definability in M. We characterize, again in terms of definability, those models M whose smallest representing topos is a Grothendieck topos. Finally, we discuss the extent to which a model can be reconstructed when its smallest representing topos is given. (shrink)

In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility (...) relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic \ ), that is, \ \ \ \supset \Box \phi \). The faithfulness also holds for normal modal logics, e.g., \, \, \, \. We shall conclude this paper with the section of some open problems and conjectures. (shrink)

M. E. Rudin proved, under CH, that for each P-point p there exists a P-point q strictly RK-greater than p. This result was proved under ${\mathfrak {p}= \mathfrak {c}}$ by A. Blass, who also showed that each RK-increasing $ \omega $ -sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-ordering. In this paper, the results cited above are proved (...) under the assumption that $\mathfrak { b}=\mathfrak {c}$. A. Blass asked in 1973 which ordinals can be embedded in the set of P-points, and pointed out that such an ordinal cannot be greater than $ \mathfrak {c}^{+}$. In this paper it is proved, under $\mathfrak {b}=\mathfrak {c}$, that for each ordinal $\alpha < \mathfrak {c}^{+}$, there is an order embedding of $ \alpha $ into P-points. It is also proved, under $\mathfrak {b}=\mathfrak {c}$, that there is an embedding of the long line into P-points. (shrink)

In the present paper the story is told of the brief and far from tranquil encounter of L.E.J. Brouwer and A. Fraenkel. The relationship which started in perfect harmony, ended in irritation and reproaches.The mutual appreciation at the outset is beyond question. All the more deplorable is the sudden outbreak of an emotional disagreement in 1927. Looking at the Brouwer–Fraenkel episode, one should keep in mind that at that time the so-called Grundlagenstreit was in full swing. An emotional man like (...) Brouwer, who easily suffered under stress, was already on edgewhen Fraenkel's book Zehn Vorlesungen Über die Grundlegung der Mengenlehre, [Fraenkel 1927] was about to appear.With the Grundlagenstreit reaching a level of personal abuse unusual in the quiet circles of pure mathematics, Brouwer was rather sensitive, where the expositions of his ideas were concerned. So when he thought that he detected instances of misconception and misrepresentation in the case of his intuitionism, he felt slighted. We will mainly look at Brouwer's reactions. since the Fraenkel letters have not been preserved.The late Mrs. Fraenkel kindly put the Brouwer letters that were in her possession at my disposal. I am grateful to the Fraenkel family for the permission to use the material.I am indebted to Andreas Blass for his valuable suggestions and corrections.Abraham Fraenkel was one of the first non-partisan mathematicians, if not the first, who developed a genuine interest in intuitionism. (shrink)

Gert H. Müller The growth of the number of publications in almost all scientific areas,· as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview ofthe existing literature, partic ularly if they do not have an extensive library available in their (...) neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg II. Non-c1assical Logics W. Rautenberg IH. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. ProofTheory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

Reviewed Works:Tomek Bartoszynski, Marion Scheepers, Set Theory, Annual Boise Extravaganza in Set Theory Conference, March 13-15, 1992, April 10-11, 1993, March 25-27, 1994, Boise State University, Boise, Idaho.R. Aharoni, A. Hajnal, E. C. Milner, Interval Covers of a Linearly Ordered Set.Eyal Amir, Haim Judah, Souslin Absoluteness, Uniformization and Regularity Properties of Projective Sets.Tomek Bartoszynski, Ireneusz Reclaw, Not Every $\gamma$-Set is Strongly Meager.Andreas Blass, Reductions Between Cardinal Characteristics of the Continuum.Claude Laflamme, Filter Games and Combinatorial Properties of Strategies.R. Daniel Mauldin, (...) Analytic non-Borel Sets Modulo Null Sets.Janusz Pawlikowski, Laver's Forcing and Outer Measure.Marion Scheepers, Meager Sets and Infinite Games.Saharon Shelah, On Some Problems in General Topology.Saharon Shelah, Remarks on $\aleph_1$-CWH not CWH First Countable Spaces.Juris Steprans, Cardinal Invariants Associated with Hausdorff Capacities. (shrink)

I present a semantics for the language of first-order additive-multiplicative linear logic, i.e. the language of classical first-order logic with two sorts of disjunction and conjunction. The semantics allows us to capture intuitions often associated with linear logic or constructivism such as sentences = games, SENTENCES = resources or sentences = problems, where “truth” means existence of an effective winning strategy.The paper introduces a decidable first-order logic ET in the above language and gives a proof of its soundness and completeness (...) with respect to this semantics. Allowing noneffective strategies in the latter is shown to lead to classical logic.The semantics presented here is very similar to Blass's game semantics. Although there is no straightforward reduction between the two corresponding notions of validity, my completeness proof can likely be adapted to the logic induced by Blass's semantics to show its decidability, which was the main problem left open in Blass's paper.The reader needs to be familiar with classical logic and arithmetic. (shrink)

Gert H. Muller The growth of the number of publications in almost all scientific areas, as in the area of logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their (...) neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises the following six volumes : I. Classical Logic W. Rautenberg II. Non-classical Logics W. Rautenberg III. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. Proof Theory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

In this paper, it is argued that metaphysics, conceived as an inquiry into the ultimate nature of mind-independent reality, is a rationally indispensable intellectual discipline, with the a priori science of formal ontology at its heart. It is maintained that formal ontology, properly understood, is not a mere exercise in conceptual analysis, because its primary objective is a normative one, being nothing less than the attempt to grasp adequately the essences of things, both actual and possible, with a view to (...) understanding as far as we can the fundamental structure of reality as a whole. Accordingly, it is urged, the deliverances of formal ontology have a modal and epistemic status akin to those of other a priori sciences, such as mathematics and logic, rather than constituting rivals to the claims of the empirical sciences, such as physics. (shrink)

This engaging volume explores and defends the claim that misanthropy is a justified attitude towards humankind in the light of how human beings both compare with and treat animals. Reflection on differences between humans and animals helps to confirm the misanthropic verdict, while reflection on the moral and other failings manifest in our treatment of animals illuminates what is wrong with this treatment. Human failings, it is argued, are too entrenched to permit optimism about the future of animals, but ways (...) are proposed in which individual people may accommodate to the truth of misanthropy through cultivating mindful, humble and compassionate relationships to animals. Drawing on both Eastern and Western philosophical traditions David E. Cooper offers an original and challenging approach to the complex field of animal ethics. (shrink)

Philosophers constantly discuss Responsibility. Yet in every discussion of which I am aware, a rather obvious point is ignored. The obvious point is that responsibility is ascribed to collectives, as well as to individual persons. Blaming attitudes are held towards collectives as well as towards individuals. Responsibility is often ascribed to nations, towns, clubs, groups, teams, and married couples. ‘Germany was responsible for the Second World War’; ‘The club as a whole is to blame for being relegated’. Such statements are (...) not rare. (shrink)

We here examine the expressive power of first order logic with generalized quantifiers over finite ordered structures. In particular, we address the following problem: Given a family Q of generalized quantifiers expressing a complexity class C, what is the expressive power of first order logic FO(Q) extended by the quantifiers in Q? From previously studied examples, one would expect that FO(Q) captures L C , i.e., logarithmic space relativized to an oracle in C. We show that this is not always (...) true. However, after studying the problem from a general point of view, we derive sufficient conditions on C such that FO(Q) captures L C . These conditions are fulfilled by a large number of relevant complexity classes, in particular, for example, by NP. As an application of this result, it follows that first order logic extended by Henkin quantifiers captures L NP . This answers a question raised by Blass and Gurevich [Ann. Pure Appl. Logic, vol. 32, 1986]. Furthermore we show that for many families Q of generalized quantifiers (including the family of Henkin quantifiers), each FO(Q)-formula can be replaced by an equivalent FO(Q)-formula with only two occurrences of generalized quantifiers. This generalizes and extends an earlier normal-form result by I. A. Stewart [Fundamenta Inform. vol. 18, 1993]. (shrink)

Cet article est un nouvel examen des objections soulevées par Leibniz dans la controverse avec Clarke contre la théorie absolutiste de l'espace et du temps. Or la plupart de ces objections sont fondées sur le principe de raison suffisante; mais Leibniz utilise aussi le principe de l'identité des indiscernables, qu'il prétend déduire du principe de raison suffisante . Ce qui m'intéresse c'est que Leibniz présente parfois deux versions de la même objection: l'une reposant uniquement sur le principe de raison suffisante, (...) l'autre uniquement sur le principe de l'identité des indiscernables. Se pose alors la question suivante: Leibniz aurait-il pu soulever toutes les objections qu'il voulait contre la théorie absolutiste, en utilisant seulement le principe de l'identité des indiscernables? Il me semble qu'il aurait certainement pu le faire. Et de plus, je crois que si Leibniz avait suivi cette voie, son raisonnement contre la théorie absolutiste aurait été beaucoup plus convaincant. Ainsi donc, je me propose de mener l'attaque de Leibniz contre la théorie absolutiste, en isolant, reformulant, et exposant systématiquement sept arguments dont il se servait ou dont il aurait pu se servir, qui sont tous fondés sur le principe de l'identité des indiscernables. (shrink)

The behavior of individuals currently living will generally have long-term consequences that affect the well-being of those who will come to live in the future. Intergenerational interdependencies of this nature raise difficult moral issues because only the current generation is in a position to decide on actions that will determine the nature of the world in which future generations will live. Although most are willing to attach some weight to the interests of future generations, many would argue that it is (...) not necessary to treat these interests as equivalent to those of the current generation. A common approach in this context is to use a system of discounting to evaluate future benefits and harms. This paper assesses the logic of discounting drawing on the writings of economists and philosophers. Much of the economic literature concerns the choice of an appropriate social discount rate. The social discount rate can be taken to reflect beliefs about the rights of future generations, a subject that has been extensively debated in the phioosophic literature. The writings of both economists and philosophers concerned with the weight to attach to the interests of future generations are reviewed and evaluated in this paper and the implications for environmental policy are discussed. (shrink)

It is known that various complexity-theoretical problems can be translated into some special spectra problems (see e.g. Fagin [Fa74] or Blass and Gurevich, [Bl-Gu86]). So questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quanti fiers in the empty vocabulary. This problem has been investigated fi rstly by Krynicki and Mostowski in [Kr-Mo 92] and [Kr- Mo 95]. All presented results can (...) be also treated as results about the expressive power of certain languages in fi nite models. (shrink)

I argue that to be compelled to do routine work is to be gravely harmed. Indeed, that pink - collar work is a more serious harm to women than rape. My purpose is to urge politically active feminists and feminist organizations to arrange their priorities accordingly and devote most of their resources to working for the elimination of sex segregation in employment.

Both articles in the November‐December 2021 issue of the Hastings Center Report reflect bioethics’ growing interest in questions of justice, or more generally, questions of how collective interests constrain individual interests. Hugh Desmond argues that human enhancement should be reconsidered in light of developments in the field of human evolution. Contemporary understandings in this area lead, he argues, to a new way of thinking about the ethics of enhancement—an approach that replaces personal autonomy with group benefit as the primary criterion (...) for deciding what enhancements are acceptable. In the second article, Johannes Kniess considers the many attempts within bioethics to draw on John Rawls's work to discuss health care access and social determinants of health, and he comes across as moderately optimistic that Rawls's theory of justice has ongoing relevance. (shrink)

Individual differences on a variety of framing and conjunction problems were examined in light of Slovic and Tversky's (1974) understanding/acceptance principle-that more reflective and skilled reasoners are more likely to affirm the axioms that define normative reasoning and to endorse the task construals of informed experts. The predictions derived from the principle were confirmed for the much discussed framing effect in the Disease Problem and for the conjunction fallacy on the Linda Problem. Subjects of higher cognitive ability were disproportionately likely (...) to avoid each fallacy. Other framing problems produced much more modest levels of empirical support. It is conjectured that the varying patterns of individual differences are best explained by two-process theories of reasoning (e.g. Evans, 1984, 1996; Sloman, 1996) conjoined with the assumption that the two processes differentially reflect interactional and analytic intelligence. (shrink)

E. J. Lowe; Are the natural numbers individuals or sorts?, Analysis, Volume 53, Issue 3, 1 July 1993, Pages 142–146, https://doi.org/10.1093/analys/53.3.142.

Business Ethics, the Environment & Responsibility, Volume 31, Issue 2, Page 453-473, April 2022.

Objects which philosophers have traditionally categorized as abstract are standardly referred to by complex noun phrases of certain canonical forms, such as ‘the set of Fs’, ‘the number of Fs’, ‘the proposition that P’, and ‘the property of being F’. It is no accident that such noun phrases are well-suited to appear in ‘Fregean’ identity-criteria, or ‘abstraction’ principles, for which Frege’s criterion of identity for cardinal numbers provides the paradigm. Notoriously, such principlesare apt to create paradoxes, and the most intuitively (...) plausible ‘Fregean’ identity-criterion for properties is afflicted by this problem. In this case, it may be possible to overcome the difficulty by modifying the criterion in a way which requires an independent account of the existence-conditions of properties, but it appears that such a strategy demands acceptance of the doctrine of immanent realism—the view that a property exists only if it is exemplified by some object. (shrink)

This paper locates its genesis in a small town called Vitebsk in Belorussia which experienced a flowering of creativity and artistic energy that led to significant modernist experimentation in the years 1917–1921. Marc Chagall, returning from the October Revolution took up the position of art commissioner and developed an academy of art that became the laboratory for Russian modernism. Chagall’s Academy, Bakhtin’s Circle, and Malevich’s experiments, artistic group UNOVIS—all in fierce dialogue with one another—made the town of Vitebsk into an (...) artistic crucible in the early twentieth century. We argue that this creative collective transformed creative energies of Russian drama, music, theatre, art, and philosophy in a distinctive contribution to modernism, structuralism and formalism that contributed richly to the social understanding of creativity itself that is so evident across Mikhail Bakhtin’s subsequent body of work, and elsewhere across the world. This paper argues that a consideration of such interplay has much potential for twenty-first century educational philosophy. (shrink)

I venture to call the attention of classical scholars to two legends about Roman Emperors gleaned amid the arid waste of theological nonsense which passed for literature among the Copts, in the hope that they may have better luck than I have had in tracing them to some classical source. The first is taken from MS. Par. Copte 131, fol. 40, a single leaf of what seems to be a geographical and historical encyclopaedia.1 The writer who is treating in a (...) very discursive way of Ethiopia, states that Nero or Domitian—a strange pair to run in double harness—caused an island in the Red Sea to be watered with oil. The description of that island is mixed up with a mention of the original divisions of the Indians—a term which as usual in early days embraces both Indians and Ethiopians,—and their subsequent changes; and as that too may be of interest to students of ancient geography, I will translate the passage in full. (shrink)

The emergence of Latin monks, and then the spread of the monastic orders of the Catholic Church in Rus-Ukraine occurred in the conditions of political-religious transformations of the nineteenth century. Acceptance of baptism from Byzantium did not mean separation from Rome. The Eastern and Western churches were still in unity at that time. The Pope remained the formal head of all Christianity. In 988, as the Nikon Chronicle attests, the ambassadors from Rome and the relics of the saints were brought (...) to the Prince of Kiev during his march to Korsun. It was about the relics of St. Clement, the Pope, found by Cyril and Methodius in the same Korsun on his return from a missionary journey to Khazaria. Two years earlier, according to a chronicle, Vladimir had received ambassadors from Rome who had invited him to adopt Christianity in Latin. There are reports that Vladimir also sent ambassadors to Rome. (shrink)

Clinical diagnostic medicine is an experimental science based on observation, hypothesis making, and testing. It is an use dynamic process that involves observation and summary, diagnostic conjectures, testing, review, observation and summary, new or revised conjectures, i.e. it is an iterative process. It can then be said that diagnostic hypotheses are also ‘observation-laden’. My aim is to enlarge on the strategies of medical diagnosis as these are meshed in training and clinical experience—that is, to describe the patterns of reasoning used (...) by experienced clinicians under different diagnostic circumstances and how these patterns of inquiry allow further insight into the evaluation and treatment of patients. I do not aim to present a theory and illustrate it with examples; I wish rather am to let a realistic example, similar to actual clinical scenarios, direct the exposition. To this end, I introduce an account of medical diagnosis—briefly comparing and contrasting it to other accounts—in order to focus on discussing the process of diagnosis through a detailed clinical case. (shrink)

Contemporary privacy theories and European discussions about data protection employ the notion of ‘personal information’ to designate their areas of concern. The notion of personal information is demarcated from non-personal information—or just information—indicating that we are dealing with a specific kind of information. However, within privacy scholarship the notion of personal information appears undertheorized, rendering the concept somewhat unclear. We argue that in an age of datafication, protection of personal information and privacy is crucial, making the understanding of what is (...) meant by ‘personal information’ more important than ever. To contribute to this aim, we analyse the conception of personal information and its nature, including the distinction between personal and non-personal information from a philosophy of language perspective. Through analyses of aboutness and relative aboutness we point to challenges related to the demarcation between personal and non-personal information, which may in practice lead to all information being personal. (shrink)

E. H. Gombrich’s bestselling history of the world for young readers tells the story of mankind from the Stone Age to the atomic bomb, focusing not on small detail but on the sweep of human experience, the extent of human achievement, and the depth of its frailty. The product of a generous and humane sensibility, this timeless account makes intelligible the full span of human history. In forty concise chapters, Gombrich tells the story of man from the stone age to (...) the atomic bomb. In between emerges a colorful picture of wars and conquests, grand works of art, and the spread and limitations of science. This is a text dominated not by dates and facts, but by the sweep of mankind’s experience across the centuries, a guide to humanity’s achievements and an acute witness to its frailties. (shrink)

Context: Phenomenology and the enactive approach pose a unique challenge to dream research: during sleep one seems to be relatively disconnected from both world and body. Movement and perception, prerequisites for sensorimotor subjectivity, are restricted; the dreamer’s experience is turned inwards. In cognitive neurosciences, on the other hand, the generally accepted approach holds that dream formation is a direct result of neural activations in the absence of perception, and dreaming is often equated with “delusions.” Problem: Can enactivism and phenomenology account (...) for the variety of dream experiences? What kinds of experiential and empirical approaches are required in order to probe into dreaming subjectivity? Investigating qualities of perception, sensation, and embodiment in dreams, as well as the relationship between the dream-world and waking-world requires a step away from a delusional or altered-state framework of dream formation and a step toward an enactive integrative approach. Method: In this article, we will focus on the “depth” of dream experiences, i.e., what is possible in the dream state. Our article is divided into two parts: a theoretical framework for approaching dreaming from an enactive cognition standpoint; and discussion of the role and strategies for experimentation on dreaming. Based on phenomenology and theories of enactivism, we will argue for the primacy of subjectivity and imagination in the formation of lived experience. Results: We propose that neurophenomenology of dreaming is a nascent discipline that requires rethinking the relative role of third-, first- and second-person methodologies, and that a paradigm shift is required in order to investigate dreaming as a phenomenon on a continuum of conscious phenomena as opposed to a break from or an alteration of consciousness. Implications: Dream science, as part of the larger enterprise of consciousness and subjectivity studies, can be included in the enactive framework. This implies that dream experiences are neither passively lived nor functionally disconnected from dreamers’ world and body. We propose the basis and some concrete strategies for an empirical enactive neurophenomenology of dreaming. We conclude that investigating dream experiences can illuminate qualities of subjective perception and relation to the world, and thus challenge the traditional subject-object juxtaposition. Constructivist content: This article argues for an interdisciplinary enactive cognitive science approach to dream studies. (shrink)

This paper assesses several prominent recent attacks on the view that epistemic justification is conceptually prior to knowledge. I argue that this view—call it the Received View (RV)—emerges from these attacks unscathed. I start with Timothy Williamson’s two strongest arguments for the claim that all evidence is knowledge (E>K), which impugns RV when combined with the claim that justification depends on evidence. One of Williamson’s arguments assumes a false epistemic closure principle; the other misses some alternative (to E>K) explanations of (...) a putative fact about the evidence a particular subject has. Next, I neutralize each of Jonathan Sutton’s three recent arguments to the conclusion that any justified belief constitutes knowledge. Finally, I consider a recent analysis of justification due to Alexander Bird, according to which justified belief is possible knowledge. I argue that Bird’s analysis delivers neither a sufficient nor (more importantly) a necessary condition for justification. [Word count: 149]. (shrink)

It is a thankless task to have to reply to Professor Murray Krieger’s “Retrospective.” Qui s’excuse, s’accuse, and since I cannot ask my readers to embark on their own retrospective of my writings and test them for consistency, I have little chance of restoring my reputation in their eyes. Hence I would have been happier to leave Professor Krieger to his agonizing, if he did not present himself the “spokesman” for a significant body of theorists who appear to have acclaimed (...) my book on Art and Illusion without ever having read it. The followers of this school of criticism—of which Professor Krieger is a prominent member—had apparently convinced themselves that the book lent support to an aesthetics in which the notions of reality and of nature had no place. They thought that I had subverted the old idea of mimesis and that all that remained were different systems of conventional signs which were made to stand for an unknowable reality. True, professor Krieger admits that I never endorsed such an interpretation of my views, and he even concedes that there are passages in Art and Illusion which contradict such an out-and-out relativism, but he wants to convince his readers that these contradictions lead precisely to the ambiguities he now proposes to analyse.If he were right that the book encourages such a misreading, all I could do would be to express my regrets for having failed to make myself sufficiently clear. Luckily I can draw comfort from the fact that unlike these literary critics, the leading archaeologist of this country, Professor Stuart Piggott, had no difficulty at all in discerning my meaning and profiting from my arguments. In his Walter Neurath Memorial Lecture of 1978, entitled Antiquity Depicted: Aspects of Archaeological Illustration, the author did me the honour of taking a statement from my book as his starting point. It is the passage at the end of part I in which I recapitulate the content of the first two chapters:What matters to us is that the correct portrait, like the useful map, is an end product on a long road through schema and correction. It is not a faithful record of a visual experience but the faithful construction of a relational mode.Neither the subjectivity of vision nor the sway of conventions need lead us to deny that such a model can be constructed to any required degree of accuracy. What is decisive here is clearly the word “required.” The form of a representation cannot be divorced from its purpose and the requirements of the society in which the given visual language gains currency.1 1. E. H. Gombrich, Art and Illusion: A Study in the Psychology of Pictorial Representation, A. W. Mellon Lectures in the Fine Arts, 1956 , p. 90. E. H. Gombrich was director of the Warburg Institute and Professor of the History of the Classical Tradition at the University of London from 1959 to 1976. His many influential works include The Story of Art, Art and Illusion, Meditations on a Hobby Horse, The Sense of Order, Ideals and Idols, The Image and the Eye, and, most recently, Tributes. His previous contributions to Critical Inquiry include “The Museum: Past, Present and Future and “Standards of Truth: The Arrested Image and the Moving Eye”. (shrink)