Mark Evan Bonds’ recent book, Absolute Music, deepens considerably the historical context within which Eduard Hanslick’s famous treatise on musical beauty can be read. This paper argues that, with the aid of this expanded context, we can understand Hanslick’s treatise to have provided contemporary and subsequent audiences with a kind of meta-programme for listening to symphonic and other non-texted music. That is to say, Hanslick’s text arguably informed and directed the way audiences came to listen to instrumental music by furnishing (...) them with imaginative constructs which could then be applied to the practice of musical listening. In much the same way as the texts which supply the poetic scenarios of so-called programme music, Hanslick’s ‘meta-programme’ became indispensable to an expanding culture of musical listening in the second half of the 19th century and beyond beyond. My claim thus contradicts the well-known formalist tenets of Hanslick’s musical aesthetics. (shrink)

Recently, cognitivist accounts about art have come under pressure to provide stronger arguments for the view that artworks can yield genuine insight and understanding. In Gregory Currie’s Imagining and Knowing: Learning from Fiction, for example, a convincing case is laid out to the effect that any knowledge gained from engaging with art must “be judged by the very standards that are used in assessing the claim of science to do the same” (Currie 2020: 8) if indeed it is to count (...) as knowledge. Cognitivists must thus rally to provide sturdier grounds for their view. The revived interest in this philosophical discussion targets not only the concept of knowledge at the heart of cognitivist and anti-cognitivist debate, but also highlights a more specific question about how, exactly, some artworks can (arguably) afford cognitive import and change how we think about the world, ourselves and the many events, persons and situations we encounter. This paper seeks to explore some of the ways in which art is capable of altering our epistemic perspectives in ways that might count as knowledge despite circumventing some standards of evidential requirement. In so doing we will contrast two alternative conceptions of how we stand to learn from art. Whereas the former is modelled on the idea that knowledge is something that can be “extracted” from our experience of particular works of art, the latter relies on a notion of such understanding as primarily borne out of a different kind of engagement with art. We shall call this the subtractive conception and cumulative conception respectively. The cumulative conception, we shall argue, better explains why at least some insights and instances of knowledge gained from art seem to elude the evidential standards called for by sceptics of cognitivism. (shrink)

Of the many difficult questions that populate the rather treacherous terrain of the philosophy of music, the one that perplexes and interests me the most often crops up in various guises in the myriad books of‘ Quotations for music lovers’ and such like. The following version may be said to capture its fundamental idea. Given that music doesn’t seem in any obvious sense to be about anything precisely, why do we seem to think that it conveys so much so strongly?

This paper provides a reading of the opera criticism of Bernard Williams in the light of his philosophical writings. Beginning with the observations that his philosophical writing lacks engagement with musical and aesthetic issues, and his operatic writing appears to present no particular philosophy of the subject, I try to draw together certain themes by mapping Williams's operatic concerns onto his philosophical project more generally. I argue that the 'excessive' nature of the artform—the idea that opera tends to exceed its (...) musico-dramatic functions—was of particular interest to Williams, partly because it resonated with his dislike of easy theoretical solutions to thorny practical issues. More specifically, Mozart's Cosi fan tutte is related, via the way the way its emotional register exceeds its dramatic context, to the issues examined by Williams in his work on moral luck. Similarly, I discuss the way Williams's essay on Debussy's Pelléas et Mélisande seems to hint at an account of the emotions which is otherwise missing from Williams's oeuvre. (shrink)

The thesis analyses the relation between Rousseau’s musical writings and elements of his moral, social and linguistic philosophy. In particular, I am concerned to demonstrate: (i.) how the core of Rousseau’s theory of musical imitation is grounded in the same analysis of the nature of man which governs his moral and social philosophy; (ii.) how this grounding does not extend to the stylistic prescriptions the justification of which Rousseau intended his musical writings to offer. The central argument draws on Rousseau’s (...) analysis of the origin of man as distinctively human. This origin extends to the awareness of moral and aesthetic value, and to communication in speech and song. Rousseau’s moral analyses of social and political life usually take the form of relating contemporary practice to the original structure in which man’s awareness of his own good is commensurate with that of the good of others. The analysis of music follows a similar model: music is to be considered good in so far as it replicates, or faithfully reflects, the original model of communication. The value of music is thereby understood to extend to moral as well as aesthetic goodness. Given the subtlety of Rousseau’s understanding of the ‘origin’, I argue that this analysis of music’s aesthetic value is powerful and far‐ reaching in its relevance for contemporary musical aesthetics. However, I also argue that while the analysis in general is good in this way, it does not entail the specific kind of musical‐stylistic preferences which Rousseau sought to use it to advance. (shrink)

In 1907, Alfred Stieglitz took what was to become one of his signature photographs, The Steerage. Stieglitz stood at the rear of the ocean liner Kaiser Wilhelm II and photographed the decks, first-class passengers above and steerage passengers below, carefully exposing the film to their reflected light. Later, in the darkroom, Stieglitz developed this film and made a number of prints from the resulting negative. The photograph is a familiar one, an enduring piece of social commentary, but what exactly is (...) The Steerage which Stieglitz has given us? It is clearer what The Steerage is not. It is distinct from each of its prints and from its negative. These may be dusty or torn without The Steerage being so, and any one of these could be destroyed without thereby destroying The Steerage itself. Nor is The Steerage the set of its prints. The set could not have had different members, while The Steerage could have had more, fewer, or different prints.1 Similar reasoning rules out the mereological sum of parts of its actual prints, for The Steerage’s prints might not have comprised just these parts. We are left with a puzzle, what sort of thing is a photograph? This puzzle is not unique to photography. Similar reasoning generates an analogous puzzle for any repeatable work of art. Novels, poems, plays, symphonies, songs, and the rest share an ontological predicament and create a 1 general puzzle concerning the ontological status of repeatable works of art. It is widely held that the puzzle has an equally general solution, one which I will argue fails for systematic reasons. Although my target here is the supposed solution to the general problem, photography will remain the central case under scrutiny. I offer it as a model for our thinking about the wider class in order to reap the benefits of thinking in terms of concrete cases. Although this risks a trade-off with the generality of my conclusions—there are important differences of detail between the cases—I hope it is clear that the considerations I appeal to in photography are not idiosyncratic but shared by the wider class.. (shrink)

Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here.

Abstract Do the central aims of epistemology, like those of moral philosophy, require that we designate some important place for those concepts located between the thin-normative and the non-normative? Put another way, does epistemology need "thick" evaluative concepts and with what do they contrast? There are inveterate traditions in analytic epistemology which, having legitimized a certain way of viewing the nature and scope of epistemology's subject matter, give this question a negative verdict; further, they have carried with them a tacit (...) commitment to what we argue to be an epistemic analogue of the reductionistic centralist thesis which Bernard Williams, in our view, successfully repudiates in ethics. In this essay, we challenge the epistemic analogue of the traditional but mistaken thesis. In offering an alternative to it which provides a comfortable home for the epistemic normativity which attends thick evaluative concepts, we align ourselves with what has been recently called the Value Turn in epistemology. From this perspective, we defend that, contrary to tradition, as influenced by centralist assumptions, epistemology does need thick evaluative concepts. Further, the sort of theories that will be able to give thick evaluative concepts an irreducible role in both belief and agent evaluation are adequately social epistemologies. What loosely refer to as second-wave of virtue epistemology is the widespread interest to provide a comfortable home for the role of thick normativity, as it is connected both with epistemic evaluation, and guidance. We recognize that, in breaking from centralism, there is a worry that a resulting anti-centralist theory will be reductionistic in the other direction, making the thick primary. We contend however that second-wave virtue epistemologies take different sources of social and epistemic value into account; they seek the 'right thickness' to ride with conception of epistemology and a field which due in part to virtue theory's resurgence, is today normative, diverse and expansive than was the traditional set of problems from which it emerged. (shrink)

While all agree that score compliance in performance is valuable, the source of this value is unclear. Questions about what authenticity requires crowd out questions about our reasons to be compliant in the first place, perhaps because they seem trivial or uninteresting. I argue that such reasons cannot be understood as ordinary aesthetic, instrumental, epistemic, or moral reasons. Instead, we treat considerations of score compliance as having a kind of final value, one which requires further explanation. Taking as a model (...) the Humean account of fidelity as an artificial virtue, I sketch a practice-theoretic account of the nature and source of such reasons, one on which we can say that they are, after all, aesthetic, but only indirectly so. (shrink)

Journal of Political Philosophy, EarlyView.

Heinrich Rickert was one of the leading neo-Kantian philosophers in Germany and a crucial figure in the discussions of the foundations of the social sciences in the first quarter of the twentieth century. His views were extremely influential, most significantly on Max Weber. The Limits of Concept Formation in Natural Science is Rickert's most important work, and it is here translated into English for the first time. It presents his systematic theory of knowledge and philosophy of science, and deals particularly (...) with historical knowledge and the problem of demarcating the natural from the human sciences. The theory Rickert develops is carefully argued and of great intrinsic interest. It departs from both positivism and neo-Hegelian idealism and is worked out by contrast to the views of others, particularly Dilthey and the early phenomenologists. (shrink)

A New Route to the Necessity of Origin’ (2004, henceforth ‘NR’), we offered an argument for the thesis that there are necessary connections between material things and their material origins. Much of the philosophical interest lay in our claim that the argument did not depend on so-called sufficiency principles for crossworld identity. It has been the verdict of much recent work on the necessity of origin that valid arguments for the thesis require some such sufficiency principle as a premise but (...) that such principles are deeply problematic.1 Finding an argument free of such principles would advance both our understanding and the plausibility of that thesis. These claims are now the subject of a pair of insightful critiques by Teresa Robertson and Graeme Forbes (2006, henceforth ‘RF’) and by Ross Cameron and Sonia Roca (2006, henceforth ‘CR’), and we welcome the opportunity to clarify and improve our account of the matter. (shrink)

The return of Hephaistos to Olympos, as a myth, concerns the establishment of a balance of power among the Olympian gods. Many visual representations of the myth in Archaic and Classical Greek art give visible form to the same theme, but they do so in a manner entirely distinct from the manner in which it is expressed in literary narratives of the tale. In this paper, I argue that vase-painters incorporated elements of Dionysiac processional ritual into representations of the return (...) of Hephaistos in order to articulate visually the principal theme of the myth. The vase-painters structured the myth along the lines of epiphanic processions in which Dionysos was escorted into the city of Athens. Like Dionysiac epiphanic processions, the procession of Hephaistos, Dionysos and the wine-god's followers is distinguished visually by drunkenness, ostentatious display of the phallus and obscene or insulting behaviour. To judge from the aetiological myths associated with them, the epiphanic processions symbolized the triumph of Dionysos over, and his belated acceptance by, those who denied his status as a god. By structuring the visual representations of the return of Hephaistos along the lines of such Dionysiac processions, artists conveyed visually the idea that the myth al so concerned the triumph of a god over those who rejected him, and his acceptance among the Olympians. It is not necessary to assume that the vase-painters relied on a detailed poetic account of the myth to create their representations of it, because they employed elements of religious spectacle, an inherently visual phenomenon, to convey the essence of the story. (shrink)

The appealing idea that knowledge is best understood as a kind of achievement faces significant criticisms, among them Matthew Chrisman’s charge that the whole project rests on a kind of ontological category mistake. Chrisman argues that while knowledge and belief are states, the kind of normativity found in, for example, Sosa’s famous ‘Triple-A’ structure of assessment is only applicable to performances, end-directed events that unfold over time, and never to states. What is overlooked, both by Chrisman and those he criticizes, (...) is a whole range of projects, those like friendship, health, marriage, and sobriety, where the end is not distinct from our pursuit of it. I suggest that such ‘inner projects’ are in fact stative achievements and thus provide a different sort of model for thinking about knowledge as an achievement. Reconceiving the project along these lines also helps to solve another outstanding problem, the charge that being an achievement is not necessary for knowledge because some knowledge, especially testimonial knowledge, is come by with little or no effort. (shrink)

If description of mental processes and evaluation of agents and their beliefs are rightly to be considered as complementary concerns on any plausible construal of the epistemological project, then this relationship cries out for explanation. For the complementarity of these concerns is hardly straightforward: One cannot epistemically evaluate a belief without knowing how it was formed, a causal or a scientific question; on the other hand, epistemic norms are and must be used to evaluate our scientific beliefs and theories, and (...) apparently then require a basis at least partly independent of scientific matters of fact. (shrink)

The explanation of the suppression of Modus Ponens inferences within the framework of linguistic pragmatics and of plausible reasoning (i.e., deduction from uncertain premises) is defended. First, this approach is expounded, and then it is shown that the results of the first experiment of Byrne, Espino, and Santamar a (1999) support the uncertainty explanation but fail to support their counterexample explanation. Second, two experiments are presented. In the first one, aimed to refute one objection regarding the conclusions observed, the additional (...) conditional premise ( if N, C ) was replaced with a statement of uncertainty ( it is not certain that N ); the answers produced by the participants remained qualitatively and quantitatively similar in both conditions. In the second experiment, a fine-grained analysis of the responses to and justifications for an evaluation task was performed. The results of both experiments strongly supported the uncertainty explanation. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Pierre Guy Mubambar réévalue ce que la tradition qualifie d'irrationnel dans la philosophie de David Hume. Il s'appuie sur le rôle que joue, dans cette philosophie, le concept de probabilité. Dans cet ouvrage, il montre comment, du point de vue épistémologique et religieux, la probabilité permet à Hume de dissoudre la causalité et la croyance au miracle. Comment décider sans trop tergiverser? L'auteur ébauche une théorie de la décision raisonnable, dans laquelle il estime que les mesures prises par la raison (...) permettent la rectification des probabilités non philosophiques. Grâce aux probabilités philosophiques, ces mesures servent la transmutation des passions violentes en passions calmes. Ainsi, peut se construire, dans la philosophie humienne, un choix spécifique qui n'est complètement ni passionnel ni rationnel, mais naturellement et inclusivement raisonnable. (shrink)

When a new piece of information contradicts a currently held belief, one has to modify the set of beliefs in order to restore its consistency. In the case where it is necessary to give up a belief, some of them are less likely to be abandoned than others. The concept of epistemic entrenchment is used by some AI approaches to explain this fact based on formal properties of the belief set (e.g., transitivity). Two experiments were designed to test the hypothesis (...) that contrary to such views, (i) belief is naturally represented by degrees rather than in an all-or-nothing manner, (ii) entrenchment is primarily a matter of content and not only a matter of form, and (iii) consequently prior degree of belief is a powerful factor of change. The two experiments used Elio and Pelletier's (1997) paradigm in which participants were presented with full simple deductive arguments whose conclusion was denied, following which they were asked to decide which premise to revise. (shrink)

Evidentialism as its leading proponents describe it has two distinct senses, these being evidentialism as a conceptual analysis of epistemic justification, and as a prescriptive ethics of belief—an account of what one ‘ought to believe’ under different epistemic circumstances. These two senses of evidentialism are related, but in the work of leading evidentialist philosophers, in ways that I think are deeply problematic. Although focusing on Richard Feldman’s ethics of belief, this chapter is critical of evidentialism in both senses. However, I (...) share with authors like Feldman and Earl Conee, that epistemology has important prescriptive functions, and that a sound, civic ethics of belief is of more than merely philosophic importance. One reason why an ethics of belief might be important to problems of practice is the need we have for tools to more effectively mediate the renewed round of ‘culture wars’ we are experiencing in Anglo-American cultures. I mean especially that grand cultural clash between science and religion, reason and faith, secularist atheism and religious fundamentalism, etc. Let us start with the genealogical question of why there is such a grand cultural debate in the first place, and why the debate especially as played out in public and popular forums and even in the courtrooms seems so volatile and so often to confusedly drag everything—beliefs, values, passions, etc., with it. These are questions that I think Sigmund Freud’s classic Civilization and its Discontents can help us understand. Freud was a major voice in criticism of the stern and often hypocritical Victorian morality, a voice pointing out the price of its sometimes high-handed, guiltinducing curtailments of the satisfactions sought by the individual. But for Freud while there are real differences in the moral demands that different societies or traditions place upon people, there is something inevitable about the conflict itself, for “replacement of the power of the individual by the power of a community constitutes the decisive step of civilization... (shrink)

While both economic and social considerations of fairness and equity play an important role in financial decision-making, it is not clear which of these two motives is more primal and immediate and which one is secondary and slow. Here we used variants of the ultimatum game to examine this question. Experiment 1 shows that acceptance rate of unfair offers increases when participants are asked to base their choice on their gut-feelings, as compared to when they thoroughly consider the available information. (...) In line with these results, Experiments 2 and 3 provide process evidence that individuals prefer to first examine economic information about their own utility rather than social information about equity and fairness, even at the price of foregoing such social information. Our results suggest that people are more economically rational at the core, but social considerations (e.g., inequality aversion) require deliberation, which under certain conditions override their self-interested impulses. (shrink)

Two notions from philosophical logic and linguistics are brought together and applied to the psychological study of defeasible conditional reasoning. The distinction between disabling conditions and alternative causes is shown to be a special case of Pollock’s (1987) distinction between ‘rebutting’ and ‘undercutting’ defeaters. ‘Inferential’ conditionals are shown to come in two varieties, one that is sensitive to rebutters, the other to undercutters. It is thus predicted and demonstrated in two experiments that the type of inferential conditional used as the (...) major premise of conditional arguments can reverse the heretofore classic, distinctive effects of defeaters. (shrink)

This essay forms the introduction for Hocquenghem’s L’après-mai des faunes. Published in January 1974, the essay reflects critically on the legacy of the events of May, 1968, and the abandonment of so-called revolutionary thought soon after. Hocquenghem calls on the left no longer to form itself simply in reaction to the bourgeois class and its values, but to find ways for turning (away) through “volutions” of action from the apathy of leftism as he has found it. Critiquing the air of (...) crisis meant to stop thinking as such, Hocquenghem “Volutions” reads as current today as when it was written. (shrink)

A review of Ernest Sosa’s book Apt Belief and Reflective Knowledge. While I think Sosa is quite right that knowledge lies on a spectrum, and that its higher but not its lower reaches require of knowers, when challenged, a strong degree of explanatory coherence (ability to understand and discursively defend the basis of their beliefs), I also point out problems with certain aspects of his account.

The critical focus of this paper is on a claim made explicitly by Gilbert Harman and accepted implicitly by numerous others, the claim that naturalism supports concurrent defense of scientific objectivism and moral relativism. I challenge the assumptions of Harman's ‘argument from naturalism' used to support this combination of positions, utilizing. Hilary Putnam’s ‘companions in guilt’ argument in order to counter it. The paper concludes that while domain-specific anti-realism is often warranted, Harman’s own views about the objectivity of facts and (...) the subjectivity of values are better seen as stemming from scientistic ideals of knowledge than from dictates of naturalism. Scientists qua scientists make value judgments, and setting aside scientistic assumptions and unrealizable conceptions of scientific objectivity should lead us to more symmetrical metaphilosophical conception of epistemic and ethical normativity than that which underlies Harman's account. (shrink)

The cover image is based on the Original Article Whistleblowing and power: A network perspective by R. Guy Thomas, https://doi.org/10.1111/beer.12290. image.

Adversaries of Moral Luck (AMLs) are at pains to explain why wrongdoers are liable to bear burdens (punishment, compensation etc.) which are related to the harm they cause, because the consequences of what we do are a matter of luck. One attempt to solve this problem suggests that wrongdoers who cause more harm are liable to bear a greater burden not because they are more blameworthy but rather because they get the short straw in a liability lottery (represented by the (...) apparently indeterminate causal process). In this paper I argue that this attempt fails on several grounds. Apart from the fact that it is hard to see how the implementation of liability lotteries can be motivated and the fact that such scheme presupposes a political order (whereas the notion of liability does not seem to presuppose one), detaching liability from the outcomes of a culpable action undermines whichever justifications there were for imposing liability in the first place. Moreover, relying on the determination of the causal process as a good indication of the wrongdoer’s degree of culpability is mistaken, because the luck brought about through the causal process is not necessarily the only element involved in cases of harmful conduct which lies beyond the wrongdoers’ control. (shrink)

In this paper, I engage with the radical critique of human rights moralism. Radical critics argue that: human rights are myopic ; human rights are demobilising ; human rights are paternalistic ; and human rights are monopolistic. I argue that critics offer important insights into the limits of human rights as a language of social justice. However, critics err insofar as they imply that human rights are irredeemably corrupted and they under-estimate the subversive potential of the moral ideas that underpin (...) the discourse. Building on the idea of human rights as claims, I set out the politicising features of human rights as they are deployed in a practical context of disagreement, conflict, and imbalances of power. I illustrate this discussion with reference to the contemporary struggles of irregular migrants. (shrink)

I take up the four issues considered by Johnson -Laird, Byrne and Girotto in their reply to Politzer. Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one and can be attenuated about the second one. However, I maintain and refine my criticisms on the last two, backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals.

The centennial of Dewey & Tuft’s Ethics (1908) provides a timely opportunity to reflect both on Dewey’s intellectual debt to utilitarian thought, and on his critique of it. In this paper I examine Dewey’s assessment of utilitarianism, but also his developing view of the good (ends; consequences), the right (rules; obligations) and the virtuous (approbations; standards) as “three independent factors in morals.” This doctrine (found most clearly in the 2nd edition of 1932) as I argue in the last sections, has (...) significant forward-going implications for debates in ethics, insofar as it functions to deflate debates among ethicists that turns on claims about the conceptual primacy of any one of these three ethical concepts over the other two. To find what “permanent value each group contributes to the clarification and direction of reflective morality” was the task Dewey set for himself. But to carry that project through demands showing also why the application of considerations of ends, rules, and virtues to problems of practice is not quite as many self-described utilitarians, deontologists, and virtue ethicists conceive it. (shrink)

Peter Lombard’s Sentences, book I, distinction 8 offers the starting point for the late medieval and Renaissance debate on the question of whether the soul is as a whole present in the whole body and in each of its parts. This paper summarizes the prehistory of Lombard’s theory that the soul is everywhere in the entire body, and analyzes the positions of two “Platonic” scholastics, the late-thirteenth-century Dominican John Quidort and the early-sixteenth-century Augustinian Giles of Viterbo.

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expres- sion (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) We hypothesized that the quantified sen- tences have an abstract underlying representation common to the formulas and their associated sets of dia- grams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people’s as- sessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne’s (1817) circles or an adaptation of Leibniz (1903/ 1988) lines as external representations and show them to support the predictions. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)