The paper defends a view of structural realism similar to that of French and Ladyman, although it differs from theirs in an important respect: I do not take indistinguishabiity of particles in quantum mechanics to have the significance they think it has. It also differs from Cao's view of structural realism, criticized in my "Critical Notice: Cao's `The Conceptual Development of 20th Century Field Theories".

At any given time, a subject has a multiplicity of conscious experiences. A subject might simultaneously have visual experiences of a red book and a green tree, auditory experiences of birds singing, bodily sensations of a faint hunger and a sharp pain in the shoulder, the emotional experience of a certain melancholy, while having a stream of conscious thoughts about the nature of reality. These experiences are distinct from each other: a subject could experience the red book without the singing (...) birds, and could experience the singing birds without the red book. But at the same time, the experiences seem to be tied together in a deep way. They seem to be unified, by being aspects of a single encompassing state of consciousness. (shrink)

This work presents a historically informed, systematic exposition of the Christology of the first seven Ecumenical Councils of undivided Christendom, from the First Council of Nicaea in 325 AD to the Second Council of Nicaea in 787 AD. Assuming the truth of Conciliar Christology for the sake of argument, Timothy Pawl considers whether there are good philosophical arguments that show a contradiction or incoherence in that doctrine. He presents the definitions of important terms in the debate and a helpful (...) metaphysics for understanding the incarnation. -/- In Defense of Conciliar Christology discusses three types of philosophical objections to Conciliar Christology. Firstly, it highlights the fundamental philosophical problem facing Christology: how can one thing be both God and man, when anything deserving to be called "God" must have certain attributes, and yet it seems that nothing that can aptly be called "man" can have those same attributes? It then considers the argument that if the Second Person of the Holy Trinity were immutable or atemporal, as Conciliar Christology requires, then that Person could not become anything, and thus could not become man. Finally, Pawl addresses the objection that if there is a single Christ then there is a single nature or will in Christ. However, if that conditional is true, then Conciliar Christology is false, since it affirms the antecedent of the conditional to be true, but denies the truth of the consequent. Pawl defends Conciliar Christology against these charges, arguing that all three philosophical objections fail to show Conciliar Christology inconsistent or incoherent. (shrink)

A variety of ideas arising in decoherence theory, and in the ongoing debate over Everett's relative-state theory, can be linked to issues in relativity theory and the philosophy of time, specifically the relational theory of tense and of identity over time. These have been systematically presented in companion papers (Saunders 1995; 1996a); in what follows we shall consider the same circle of ideas, but specifically in relation to the interpretation of probability, and its identification with relations in the Hilbert (...) Space norm. The familiar objection that Everett's approach yields probabilities different from quantum mechanics is easily dealt with. The more fundamental question is how to interpret these probabilities consistent with the relational theory of change, and the relational theory of identity over time. I shall show that the relational theory needs nothing more than the physical, minimal criterion of identity as defined by Everett's theory, and that this can be transparently interpreted in terms of the ordinary notion of the chance occurrence of an event, as witnessed in the present. It is in this sense that the theory has empirical content. (shrink)

Disorders of volition are often accompanied by, and may even be caused by, disruptions in the phenomenology of agency. Yet the phenomenology of agency is at present little explored. In this paper we attempt to describe the experience of normal agency, in order to uncover its representational content.

This article examines the relationship between Jeremy Waldron’s supersession thesis and compensation. Recently, Waldron has argued that claims for material compensation for the original injustice cannot be superseded. He limits supersession to issues of restitution. Waldron’s supersession thesis is frequently cited by opponents of claims based on historical injustice, so his view of compensation warrants close examination. In our article, we explain the details of Waldron’s ‘simple model’ of compensation, offer an internal critique of it, and try to sympathetically reconstruct (...) it. We contend that a crucial claim about this model does not work; his model would result in many more backward-looking compensatory claims than he realizes. Waldron’s allowing for material compensation claims from historical injustice is in tension with, or incompatible with, his long-expressed view that the spirit of the supersession thesis is that justice should be forward-looking and look to present-day costs. We have argued elsewhere that the abstract possibility that restitution claims may be superseded due to changing circumstances (what we call the ‘supersession thesis proper’) is separable from the question of whether justice has a forward-looking or backward-looking orientation. We argue here that Waldron’s model of compensation can best be made sense of through our distinction of ‘full supersession’ and ‘partial supersession.’ This allows us to show that Waldron’s model relies on a more strongly backward-looking orientation than he seems to endorse in his earlier works on restitution and his most recent article discussing compensation. We conclude by offering external criticisms of Waldron’s model of compensation. (shrink)

This is a self-contained introduction to the Everett interpretation of quantum mechanics. It is the introductory chapter of Many Worlds? Everett, quantum theory, and reality, S. Saunders, J. Barrett, A. Kent, and D. Wallace, Oxford University Press.

In this paper we defend the doxastic conception of delusions against the metacognitive account developed by Greg Currie and collaborators. According to the metacognitive model, delusions are imaginings that are misidentified by their subjects as beliefs: the Capgras patient, for instance, does not believe that his wife has been replaced by a robot, instead, he merely imagines that she has, and mistakes this imagining for a belief. We argue that the metacognitive account is untenable, and that the traditional conception of (...) delusions as beliefs should be retained. (shrink)

This article adapts John Rawls’s writings, arguing that past injustice can change what we ought to publicly affirm as the standard of justice today. My approach differs from forward-looking approaches based on alleviating prospective disadvantage and backward-looking historical entitlement approaches. In different contexts, Rawls’s own concern for the ‘social bases of self-respect’ and equal citizenship may require public endorsement of different principles or specifications of the standard of justice. Rawls’s difference principle focuses on the least advantaged socioeconomic group. I argue (...) that a historicized difference principle considers the relative standing of racial, gender, and other historically stigmatized groups; provides their members assurance by weakening incentives to manipulate justice to another group’s advantage; and may result in policies resembling reparations, though justified by forward-looking considerations of self-respect and public assurance. I then examine how disrespectful justifications were historically used to forcibly include indigenous peoples as citizens. While Rawls thinks providing citizens one package of basic liberties signals respect, indigenous self-government could better support self-respect. I invoke Rawlsian international justice, which calls for mutual respect between peoples. Indigenous peoples’ status should reflect their past and persisting peoplehood, providing assurance by weakening incentives to unjustly transform international into domestic contexts. (shrink)

1 Department of Philosophy, University of Dundee, Dundee DD1 4HN. [email protected].

We discuss three varieties of affective dynamics. In each case, we suggest how these affective dynamics should be operationalized and measured in daily life using time-intensive methods, like ecological momentary assessment or ambulatory assessment, and recommend time-sensitive analyses that take into account not only the variability but also the temporal dependency of reports. Studies that explore how these affective dynamics are associated with psychological disorders and symptoms are reviewed, and we emphasize that these affective processes are within a nexus of (...) other components of emotion regulation. (shrink)

This paper argues that there are important irrational elements to love. In the philosophical literature, we typically find that love is either thought of as rational or arational and that any irrational elements are thought to be defective, or extraneous to love itself. We argue, on the contrary, that irrationality is in part connected to what we find valuable about love. -/- We focus on 3 basic elements of love: -/- 1) Whom you love 2) How much you love them (...) 3) How much of a role love plays in your life -/- And in each case, we argue that love can be irrational and valuable. (shrink)

Nietzsche consistently valorizes artistic falsehoods. On standard interpretations, this is because art provides deceptive yet salutary fictions that help us affirm life. This reading conflicts, however, with Nietzsche’s insistence that life-affirmation requires untrammeled honesty. I present an alternative interpretation which navigates the interpretive impasse. With special attention to the influence of Friedrich Schiller, the paper argues for three claims: (1) Nietzsche does not hold that art is false because it “beautifies,” but because it produces mere semblances of, its objects; (2) (...) these semblances are essentially non-deceptive; (3) he values artistic illusions because they dispose us positively to illusion more generally. Such ‘evaluative reorientation,’ I argue, is not merely consistent with, but integral to, achieving Nietzsche’s ideal of honesty. (shrink)

Frege puzzles exploit cognitive differences between co-referential terms. Traditionally, they were handled by some version of Frege’s distinction between sense and reference, which avoided disruptive consequences for epistemology. However, the Fregean programme did not live up to its original promise, and was undermined by the development of theories of direct reference; for semantic purposes, its prospects now look dim. In particular, well-known analogues of Frege puzzles concern pairs of uncontentious synonyms; attempts to deal with them by distinguishing idiolects or postulating (...) ‘narrow contents’ or elaborate forms of context-sensitivity are inadequate or semantically implausible. Although ascriptions of knowledge, belief, and other attitudes are ubiquitous in epistemology, epistemologists have not properly come to terms with the surprising consequences of anti-Fregean semantic accounts of attitude ascriptions. In ‘A Puzzle about Belief ’, Saul Kripke shows that natural-seeming disquotational principles for ascribing belief lead to apparently unacceptable consequences, including outright contradictions, in problem cases. Such disquotation principles, I argue, are best regarded not as conceptual connections but just as heuristics in the psychological sense, quick and easy ways of assessing belief ascriptions, usually accurate under normal conditions but far from 100% reliable. I discuss similar heuristics for ascribing knowledge and other attitudes. That the principles have a merely heuristic status need not be pre-theoretically manifest to their users. This view vindicates Kripke’s conclusion that it would be wrong-headed to draw semantic conclusions from Frege puzzles. I discuss the epistemological consequences of an anti-Fregean approach to Frege puzzles, including for Kripke’s cases of the contingent a priori and the necessary a posteriori, but also for evidence, for epistemic modalities, and for epistemic and subjective conceptions of probability. Anna Mahtani’s recent identification of Frege puzzles for the ex ante Pareto Principle as used in welfare economics provides an interesting example. I suggest a model-building methodology as the most promising way of handling at least some of the difficulties. A final issue is the choice between different anti-Fregean approaches to semantics, from very coarse-grained intensional approaches on which sentences express functions from possible worlds to truth-values to more fine-grained hyperintensional approaches on which sentences express functions from possible or impossible worlds to truth-values or else Russellian structured propositions. Some of the hyperintensional theories violate semantic compositionality. More generally, since our attitude ascriptions rely on heuristics, they should be expected to exhibit some level of error; although hyperintensional approaches may be able slightly to reduce the level of postulated error, they do so at the cost of vastly increased theoretical complexity, and so have weak explanatory power. Methodologically, a simple intensional approach does better. (shrink)

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject.

According to the Fragmentation Analysis, epistemic akrasia is a state of conflict between beliefs formed by the linguistic and non-linguistic belief-formation systems, and epistemic akrasia is irrational because it is a state of conflict between beliefs so formed. I argue that there are cases of higher-order epistemic akrasia, where both beliefs are formed by the linguistic belief-formation system. Because the Fragmentation Analysis cannot accommodate this possibility, the Fragmentation Analysis is incorrect. I consider three objections to the possibility of higher-order epistemic (...) akrasia. Along the way, I offer a revision of the Fragmentation Analysis that can allow for the possibility of higher-order akrasia while avoiding the problems I point out for the original view. (shrink)

Kant limits cosmopolitan right to a universal right of hospitality, condemning European imperial practices towards indigenous peoples, while allowing a right to visit foreign countries for the purpose of offering to engage in commerce. I argue that attempts by contemporary theorists such as Jeremy Waldron to expand and update Kant’s juridical category of cosmopolitan right would blunt or erase Kant’s own anti-colonial doctrine. Waldron’s use of Kant’s category of cosmopolitan right to criticize contemporary identity politics relies on premises that upset (...) Kant’s balanced right to hospitality. An over-extensive right to visit can invoke “Kantian” principles that Kant himself could not have consistently held, without weakening his condemnation of European settlement. I construct an alternative spirit of cosmopolitan right more favorable to the contemporary claims of indigenous peoples. Kant’s analysis suggests there are circumstances when indigenous peoples may choose whether to engage in extensive cultural interaction, and reasonably refuse the risks of subjecting their claims to debate in democratic politics in a unitary public. Cosmopolitan right accorded respect to peoples; any “domestic” adaptation of cosmopolitan right should respect indigenous peoples as peoples, absent a serious public explanation by a democratic state for why it has now become appropriate to treat indigenous peoples merely as individual citizens. (shrink)

Divine Action and Modern Science considers the relationship between the natural sciences and the concept of God acting in the world. Nicholas Saunders examines the Biblical motivations for asserting a continuing notion of divine action and identifies several different theological approaches to the problem. He considers their theoretical relationships with the laws of nature, indeterminism, and probabilistic causation. His book then embarks on a radical critique of current attempts to reconcile special divine action with quantum theory, chaos theory and (...) quantum chaos. As well as considering the implications of these problems for common interpretations of divine action, Saunders also surveys and codifies the many different theological, philosophical and scientific responses to divine action. The conclusion reached is that we are still far from a satisfactory account of how God might act in a manner that is consonant with modern science despite the copious recent scholarship in this area. (shrink)

Timothy Chappell develops a picture of what philosophical ethics can be like, once set aside from conventional moral theory. His question is 'How are we to know what to do?', and the answer he defends is 'By developing our moral imaginations'--a key part of human excellence, which plays many roles in our practical and evaluative lives.

The growing diffusion of perspectivism within the debate on information system ontologies [ISOs] does not correspond to a thorough analysis of what perspectivism specifically consists of. This paper aims to fill this void. First, I show what supporting perspectivism in information system ontologies [PISO] means in terms of (minimal) claims and implications; then I argue that the definitions of ISO implicitly assume PISO’s (minimal) claims or, in other words, that ISOs presuppose and maintain PISO. Section 2 presents the main definitions (...) of ISO. Section 3 specifies what claims are common to all perspectivists in ISO. Sects. 4–7 analyze the implications of those claims. Section 8 explores the chance of multiple perspectivisms within ISOs’ domain. Finally, Sects. 9–10 assume that, if PISO’s (minimal) claims and (their) implications can be inferred from ISO’s definitions, then ISOs are perspectivist, or PISO’s minimal claims are assumptions underlying ISOs. (shrink)

This book is intended as a philosophical introduction to geo-ontologies, in response to their increasing diffusion within the contemporary debate, where philosophy plays a fundamental, though still unexplored, role. Accordingly, the first part offers a short overview of the ontological background of geo-ontologies, which comprehends computer science, philosophy and geography. The second part is devoted to describe the ontology of geography, to define notions such as geographical entities and boundaries, and to trace some philosophical tools useful for spatial representation. The (...) third part investigates the emerging of geo-ontologies from the spatial turn and is concerned with a taxonomy for geo-ontologies grounded on some fundamental geographical distinctions. Finally, the last part presents the emergence of Digital Humanities and the consequent proliferation of geographical projects focused on the ancient world, in particular Greek and Roman. (shrink)

Call a term ‘pseudo-singular’ if it is syntactically singular but semantically plural. ‘The pair who wrote Principia’ is a good example, standing as it does for the two individuals, Whitehead and Russell. In this journal (2021), Eric Snyder and Stewart Shapiro launched an attack on the idea, calling it ‘linguistically and logically untenable.’ In this reply we rebut every one of their criticisms.

Timothy Chappell’s new translation of the Theaetetus is presented here in short sections of text, each preceded by a summary of the argument and followed by his philosophical commentary on it. Introductory remarks discuss Plato and his works, his use of dialogue, the structure of the Theaetetus, and alternative interpretations of the work as a whole. A glossary and bibliography are provided.

Effective Altruism encourages affluent people to make significant donations to improve the wellbeing of the world’s poor, using quantified and observational methods to identify the most efficient charities. Critics argue that EA is inattentive to the systemic causes of poverty and underestimates the effectiveness of individual contributions to systemic change. EA claims to be open to systemic change but suggests that systemic critiques, such as the socialist critique of capitalism, are unhelpfully vague and serve primarily as hypocritical rationalizations of continued (...) affluence. I reformulate the systemic change objection, rebut the charges of vagueness and bad faith and argue that charity may not be worth doing at all from a purely altruistic perspective. In order to take systemic change seriously, EA must repudiate its narrowly empiricist approach, embrace holistic, interpretive social analysis and make inevitably controversial judgments about the complex dynamics of collective action. These kinds of evidence and judgment cannot be empirically verified but are essential to taking systemic change seriously. EA is thereby forced to sacrifice its a-political approach to altruism. I also highlight the importance of quotidian, extra-political contributions to perpetuating or changing harmful social practices. Radical efforts to resist, subvert and reconstruct harmful social practices, such as those involved in economic decision-making, could be just as effective and demanding as charity. But such efforts may be incompatible with extensive philanthropy, because they can require people to retain some level of affluence for strategic reasons but to repudiate both the acquisition of significant wealth and charity as is currently organized. The wealth and status of some critics of charity may indeed be incompatible with effectively contributing to social change, but the altruistic merits of charity are neither as obvious nor as easily demonstrated as EA believes. (shrink)

According to ontological perspectivism, there can be, in principle, multiple and alternative perspectives on the world that can be sliced, systematized, and conceptualized in different ways. Surely, such an ontological position has many categorial implications, which may vary depending on different disciplinary contexts. This paper explores parts of these implications in the realm of geography. In particular, it aims at discussing the ontological categories that one might use to describe the geographical world in an overarching perspective – that is, the (...) perspective that puts toether all the partial views coming from the different branches of the geographical investigation. We will see that if the overarching perspective is expected to include all the views on the geographical world, then such a perspective should be all-embracing in terms of contents and categories. This means that the overarching perspective might also comprehend inconsistencies that derive from how the various partial perspectives conceptualize differently the geographical world. (shrink)

First published Sat Apr 5, 2003; most recent substantive revision Wed Aug 22, 2018. -/- Samuel Clarke (1675–1729) was the most influential British philosopher in the generation between Locke and Berkeley. His philosophical interests were mostly in metaphysics, theology, and ethics.

It is not my claim that the ‘L¨ owenheim-Skolem paradox’ is an antinomy in formal logic; but I shall argue that it is an antinomy, or something close to it, in philosophy of language. Moreover, I shall argue that the resolution of the antinomy—the only resolution that I myself can see as making sense—has profound implications for the great metaphysical dispute about realism which has always been the central dispute in the philosophy of language.

Despite their recent development, geo-ontologies represent a complicated conundrum for the different experts involved in their design. Computer scientists use ontologies for describing the meaning of data and their semantics in order to make information resources built for humans understandable also for artificial agents. Geographers pursue conceptualizations that describe the domain of interest in a way that should be accessible, informative, and complete for their final recipients. In this context, philosophers are not required to sketch the historical background of ontology. (...) Rather, they should offer conceptual solutions for carving nature at the joints and choosing how best to categorize and classify the different entities belonging to the geographical domain in question. Accordingly, the aim of this paper is to combine assumptions and requirements coming from these different areas of research in order to show what different categories might potentially complete the current domain of geo-ontologies. (shrink)

In the domain of information systems ontologies, the notion of completeness refers to ontological contents by demanding that they be exhaustive with respect to the domain that the ontology aims to represent. The purpose of this paper is to analyze such a notion, by distinguishing different varieties of completeness and by questioning its consistency with the open-world assumption, which formally assumes the incompleteness of conceptualizations on information systems ontologies.

According to Gamper, one function of science is to determine how the world is. Science, Gamper continues, rests on a set of basic assumptions, and the gap between basic assumptions and science should be filled by ontological frameworks that accommodates the modal properties of such assumptions. Different frameworks may surely suggest different modal properties. Thus, in so far as we use different basic assumptions, we can have different ontologies with different modal properties. Ontologies affect, in turn, science, which, however, has (...) the power to falsify the ontological frameworks. The aim of this article is to show a possible trouble of Gamper's proposal, here considered as applied to the geographical debate. (shrink)

The current (still limited) use of the notion of informativeness in the domain of information system ontologies seems to indicate that such ontologies are informative if and only if they are understandable for their final recipients. This paper aims at discussing some theoretical issues emerging from that use which, as we will see, connects the informativeness of information system ontologies to their representational primitives, domains of knowledge, and final recipients. Firstly, we maintain that informativeness interacts not only with the actual (...) representational primitives, but also with their variability over time. Secondly, we discuss the correspondence between representational primitives and domains of knowledge of those ontologies. Finally, we explore the possibility of an epistemological discrepancy between human beings and software systems on the understanding of ontological contents. (shrink)

Greek and Roman Philosophy After Aristotle brings together over twenty-five of the most important works of Western philosophy written from 322 B.C.E. — the death of Aristotle — to the close of the third century C.E. Eminent philosopher Jason Saunder's choices for this concise volume emphasize the range and significance of the leading philosophers of the Hellenistic Age. Supplemented by Dr. Saunder's enlightening introduction, descriptive notes, and extensive bibliography, these readings provide an essential introduction for students and general readers alike (...) to the enormous influence of Greek philosophy on the formative years of Christianity as well as the early Christians' distrust of it. Published initially in 1966 as part of The Free Press paperback series Readings in the History of Philosophy, this affordable volume introduces Lucretius, Epicurus, Epictetus and Stoicism, Sextus Empiricus, Lucian, Philo of Alexanderia, and Plotinus, as well as seminal figures from early Christian thought, including St. Paul and Clement of Alexandria. JASON L. SAUNDERS held positions in philosophy at the University of California at San Diego, and at The City College of New York. Dr. Saunders was the author of The History and Philosophy of Ancient and Renaissance Stoicism, Greek and Latin Philosophy of Aristotle, Philosophy of Neo Stoicism, and Justus Lipsius: The Philosopher of Renaissance Stoicism. [Back cover text from 1994 reprint.]. (shrink)

Both Kant and James claim to limit the role of knowledge in order to make room for faith. In this paper, we argue that despite some similarities, their attempts to do this come apart. Our main claim is that, although both Kant and James justify our adopting religious beliefs on practical grounds, James believes that we can—and should—subsequently assess such beliefs on the basis of evidence. We offer our own account of this evidence and discuss what this difference means for (...) their accounts of religious belief. (shrink)

Unconscious processing of stimuli with emotional content can bias affective judgments. Is this subliminal affective priming merely a transient phenomenon manifested in fleeting perceptual changes, or are long-lasting effects also induced? To address this question, we investigated memory for surprise faces 24 h after they had been shown with 30-ms fearful, happy, or neutral faces. Surprise faces subliminally primed by happy faces were initially rated as more positive, and were later remembered better, than those primed by fearful or neutral faces. (...) Participants likely to have processed primes supraliminally did not respond differentially as a function of expression. These results converge with findings showing memory advantages with happy expressions, though here the expressions were displayed on the face of a different person, perceived subliminally, and not present at test. We conclude that behavioral biases induced by masked emotional expressions are not ephemeral, but rather can last at least 24 h. (shrink)

According to a common view, animals have moral status. Further, a standard defense of this view is the Argument from Consciousness: animals have moral status because they are conscious and can experience pain and it would be bad were they to experience pain. In a series of papers :277–291, 2015a, J Agric Environ Ethics 28:11270–1138, 2015b, J Agric Environ Ethics 30:37–54, 2017), Timothy Hsiao claims that animals do not have moral status and criticizes the Argument from Consciousness. This short (...) paper defends the Argument from Consciousness by providing two simple responses to Hsiao’s criticism. (shrink)

Sometimes, two unfair distributions cancel out in aggregate. Paradoxically, two distributions each of which is fair in isolation may give rise to aggregate unfairness. When assessing the fairness of distributions, it therefore matters whether we assess transactions piecemeal or focus only on the overall result. This piece illustrates these difficulties for two leading theories of fairness before offering a formal proof that no non-trivial theory guarantees aggregativity. This is not intended as a criticism of any particular theory, but as a (...) datum that must be taken into account in constructing a theory of fairness. (shrink)

The degree to which the early dharma literature was an extrapolation from the earlier ritual codes can be seen from a number of shared features of form and content. One of these that has not received more than passing notice is the fact that the Dharmaśāstric principle of regarding customary norms as a valid basis of dharma, both in general and in limited spheres, has its origins in ritual rules in the śrautasūtras and gṛhyasūtras. Passages from the Baudhāyanaśrautasūtra and numerous (...) gṛhyasūtras show that already in these rulebooks established practices of particular social groups were accepted as a valid authority in certain contexts where explicit textual warrant was lacking, and that a further distinction was there made between the general norms of experts and the valid particular norms of locality or social group. (shrink)

Skolem's Paradox involves a seeming conflict between two theorems from classical logic. The Löwenheim Skolem theorem says that if a first order theory has infinite models, then it has models whose domains are only countable. Cantor's theorem says that some sets are uncountable. Skolem's Paradox arises when we notice that the basic principles of Cantorian set theory—i.e., the very principles used to prove Cantor's theorem on the existence of uncountable sets—can themselves be formulated as a collection of first order sentences. (...) How can the very principles which prove the existence of uncountable sets be satisfied by a model which is itself only countable? How can a countable model satisfy the first order sentence which says that there are uncountably many mathematical objects—e.g., uncountably many real numbers? (shrink)