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.

This paper concerns Tarski’s use of the term “model” in his 1936 paper “On the Concept of Logical Consequence.” Against several of Tarski’s recent defenders, I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski’s detractors, I argue that this non-standard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski’s ω-rule example.

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)

I present two generalizations of Putnam's model-theoretic argument against realism. The first replaces Putnam's model theory with some new, and substantially simpler, model theory, while the second replaces Putnam's model theory with some more accessible results from astronomy. By design, both of these new arguments fail. But the similarities between these new arguments and Putnam's original arguments illuminate the latter's overall structure, and the flaws in these new arguments highlight the corresponding flaws in Putnam's arguments.

In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge this (...) final argument. Whatever other faults deflationism may have, the T-schema does provide an implicit definition of the truth predicate. Or so, at any rate, I shall argue. (shrink)

In his new paper, “Eligibility and Inscrutability,” J. R. G. Williams presents a surprising new challenge to David Lewis’ theory of interpretation. Although Williams frames this challenge primarily as a response to Lewis’ criticisms of Putnam’s model-theoretic argument, the challenge itself goes to the heart of Lewis’ own account of interpretation. Further, and leaving Lewis’ project aside for a moment, Williams’ argument highlights some important—and some fairly general—points concerning the relationship between model theory and semantic determinacy.

This paper concerns Tarski's use of the term "model" in his 1936 paper "On the Concept of Logical Consequence." Against several of Tarski's recent defenders, I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski's detractors, I argue that this non-standard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski's $\omega$-rule example.

The Lowenheim-Skolem theorems say that if a first-order theory has infinite models, then it has models which are only countably infinite. Cantor's theorem says that some sets are uncountable. Together, these theorems induce a puzzle known as Skolem's Paradox: the very axioms of set theory which prove the existence of uncountable sets can be satisfied by a merely countable model. ;This dissertation examines Skolem's Paradox from three perspectives. After a brief introduction, chapters two and three examine several formulations of Skolem's (...) Paradox in order to disentangle the roles which set theory, model theory, and philosophy play in these formulations. In these chapters, I accomplish three things. First, I clear up some of the mathematical ambiguities which have all too often infected discussions of Skolem's Paradox. Second, I isolate a key assumption upon which Skolem's Paradox rests, and I show why this assumption has to be false. Finally, I argue that there is no single explanation as to how a countable model can satisfy the axioms of set theory ;In chapter four, I turn to a second puzzle. Why, even though philosophers have known since the early 1920's that Skolem's Paradox has a relatively simple technical solution, have they continued to find this paradox so troubling? I argue that philosophers' attitudes towards Skolem's Paradox have been shaped by the acceptance of certain, fairly specific, claims in the philosophy of language. I then tackle these philosophical claims head on. In some cases, I argue that the claims depend on an incoherent account of mathematical language. In other cases, I argue that the claims are so powerful that they render Skolem's Paradox trivial. In either case, though, examination of the philosophical underpinnings of Skolem's Paradox renders that paradox decidedly unparadoxical. ;Finally, in chapter five, I turn away from "generic" formulations of Skolem's Paradox to examine Hilary Putnam's "model-theoretic argument against realism." I show that Putnam's argument involves mistakes of both the mathematical and the philosophical variety, and that these two types of mistake are closely related. Along the way, I clear up some of the mutual charges of question begging which have characterized discussions between Putnam and his critics. (shrink)

In an earlier paper, I claimed that one version of Putnam's model-theoretic argument against realism turned on a subtle, but philosophically significant, mathematical mistake. Recently, Luca Bellotti has criticized my argument for this claim. This paper responds to Bellotti's criticisms.

This note concerns a recent paper by Hud Hudson on the nature of 'receptacles'. It simplifies the mathematics in Hudson's paper, and it eliminates almost all of the topology in Hudson's arguments.

odel’s theorem than he has often been credited with. Substantively, they find in Wittgenstein’s remarks “a philosophical claim of great interest,” and they argue that, when this claim is properly assessed, it helps to vindicate some of Wittgenstein’s broader views on G¨.

In this dissertation we study two-cardinal phenomena—both of the admitting cardinals variety and of the Chang’s Conjecture variety—under the assumption that all our models have stable theories. All our results involve two, relatively widely accepted generalizations of the traditional definitions in this area. First, we allow the relevant subsets of our models to be picked out by (perhaps infinitary) partial types; second we consider δ-cardinal problems as well as two-cardinal problems.

Over the years, Skolem’s Paradox has generated a fairly steady stream of philosophical discussion; nonetheless, the overwhelming consensus among philosophers and logicians is that the paradox doesn’t constitute a mathematical problem (i.e., it doesn’t constitute a real contradiction). Further, there’s general agreement as to why the paradox doesn’t constitute a mathematical problem. By looking at the way firstorder structures interpret quantifiers—and, in particular, by looking at how this interpretation changes as we move from structure to structure—we can give a technically (...) adequate “solution” to Skolem’s Paradox. So, whatever the philosophical upshot of Skolem’s Paradox may be, the mathematical side of Skolem’s Paradox seems to be relatively straightforward. (shrink)

This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B |<κ(T ) pieces, Ai | i < |B |<κ(T ) , such that for each Ai there is a Bi ⊆ B where |Bi| < κ(T ) and Ai..

This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B|$^{ |B|, then we try to find A' $\subset$ A and B' $\subset$ B such that |A'| is as large as possible, |B'| is as small as possible, and A' $\&2ADD;$ $\underset{B'}$ B. We prove some positive results in this direction, and we discuss the optimality of these results under ZFC (...) + GCH. (shrink)

We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ , λ ). We also prove that every “reasonable” variant of Chang’s Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the δ-cardinal case for arbitrary ordinals δ.

We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some must admit every. We also prove that every "reasonable" variant of Chang's Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the $\delta$-cardinal case for arbitrary ordinals $\delta$.

You’ll be pleased to know that I don’t intend to use these remarks to comment on all of the papers presented at this conference. I won’t try to show that one paper was right about this topic, that another was wrong was about that topic, or that several of our conference participants were talking past one another. Nor will I try to adjudicate any of the discussions which took place in between our sessions. Instead, I’ll use these remarks to make (...) two simple points: one about logicism in the 20th century and one about neo-logicism here at the start of the 21st. (shrink)

Recent work on inference to the best explanation has come to an impasse regarding the proper way to coordinate the theoretical virtues in explanatory inference with probabilistic confirmation theory, and in particular with aspects of Bayes's Theorem. I argue that the theoretical virtues are best conceived heuristically and that such a conception gives us the resources to explicate the virtues in terms of ceteris paribus theorems. Contrary to some Bayesians, this is not equivalent to identifying the virtues with likelihoods or (...) priors per se; the virtues may be more accessible epistemically than likelihoods or priors. I then prove a ceteris paribus theorem regarding theoretical consilience, use it to correct a recent application of Reichenbach's common cause principle, and apply it to a test case of scientific reasoning. Explanation and confirmation The heuristic conception of theoretical virtues Abduction and the accessibility of explanatory power Evidential and theoretical consilience A test case: gravitational lensing Conclusion Thus natural science appears completely to lose from sight the large and general questions; but all the more splendid is the success when, groping in the thicket of special questions, we suddenly find a small opening that allows a hitherto undreamt of outlook on the whole. (L. Boltzmann, Theoretical Physics and Philosophical Problems). (shrink)

This chapter contains sections titled: Introduction Goal and Scope of the Argument The Concept of a Miracle Textual Assumptions Background Facts: Death and Burial The Salient Facts: W, D, and P Probabilistic Cumulative Case Arguments: Nature and Structure The Testimony of the Women: Bayes Factor Analysis The Testimony of the Disciples: Bayes Factor Analysis The Conversion of Paul: Bayes Factor Analysis The Collective Force of the Salient Facts Independence Hume's Maxim and Worldview Worries Plantinga's Principle of Dwindling Probabilities Knavery, Folly, (...) and the Love of Wonder Conclusion References. (shrink)

Two long-standing arguments in cognitive science invoke the assumption that holistic inference is computationally infeasible. The first is Fodor’s skeptical argument toward computational modeling of ordinary inductive reasoning. The second advocates modular computational mechanisms of the kind posited by Cosmides, Tooby and Sperber. Based on advances in machine learning related to Bayes nets, as well as investigations into the structure of scientific and ordinary information, I maintain neither argument establishes its architectural conclusion. Similar considerations also undermine Fodor’s decades-long diagnosis of (...) artificial intelligence research as confounded by an inability to circumscribe the amount of information relevant to inferential processes. This diagnosis is particularly inapposite with respect to Bayes nets, since one of their strengths as machine learning systems has been their capacity to reason probabilistically about large data sets whose size overwhelms the capacities of individual human reasoners. A general moral follows from these criticisms: Insights into artificial and human cognitive systems are likely to be cultivated by focusing greater attention on the structure and density of connections among items of information that are available to them. (shrink)

In a recent article, David Kyle Johnson has claimed to have provided a ‘refutation’ of skeptical theism. Johnson’s refutation raises several interesting issues. But in this note, I focus on only one—an implicit principle Johnson uses in his refutation to update probabilities after receiving new evidence. I argue that this principle is false. Consequently, Johnson’s refutation, as it currently stands, is undermined.

The formal representation of the strength of witness testimony has been historically tied to a formula — proposed by Condorcet — that uses a factor representing the reliability of an individual witness. This approach encourages a false dilemma between hyper-scepticism about testimony, especially to extraordinary events such as miracles, and an overly sanguine estimate of reliability based on insufficiently detailed evidence. Because Condorcet’s formula does not have the resources for representing numerous epistemically relevant details in the unique situation in which (...) testimony is given, many late 19th century thinkers like Venn turned away from the probabilistic analysis of testimony altogether. But a more nuanced approach using Bayes factors provides a better, more flexible, formalism for representing the evidential force of testimony. (shrink)

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

This is not your psychoanalyst's unconscious.

Knepper criticizes existing efforts in the philosophy of religion for being out of step with, and therefore useless to, the academic study of religion, then forwards a new program for philosophy of religion that is in step with, and therefore useful to, the academic study of religion.

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)

A pocket-sized collection of mindfulness practices anyone can do anytime--from the author of Mindful Eating. Mindfulness can reduce stress, improve physical health and quality of life, and give you deep insight. Meditation practice is one way to do it, but not the only way. In fact, there are easy ways to fit it into your everyday life. Jan Chozen Bays provides here 25 practices that can be used on the go to cultivate mindfulness. The three-breath practice, the mindfulness of (...) entering rooms, offering compliments, tasting your food one careful bite at a time--these deceptively simple practices can have a cumulative effect for the better. The book is an abridgment of Bays's longer collection How to Train a Wild Elephant: And Other Adventures in Mindfulness. (shrink)

Second-order logic and modal logic are both, separately, major topics of philosophical discussion. Although both have been criticized by Quine and others, increasingly many philosophers find their strictures uncompelling, and regard both branches of logic as valuable resources for the articulation and investigation of significant issues in logical metaphysics and elsewhere. One might therefore expect some combination of the two sorts of logic to constitute a natural and more comprehensive background logic for metaphysics. So it is somewhat surprising to find (...) that philosophical discussion of secondorder modal logic is almost totally absent, despite the pioneering contribution of Barcan. (shrink)

In this global introduction to philosophy of religion you begin not with a single tradition, but with religious philosophies from East Asia, South Asia, West Africa, and Native North America, alongside the classical Abrahamic and modern European traditions. Matching this diversity of traditions, chapters are organized around questions that acknowledge there is no single understanding of any god or ultimate reality. Instead you approach six different traditions of philosophizing about religion by asking questions about the journeys of both the self (...) and the cosmos such as "What is my path?" and "Where did the cosmos come from?" Accompanied by introductory materials and an extensive glossary, each chapter includes learning objectives, questions for discussion, and suggested primary and secondary sources. The categories of religion and philosophy are interrogated throughout. Equipped with study tools and universal questions about the self and the cosmos, Philosophies of Religion: A Global and Critical Introduction shows you how to philosophize about religions around the world. (shrink)

On method, discursive logics, and epistemology -- Questions of medieval discursive practice -- From the middle ages to the (w)hole of Utopia -- Kepler, his Dream, and the analysis and pattern of thought -- Campanella and Bacon: concerning structures of mind -- The masculine birth of time -- Cyrano and the experimental discourse -- The myth of sun and moon -- The difficulty of writing -- Crusoe rights his story -- Gulliver's critique of Euclid -- Emergence, consolidation, and dominance of (...) a discourse. (shrink)

Skeptical theism is a family of responses to the evidential problem of evil. What unifies this family is two general claims. First, that even if God were to exist, we shouldn’t expect to see God’s reasons for permitting the suffering we observe. Second, the previous claim entails the failure of a variety of arguments from evil against the existence of God. In this essay, we identify three particular articulations of skeptical theism—three different ways of “filling in” those two claims—and describes (...) their role in responding to evidential arguments of evil due to William Rowe and Paul Draper. But skeptical theism has been subject to a variety of criticisms, several of which raise interesting issues and puzzles not just in philosophy of religion but other areas of philosophy as well. Consequently, we discuss some of these criticisms, partly with an eye to bringing out the connections between skeptical theism and current topics in mainstream philosophy. Finally, we conclude by situating skeptical theism within our own distinctive methodology for evaluating world views, what we call “worldview theory versioning.”. (shrink)

The paper explores the main competing interpretations of Aristotle's view of the relation between happiness and external goods in the Nicomachean Ethics. On the basis of a careful analysis of what Aristotle says in the Nicomachean Ethics (and other works such as the Eudemian Ethics, Politics, Rhetoric, etc.) it is argued that it is likely that Aristotle takes at least some external goods to be actual constituents of happiness provided that (1) they are accompanied by virtuous activity and (2) the (...) agent enjoying and using those external goods does so in ways compatible with the continuous aim of acting virtuously. (shrink)

This is the first single volume to offer a comprehensive and systematic account of British and American aesthetics from the early eighteenth century to the late twentieth century.

The chapter argues that a model‐building methodology like that widespread in contemporary natural and social science already plays a significant role in philosophy. One neglected form of progress in philosophy over the past fifty years has been the development of better and better formal models of significant phenomena. Examples are given from both philosophy of language and epistemology. Philosophy can do still better in the future by applying model‐building methods more systematically and self‐consciously, with consequent readjustments to its methodology. Although (...) it is neither likely nor desirable for model‐building to become the sole or even main philosophical method, its use enhances the power and reliability of philosophical thinking. (shrink)

Lately in the past couple of years, there are an increasing in the normal rate of playing computer games or video games compared to the E-learning content that are introduced for the safety of our children, and the impact of the video game addictiveness that ranges from (Musculoskeletal issues, Vision problems and Obesity). Furthermore, this paper introduce an intelligent tutoring system for both parent and their children for enhancement the experience of gaming and tell us about the health problems and (...) how we can solve them, with an easy user interface that way can our children be happy and excited about the information and their health. (shrink)

Things in common: an introduction -- Life -- Specters -- Subscendence -- Species -- Kindness.