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)

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 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 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 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.

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)

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 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 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 $\delta$.

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¨.

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..

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.

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)

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.

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)

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)

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)

The author argues that all forms of life are interconnected and that no being, construct, or object can exist independently from the ecological entanglement, nor does "nature" exist as an entity separate from the uglier or more synthetic elements of life. Realizing this interconnectedness is what the author calls the ecological thought. He investigates the philosophical, political, and aesthetic implications of this interconnectedness.

Humean arguments from evil are some of the most powerful arguments against Theism. They take as their data what we know about good and evil. And they argue that some rival to Theism better explains, or otherwise predicts, that data than Theism. However, this paper argues that there are many problems with various methods for defending Humean arguments. I consider Philo’s original strategy; modern strategies in terms of epistemic probability; phenomenological strategies; and strategies that appeal to scientific and metaphysical explanations. (...) None of these methods have been sufficiently developed to provide a clear and distinctive defense of Humean arguments. Defenders of Humean arguments need to spend more time on the underlying methodology of their arguments. (shrink)

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)

When I take off my glasses, the world looks blurred. When I put them back on, it looks sharpedged. I do not think that the world really was blurred; I know that what changed was my relation to the distant physical objects ahead, not those objects themselves. I am more inclined to believe that the world really is and was sharp-edged. Is that belief any more reasonable than the belief that the world really is and was blurred? I see more (...) accurately with my glasses on than off, so visual appearances when they are on have some cognitive priority over visual appearances when they are off. If I must choose which kind of visual appearance to take at face value, I will choose the sharp-edged look. But what should I think when I see a mist, which looks very blurred however well I am seeing? Indeed, why choose to take any of the looks at face value? Why not regard all the choices as illegitimate projections of ways of seeing the world onto the world itself? (shrink)

Two opposing tendencies in the philosophy of language go by the names of ‘referentialism’ and ‘inferentialism’ respectively. In the crudest version of the contrast, the referentialist account of meaning gives centre stage to the referential semantics for a language, which is then used to explain the inference rules for the language, perhaps as those which preserve truth on that semantics (since a referential semantics for a language determines the truth-conditions of its sentences). By contrast, the inferentialist account of meaning gives (...) centre stage to the inference rules for the language, which are then used to explain its referential semantics, perhaps as the semantics on which the rules preserve truth. On pain of circularity, we cannot combine both directions of explanation. (shrink)

This paper discusses the nature and the status of inference to the best explanation. We outline the foundational role given IBE by its defenders and the arguments of critics who deny it any place at all ; argue that, on the two main conceptions of explanation, IBE cannot be a foundational inference rule ; sketch an account of IBE that makes it contextual and dependent on substantive empirical assumptions, much as simplicity seems to be ; show how that account avoids (...) the critics ' complaints and leaves IBE an important role ; and sketch how our account can clarify debates over IBE in arguments for scientific realism. (shrink)

This paper challenges the soundness of the two-dimensional conceivability argument against the derivation of phenomenal truths from physical truths in light of a hyperintensional, ground-theoretic regimentation of the ontology of consciousness. The regimentation demonstrates how ontological dependencies between truths about consciousness and about physics cannot be witnessed by epistemic constraints, when the latter are recorded by the conceivability—i.e., the epistemic possibility—thereof. Generalizations and other aspects of the philosophical significance of the hyperintensional regimentation are further examined.

The fundamental freedoms of speech, conscience, privacy, and religion are now an essential part of the fabric of contemporary society, set down in our most basic laws and regularly invoked in our political and cultural debates. These freedoms play a vital role in securing the spaces and opportunities within which people are able to pursue their own lives in their own ways. Independence of Mind takes this accepted thought a step further, by exploring the ways in which the fundamental freedoms (...) help us to achieve something even more profound, by enabling us to arrive at beliefs, convictions and voices of our own, so that we truly come to think, believe and speak for ourselves in the rich and various ways that the freedoms then protect. Privacy grants us the distance and refuge from others necessary to develop views of our own; freedom of speech calls on us to imagine ways of expressing ourselves that are both true to the views we have developed and innovative in their own right; freedom of conscience enables each of us to create a distinctive rational personality in which to embed the convictions that we wish to treat as non-negotiable; freedom of religion allows groups of us to endorse certain beliefs as articles of faith, free from the full demands of rational scrutiny. Much has been written about the political and legal implications of the fundamental freedoms and their entrenchment in bills of rights. This is the first book to undertake a comprehensive philosophical examination of their moral bases. It offers a penetrating analysis of what makes these particular freedoms matter to us in the ways that they do, and of the true significance of their entrenchment in law. (shrink)

Yet recent thinkers have expressed deep reservations about the concept and the term has become marginalized in the humanities and social sciences.Eschewing this ...

Previous research has suggested that bodily signals from internal organs are associated with diverse cortical and subcortical processes involved in sensory-motor functions, beyond homeostatic reflexes. For instance, a recent study demonstrated that the preparation and execution of voluntary actions, as well as its underlying neural activity, are coupled with the breathing cycle. In the current study, we investigated whether such breathing-action coupling is limited to voluntary motor action or whether it is also present for mental actions not involving any overt (...) bodily movement. To answer this question, we recorded electroencephalography (EEG), electromyography (EMG), and respiratory signals while participants were conducting a voluntary action paradigm including self-initiated motor execution (ME), motor imagery (MI), and visual imagery (VI) tasks. We observed that the voluntary initiation of ME, MI, and VI are similarly coupled with the respiration phase. In addition, EEG analysis revealed the existence of readiness potential (RP) waveforms in all three tasks (i.e., ME, MI, VI), as well as a coupling between the RP amplitude and the respiratory phase. Our findings show that the voluntary initiation of both imagined and overt action is coupled with respiration, and further suggest that the breathing system is involved in preparatory processes of voluntary action by contributing to the temporal decision of when to initiate the action plan, regardless of whether this culminates in overt movements. -/- . (shrink)

This book presents in translation writings by six medieval philosophers which bear on the subject of conscience. Conscience, which can be considered both as a topic in the philosophy of mind and a topic in ethics, has been unduly neglected in modern philosophy, where a prevailing belief in the autonomy of ethics leaves it no natural place. It was, however, a standard subject for a treatise in medieval philosophy. Three introductory translations here, from Jerome, Augustine and Peter Lombard, present the (...) loci classici on which subsequent discussions drew; there follows the first complete treatise on conscience, by Philip the Chancellor, while the two remaining translations, from Bonaventure and Aquinas, have been chosen as outstanding examples of the two main approaches which crystallised during the thirteenth century. (shrink)

Plagiarism detection is the process of finding similarities on electronic based documents. Recently, this process is highly required because of the large number of available documents on the internet and the ability to copy and paste the text of relevant documents with simply Control+C and Control+V commands. The proposed solution is to investigate and develop an easy, fast, and multi-language support plagiarism detector with the easy of one click to detect the document plagiarism. This process will be done with the (...) support of intelligent system that can learn, change and adapt to the input document and make a cross-fast search for the content on the local repository and the online repository and link the content of the file with the matching content everywhere found. Furthermore, the supported document type that we will use is word, text and in some cases, the pdf files –where is the text can be extracting from them- and this made possible by using the DLL file from Word application that Microsoft provided on OS. The using of DLL will let us to not constrain on how to get the text from files; and will help us to apply the file on our Delphi project and walk throw our methodology and read the file word by word to grantee the best working scenarios for the calculation. In the result, this process will help in the uprising the documents quality and enhance the writer experience related to his work and will save the copyrights for the official writer of the documents by providing a new alternative tool for plagiarism detection problem for easy and fast use to the concerned Institutions for free. (shrink)

This essay defends an epistemicist response to the phenomenon of vagueness concerning moral terms. I outline a traditional model of - and then two novel approaches to - epistemicism about moral predicates, and I demonstrate how the foregoing are able to provide robust explanations of the source of moral, as epistemic, indeterminacy. The first approach to moral epistemicism concerns the extensions of moral predicates, as witnessed by the non-transitivity of a value-theoretic sorites paradox. The second approach to moral epistemicism is (...) induced by the status of moral dilemmas in the epistemic interpretation of two-dimensional semantics. I examine the philosophical significance of the foregoing, and compare the proposal to those of ethical expressivism, constructivism, and scalar act-consequentialism. Finally, I examine the status of moral relativism in light of the epistemicist models of moral vagueness developed in the paper. (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.