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.

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 justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, (...) and weak updating axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability. (shrink)

The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, (...) and weak updating axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability. (shrink)

We show that a quantum system admits hidden variables if and only if there is a rich set of states which satisfy a Bayesian rule. The result is proved using a relationship between Bayesian type states and dispersion-free states. Various examples are presented. In particular, it is shown that for classical systems every state is Bayesian and for traditional Hilbert space quantum systems no state is Bayesian.

Jeffrey conditioning is said to provide a more general method of assimilating uncertain evidence than Bayesian conditioning. We show that Jeffrey learning is merely a particular type of Bayesian learning if we accept either of the following two observations: – Learning comprises both probability kinematics and proposition kinematics. – What can be updated is not the same as what can do the updating; the set of the latter is richer than the set of the former. We address the problem of (...) commutativity and isolate commutativity from invariance upon conditioning on conjunctions. We also present a disjunctive model of Bayesian learning which suggests that Jeffrey conditioning is better understood as providing a method for incorporating unspecified but certain evidence rather than providing a method for incorporating specific but uncertain evidence. The results also generalize over many other subjective probability update rules, such as those proposed by Field and Gallow. (shrink)

Based on the theory of dialectical structures, I review the concept of degree of justification of a partial position a proponent may hold in a controversial debate. The formal concept of degree of justification dovetails with our pre-theoretic intuitions about a thesis' strength of justification. The central claim I'm going to defend in this paper maintains that degrees of justification, as defined within the theory of dialectical structures, correlate with a proponent position's verisimilitude. I vindicate this thesis with the results (...) of simulations of controversial argumentation. (shrink)

The generalized Bayes’ rule (GBR) can be used to conduct ‘quasi-Bayesian’ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walley’s theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozman’s linear programming formulation of the (...) GBR. Examples are provided to demonstrate how the GBR can be applied in practice. These examples also illustrate the effects of prior imprecision and prior-data conflict on the precision of the posterior probability distribution. (shrink)

This article compares inference to the best explanation with Bayes’s rule in a social setting, specifically, in the context of a variant of the Hegselmann–Krause model in which agents not only update their belief states on the basis of evidence they receive directly from the world, but also take into account the belief states of their fellow agents. So far, the update rules mentioned have been studied only in an individualistic setting, and it is known that in such a (...) setting both have their strengths as well as their weaknesses. It is shown here that in a social setting, inference to the best explanation outperforms Bayes’s rule according to every desirable criterion. 1 What Is Inference to the Best Explanation?2 Judging the Rules—By Which Lights?3 From an Individualistic to a Social Perspective 3.1 The Hegselmann–Krause model 3.2 A probabilistic extension of the Hegselmann–Krause model 3.3 Simulations4 Results and Discussion5 Interpretation6 Conclusion. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same (...) axioms: "responsiveness", which requires that revised beliefs incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is (...) explicitly inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. (shrink)

Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed for, persons in many important contexts including law, medical diagnosis, and intelligence analysis. The complexity of these tasks can often be captured and represented by graphical structures now called inference networks. These networks are directed acyclic graphs, consisting of nodes, representing relevant hypotheses, items of evidence, and unobserved variables, and arcs joining (...) some of the nodes, representing dependency relations among them. This chapter describes and comments on two different approaches to inference network construction. In the first approach, a DAG network structure is explicitly constructed as a vehicle for probabilistic analyses. Since the associated computations can be regarded as generalising the use of Bayes' rule, such networks are commonly called Bayesian networks. The second approach stems from the work of the American jurist John H. Wigmore who was the very first person to attempt a systematic study of inference networks. (shrink)

When preferences are such that there is no unique additive prior, the issue of which updating rule to use is of extreme importance. This paper presents an axiomatization of the rule which requires updating of all the priors by Bayes rule. The decision maker has conditional preferences over acts. It is assumed that preferences over acts conditional on event E happening, do not depend on lotteries received on Ec, obey axioms which lead to maxmin expected utility representation (...) with multiple priors, and have common induced preferences over lotteries. The paper shows that when all priors give positive probability to an event E, a certain coherence property between conditional and unconditional preferences is satisfied if and only if the set of subjective probability measures considered by the agent given E is obtained by updating all subjective prior probability measures using Bayes rule. (shrink)

At the very end of the 19th century, Gabriele Tarde wrote that all society was a product of imitation and innovation. This view regarding the development of society has, to a large extent, fallen out of favour, and especially so in those areas where the rational actor model looms large. I argue that this is unfortunate, as models of imitative learning, in some cases, agree better with what people actually do than more sophisticated models of learning. In this paper, I (...) contrast the behaviour of imitative learning with two more sophisticated learning rules (one based on Bayesian updating, the other based on the Nash-Brown-von Neumann dynamics) in the context of social deliberation problems. I show for two social deliberation problems, the Centipede game and a simple Lewis sender-receiver game, that imitative learning provides better agreement with what people actually do, thus partially vindicating Tarde. (shrink)

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than (...) Jeffrey's examples of uncertain perception might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)

Legal reasoning on the requirements and application of law has been studied for centuries, but in this subject area the legal profession maintains predominantly the same stance it did in the time of the Ancient Greeks. There is a gap between the standards of proof, one which has been always demonstrated by percentages and in terms of the evaluation of these standards by percentages by mathematical or statistical methods. One method to fill the gap is Bayes theorem that describes an (...) event’s probability based on conditions that might be related to an event. Bayes theorem can help to establish or confirm a relation between facts and rules if there is sufficient other evidence that connect a party in a procedure with a considered legal action. (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)

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)

M. Cüneyt Kaya, Bir ve Çok Âmirî Felsefesinde Tanrı ve Âlem, İstanbul: Klasik Yayınları, 2017, 195 s.

In order to explore whether and how Jewish teachings influence the attitudes of strictly-orthodox Jews to clinical trials, 10 strictly-orthodox Jews were purposively selected and interviewed, using a semi-structured schedule. Relevant literature was searched for similar studies and for publications covering relevant Jewish teachings. Thematic analysis was used to analyse transcribed interviews and explore relationships between attitudes and Jewish teachings identified in the review. Participants’ attitudes were influenced in a variety of ways: by Jewish teachings on the over-riding importance of (...) preserving life—the need to avoid risks affecting life and health, while taking risks to preserve life—and the religious obligation to help others, as well as by previous experience. Attitudes mirrored those in the general population, enabling many participants to reach conclusions that did not differ materially from those of the general population or research ethics committees. (shrink)

In everyday life, people typically observe fragments of causal networks. From this knowledge, people infer how novel combinations of causes they may never have observed together might behave. I report on 4 experiments that address the question of how people intuitively integrate multiple causes to predict a continuously varying effect. Most theories of causal induction in psychology and statistics assume a bias toward linearity and additivity. In contrast, these experiments show that people are sensitive to cues biasing various integration rules. (...) Causes that refer to intensive quantities (e.g., taste) or to preferences (e.g., liking) bias people toward averaging the causal influences, whereas extensive quantities (e.g., strength of a drug) lead to a tendency to add. However, the knowledge underlying these processes is fallible and unstable. Therefore, people are easily influenced by additional task‐related context factors. These additional factors include the way data are presented, the difficulty of the inference task, and transfer from previous tasks. The results of the experiments provide evidence for causal model and related theories, which postulate that domain‐general representations of causal knowledge are influenced by abstract domain knowledge, data‐driven task factors, and processing difficulty. (shrink)

The Transatlantic slave trade radically impaired Africa's potential to develop economically and maintain its social and political stability. The arrival of Europeans on the West African Coast and their establishment of slave ports in various parts of the continent triggered a continuous process of exploitation of Africa's human resources, labor, and commodities. This exploitative commerce influenced the African political and religious aristocracies, the warrior classes and the biracial elite, who made small gains from the slave trade, to participate in the (...) oppression of their own people. The Europeans, on the other hand, greatly benefited from the Atlantic trade, since it allowed them to amass the raw materials that fed the Industrial Revolution to the detriment of African societies whose capacity to transform their modes of production into a viable entrepreneurial economy was severely halted. (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.

The information explosion and digital modes of learning often combine to inform the quest for the best ways of transforming information in digital form for pedagogical purposes. This quest has become more urgent and pervasive with the ‘turn’ to online learning in the context of COVID-19. This can result in linear, asynchronous, transmission-based modes of teaching and learning which commodify, package and deliver knowledge for individual ‘customers’. The primary concerns in such models are often technical and economic – technology as (...) a cost-effective ‘solution’ to educational challenges. In this paper I argue for the importance of dialogic learning space in teaching and learning by means of Information and Communication Technologies, whether in the form of fully online learning, blended learning or face-to-face encounters using ICT affordances. Although the 20th Century theorists Mikhail Bakhtin (1895–1975) and Hans-Georg Gadamer (1900–2002) produced their seminal works before the advent of ICTs, they were both concerned with the quality and authenticity of human engagement with texts and with other persons and contexts. Besides a shared interest in dialogue as an ontological feature of human life and being, they both used spatiotemporal concepts for understanding and interpreting texts. The article draws on Gadamer’s notions of dialogue and horizon, and Bakhtin’s notions of dialogue and chronotope, to conceptualize dialogic possibilities for online education. Its purpose is to provide a framework, grounded in Bakhtin’s and Gadamer’s ideas, for a dialogic approach to online teaching and learning in higher education. (shrink)

Some arguments are good; others are not. How can we tell the difference? This article advances three proposals as a partial answer to this question. The proposals are keyed to arguments conditioned by different degrees of uncertainty: mild, where the argument’s premises are hedged with point-valued probabilities; moderate, where the premises are hedged with interval probabilities; and severe, where the premises are hedged with non-numeric plausibilities such as ‘very likely’ or ‘unconfirmed’. For mild uncertainty, the article proposes to apply a (...) principle referred to as ‘Jeffrey’s rule’, for the principle is a generalization of Jeffrey conditionalization. For moderate uncertainty, the proposal is to extend Jeffrey’s rule for use with probability intervals. For severe uncertainty, the article proposes that even when lack of probabilistic information prevents the application of Jeffrey’s rule, the rule can be adapted to these conditions with the aid of a suitable plausibility measure. Together, the three proposals introduce an approach to argument evaluation that complements established frameworks for evaluating arguments: deductive soundness, informal logic, argumentation schemes, pragma-dialectics, and Bayesian inference. Nevertheless, this approach can be looked at as a generalization of the truth and validity conditions of the classical criterion for sound argumentation. (shrink)

This fine book is a comprehensive and careful survey of the current situation in the methodology of economics. It is directed primarily at economists and students of economics. Indeed, the economist who reads it with the care it deserves will have a better grip on matters of methodology in economics than most philosophers of science, but philosophers and historians of science will also find the work rewarding and interesting. Though a few examples may be beyond the economically untutored reader, they (...) are not essential to the exposition, and other examples are accessible and enlightening: the brief discussions of Paul Samuelson's revealed preference approach and Julie Nelson's criticism of Gary Becker's work on economics of the family are good instances. Chapter 2, “The Methodological Tradition in Economics,” is a calm and brief introduction to its subject.Until quite recently practicing scientists, economists among them, and philosophers of science presupposed several strong theses about science and knowledge: that all genuine knowledge is scientific; that the objects of this knowledge are eternal and free of context; that all knowledge and all science is one, unified at least by a common scientific method; that, though not infallible, this method is progressive—it approaches truth as a limit—and operates in independence of the nonscientific beliefs and values of its practitioners. These principles cannot be presupposed today. Those who would accept any of them must be ready to meet serious criticisms. The import of this contemporary Methodenstreit as it affects economics is the dominant theme of Reflection without Rules. The reader is left with the conviction that the science of economics and the study of its methodology are inseparable and that it was only dedicated and myopic attachment to The Legend that kept this messy business at bay. Nor can there be any return to the age of innocent division of labor—economists to economics, philosophers to methodology.There are too many topics treated in the book even to list in a brief review. There are calm and clear accounts of Thomas Kuhn's work; of logical positivism ; of the deep effects of the collapse of The Legend on Walrasian equilibrium models; of Daniel Hausman's work on the nature of economics; of the strong program, which strives to reduce scientific activity to the effects of the social interests of scientists; of Alvin Goldman's reliabilism and social epistemology ; and of the important differences between pre‐ and post‐Legend views of science and knowledge.The question of values in science arises for economics in a special and pointed way, for economics studies many sorts of values. It also, at least since Adam Smith, deals in the unintended collective consequences of individual intentional actions. Economics evidently consists in the largely unintended consequences of the intentional actions of individual economists, and, once The Legend is discredited, economics is seen to navigate the very currents that it studies. This opens the door to the virtuous possibility of self‐criticism in tune with the strong naturalism of contemporary epistemology.It is not the least virtue of Reflection without Rules that its author wears his impressive erudition gracefully and well. The book is sophisticated and at the same time naive in the best sense. It will fortunately be the standard reference for work in the methodology of economics for some time to come. (shrink)

All research is immersed in the competition for knowledge, but this is not always governed by fairness. In this opinion article, I elaborate on indicators of unfairness to be found in both evaluation guides and evaluation panels, and I spontaneously offer a number of rules of thumb meant to keep it at bay. Although they are explicitly offered to the Portuguese Foundation for Science and Technology (FCT) and in particular to the evaluation panel for Philosophy, Ethics and Religion of FCT's (...) fifth edition of their Individual Call to Scientific Employment Stimulus, here used as concrete illustrations of unfairness, my rules of thumb are guaranteed to promote fairness in the competition for knowledge in general. (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)

Largely due to the difficulty of observing behavior, empirical business ethics research relies heavily on the scenario methodology. While not disputing the usefulness of the technique, this paper highlights the importance of a careful assessment of the fit between the context of the situation described in the scenario and the knowledge and experience of the respondents. Based on a study of online auctions, we provide evidence that even respondents who have direct knowledge of the situation portrayed in the scenario may (...) develop significantly different assessments of the level of unethical behavior. Further, those assessments may be conditioned in different ways by the same moderating variables. We conclude that care should be exercised when recruiting respondents to choose only those who can be expected to understand the scenario in its true context and that separate analyses should be conducted for groups of respondents who have different perspectives within that context. (shrink)

Largely due to the difficulty of observing behavior, empirical business ethics research relies heavily on the scenario methodology. While not disputing the usefulness of the technique, this paper highlights the importance of a careful assessment of the fit between the context of the situation described in the scenario and the knowledge and experience of the respondents. Based on a study of online auctions, we provide evidence that even respondents who have direct knowledge of the situation portrayed in the scenario may (...) develop significantly different assessments of the level of unethical behavior. Further, those assessments may be conditioned in different ways by the same moderating variables. We conclude that care should be exercised when recruiting respondents to choose only those who can be expected to understand the scenario in its true context and that separate analyses should be conducted for groups of respondents who have different perspectives within that context. (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.

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.

PurposeAs interest in technology ethics is increasing, so is the interest in bringing schools of ethics from non-Western philosophical traditions to the field, particularly when it comes to information and communication technology. In light of this development and recent publications that result from it, this paper aims to present responds critically to recent work on Confucian virtue ethics (CVE) and technology.Design/methodology/approachFour critiques are presented as theoretical challenges to CVE in technology, claiming that current literature insufficiently addresses: overall applicability, collective ethics (...) issues, epistemic overconfidence within technology corporations and amplification of epistemic overconfidence by the implementation of CVE. These challenges make use of general CVE literature and work on technology critique, political philosophy, epistemology and business ethics.FindingsImplementing CVE in technology may yield some benefits, but these may be outweighed by other outcomes, include strengthening hierarchies, widening inequities, increasing, rather than limiting, predictive activity, personal data collection, misinformation, privacy violations and challenges to the democratic process.Originality/valueThough not directly advocating against CVE, the paper reveals hitherto unidentified and serious issues that should be addressed before CVE are used to inform ethics guidelines or regulatory policies. It also serves as a foundation for further inquiry into how Eastern philosophy more broadly can inform technology ethics in the West. (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 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.

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.