Online research in philosophy

It is widely believed that the so-called knowledge account of assertion best explains why sentences such as “It’s raining in Paris but I don’t believe it” and “It’s raining in Paris but I don’t know it” appear odd to us. I argue that the rival rational credibility account of assertion explains that fact just as well. I do so by providing a broadly Bayesian analysis of the said type of sentences which shows that such sentences cannot express rationally held beliefs. (...) As an interesting aside, it will be seen that these sentences also harbor a lesson for Bayesian epistemology itself. (shrink)

Hunting Causes and Using Them argues that causation is not one thing, as commonly assumed, but many. There is a huge variety of causal relations, each with different characterizing features, different methods for discovery and different uses to which it can be put. In this collection of new and previously published essays, Nancy Cartwright provides a critical survey of philosophical and economic literature on causality, with a special focus on the currently fashionable Bayes-nets and invariance methods – and it (...) exposes a huge gap in that literature. Almost every account treats either exclusively how to hunt causes or how to use them. But where is the bridge between? It’s no good knowing how to warrant a causal claim if we don’t know what we can do with that claim once we have it. This book will interest philosophers, economists and social scientists. (shrink)

According to the Bayesian view, scientific hypotheses must be appraised in terms of their posterior probabilities relative to the available experimental data. Such posterior probabilities are derived from the prior probabilities of the hypotheses by applying Bayes'theorem. One of the most important problems arising within the Bayesian approach to scientific methodology is the choice of prior probabilities. Here this problem is considered in detail w.r.t. two applications of the Bayesian approach: (1) the theory of inductive probabilities (TIP) developed by (...) Rudolf Carnap and other epistomologists and (2) the analysis of the multinational inferences provided by Bayesian statstics (BS). ... Zie: Summary. (shrink)

J. Richard Gott III (1993) has used the “Copernican principle” to derive a probability density function for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. John Leslie (1996) and others have used an apparently similar probabilistic argument, the “Doomsday Argument,” to claim that conventional predictions of longevity must be adjusted, based on Bayes’ Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions—his (...) delta t formula—is mathematically equivalent to Laplace’s famous (and notorious) ‘rule of succession’; moreover, Gott’s delta t formula is a plausible worst-case (if one favors greater longevity) bound in some contexts. On the other hand, the Doomsday Argument is fallacious: the argument’s Bayesian formalism is stated in terms of total duration, but all attempted real-life applications of the argument—with one exception, an application by Gott 1994—actually plug in prior probabilities for future duration; moreover, the Self-Sampling Assumption, an essential premise of the Doomsday Argument, is contradicted by the prior information in all known real-life cases. But rejecting the Doomsday Argument does not entail rejecting the possibility of learning about the future from the past. Applying the work of Bruce M. Hill (1968, 1988, 1993) and Frank P.A. Coolen (1998, 2006) in the field of non-parametric predictive inference, I propose and defend an alternative methodology for quantifying how past longevity of any phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity. This methodology forms the basis of a calculus of induction. (shrink)

In the last published round of his debate with Walter Block on economic methodology,1 Bryan Caplan introduces Bayes’ Rule as ‘a cure for methodological schizofrenia’. Block had raised the question ‘Why do economists react so violently to empirical evidence against the conventional view of the minimum wage’s effect?’ and answered it with the suggestion that economists do so because they are covert praxeologists. This means that they base most of their economic arguments on conclusions derived from their a priori (...) understanding of human action, although, as methodologists, they prefer to maintain that their arguments are merely appropriately qualified generalisations of empirical observations. Against this, Caplan maintained that neoclassical economists are Bayesians with some strong prior beliefs, which lead them to ascribe low probability to any statement that goes against the strongly held consensus. Presumably, there is such a strongly held consensus with respect to the minimum wage effect. Caplan concluded that ‘[t]he Bayesian position stakes out a compelling middle ground between atheoretical positivism and praxeology. On the one hand, the Bayesian view emphasizes that few propositions are known with certainty, and that we should adjust our probabilities as new information comes in. On the other hand, the Bayesian view recognizes that the rational view is not an average of past empirical findings, much less a naïve faith in the last prominent study.’ (C, p.83) Caplan’s references to Bayes should be considered carefully before we accept that Bayesianism makes for a middle ground—let alone a compelling one— between positivism and praxeology. The image of a middle ground may be soothing, but it is no more than a metaphor. Whether it makes sense in this context, is an altogether different matter.. (shrink)

Preface for instructors -- Preface for students (you really should read it) -- What is logic about? -- Sentential logic basics -- Sentential logic proofs -- More sentential logic : contradictions, tautologies and assumptions -- Predicate logic basics -- Proofs in predicate logic -- Probability : the basic rules of life -- The theorem of Dr. Bayes -- Probability illusions : why we are so bad at inductive reasoning -- Studies have shown ... or have they? -- Inference to (...) the best explanation -- Rhetoric : the art of persuasion -- Won't get fooled again (fallacies and other foibles) -- Spin, spin, spin (or how not to be a sucker) -- Everything you know is wrong! : pseudoscience and bogus scholarship. (shrink)

Is the restricted, consistent, version of the T-scheme sufficient for an ‘implicit definition’ of truth? In a sense, the answer is yes (Haack 1978 , Quine 1953 ). Section 4 of Ketland 1999 mentions this but gives a result saying that the T-scheme does not implicitly define truth in the stronger sense relevant for Beth’s Definability Theorem. This insinuates that the T-scheme fares worse than the compositional truth theory as an implicit definition. However, the insinuation is mistaken. For, as Bays (...) rightly points out, the result given extends to the compositional truth theory also. So, as regards implicit definability, both kinds of truth theory are equivalent. Some further discussion of this topic is mentioned (Gupta 2008 , Ketland 2003 , McGee 1991 ), all in agreement with Bays’s analysis. (shrink)

“I can’t read. Show me” is a student’s cry heard by teachers of the arts in all kinds of classes. Demonstrating a particular process one on one is a very effective way to learn, but sometimes teachers need a way for students to take notes or follow a guide to aid in remembering a complex technique. Notation systems have developed as the educational solution to this need.1 Adela Bay, a private piano teacher, relates in her book’s dedication the reason she (...) developed a notation system for her music students, saying they were “intimidated by traditional music instruction.”2 In the arts, written notations are available from places and times that most people cannot visit in order to learn a particular technique.3 .. (shrink)

This essay is a response to Michael Martin’s “Why the Resurrection Is Initially Improbable,” Philo, Vol. 1, No.1. I argue that Martin has not succeeded in achieving his aim of showing that the Resurrection is initially improbable and thus, by Bayes’s Theorem, implausible. I respond to five of Martin’s arguments: (1) the “particular time and place argument”; (2) the claim that there is no plausible Christian theory of why Jesus should have been incarnated and resurrected; (3) the claim that (...) the Resurrection accounts in the New Testament are unreliable; (4) Martin’s assumptions about how one establishes the initial probability of Resurrection; and (5) the use Martin makes of Bayes’s Theorem to discredit belief in the Resurrection. (shrink)

The paper aims at describing the discussion about the model-theorethic argument of Hilary Putnam in the past thirty years. First of all it presents the view of Timothy Bays, who through scrupulous examination of the formal side of the argument demonstrates that in fact it has very little in common with the model-theory. It is rather a simple and purely philosophical argument, which isn't more reliable and conclusive than any other argument in philosophy. Putnam tries to block the answer of (...) followers of the causal theory of reference by insisting that it is "just more theory", which could be erased by argument like any other language structure. In response meta-physical realists, like David Lewis and James Van Cleve, claim that "it is not causal language that fixes reference; it is causation itself". David Leech Anderson agrees with metaphysical realists that in principle causal theory could fix the reference, but in his opinion we do not have reliable and substantive theory of that kind, and it doesn't even seem probable that we will have such a theory in future. In conclusion, I agree with Putnam that the metaphysical realist says that "we-know-not-what fixes the reference relation we-know-not-how", and he doesn't have any chance of avoiding the demolition by the model-theorethic argument, because he still tries to separate sharply the realms of language and reality. (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)

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)

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)

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..