The word ‘probability’ in ordinary language has two different senses, here called inductive and physical probability. This paper examines the concept of inductive probability. Attempts to express this concept in other words are shown to be either incorrect or else trivial. In particular, inductive probability is not the same as degree of belief. It is argued that inductive probabilities exist; subjectivist arguments to the contrary are rebutted. Finally, it is argued that inductive probability is an important concept and that it (...) is a mistake to try to replace it with the concept of degree of belief, as is usual today. (shrink)

Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...) ways a return to Carnap's conception of confirmation, though there are also important differences between my analysis and his. My analysis includes new accounts of what evidence is and of the indexicality of confirmation claims. Finally, I defend my analysis against Achinstein's criticisms of the relevance concept of confirmation. (shrink)

Hempel's paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a variety (...) of other responses and is shown to differ from all of them. (shrink)

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap's inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

Bayesian confirmation theory offers an explicatum for a pretheoretic concept of confirmation. The “problem of irrelevant conjunction” for this theory is that, according to some people's intuitions, the pretheoretic concept differs from the explicatum with regard to conjunctions involving irrelevant propositions. Previous Bayesian solutions to this problem consist in showing that irrelevant conjuncts reduce the degree of confirmation; they have the drawbacks that (i) they don't hold for all ways of measuring degree of confirmation and (ii) they don't remove the (...) conflict with intuition but merely “soften the impact” (as Fitelson has written). A better solution, which avoids both these drawbacks, is to show that the intuition is wrong. (shrink)

Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...) the empirical significance of sentences. However, his criteria for sentences—translatability, verifiability, falsifiability, confirmability—are usable, and under the assumptions needed for the Carnap sentence approach, verifiability, falsifiability, and translatability become equivalent. As a result of the Carnap sentence approach, metaphysics is rendered analytic. (shrink)

Abstract Artificial language philosophy (also called ‘ideal language philosophy’) is the position that philosophical problems are best solved or dissolved through a reform of language. Its underlying methodology—the development of languages for specific purposes—leads to a conventionalist view of language in general and of concepts in particular. I argue that many philosophical practices can be reinterpreted as applications of artificial language philosophy. In addition, many factually occurring interrelations between the sciences and philosophy of science are justified and clarified by the (...) assumption of an artificial language methodology. (shrink)

It has been argued that our concepts can be disrupted or challenged by technology or normative concerns, which raises the question of whether we can create, design, engineer, or define more robust concepts that avoid counterexamples and conceptual challenges that can lead to conceptual disruption. In this paper, it is argued that we can. This argument is presented through a case study of a definition in the technological domain.

(1) The aim of the paper is to develop a reduction of fallacy theory, i.e. to 'deduce' fallacy theory from a positive theory of argumentation which provides exact criteria for valid and adequate argumentation. Such reductionism has several advantages compared to an unsystematic action, which is quite usual in current fallacy but which at least in part is due to the poor state of positive argumentation theory itself. (2) After defining 'fallacy' (3) some principle ideas and (4) the exact criteria (...) for (argumentatively) valid and adequate arguments of the 'practical theory of argumentation' of the author are expounded. These criteria will be used as the positive basis for the following reduction. (5) In the main part of the paper a systematization, definition and explanation of the main types and many subforms of fallacies of argumentative validity and (6) adequacy is developed, following the list of positive conditions of validity and adequacy. In addition to many new types of fallacies, this systematization contains the most important of the traditionally known and named fallacies; these are explained and the criteria for some of them are corrected or put more precisely. (shrink)

This paper develops an account of scientific objectivity for a relativist theory of evidence. It briefly reviews the character and shortcomings of empiricist and wholist treatments of theory acceptance and objectivity and argues that the relativist account of evidence developed by the author in an earlier essay offers a more satisfactory framework within which to approach questions of justification and intertheoretic comparison. The difficulty with relativism is that it seems to eliminate objectivity from scientific method. Reconceiving objectivity as a function (...) of the social character of science, rather than of individually practiced methods, allows us to claim that science is objective even if relativism is true, and provides a more realistic account of scientific objectivity than is possible on either the empiricist or the wholist accounts. (shrink)

This paper provides a new argument for the relevance of empirical research to moral and political philosophy and a novel defense of the positive program in experimental philosophy. The argument centers on the idea that normative concepts used in moral and political philosophy can be evaluated in terms of their fruitfulness in solving practical problems. Empirical research conducted with an eye to the practical problems that are relevant to particular concepts can provide evidence of their fruitfulness along a number of (...) dimensions. An upshot of the argument is that philosophers should not only engage with but must also be involved in conducting experimental studies that examine the practical roles that normative concepts can play. Rather than just clearing the way for philosophical work to be done, the argument has the further implication that empirical research will be required to advance at least some important debates in moral and political philosophy. (shrink)

In the burgeoning philosophical literature on conceptual engineering improving our concepts is typically portrayed as the hallmark activity of the field. However, Herman Cappelen has challenged the idea that we can know how and why conceptual changes occur well enough to actively intervene in revising our concepts; the mechanisms of conceptual change are typically inscrutable to us. If the ‘inscrutability challenge’ is correct, the practical aspect of conceptual engineering may seem to be undermined, but I argue that endorsing such pessimism (...) would be a mistake. Even if the inscrutability challenge is correct, conceptual engineers often have good reasons to try to preserve existing concepts. I examine several cases where concept preservation is important and draw lessons about this activity for conceptual engineers. (shrink)

Scientists often diverge widely when choosing between research programs. This can seem to be rooted in disagreements about which of several theories, competing to address shared questions or phenomena, is currently the most epistemically or explanatorily valuable—i.e. most successful. But many such cases are actually more directly rooted in differing judgments of pursuit-worthiness, concerning which theory will be best down the line, or which addresses the most significant data or questions. Using case studies from 16th-century astronomy and 20th-century geology and (...) biology, I argue that divergent theory choice is thus often driven by considerations of scientific process, even where direct epistemic or explanatory evaluation of its final products appears more relevant. Broadly following Kuhn’s analysis of theoretical virtues, I suggest that widely shared criteria for pursuit-worthiness function as imprecise, mutually-conflicting values. However, even Kuhn and others sensitive to pragmatic dimensions of theory ‘acceptance’, including the virtue of fruitfulness, still commonly understate the role of pursuit-worthiness—especially by exaggerating the impact of more present-oriented virtues, or failing to stress how ‘competing’ theories excel at addressing different questions or data. This framework clarifies the nature of the choice and competition involved in theory choice, and the role of alternative theoretical virtues. (shrink)

The accuracy-first program attempts to ground epistemology in the norm that one’s beliefs should be as accurate as possible, where accuracy is measured using a scoring rule. We argue that considerations of scientific progress suggest that such a monism about epistemic value is untenable. In particular, we argue that counterexamples to the standard scoring rules are ubiquitous in the history of science, and hence that these scoring rules cannot be regarded as a precisification of our intuitive concept of epistemic value.

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully (...) support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. (shrink)

Weighted averaging is a method for aggregating the totality of information, both regimented and unregimented, possessed by an individual or group of individuals. The application of such a method may be warranted by a theorem of the calculus of probability, simple conditionalization, or Jeffrey's formula for probability kinematics, all of which average in terms of the prior probability of evidence statements. Weighted averaging may, however, be applied as a method of rational aggregation of the probabilities of diverse perspectives or persons (...) in cases in which the weights cannot be articulated as the prior probabilities of statements of evidence. The method is justified by Wagner's Theorem exhibiting that any method satisfying the conditions of the Irrelevance of Alternatives and Zero Unanimity must, when applied to three or more alternatives, be weighted averaging. (shrink)

In Carnap’s autobiography, he tells the story how one night in January 1931, “the whole theory of language structure” in all its ramifications “came to [him] like a vision”. The shorthand manuscript he produced immediately thereafter, he says, “was the first version” of Logical Syntax of Language. This document, which has never been examined since Carnap’s death, turns out not to resemble Logical Syntax at all, at least on the surface. Wherein, then, did the momentous insight of 21 January 1931 (...) consist? We seek to answer this question by placing Carnap’s shorthand manuscript in the context of his previous efforts to accommodate scientific theories and metalinguistic claims within Wittgenstein’s Tractatus theory of meaning. The breakthrough of January 1931 consists, from this viewpoint, in the rejection of the Tractatus theory in favor of the meta-mathematical perspective of Hilbert, Gödel, and Tarski. This was not yet the standpoint of the published Logical Syntax, as we show, but led naturally to the “principle of tolerance” and thus to Carnap’s mature philosophy, in which the inconsistencies between this first view and the principle of tolerance, which survived into the published Syntax, were overcome. (shrink)

Kolmogorov's account in his [1933] of an absolute probability space presupposes given a Boolean algebra, and so does Rényi's account in his [1955] and [1964] of a relative probability space. Anxious to prove probability theory ‘autonomous’. Popper supplied in his [1955] and [1957] accounts of probability spaces of which Boolean algebras are not and [1957] accounts of probability spaces of which fields are not prerequisites but byproducts instead.1 I review the accounts in question, showing how Popper's issue from and how (...) they differ from Kolmogorov's and Rényi's, and I examine on closing Popper's notion of ‘autonomous independence’. So as not to interrupt the exposition, I allow myself in the main text but a few proofs, relegating others to the Appendix and indicating as I go along where in the literature the rest can be found. (shrink)

This paper studies the extent to which probability functions are recursively definable. It proves, in particular, that the (absolute) probability of a statement A is recursively definable from a certain point on, to wit: from the (absolute) probabilities of certain atomic components and conjunctions of atomic components of A on, but to no further extent. And it proves that, generally, the probability of a statement A relative to a statement B is recursively definable from a certain point on, to wit: (...) from the probabilities relative to that very B of certain atomic components and conjunctions of atomic components of A, but again to no further extent. These and other results are extended to the less studied case where A and B are compounded from atomic statements by means of `` ∀ '' as well as `` ∼ '' and "&". The absolute probability functions considered are those of Kolmogorov and Carnap, and the relative ones are those of Kolmogorov, Carnap, Renyi, and Popper. (shrink)

This paper investigates the relation between Carnap and Quine’s views on analyticity on the one hand, and their views on philosophical analysis or explication on the other. I argue that the stance each takes on what constitutes a successful explication largely dictates the view they take on analyticity. I show that although acknowledged by neither party (in fact Quine frequently expressed his agreement with Carnap on this subject) their views on explication are substantially different. I argue that this difference not (...) only explains their differences on the question of analyticity, but points to a Quinean way to answer a challenge that Quine posed to Carnap. The answer to this challenge leads to a Quinean view of analyticity such that arithmetical truths are analytic, according to Quine’s own remarks, and set theory is at least defensibly analytic. (shrink)

Academic and corporate research departments alike face a crucial dilemma: to exploit known frameworks or to explore new ones; to specialize or to innovate? Here I show that these two conflicting epistemic desiderata are sufficient to explain pluralistic ignorance and its boom-and-bust-like dynamics, exemplified in the collapse of the efficient markets hypothesis as a modern risk management paradigm in 2007. The internalist nature of this result, together with its robustness, suggests that pluralistic ignorance is an inherent feature rather than a (...) threat to the rationality of epistemic communities. (shrink)

Objective Bayesians hold that degrees of belief ought to be chosen in the set of probability functions calibrated with one’s evidence. The particular choice of degrees of belief is via some objective, i.e., not agent-dependent, inference process that, in general, selects the most equivocal probabilities from among those compatible with one’s evidence. Maximising entropy is what drives these inference processes in recent works by Williamson and Masterton though they disagree as to what should have its entropy maximised. With regard to (...) the probability function one should adopt as one’s belief function, Williamson advocates selecting the probability function with greatest entropy compatible with one’s evidence while Masterton advocates selecting the expected probability function relative to the density function with greatest entropy compatible with one’s evidence. In this paper we discuss the significant relative strengths of these two positions. In particular, Masterton’s original proposal is further developed and investigated to reveal its significant properties; including its equivalence to the centre of mass inference process and its ability to accommodate higher order evidence. (shrink)

We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.

In 1990 Edward Craig published a book called Knowledge and the State of Nature in which he introduced and defended a genealogical approach to epistemology. In recent years Craig’s book has attracted a lot of attention, and his distinctive approach has been put to a wide range of uses including anti-realist metaepistemology, contextualism, relativism, anti-luck virtue epistemology, epistemic injustice, value of knowledge, pragmatism and virtue epistemology. While the number of objections to Craig’s approach has accumulated, there has been no sustained (...) attempt to develop answers to these objections. In this paper we provide answers to seven important objections in the literature. (shrink)

Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in (...) philosophy”—to adapt Wigner’s phrase—is analogous to that of mathematical explanations in science. As success-criteria for mathematical philosophy, we propose that it should be correct, responsive, illuminating, promising, relevant, and adequate. (shrink)

Philosophical analyses of scientific concepts are legion. However, this literature is replete with methodological errors that have largely gone unnoticed. Five distinct projects are conflated which has led to faulty inferences, ambiguities, and mischaracterizations. There has also been some recent enthusiasm for approaches that attempt to rectify problematic scientific concepts but the motivations for these approaches are questionable. I am hopeful that by bringing these various issues to light that it will lead practitioners to be more explicit about their aims (...) and subsequently result in better analyses. (shrink)

We will show that almost all nonassociative relation algebras are symmetric and integral (in the sense that the fraction of both labelled and unlabelled structures that are symmetric and integral tends to $1$ ), and using a Fraïssé limit, we will establish that the classes of all atom structures of nonassociative relation algebras and relation algebras both have $0$ – $1$ laws. As a consequence, we obtain improved asymptotic formulas for the numbers of these structures and broaden some known probabilistic (...) results on relation algebras. (shrink)

Mark Siebel has presented a compelling argument against Branden Fitelson’s probabilistic measure of coherence. The present paper shows how Siebel’s argument can be strengthened and thereby extended to an argument against a huge class of coherence measures from the literature including William Roche’s average mutual firmness account, which has not been challenged up to now.

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s coherence measure based on Douven and Meijs’ average mutual support approach and the (...) conditional probability. (shrink)

The probabilistic support relation is known to violate transitivity. But over the years, philosophers have identified various conditions under which it does not, most notably screening-off and weak screening-off. In this short discussion note, I wish to highlight another condition that, unfortunately, is often neglected in the literature. This condition is due to Mary Hesse who recognized its transitivity-ensuring property long before other conditions entered the stage. I show that her condition is logically independent of screening-off and weak screening-off, but (...) that, just like the two aforementioned, it entails the recently proposed very weak screening-off condition due to Jeanne Peijnenburg and David Atkinson. (shrink)

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to investigate Carnap’s measure (...) regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures satisfy and violate the same adequacy constraints, despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and perform similarly in a series of test cases for probabilistic coherence measures. (shrink)

Changing weather conditions and barometer changes usually coincide. Accordingly, the propositions that my barometer falls and that the weather conditions deteriorate are quite coherent—especially under the assumption that there is a drop in atmospheric pressure. Nevertheless, scenarios like these involving common causes turn out to be highly problematic for a prominent class of probabilistic coherence measures, namely, those explicating coherence based on the idea of relevance-sensitivity. In this article, we show that none of these measures accords with the intuition that (...) in the light of a common cause, two propositions referring to the cause’s effects should turn out to be coherent. This result casts doubts on the view that these measures can be considered proper explications of the concept of coherence. 1Introduction2Relevance-Sensitive Coherence Measures3Common Causes, Screening-off, and Coherence4Discussion 4.1Multiple explications of coherence4.2Conditionalization versus set expansion5Conclusion. (shrink)

This paper presents a symmetry condition for probabilistic measures of confirmation which is weaker than commutativity symmetry, disconfirmation commutativity symmetry but also antisymmetry. It is based on the idea that for any value a probabilistic measure of confirmation can assign there is a corresponding case where degrees of confirmation are symmetric. It is shown that a number of prominent confirmation measures such as Carnap’s difference function, Rescher’s measure of confirmation, Gaifman’s confirmation rate and Mortimer’s inverted difference function do not satisfy (...) this condition and instead exhibit a previously unnoticed and rather puzzling behavior in certain cases of disconfirmation. This behavior also carries over to probabilistic measures of information change, causal strength, explanatory power and coherence. (shrink)

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

The Uniqueness Thesis holds, roughly speaking, that there is a unique rational response to any particular body of evidence. We first sketch some varieties of Uniqueness that appear in the literature. We then discuss some popular views that conflict with Uniqueness and others that require Uniqueness to be true. We then examine some arguments that have been presented in its favor and discuss why permissivists find them unconvincing. Last, we present some purported counterexamples that have been raised against Uniqueness and (...) discuss some possible reasons why proponents of Uniqueness might find these similarly unconvincing. (shrink)

A common objection to the very idea of conceptual engineering is the topic continuity problem: whenever one tries to “reengineer” a concept, one only shifts attention away from one concept to another. Put differently, there is no such thing as conceptual revision: there’s only conceptual replacement. Here, I show that topic continuity is compatible with conceptual replacement. Whether the topic is preserved in an act of conceptual replacement simply depends on what is being replaced (a conceptual tool or a conceptual (...) role) and what the topic under discussion is. Thus, the topic continuity problem only arises from a failure to specify these two things. (shrink)

It is widely believed that some a priori necessary truths are not analytic in the sense of transformable by substitution of synonyms into logical truths. One much-cited example comes from the supposed incompatibility between colour predicates. The idea is that sentences like “Nothing is both blue all over (or uniformly or at a point) and also red” are not transformable into a logical truth in the same way as “Nothing is both a bachelor and married” because the requisite conceptual link (...) between “bachelor” and “not married” is absent between “blue” and “not red”. This paper examines whether colour exclusion may be more like the bachelor case than it initially appears. It transpires that the most promising line of thought is not, however, as has been argued at length in the literature, that “blue” in some more or less convoluted way manages to mean “not red”. Instead it is suggested that the requisite conceptual link may reside in the oft-ignored qualifications (“all over”, “uniformly”, etc.), without which there is no incompatibility in the first place. (shrink)

I will defend explication, in a Carnapian sense, as a strategy for revisionary ontologists and radical sceptics. The idea is that these revisionary philosophers should explicitly commit to using expressions like “S knows that p” and “Fs exist” differently from how these expressions are used in everyday contexts. I will first motivate this commitment for these revisionary philosophers. Then, I will address the main worries that arise for this strategy: the unintelligibility worry and the topic shift worry. I will focus (...) on the latter worry and provide a solution that makes use of a distinction between practically and theoretically oriented beliefs. On my view, the revisionary philosophers who admit to departing from the everyday language can still criticize everyday knowledge and existence claims, by arguing that while the language embedded in these claims is suitable for beliefs-1, it is not suitable for beliefs-2. (shrink)

The nature of the distinction between rational andnon-rational accounts of the development of science isanalyzed. These two kinds of accounts differ mostlyin the status which they give to methodologicalprinciples. It is shown that there are severaldimensions with respect to which the status of suchprinciples can resemble more or less the kind ofstatus that a paradigmatic rational account would givethem. It is concluded that, under the most plausibledefinitions of a rational account, the extent to whicha philosophical account of scientific change isrational (...) is a matter of degree, and that there is nosuch clear distinction between the two kinds ofaccounts which some supporters of rational and ofnon-rational accounts have assumed to exist. (shrink)