The Logic of Theory Assessment

This paper starts by indicating the analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel’s cake and eat it too — in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, α is an acceptable theory for evidence β if and only if α is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap’s positive relevance account, thereby shedding new light on Carnap’s analysis as well as solving another problem of confirmation theory. A precursor of this paper has appeared as “The Logic of Confirmation and Theory Assessment” in L. Běhounek & M. Bílková (eds.), The Logica Yearbook 2004, Prague: Filosofia, 2005, 161–176.     

Hempel’s logic of confirmation

This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel’s cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap’s analysis.     

Why Bayesians Needn’t Be Afraid of Observing Many Non-black Non-ravens

According to Hempel??s raven paradox, the observation of one non-black non-raven confirms the hypothesis that all ravens are black. Bayesians such as Howson and Urbach (Scientific reasoning: the Bayesian approach, 2nd edn. Open Court, Chicago, 1993) claim that the raven paradox can be solved by spelling out the concept of confirmation in the sense of the relevance criterion. Siebel (J Gen Philos Sci 35:313?C329, 2004) disputes the adequacy of this Bayesian solution. He claims that spelling out the concept of confirmation in the relevance sense lets the raven paradox reappear as soon as numerous non-black non-ravens are observed. It is shown in this paper that Siebel??s objection to the Bayesian solution is flawed. Nevertheless, the objection made by Siebel may give us an idea of how Bayesians can successfully handle situations in which we observe more than one non-black non-raven.     

Grounding and the explanatory role of generalizations

According to Hempel’s (Aspects of scientific explanation and other essays. The Free Press, New York, 1965) influential theory of explanation, explaining why some a is G consists in showing that the truth that a is G follows from a law-like generalization to the effect that all Fs are G together with the initial condition that a is F. While Hempel’s overall account is now widely considered to be deeply flawed, the idea that some generalizations play the explanatory role that the account predicts is still often endorsed by contemporary philosophers of science. This idea, however, conflicts with widely shared views in metaphysics according to which the generalization that all Fs are G is partially explained by the fact that a is G. I discuss two solutions to this conflict that have been proposed recently, argue that they are unsatisfactory, and offer an alternative.     

Axiomatic Theories of Partial Ground I

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground.     

Filtering Theories of Truth: Compositionality as a Criterion

The traditional way to filter out the implausible candidate solutions to the semantic paradoxes is to appeal to the so-called “cost/benefit analyses.” Yet it is often tedious and controversial to carry out such analyses in detail. Facing this, it would be helpful for us to rely upon some principles to filter out at least something, if not everything, from them. The proposal in this paper is thereby rather simple: We may use principles of compositionality as a “filter” for this purpose. The paper has four sections. In Section 2, the author uses the filter to examine Kripke’s fixed-point theory and to thereby show how it works. In Section 3, the author gives more examples from the classical theories of truth to demonstrate the power of the filter. In Section 4, the author addresses the skepticism concerning whether there is any consistent or non-trivial theory of truth that can survive this filtering procedure. A “nearly sufficient” condition for a theory of truth to survive this test is discussed in order to show that at least some consistent or non-trivial theories of truth do indeed survive the filtering procedure.     

Second-order probability affects hypothesis confirmation

Bayesian confirmation measures give numerical expression to the impact of evidence E on a hypothesis H. All measures proposed to date are formal—that is, functions of the probabilities Pr(E∧H), Pr(E∧¬H), Pr(¬E∧H), Pr(¬E∧¬H), and nothing more. Experiments reported in Tentori, Crupi, and Osherson (2007) suggest that human confirmation judgment is not formal, but this earlier work leaves open the possibility that formality holds relative to a given semantic domain. The present study discredits even this weaker version of formality by demonstrating the role in confirmation judgments of a probability distribution defined over the possible values of Pr(E∧H), Pr(E∧¬H), Pr(¬E∧H), and Pr(¬E∧¬H)—that is, a second-order probability. Specifically, when for each of the latter quantities a pointwise value is fixed with a maximal second-order probability, evidence impact is rated in accordance with formal and normatively credible confirmation measures; otherwise evidence impact is systematically judged as more moderate.     

Adding a Conditional to Kripke’s Theory of Truth

Kripke’s theory of truth (Kripke, The Journal of Philosophy72(19), 690–716; 1975) has been very successful but shows well-known expressive difficulties; recently, Field has proposed to overcome them by adding a new conditional connective to it. In Field’s theories, desirable conditional and truth-theoretic principles are validated that Kripke’s theory does not yield. Some authors, however, are dissatisfied with certain aspects of Field’s theories, in particular the high complexity. I analyze Field’s models and pin down some reasons for discontent with them, focusing on the meaning of the new conditional and on the status of the principles so successfully recovered. Subsequently, I develop a semantics that improves on Kripke’s theory following Field’s program of adding a conditional to it, using some inductive constructions that include Kripke’s one and feature a strong evaluation for conditionals. The new theory overcomes several problems of Kripke’s one and, although weaker than Field’s proposals, it avoids the difficulties that affect them; at the same time, the new theory turns out to be quite simple. Moreover, the new construction can be used to model various conceptions of what a conditional connective is, in ways that are precluded to both Kripke’s and Field’s theories.     

A Temporal Semantics for Basic Logic

In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t-norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se. In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas can be interpreted as modal formulas over a flow of time, where the logic of each instant is ?ukasiewicz, with a finite or infinite number of truth values. As a main result, we obtain validity with respect to all flows of times that are non-branching to the future, and completeness with respect to all finite linear flows of time, or to an appropriate single infinite linear flow of time. It may be argued that this reduces the problem of establishing a meaningful interpretation of the truth values in BL logic to the analogous problem for ?ukasiewicz logic.     

Internet stings directed at pedophiles: A study in philosophy and law

This article is published under rules given in “Multiple Publication Reconsidered,”Journal of Information Ethics 7 (Fall 1998): (2)47-53 and “Multiple Publication Reconsidered II,”Journal of Information Ethics 15 (Spring 2006): (1)5-7 and is substantially revised from 15Widener Law Journal 47 (2005), per refereeing, and also has an additional final section. The article is intended to, in Sections I and II, flesh out and put within a metaphilosophical framework the theoretical argument first made in 2002 in “Do Internet Stings Directed at Pedophiles Capture Offenders or Create Offenders? And Allied Questions” (Sexuality &; Culture 6(4): 73–100), with some modifications (See note 14). Where there are differences, I stand by this version as the final version of the argument. Section III addresses three experimental or empirical studies which might be thought to contradict or confirm the data of the 2002 study. Section IV compares what we have done with the one other jurisprudential argument made by Summer 2005. Section V discusses why, despite the evidence and the arguments, these sting operations are popular with prosecutors and the public alike. Section VI comments on why my empirical study dating to 2002 does not appear to have gained wide acceptance, and what, if anything, can be said about this.     

Simplicity as a criterion of theory choice in metaphysics

Metaphysicians frequently appeal to the idea that theoretical simplicity is truth conducive in metaphysics, in the sense that, all other things being equal, simpler metaphysical theories are more likely to be true. In this paper I defend the notion that theoretical simplicity is truth conducive in metaphysics, against several recent objections. I do not give any direct arguments for the thesis that simplicity is truth conducive in metaphysics, since I am aware of no such arguments. I do argue, however, that there is no special problem with the notion that simplicity is truth conducive in metaphysics. More specifically, I argue that if you accept the idea that simplicity is truth conducive in science, then it would be objectionably arbitrary to reject the idea that simplicity is truth conducive in metaphysics.     

Radical interpretation and the permutation principle

Davidson has claimed that to conclude that reference is inscrutable, one must assume that If some theory of truth ... is satisfactory in the light of all relevant evidence ... then any theory that is generated from the first theory by a permutation will also be satisfactory in the light of all relevant evidence. However, given that theories of truth are not directly read off the world, but rather serve as parts of larger theories of behavior, this assumption is far from self-evident. A proper understanding of the role truth theories play in theories of interpretation makes the inscrutability of reference much less wide-spread than Davidson suggests, and, as a result, the radical interpretation methodology is much less likely to saddle its defenders with counterintuitive cases of indeterminacy than is commonly supposed.     

A Unification of Two Approaches to Vagueness: The Boolean Many-Valued Approach and the Modal-Precisificational Approach

The Boolean many-valued approach to vagueness is similar to the infinite-valued approach embraced by fuzzy logic in the respect in which both approaches seek to solve the problems of vagueness by assigning to the relevant sentences many values between falsity (or 0) and truth (or 1), but while the fuzzy-logic approach postulates linearly-ordered values (or ‘degrees’) between 0 and 1, the Boolean approach assigns to sentences values in a many-element (including infinite-element) complete Boolean algebra. On the modal-precisificational approach represented by Kit Fine, if a (vague) sentence is indeterminate in truth value in some world (possibly the actual world), it is taken to be true in one precisified world accessible from that world and false in another. This paper points to a way to unify these two approaches to vagueness by showing that Fine’s version of the modal-precisificational approach can be combined with the Boolean many-valued approach instead of supervaluationism, one of the most popular approaches to vagueness.     

Naive and refined truth approximation

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.In Section 2 general constraints are formulated for the notions of structurelikeness and truthlikeness of structures.In Section 3 a refined definition of truthlikeness of theories is presented, based on the notion of structurelikeness, using a sophisticated version of the conceptual justification for the naive definition.In Section 4 it is shown that idealization and concretization is a special kind of potentially refined truth approximation.I would like to acknowledge that van Benthem (1987) played in several respects a crucial role in the research for a new refined definition. Moreover, I like to thank David Miller, Ilkka Niiniluoto, and two referees for their comments on an earlier version. One of the referees notes that the Miller version of the naive approach (in model-theoretic terms, and identifying the truth with the truth about the actual world) has been criticised on several occasions for its failure to accommodate likeness between structures by Oddie (notably Oddie, 1986). The idea that likeness between structures should be a guiding idea behind truthlikeness is said to be a constant theme of Oddie's work. All this may well be true, but I should add however that Oddie's publications did not play any role in my research. The local references to Oddie are based on the suggestions by the referee.     

You Ought to Know Better: the Morality of Political Engagement

I argue that, from the liberal perspective, citizens have a pro tanto moral duty to cultivate and maintain a readiness to participate in politics when such an action is called for from the moral perspective—I will call it “the pro tanto duty of political engagement.” It requires a citizen to (i) monitor what the government is doing (or not doing), (ii) evaluate its actions, and (iii) learn what she can do to intervene politically. In Section 1, I will discuss some doubts on the pro tanto duty of political engagement. In Section 2, I will describe Alexander Guerrero’s account of culpable ignorance and argue from his account that the pro tanto duty of political engagement is derived from a general moral duty to properly manage one’s morally relevant beliefs. In Section 3, I will argue that to properly assess the moral significance of any government policy or policy proposal, one must learn about the lives and personal values of those who would be affected by the policy.     

Principles for Object-Linguistic Consequence: from Logical to Irreflexive

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by (Beall and Murzi, Journal of Philosophy, 3 pp. 143–65 (2013)) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion of logical consequence: we study the corresponding theory of validity (and some of its variants) by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth (strong Kleene version). Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence.     

The aesthetic realism of Mikhail Lifshits: art,history and the communist ideal

The aesthetics of Mikhail Lifshits may be characterised as a quest for pravda (truth/justice) in art. The article discusses his assessment of the fate of art in the communist revolution and his view on revolution through the prism of classical art. Pondering the metaphysical foundations of his realist aesthetics, Lifshits offered a naturalistic version of the theory of reflection based on the contradistinction of “big” and “small” being.     

The redundancy problem: From knowledge-infallibilism to knowledge-minimalism

Among the epistemological ideas commonly associated with the Descartes of the Meditations, at any rate, is a knowledge-infallibilism. Such an idea was seemingly a vital element in Descartes’s search for truth within that investigative setting: only a true belief gained infallibly (as we would now describe it) could be knowledge, as the Meditations conceived of this. Contemporary epistemologists are less likely than Descartes was to advocate our ever seeking knowledge-infallibility, if only because most are doubtful as to its ever being available. Still, they would agree—in a seemingly Cartesian spirit—that if infallible knowledge was available then it would be a stronger link to truth than fallible knowledge ever manages to be. But this paper argues that infallible knowledge lacks that supposed advantage over fallible knowledge. Indeed, we will see why we should move even further away from the epistemological model at the heart of the Meditations: we should adopt knowledge-minimalism, by conceiving of a belief’s being true as always sufficient for its being knowledge—this, for any belief.     

Positioning Implicit Theories of Well-Being Within a Positivity Framework

Two studies with 230 and 363 Canadian undergraduate students tested the relationship between incremental theories of well-being (i.e., beliefs regarding the malleability of well-being) and a positive mental outlook. In Study 1, incremental theories of well-being were associated with Prioritizing Positivity (purposely incorporating pleasant activities into one’s daily routine) and showed a positive relationship with several other indicators of positive mental functioning (e.g., intrinsic motivation, eudaimonic motivation). In Study 2, incremental theories of well-being were associated with Positivity (viewing life and experiences with a positive outlook) and were positively correlated with additional indicators of positive mental functioning (e.g., harmony in life, self-compassion). In both studies, the relationship between incremental theories of well-being and both hedonic and eudaimonic well-being held true across different measures. A synthesis of major results using a Bayesian meta-analytic procedure suggested a moderate association between an incremental well-being mindset and well-being. Results of these studies help to situate incremental views toward well-being within a broad positivity framework, and to expand the nomological web of correlates of implicit theories of well-being.     

Toward a postmodern correspondence theory of truth

The correspondence theory of truth no longer holds the privileged place it once held. In a postmodern world there simply does not appear to be any objective reality to which our ideas might correspond in order to be true. Thus, today other theories of truth have become popular. Most theists bemoan the loss of correspondence and muster arguments to oppose the postmodern perspective. This paper argues that even given the postmodern perspective of our age a correspondence theory of truth is still a viable.