The psychological side of Hempel’s paradox of confirmation

People often test hypotheses about two variables (X andY), each with two levels (e.g.,X1 andX2). When testing “IfX1, thenY1,” observing the conjunction ofX1 andY1 is overwhelmingly perceived as more supportive than observing the conjunction ofX2 andY2, although both observations support the hypothesis. Normatively, theX2&Y2 observation provides stronger support than theX1&Y1 observation if the former is rarer. Because participants in laboratory settings typically test hypotheses they are unfamiliar with, previous research has not examined whether participants are sensitive to the rarity of observations. The experiment reported here showed that participants were sensitive to rarity, even judging a rareX2&Y2 observation more supportive than a commonX1&Y1 observation under certain conditions. Furthermore, participants’ default strategy of judgingX1&Y1 observations more informative might be generally adaptive because hypotheses usually regard rare events.     

Field’s logic of truth

T. M. Scanlon’s buck-passing account of value (BPA) has been subjected to a barrage of criticisms. Recently, to be helpful to BPA, Roger Crisp has suggested that a number of these criticisms can be met if one makes some revisions to BPA. In this paper, I argue that if advocates of the buck-passing account accepted these revisions, they would effectively be giving up the buck-passing account as it is typically understood, that is, as an account concerned with the conceptual priority of reasons or the right vis-à-vis value or the good. I conclude by addressing some of the broader implications of my arguments for the current debate about the buck-passing account of value.     

Hegel’s logic of finitude

In ??Violence and Metaphysics?? Jacques Derrida suggests that ??the only effective position to take in order not to be enveloped by Hegel would seem to be??to consider false-infinity??irreducible.?? Inversely, refuting the charge of logocentrism associated with Hegelian true infinity (wahrhafte Unendlichkeit) would involve showing that Hegel??s speculative logic does not establish the infinity of being exempt from the negativity of the finite. This paper takes up Derrida??s challenge, and argues that true infinity is crucial to Hegel??s understanding of ideality as a question of normative authority, which does not fall prey to logocentrism. Through an exposition of the dialectic of the finite and the infinite in Hegel??s Science of Logic, I argue that true infinity is not an ontological category that eliminates division, but rather refers to the metalogical standpoint involved in a philosophical account of determinacy. Although fully achieved at the end of the Logic, the metalogical standpoint that Hegel elaborates in the Seinslogik under the banner of the true infinite already clarifies that determinacy is a product of normative authority that is itself precarious.     

The logic of Simpson’s paradox

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal (and questionable) account of the first two questions. We argue that the “how to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”     

Monsters in Kaplan’s logic of demonstratives

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to contain monsters. For similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift.     

Formality of logic and Frege’s Begriffsschrift

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’.     

Revisiting Reichenbach’s logic

Synthese - In this paper we show that, when analyzed with contemporary tools in logic—such as Dunn-style semantics, Reichenbach’s three-valued logic exhibits many interesting features,...     

Prior’s defence of Hintikka’s theorem. A discussion of Prior’s ‘The logic of obligation and the obligations of the logician’

In his paper, The logic of obligation and the obligations of the logician, A.N. Prior considers Hintikka??s theorem, according to which a statement cannot be both impossible and permissible. This theorem has been seen as problematic for the very idea of a logic of obligation. However, Prior rejects the view that the logic of obligation cannot be formalised. He sees this resistance against such a view as an important part of what could be called the obligation of the logician. Prior argues that Hintikka??s theorem should not be seen as something paradoxical. On the contrary, it should be seen as a fully acceptable consequence of a basic and reasonable assumption in deontic logic, namely Hintikka??s rule.     

Why ‘non-mental’ won’t work: on Hempel’s dilemma and the characterization of the ‘physical’

Recent discussions of physicalism have focused on the question how the physical ought to be characterized. Many have argued that any characterization of the physical should include the stipulation that the physical is non-mental, and others have claimed that a systematic substitution of ‘non-mental’ for ‘physical’ is all that is needed for philosophical purposes. I argue here that both claims are incorrect: substituting ‘non-mental’ for ‘physical’ in the causal argument for physicalism does not deliver the physicalist conclusion, and the specification that the physical is non-mental is irrelevant to the task of formulating physicalism as a substantive, controversial thesis.

Axiomatization of ‘Peircean’ branching-time logic

The branching-time logic called Peircean by Arthur Prior is considered and given an infinite axiomatization. The axiomatization uses only the standard deduction rules for tense logic.     

Soames on Russell’s logic: a reply

In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.