Proof uses forcing on perfect trees for 2-quantifier sentences in the language of arithmetic. The result extends to exact pairs for the hyperarithmetic degrees.

In an attempt to give a unified account of common properties of various resource bounded reducibilities, we introduce conditions on a binary relation ≤r between subsets of the natural numbers, where ≤r is meant as a resource bounded reducibility. The conditions are a formalization of basic features shared by most resource bounded reducibilities which can be found in the literature. As our main technical result, we show that these conditions imply a result about exact pairs which has been previously (...) shown by Ambos-Spies [2] in a setting of polynomial time bounds: given some recursively presentable ≤r-ideal I and some recursive ≤r-hard set B for I which is not contained in I, there is some recursive set C, where B and C are an exact pair for I, that is, I is equal to the intersection of the lower ≤r-cones of B and C, where C is not in I. In particular, if the relation ≤r is in addition transitive and there are least sets, then every recursive set which is not in the least degree is half of a minimal pair of recursive sets. (shrink)

TheK-trivial sets form an ideal in the Turing degrees, which is generated by its computably enumerable members and has an exact pair below the degree of the halting problem. The question of whether it has an exact pair in the c.e. degrees was first raised in [22, Question 4.2] and later in [25, Problem 5.5.8].We give a negative answer to this question. In fact, we show the following stronger statement in the c.e. degrees. There exists aK-trivial (...) degreedsuch that for all degreesa, bwhich are notK-trivial anda > d, b > dthere exists a degreevwhich is notK-trivial anda > v, b > v. This work sheds light to the question of the definability of theK-trivial degrees in the c.e. degrees. (shrink)

Interactionists hold that non-spatial objects causally interact with physical objects. Interactionists have traditionally grappled with the puzzle of how such interaction is possible. More recently, Jaegwon Kim has presented interactionists with a more daunting threat: the pairing argument, which purports to refute interactionism by showing that non-spatial objects cannot stand in causal relations. After reviewing that argument, I develop a challenge to it on behalf of the interactionist. The challenge poses a dilemma: roughly, either haecceities exist or they do not. (...) I argue that the pairing argument fails in either case. While the challenge does not explain exactly how the pairing argument goes wrong, it shows that the argument fails. The challenge also explains the difficulty in pinpointing the pairing argument’s failure: exactly how the pairing argument fails depends on difficult issues concerning the nature of objects. (shrink)

According to Frege, n=Kn, where n is any cardinal number and Kn is the class of all n-tuples. According to Von Neumann, n=Kpn, where Kpn is the class of all of n's predecessors. These analyses are prima facie incompatible with each other, given that Kn≠Kpn, for n>0. In the present paper it is shown that these analyses are in fact compatible with each other, for the reason that each analysis can and ultimately must be interpreted as being to the effect (...) that n=Cn, where Cn is the class of all ordered pairs <Kn#,Rn#>, where Kn# is an arbitrary class and Rn# is an arbitrary relation such that a class k has n-many members exactly if k bears Rn# to Kn#. (shrink)

Ptolemy reports three dated lunar eclipses observed by Hipparchus, and also refers to two more, without identifying them, which Hipparchus compared with two earlier counterparts (apparently, observed in Mesopotamia) to assess the validity of the Babylonian period relations of the lunar motion. Also, in Pliny the Elder’s Historia naturalis, we are told that a horizontal lunar eclipse (selenelion) at sunrise and moonset was reported (observed?) by Hipparchus. Reviewing a paper by G.J. Toomer in 1980, it is shown that the pairs (...) of the eclipses were, almost certainly, the ones occurring on “31 January 486 b.c. and 27 January 141 b.c.” and “19 November 502 b.c. and 14 November 157 b.c.”; and if Hipparchus observed from St. Stephen’s Hill in Rhodes, the most probable candidate for the selenelion at moonset was the lunar eclipse of 7 February 142 b.c., although he also had the chance to observe any of the four others, occurring on 3 July 150 b.c., 10 April 145 b.c., 26 November 139 b.c., and 15 November 138 b.c., on a sufficiently elevated mountain on the island. (shrink)

L’évaluation scientifique a toujours fait partie du paysage de la recherche en sciences exactes si l’on entend par là l’existence de procédures pertinentes d’examen par les pairs – qu’il s’agisse de la soumission d’un article à une revue scientifique, du recrutement et de l’affectation thématique d’un chercheur, ou du financement de programmes de recherche nécessitant..

TOT states may be viewed as a temporary and reversible microamnesia. We investigated the effects of lorazepam on TOT states in response to general knowledge questions. The lorazepam participants produced more commission errors and more TOTs following commission errors than the placebo participants . The resolution of the TOTs was unimpaired by the drug. Neither feeling-of-knowing accuracy nor recognition were affected by lorazepam. The higher level of incorrect recalls produced by lorazepam participants may be due to the fact that they (...) were more frequently temporarily unable to access a known item. For some of these items, the awareness of the retrieval failure resulted in a commission TOT . The resolution of the TOT conflict is discussed in the light of the anxiolytic and anticonflict effects of lorazepam. The data are discussed in terms of contemporary theories of TOTs and the effects that benzodiazepines have on semantic memory. (shrink)

Background: Walking while performing a secondary task walking) increases cognitive workload in young adults. To date, few studies have used neurophysiological measures in combination to subjective measures to assess cognitive workload during a walking task. This combined approach can provide more insights into the amount of cognitive resources in relation with the perceived mental effort involving in a walking task.Research Question: The objective was to examine cognitive workload in young adults during walking conditions varying in complexity.Methods: Twenty-five young adults performed (...) four conditions: usual walking, simple DT walking, complex DT walking and standing while subtracting. During the walking task, mean speed, cadence, stride time, stride length, and their respective coefficient of variation were recorded. Cognitive workload will be measured through changes in oxy- and deoxy-hemoglobin during walking in the dorsolateral prefrontal cortex and perceived mental demand score from NASA-TLX questionnaire.Results: In young adults, ΔHbO2 in the DLPFC increased from usual walking to both DT walking conditions and standing while subtracting condition. ΔHbO2 did not differ between the simple and complex DT and between the complex DT and standing while subtracting condition. Perceived mental demand gradually increased with walking task complexity. As expected, all mean values of gait parameters were altered according to task complexity. CV of speed, cadence and stride time were significantly higher during DT walking conditions than during usual walking whereas CV of stride length was only higher during complex DT walking than during usual walking.Significance: Young adults had greater cognitive workload in the two DT walking conditions compared to usual walking. However, only the mental demand score from NASA-TLX questionnaire discriminated simple from complex DT walking. Subjective measure provides complementary information to objective one on changes in cognitive workload during challenging walking tasks in young adults. These results may be useful to improve our understanding of cognitive workload during walking. (shrink)

An Exact Pair for the Arithmetic Degrees whose join is not a Weak Uniform Upper Bound, in the Recursive Function Theory-Newsletters, No. 28, August-September 1982.

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings (...) via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs. (shrink)

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.

We show that the elementary theory of the recursively enumerable tt-degrees has the same computational complexity as true first-order arithmetic. As auxiliary results, we prove theorems about exact pairs and initial segments in the tt-degrees.

A set A is symmetric enumeration (se-) reducible to a set B (A ≤\sb se B) if A is enumeration reducible to B and \barA is enumeration reducible to \barB. This reducibility gives rise to a degree structure (D\sb se) whose least element is the class of computable sets. We give a classification of ≤\sb se in terms of other standard reducibilities and we show that the natural embedding of the Turing degrees (D\sb T) into the enumeration degrees (D\sb e) (...) translates to an embedding (ι\sb se) into D\sb se that preserves least element, suprema, and infima. We define a weak and a strong jump and we observe that ι\sb se preserves the jump operator relative to the latter definition. We prove various (global) results concerning branching, exact pairs, minimal covers, and diamond embeddings in D\sb se. We show that certain classes of se-degrees are first-order definable, in particular, the classes of semirecursive, Σ\sb n ⋃ Π\sb n, Δ\sb n (for any n \in ω), and embedded Turing degrees. This last result allows us to conclude that the theory of D\sb se has the same 1-degree as the theory of Second-Order Arithmetic. (shrink)

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform (...) upper bounds on I never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. (shrink)

The degree structure of functions induced by a polynomial-time reducibility first introduced in G. Miller's work on the complexity of prime factorization is investigated. Several basic results are established including the facts that the degrees restricted to the sets do not form an upper semilattice and there is a minimal degree, as well as density for the low degrees, a weak form of the exact pair theorem, the existence of minimal pairs and the decidability of the Π2 theory (...) of the low degrees. (shrink)

The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first (...) part, we tested whether the processing of metric vs topological relations yielded the same hemispheric specialization as the processing of coordinate vs categorical relations. In the second part, we investigated the specific performance patterns for the processing of five pairs of exact/co-exact relations, where stimuli for the co-exact relations were divided into three categories depending on their distance from the exact case. Regarding the processing of metric vs topological relations, hemispheric differences were found for only a few of the stimuli used, which may indicate that other processing mechanisms might be at play. Regarding the processing of exact vs co-exact relations, results show that the level of agreement among participants in judging co-exact relations decreases with the distance from the exact case, and this for the five pairs of exact/co-exact relations tested. The philosophical implications of these empirical findings for the epistemological analysis of Euclid's diagram-based geometric practice are spelled out and discussed. (shrink)

Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation (...) to the other key supports of his idealism. The paper’s central finding is that Kant’s idealist argument from incongruent counterparts rests essentially on his theory of freedom. The surprising result sheds new light on deep and overlooked links among the pillars of transcendental idealism, pointing the way to a comprehensive and unified reading of Kant’s system of idealist arguments. (shrink)

I think that there are good reasons to adopt a relativist semantics for epistemic modal claims such as ``the treasure might be under the palm tree'', according to which such utterances determine a truth value relative to something finer-grained than just a world (or a <world, time> pair). Anyone who is inclined to relativise truth to more than just worlds and times faces a problem about assertion. It's easy to be puzzled about just what purpose would be served by (...) assertions of this kind, and how to understand what we'd be up to in our use of sentences like ``the treasure might be under the palm tree'', if they have such peculiar truth conditions. After providing a very quick argument to motivate a relativist view of epistemic modals, I bring out and attempt to resolve this problem in making sense of the role of assertions with relativist truth conditions. Solving this problem should be helpful in two ways: first, it eliminates an apparently forceful objection to relativism, and second, spelling out the relativist account of assertion and communication will help to make clear just what the relativist position is, exactly, and why it's interesting. (shrink)

One lists the distinct pairs of categorical premises formulable via only the positive terms, S,P,M, by constructing a six by six matrix obtained by pairing the six categorical P-premises, A, O, A, O, where P* ∈ {P,P′}, with the six, similar, categorical S-premises. One shows how five rules of valid syllogism, select only 15 distinct PCPs that entail logical consequences belonging to the set L+: = {A, O, A, E, O, I}. The choice of admissible LCs can be regarded as (...) a condition separated from the conditions contained in the RofVS: the usual eight PCPs that generate valid syllogisms are obtained when the only admissible LCs belong to the set L: = {A, E, O, I} and no existential imports are addressed. A 64 PCP-matrix obtains when both PCPs and LCs may contain indefinite terms—the positive, S,P,M, terms, and their complementary sets, S′,P′, M′, in the universe of discourse, U, called the negative terms. Now one can accept eight LCs: A, I, where P* ∈ {P,P′}, S* ∈ {S,S′}, and there are 32 conclusive PCPs, entailing precise, “one partitioning subset of U” LCs. The four rules of conclusive syllogisms predict the less precise LCs, left after eliminating the middle term from the exact LCs. The RofCS also predict that the other 32 PCPs of the 64 PCP-matrix are non-conclusive. The RofVS and the RofCS are generalized, and arguments are given, for also accepting as valid syllogisms the conclusive syllogisms formulable via positive terms which entail the LCs A and O. (shrink)

Recently two pairs of authors have aimed to vindicate the longstanding "orthodox" or conventional claim that a first-class constraint generates a gauge transformation in typical gauge theories such as electromagnetism, Yang-Mills and General Relativity, in response to the Lagrangian-equivalent reforming tradition, in particular Pitts, _Annals of Physics_ 2014. Both pairs emphasize the coherence of the extended Hamiltonian formalism against what they take to be core ideas in Pitts 2014, but both overlook Pitts 2014's sensitivity to ways that one might rescue (...) the claim in question, including an additive redefinition of the electrostatic potential. Hence the bulk of the paper is best interpreted as arguing that the longstanding claim about separate first-class constraints is _either false or trivial_---de-Ockhamization (using more when less suffices by splitting one quantity into the sum of two) being trivial. Unfortunately section 9 of Pitts 2014, a primarily verbal argument that plays no role in other works, is refuted. Pooley and Wallace's inverse Legendre transformation to de-Ockhamized electromagnetism with an additively redefined electrostatic potential, however, opens the door to a precisely analogous calculation introducing a photon mass, which shows that a _second-class primary_ constraint generates a 'gauge transformation' in the exactly same sense---a _reductio ad absurdum_ of the orthodox claim that a first-class constraint generates a gauge transformation _and a second-class constraint does not_. A _reductio_ using massive electromagnetism was presaged in Pitts 2014. Gauge freedom by de-Ockhamization does not require any constraints at all, first-class or second-class, because any dynamical variable in any Lagrangian can be de-Ockhamized into exhibiting trivial additive artificial gauge freedom by splitting one quantity into the sum of two. Physically interesting gauge freedom, however, is typically generated by a tuned sum of first-class constraints, not each first-class constraint alone. (shrink)

In non‐literal uses of language, the content an utterance communicates differs from its literal truth conditions. Loose talk is one example of non‐literal language use (amongst many others). For example, what a loose utterance of (1) communicates differs from what it literally expresses: (1) Lena arrived at 9 o'clock. Loose talk is interesting (or so I will argue). It has certain distinctive features which raise important questions about the connection between literal and non‐literal language use. This paper aims to (i.) (...) introduce a range of novel data demonstrating certain overlooked features of loose talk, and (ii.) develop a new theory of the phenomenon which accounts for these data. In particular, this theory is motivated by the need to explain minimal pairs such as (2)-(3): (2) Lena arrived at 9 o'clock, but she did not arrive at 9 o'clock exactly. (3) ?? Lena did not arrive at 9 o'clock exactly, but she arrived at 9 o'clock. (2) and (3) agree in their truth conditions. Yet they differ in felicity. As such, they constitute a problem for any account which hopes to predict the acceptability of the loose use of a sentence from its truth conditions and the context of utterance alone. Instead, it will be argued, to explain loose talk phenomena we must posit an additional layer of meaning outstripping truth conditions. This layer of meaning is shown to exhibit a range of properties, all of which point to its being semantically encoded. Thus, if correct, the theory provides a new example of how semantic meaning must extend beyond literal, truth‐conditional content. (shrink)

"This admirable volume of readings is the first of a pair: the editors are to be applauded for placing the philosophy of color exactly where it should go, in ...

Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...) per unit of resource devoted to them than each of the other available interventions, including those that focus on the health and well-being of the current population. In this paper, I argue that, even if we grant the consequentialist ethics upon which this argument depends, and even if we grant one of the axiologies that are typically paired with that ethics to give the argument, we are not morally required to choose an option that maximises expected utility; indeed, we might not even be permitted to do so. Instead, I will argue, if the argument's consequentialism is correct, we should choose using a decision theory that is sensitive to risk, and allows us to give greater weight to worse-case outcomes than expected utility theory does. And, I will show, such decision theories do not always recommend longtermist interventions. Indeed, sometimes, they recommend exactly the opposite: sometimes, they recommend hastening human extinction. Many, though not all, will take this as a reductio of the consequentialism or the axiology of the argument. I remain agnostic on the conclusion we should draw. (shrink)

A thought-provoking comparative take on two seminal thinkers in Christian history In this book -- the first volume in the Kierkegaard as a Christian Thinker series -- Lee Barrett offers a novel comparative interpretation of early church father Augustine and nineteenth-century philosopher-theologian Soren Kierkegaard. Though these two intellectual giants have been paired by historians of Western culture, the exact nature of their similarities and differences has never before been probed in detail. Barrett demonstrates that on many essential theological levels (...) Augustine and Kierkegaard were more convergent than divergent. Most significantly, their parallels point to a distinctive understanding of the Christian life as a passion for self-giving love. Approaching Kierkegaard through the lens of Augustine, Barrett argues, enables the theme of desire for fulfillment in God to be seen as much more central to Kierkegaard's thought than previously imagined. (shrink)

Across cultures people construct spatial representations of time. However, the particular spatial layouts created to represent time may differ across cultures. This paper examines whether people automatically access and use culturally specific spatial representations when reasoning about time. In Experiment 1, we asked Hebrew and English speakers to arrange pictures depicting temporal sequences of natural events, and to point to the hypothesized location of events relative to a reference point. In both tasks, English speakers (who read left to right) arranged (...) temporal sequences to progress from left to right, whereas Hebrew speakers (who read right to left) arranged them from right to left, replicating previous work. In Experiments 2 and 3, we asked the participants to make rapid temporal order judgments about pairs of pictures presented one after the other (i.e., to decide whether the second picture showed a conceptually earlier or later time-point of an event than the first picture). Participants made responses using two adjacent keyboard keys. English speakers were faster to make “earlier” judgments when the “earlier” response needed to be made with the left response key than with the right response key. Hebrew speakers showed exactly the reverse pattern. Asking participants to use a space-time mapping inconsistent with the one suggested by writing direction in their language created interference, suggesting that participants were automatically creating writing-direction consistent spatial representations in the course of their normal temporal reasoning. It appears that people automatically access culturally specific spatial representations when making temporal judgments even in nonlinguistic tasks. (shrink)

We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect (...) predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel _indirect_ illusory inferences from disjunction bear a structural similarity to seemingly unrelated _probabilistic reasoning_ problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory. (shrink)

In this paper I argue that according to Malebranche mental attention is the corrective to epistemic error and moral lapse and constitutes the essence of human freedom. Moreover, I show how this conception of human freedom is both morally significant and compatible with occasionalism. By attending to four distinctions made by Malebranche throughout his writings we can begin to understand first, what it means for human beings to exercise their freedom in a way that has some meaningful consequence, and second, (...) how this meaningful consequence does not conflict with occasionalism. The distinctions are: mind/matter, nothing/real, moral/physical, union of the human mind with God/union of the human mind with the human body. By getting clear about how Malebranche sees the overlap between and interconnection among these distinctions we can get a better handle on the metaphysical nature of human freedom, what kind of power it confers on us, and what it entails. I will discuss each distinction is turn starting in 1) with the mind/matter distinction. This first pair will be analyzed by way of a comparison between extended things and thinking things introduced by Malebranche early in *The Search After Truth.* Taking note of where the comparison breaks down, and why, leads directly into 2) where I discuss the nothing/real distinction. This pair is discussed at length in the first Elucidation to *The Search*, the stated objective of which is to clarify what was written in the course of the comparison between mind and matter at the outset of *The Search.* In 3) I analyze the moral/physical distinction, developed in Malebranche’s final work *Réflexions sur la prémotion physique*, and suggest that this pair exactly parallels the nothing/real distinction. In 4) I suggest that the only way to fully understand what is a stake with these distinctions and what Malebranche is trying to do with them is by looking at them in relation to the most important distinction of them all –between the union of the mind and God/union of the mind and body. I conclude in 5) by suggesting a way to understand our power to unite our minds to God. This power does not conflict with occasionalism because it is neither an efficient cause nor does it produce any real effects. It does, nevertheless, have a meaningful role in our moral lives. (shrink)

Although the study of reasons plays an important role in both epistemology and moral philosophy, little attention has been devoted to the question of how, exactly, reasons interact to support the actions or conclusions they do. In this book, John F. Horty attempts to answer this question by providing a precise, concrete account of reasons and their interaction, based on the logic of default reasoning. The book begins with an intuitive, accessible introduction to default logic itself, and then argues that (...) this logic can be adapted to serve as a foundation for a concrete theory of reasons. Horty then shows that the resulting theory helps to explain how the interplay among reasons can determine what we ought to do by developing two different deontic logics, capturing two different intuitions about moral conflicts.In the central part of the book, Horty elaborates the basic theory to account for reasoning about the strength of our own reasons, and also about the related concepts of undercutting defeaters and exclusionary reasons. The theory is illustrated with an application to particularist arguments concerning the role of principles in moral theory. The book concludes by introducing a pair of issues new to the philosophical literature: the problem of determining the epistemic status of conclusions supported by separate but conflicting reasons, and the problem of drawing conclusions from sets of reasons that can vary arbitrarily in strength, or importance. (shrink)

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets (...) of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

The notion that visual attention can operate over visual objects in addition to spatial locations has recently received much empirical support, but there has been relatively little empirical consideration of what can count as an `object' in the ®rst place. We have investi- gated this question in the context of the multiple object tracking paradigm, in which subjects must track a number of independently and unpredictably moving identical items in a ®eld of identical distractors. What types of feature clusters can (...) be tracked in this manner? In other words, what counts as an `object' in this task? We investigated this question with a technique we call target merging: we alter tracking displays so that distinct target and distractor loca- tions appear perceptually to be parts of the same object by merging pairs of items (one target with one distractor) in various ways ± for example, by connecting item locations with a simple line segment, by drawing the convex hull of the two items, and so forth. The data show that target merging makes the tracking task far more dif®cult to varying degrees depending on exactly how the items are merged. The effect is perceptually salient, involving in some conditions a total destruction of subjects' capacity to track multiple items. These studies provide strong evidence for the object-based nature of tracking, con®rming that in some contexts attention must be allocated to objects rather than arbitrary collections of features. In addition, the results begin to reveal the types of spatially organized scene components that can be independently attended as a function of properties such as connectedness, part struc- ture, and other types of perceptual grouping. q 2001 Elsevier Science B.V. All rights reserved. (shrink)

The so-called ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically: $${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$ The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is . I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new (...) argument against it. I appeal to an old triviality result of mine against ‘Stalnaker’s Thesis’ that the probability of a conditional equals the corresponding conditional probability. I showed that for all finite-ranged probability functions, there are strictly more distinct values of conditional probabilities than there are distinct values of probabilities of conditionals, so they cannot all be paired up as Stalnaker’s Thesis promises. Conditional probabilities are too fine-grained to coincide with probabilities of conditionals across the board. If the assertibilities of conditionals are to coincide with conditional probabilities across the board, then assertibilities must be finer-grained than probabilities. I contend that this is implausible—it is surely the other way round. I generalize this argument to other interpretations of ‘ As ’, including ‘acceptability’ and ‘assentability’. I find it hard to see how any such figure of merit for conditionals can systematically align with the corresponding conditional probabilities. (shrink)

In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. Then, (...) we explore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way. How should those credences hang together? How should the credences change in response to evidence? And how should those credences guide the person’s actions? This is the approach of the first six chapters of this handbook. In the second half, we consider different representations—the set of propositions a person believes; their ranking of propositions by their plausibility. And in each case we ask again what the norms are that govern a person so represented. Or, we might represent them as having both credences and full beliefs, and then ask how those two representations should interact with one another. This handbook is incomplete, as such ventures often are. Formal epistemology is a much wider topic than we present here. One omission, for instance, is social epistemology, where we consider not only individual believers but also the epistemic aspects of their place in a social world. Michael Caie’s entry on doxastic logic touches on one part of this topic, but there is much more. Relatedly, there is no entry on epistemic logic, nor any on knowledge more generally. There are still more gaps. These omissions should not be taken as ideological choices. This material is missing, not because it is any less valuable or interesting, but because we v failed to secure it in time. Rather than delay publication further, we chose to go ahead with what is already a substantial collection. We anticipate a further volume in the future that will cover more ground. Why an open access handbook on this topic? A number of reasons. The topics covered here are large and complex and need the space allowed by the sort of 50 page treatment that many of the authors give. We also wanted to show that, using free and open software, one can overcome a major hurdle facing open access publishing, even on topics with complex typesetting needs. With the right software, one can produce attractive, clear publications at reasonably low cost. Indeed this handbook was created on a budget of exactly £0 (≈ $0). Our thanks to PhilPapers for serving as publisher, and to the authors: we are enormously grateful for the effort they put into their entries. (shrink)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof rules has (...) a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

Philosophers often talk as though each ability is held by exactly one agent. This paper begins by arguing that abilities can be held by groups of agents, where the group is not an agent. I provide a new argument for—and a new analysis of—non-agentive groups’ abilities. I then provide a new argument that, surprisingly, obligations are different: non-agentive groups cannot bear obligations, at least not if those groups are large-scale such as ‘humanity’ or ‘carbon emitters.’ This pair of conclusions (...) is important, since philosophers who endorse large-scale non-agentive groups’ abilities almost universally endorse their obligations. More importantly, the twin arguments (one for abilities, one against obligations) make the following novel contribution: abilities imply agency-involving explanations, while obligations imply action-guidance. This general conclusion should be of interest beyond social ontology. (shrink)

Stanley Cavell isn't the first to arrive at philosophy through a life with music. Nor is he the first whose philosophical practice bears the marks of that life. Much of Cavell's life with music is confirmed for the world in his philosophical autobiography Little Did I Know. A central moment in that book is Cavell's describing the realization that he was to leave his musical career behind – for what exactly, he did not yet know. He connects the memory-shock of (...) this leaving with "the work of mourning." How does such a life out of music inform Cavell's philosophical sensibility? The thought I follow in this essay is that Cavell's distinctive orientation in philosophy – call this his lifelong coming to terms with his abandoning a life in music – is guided in part by an interest in those moments in experience where words seem to run out, or veer toward nonsense, leaving in their wake touchstones of ecstasy. I explore this idea by summarizing my exchange with Stanley Cavell years ago when I asked him whether certain passages from his essay "Music Discomposed" are depictions of the unsayable. Cavell's response is elaborated, or qualified, by considering a pair of moments in Little Did I Know where words appear to run out. I conclude by discussing culminating thoughts on the burden borne by words and their failure that appear in Cavell's late essay on music, "Impressions of Revolution.". (shrink)

Philosophers often talk as though each ability is held by exactly one agent. This paper begins by arguing that abilities can be held by groups of agents, where the group is not an agent. I provide a new argument for—and a new analysis of—non-agentive groups’ abilities. I then provide a new argument that, surprisingly, obligations are different: non-agentive groups cannot bear obligations, at least not if those groups are large-scale such as ‘humanity’ or ‘carbon emitters.’ This pair of conclusions (...) is important, since philosophers who endorse large-scale non-agentive groups’ abilities almost universally endorse their obligations. More importantly, the twin arguments (one for abilities, one against obligations) make the following novel contribution: abilities imply agency-involving explanations, while obligations imply action-guidance. This general conclusion should be of interest beyond social ontology. (shrink)

In his paper, ‘Patients, doctors and risk attitudes’, Makins argues that doctors, when choosing a treatment for their patient, need to follow their risk profile.1 He presents a pair of fictitious diseases facing a patient who either has ‘exemplitis’, which requires no treatment or ‘caseopathy’, which is severe and disabling and for which there is a treatment with unpleasant side effects. The doctor needs to decide whether the patient should pursue the unpleasant treatment, just in case he has caseopathy. (...) Makins believes that rational-choice theory is a productive way to approach this problem. This theory frames all decisions as gambles. Each possible gamble (eg, not to pursue treatment) leads, probabilistically, to a set of outcomes (life with no disease and no side effects, but also, possibly, life with a disabling disease, since no treatment is taken). Utilities of these outcomes and probabilities that they will happen are combined to yield a number—expected utility. One is supposed to gamble—to make a choice—in a way that maximises this expected utility. Makins takes this framework for granted and is focused on an additional complication, the patient’s risk preference. He believes that, in his hypothetical example, even if expected utility were exactly the same, withholding treatment …. (shrink)

Linguistic repetitions in children are conceptualized as negative in children with autism – echolalia, without communicative purpose – and positive in typically developing (TD) children – linguistic alignment involved in shared engagement, common ground and language acquisition. To investigate this apparent contradiction we analyzed spontaneous speech in 67 parent–child dyads from a longitudinal corpus (30 minutes of play activities at 6 visits over 2 years). We included 32 children with autism and 35 linguistically matched TD children (mean age at recruitment (...) 32.76 and 20.27 months). We found a small number of exact repetitions in both groups (roughly 1% of utterances across visits), which increased over time in children with autism and decreased in the TD group. Partial repetitions were much more frequent: children reused caregivers' words at high rates regardless of diagnostic group (24% of utterances at first visit), and this increased in frequency (but not level) over time, faster for TD children (at final visit: 33% for autism, 40% for TD). The same happened for partial repetition of syntax and semantic alignment. However, chance alignment (as measured by surrogate pairs) also increased and findings for developmental changes were reliable only for syntactic and semantic alignment. Children with richer linguistic abilities also displayed a higher tendency to partially re–use their caregivers' language (alignment rates and semantic alignment). This highlights that all children commonly re–used the words, syntax, and topics of their caregivers, albeit with some quantitative differences, and that most repetition was at least potentially productive, with repeated language being re–contextualized and integrated with non–repeated language. The salience of echolalia in ASD might be partially explained by slight differences in frequency, amplified by lower semantic alignment, persistence over time, and expectations of echolalia. More in–depth qualitative and quantitative analyses of how repetitions are used and received in context are needed. (shrink)

In De Interpretatione 6-9, Aristotle considers three logical principles: the principle of bivalence, the law of excluded middle, and the rule of contradictory pairs (according to which of any contradictory pair of statements, exactly one is true and the other false). Surprisingly, Aristotle accepts none of these without qualification. I offer a coherent interpretation of these chapters as a whole, while focusing special attention on two sorts of statements that are of particular interest to Aristotle: universal statements not made (...) universally and future particular statements. With respect to the former, I argue that Aristotle takes them to be indeterminate and so to violate the rule of contradictory pairs. With respect to the latter, the subject of the much discussed ninth chapter, I argue that the rule of contradictory pairs, and not the principle of bivalence, is the focus of Aristotle's refutation. Nevertheless, Aristotle rejects bivalence for future particular statements. (shrink)

We illustrate an explicit counterexample to Bell's theorem by constructing a pair of dichotomic variables that exactly reproduce the EPR-Bohm correlations in a manifestly local-realistic manner.

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single (...) particle consists of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

The term 'essentialism' in its popular usage is usually qualified in some way, as in 'biological essentialism', 'gender essentialism' and 'social essentialism'. The essentialist theses were defended on the grounds that denying them leads, under plausible assumptions, to pairs of worlds containing objects which are intrinsic and spatio‐temporal duplicates and yet which are numerically distinct. This chapter outlines some technical difficulties in getting the definitions of 'essential property' and 'individual essence' exactly right. It explains the idea of a metaphysically essential (...) property in terms of Aristotle's 'essential/accidental' contrast. A popular idea is to invoke the notion, which has its roots in Aristotle's theory of essence and accident, of a substance sortal. A different way of developing a sortal‐based account of essential kinds is suggested by David Wiggins, who argues that it is only ultimate sortals that represent essential properties, where an ultimate sortal is the most general sortal corresponding to a given principle of individuation. (shrink)

Jacques Ellul, by far the most significant author in the serious discussions on the interface between religion and technology, is apparently not known to the science‐and‐religion field. The reason is the imprecise use of the terminology. In scientific formulation the relationship can be summarized as technology /religion:: science/theology. The first pair are robust three‐dimensional templates of most human experience; the second pair are linear, abstract concerns of a minority of citizens. In the parallel community—now well developed throughout academia—of (...) science, technology, and society, where the technology/religion matters have been discussed more than the science/religion pair, John Caiazza's point that “techno‐secularism is the real problem” has been front and center for some decades. Among the theologians most aware of this, Raimundo Panikkar, Langdon Gilkey, and Huston Smith, Smith is the one who has taken the case much further than Caiazza, recognizing the danger of the real theological challenge from the religion of scientism and actively working against it. I write from a unique background among those involved in this debate—that of being deeply embedded simultaneously both in the modern science and technology establishment and in the reform of the religious enterprise for fifty years. I make the case that matters are worse than even Smith posits. He shows that scientism as a fundamentalist modern secularism serves the exact function of the theology behind the practiced religion of America and the West, that is, technology. An unexpected ray of hope has appeared in the sudden emergence of whole‐person healing (also known as complementary and alternative medicine), which is used regularly by well over half the population. This reintroduction of the spiritual dimension into this key technology of health will certainly be a major turning point. (shrink)

A linguistic theory is correct exactly to the extent that it is the explicit statement of a body of knowledge possessed by a designated language-user. This popular psychological conception of the goal of linguistic theorizing is commonly paired with a preference for idiolectal over social languages, where it seems to be in the nature of idiolects that the beliefs one holds about one’s own are ipso facto correct. Unfortunately, it is also plausible that the correctness of a genuine belief cannot (...) consist merely in that belief’s being held. This paper considers how best to eliminate this tension. (shrink)

Both and agree that there are universals—that qualities are universals. To say that the quality white is a universal is to say, in part, that one and the same thing is connected in some way to both Plato and Socrates and accounts for the truth of the sentences "Plato is white" and "Socrates is white." To put it another way, the term "white" in both sentences refers to the same entity. What arguments are there for such a view? Russell elegantly (...) put forth the classic argument in "On the Relations of Universals to Particulars." To deny universals is to assert that the quality attributed to Socrates is not one and the same with the quality attributed to Plato. The quality "in" each is numerically distinct and, furthermore, no one thing accounts for these distinct qualities being of the same kind. [I mention this latter point since one might, on a version of, hold that there are particular qualities as well as universal qualities. The former account for the whiteness of particular patches; the latter for such particular whitenesses being just that.] One must then hold that such particular qualities are related in some way, since they are the entities in virtue of which we truly assert that both things are white. One must then specify such a relation. The obvious point is that such a relation will either be taken as a universal or a particular instance. If a particular then the original problem recurs when we introduce a third white patch or a pair of black patches. If admitted as a universal then the view finally accepts universals, albeit relational ones. No other alternative can answer the original question—to account for Socrates and Plato having the same color. That is, no alternative acknowledging only individuals—that denies the two patches are connected, in some way, to one and the same entity—can prevent the recurrence of exactly the same kind of question we started out with. Let us consider the case of particulars. One may argue that just as universals account for the sameness of quality, something must account for the difference of two patches which, conceivably, have all their nonrelational qualities in common. This something, the ground of numerical difference, is considered to be a substratum which stands in a unique relation or connection with universals to form or constitute facts and the things we started out with, Plato and Socrates. These ordinary things are thought of as composed of a substratum and universals connected together. Facts about such things may be composed of the substratum and one universal. The facts are about the things since the same substratum is a constituent of both sorts of entities. Such substrata account for the difference of the two patches; for there being two and not one thing. These substrata, in turn, are held to be simply different. At this point one may balk. If substrata are held to be simply different, why bother with them at all? Why not hold that Socrates and Plato are composites, not classes, of universals, and that they are different composites of the same universals? They just simply differ. If substrata can simply differ, why may not composites of universals simply differ? The proponent of substrata must retort that since Plato and Socrates are composite entities they cannot simply differ but must be held to differ in a constituent. Only simple entities can simply differ. Let me call this assertion the axiom of difference. The first point to note is that it is a necessary assumption in the argument to establish the need for substrata in an adequate ontology. We must then inquire why some accept, implicitly or explicitly, such an axiom. (shrink)

Across eight experiments (N = 2310), we studied whether people would prioritize rescuing individuals who may be thought to contribute more to society. We found that participants were generally dismissive of general rules that prioritize more socially beneficial individuals, such as doctors instead of unemployed people. By contrast, participants were more supportive of one-off decisions to save the life of a more socially beneficial individual, even when such cases were the same as those covered by the rule. This generality effect (...) occurred robustly even when controlling for various factors. It occurred when the decision-maker was the same in both cases, when the pairs of people differing in the extent of their indirect social utility was varied, when the scenarios were varied, when the participant samples came from different countries, and when the general rule only covered cases that are exactly the same as the situation described in the one-off condition. The effect occurred even when the general rule was introduced via a concrete precedent case. Participants' tendency to be more supportive of the one-off proposal than the general rule was significantly reduced when they evaluated the two proposals jointly as opposed to separately. Finally, the effect also occurred in sacrificial moral dilemmas, a general phenomenon occurring in multiple moral contexts. We discuss possible explanations of the effect, including concerns about negative consequences of the rule and a deontological aversion against making difficult trade-off decisions unless they are absolutely necessary. (shrink)