We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by (...) number of symbols or by number of inferences, for tree-like or dag-like proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs. (shrink)

This article analyzes the relationship between the structure of federal Title IX investigations and the existing evidence addressing the emotional and mental health needs of sexual harassment and sexual assault victims. The article argues that federal requirements for investigating sexual harassment should be restructured so as to address the challenges stigma poses for the realization of Title IX's objectives.

This particular roundtable falls at the end of a four-year networking project (COST Action IS1307 New Materialism: Networking European Scholarship on ‘How Matter Comes to Matter’) and reflects upon the genealogies of new materialism and how these flow into the individual working practices of participants. The texts below were contributed remotely via email by members of the group, following face-to-face meetings in Barcelona, Maribor, Warsaw, Liverpool, Paris and Utrecht. Authors were unaware of each other’s responses and in this way the (...) dialogue has unfolded a little like a game of Exquisite Corpse or Consequences, with questions acting like a trail of breadcrumbs to follow. Accordingly, the text is the product of a partially bounded experimental system ‘designed to give unknown answers to questions that the experimenters themselves are not yet able to clearly ask’ (Rheinberger 1997: 28). Thus, it both ruminates upon work to date and is intended to generate novel responses from authors and readers alike. (shrink)

This paper studies the complexity of constant depth propositional proofs in the cedent and sequent calculus. We discuss the relationships between the size of tree-like proofs, the size of dag-like proofs, and the heights of proofs. The main result is to correct a proof construction in an earlier paper about transformations from proofs with polylogarithmic height and constantly many formulas per cedent.

We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory [Formula: see text] is consistent with the conjecture that [Formula: see text], i.e. some problem that is solvable in non-deterministic exponential time does not have polynomial size circuits. We suggest this is the best currently available evidence for the truth of the conjecture. The same techniques establish the same results with [Formula: see text] replaced (...) by the class of problems decidable in non-deterministic barely superpolynomial time such as [Formula: see text]. Additionally, we establish a magnification result on the hardness of proving circuit lower bounds. (shrink)

Across species, animals have an intrinsic drive to approach appetitive stimuli and to withdraw from aversive stimuli. In affective science, influential theories of emotion link positive affect with strengthened behavioural approach and negative affect with avoidance. Based on these theories, we predicted that individuals’ positive and negative affect levels should particularly influence their behaviour when innate Pavlovian approach/avoidance tendencies conflict with learned instrumental behaviours. Here, across two experiments – exploratory Experiment 1 (N = 91) and a preregistered confirmatory Experiment 2 (...) (N = 335) – we assessed how induced positive and negative affect influenced Pavlovian-instrumental interactions in a reward/punishment Go/No-Go task. Contrary to our hypotheses, we found no evidence for a main effect of positive/negative affect on either approach/avoidance behaviour or Pavlovian-instrumental interactions. However, we did find evidence that the effects of induced affect on behaviour were moderated by individual differences in self-reported behavioural inhibition and gender. Exploratory computational modelling analyses explained these demographic moderating effects as arising from positive correlations between demographic factors and individual differences in the strength of Pavlovian-instrumental interactions. These findings serve to sharpen our understanding of the effects of positive and negative affect on instrumental behaviour. (shrink)

Definitions of health and disease are of more than theoretical interest. Understanding what it means to be healthy has implications for choices in medical treatment, for ethically sound informed consent, and for accurate assessment of policies or programs. This deeper understanding can help us create more effective public policy for health and medicine. It is notable that such contentious legal initiatives as the Americans with Disability Act and the Patients' Bill of Rights fail to define adequately the medical terms on (...) which their effectiveness depends. In Ethics and the Metaphysics of Medicine, Kenneth Richman develops an "embedded instrumentalist" theory of health and applies it to practical problems in health care and medicine, addressing topics that range from the philosophy of science to knee surgery."Embedded instrumentalist" theories hold that health is a match between one's goals and one's ability to reach those goals, and that the relevant goals may vary from individual to individual. This captures the normative implications of the term health while avoiding problematic relativism. Richman's embedded instrumentalism differs from other theories of health in drawing a distinction between the health of individuals as biological organisms and the health of individuals as moral agents. This distinction illuminates many difficulties in patient-provider communication and helps us understand conflicts between promoting health and promoting ethically permissible behavior. After exploring, expanding, and defending this theory in the first part of the book, Richman examines its ethical implications, discussing such concerns as the connection between medical beneficence and respect for autonomy, patient-provider communication, living wills, and clinical education. (shrink)

The concept of lying is generally assumed to be closely related to the concept of assertion. However, the literature on lying has focused almost exclusively on lies expressed by unqualified assertions. Sometimes a speaker chooses to qualify her assertion by hedging, making her utterance a hedged declarative. This paper defends the thesis that lies can be expressed by untruthful hedged declaratives, and explores the implications of this thesis for the definition of lying. Many standard approaches to the definition of lying (...) allow lies to be expressed by untruthful hedged declaratives, which may explain why these cases have been ignored in the literature. However, untruthful hedged declaratives present a problem for a recently-proposed theory that analyzes lying in terms of the Knowledge Norm of Assertion. According to this theory, a necessary condition on lying is that in asserting that p, the speaker represents herself as knowing that p; however, in making an untruthful hedged declarative a speaker represents herself as having an epistemic attitude weaker than knowledge. The fact that such a theory fails to adequately explain untruthful hedged declaratives provides a reason to prefer alternative theories of lying. The discussion draws out some important observations about the concepts of lying, assertion, belief, and the relations between them. (shrink)

Is time necessary for causation? We argue that, given a counterfactual theory of causation, it is not. We defend this claim by considering cases of counterfactual dependence in quantum mechanics. These cases involve laws of nature that govern entanglement. These laws make possible the evaluation of causal counterfactuals between space-like separated entangled particles. There is, for the proponent of a counterfactual theory of causation, a possible world in which causation but not time exists that can be reached by ‘stripping out’ (...) time from the actual world, leaving quantum mechanical laws intact. (shrink)

Michelle Garcia Winner’s Social Thinking Curriculum is widely used by schools across the USA and has garnered attention internationally. The curriculum addresses social language and behavior deficits among those on the autism spectrum. Although many embrace this curriculum without reservation, the emphasis on social conformity, including avoiding behaviors that make others uncomfortable, merits scrutiny. Individuals who have difficulty understanding social cues and conventions can derive tremendous benefit from learning to fit in, for example, or learning what is likely to make (...) others uncomfortable and why. However, too much emphasis on pleasing others can reinforce undesirable tendencies. For example, autism is already linked to avoidant personality disorder. An emphasis on avoiding making others uncomfortable may also inhibit the development of principled ethical thinking and action. Reframing social thinking to treat it not (or not only) as an end in itself, but as a way to achieve a variety of social and personal goals would go a long way toward addressing the weaknesses of the Social Thinking Curriculum. (shrink)

Sam Harris dismantles the most common justification for religious faith--that a moral system cannot be based on science.

As a neurodevelopmental condition that affects cognitive functioning, autism has been used as a test case for theories of moral responsibility. Most of the relevant literature focuses on autism’s impact on theory of mind and empathy. Here I examine aspects of autism related to executive function. I apply an account of how we might fail to be reasons responsive to argue that autism can increase the frequency of excuses for transgressive behavior, but will rarely make anyone completely exempt from moral (...) responsibility in general. On this account, although excuses may apply more often to autists than to others, the excuses that apply to autists are just the same excuses that can apply to anyone. (shrink)

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

This paper responds to Goodwin Liu's argument in Volume II of this Journal that a pedagogy must be supported by an appropriate theory of knowledge, and that the epistemology which best supports the service-learning pedagogy is anti-foundational pragmatism. The author shows that Liu's characterization of the pragmatist model of knowledge does not avoid the dualism which he sees as a fault of the traditional epistemology. After suggesting a remedy to this, the author then extends Liu's argument by indicating the limits (...) to what the appropriately modified epistemological support will sanction. These limits are shown to be more restrictive than Liu suggests. The result is an improved philosophical justification of the service-learning pedagogy and some suggestions for evaluating proposed curriculum. (shrink)

We consider two categorical syllogisms, valid or invalid, to be equivalent if they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. For a more natural development, using group-theoretic methods, the space of syllogisms is enlarged to include nonstandard syllogisms, and various groups of transformations (...) on that space are studied. (shrink)

Whether to treat autism as exculpatory in any given circumstance appears to be influenced both by models of autism and by theories of moral responsibility. This article looks at one particular combination of theories: autism as theory of mind challenges and moral responsibility as requiring appropriate experience of the reactive attitudes. In pursuing this particular combination of ideas, we do not intend to endorse them. Our goal is, instead, to explore the implications of this combination of especially prominent ideas about (...) autism and about moral responsibility. These implications can be quite serious and practical for autists and those who interact directly with autists, as well as for broader communities as they attend to the fair, compassionate, and respectful treatment of increasing numbers of autistic adults. We find that these theories point to a limited range of situations in which autists should not be blamed for transgressive actions for which neurotypical individuals should be blamed. We build on what others have written on these issues by bringing in a recent cognitive model of the role theory of mind plays in empathy, by discussing the social implications of the theoretical findings, and by raising questions about the compatibility of reactive attitude theories of moral responsibility with the neurodiversity approach to autism. (shrink)

A fragmented and unfirnished exploration into the realist and anti-realist debate in mathematics. And the subsequent exploration of how novelty and creation works on a fundemental epistemic scale. The paper puts forth two major frameworks that attempt to bridge realism and anti-realism and provides a novel solution to the epistemic problem of true novelty and idea generation.

In an earlier Dissecting Bioethics contribution, Debra J. H. Mathews, Joseph J. Fins, and Eric Racine challenge standard ways of thinking about the therapeutic misconception in the context of consent for research participation. They propose that instead of demanding “rational congruence” between how researchers and participants conceive of a given protocol, we should accept a less stringent standard of “reasonable coherence.” While Mathews, Fins, and Racine (MFR) provide some important insights, their proposal needs refinement. There is room for a wide (...) but not unlimited range of participant hopes and motivations. However, their model of reasonable coherence is too weak a standard for whether participants have adequate understanding of the scientific goals of a protocol. By the time participants are recruited for medical research, the goals of the protocol, having been set and agreed to through accepted scientific processes, are no longer open for alternate interpretations. This paper discusses this and other objections to MFR’s proposal. It then suggests that a concept of “deal breakers” might be useful in this context. (shrink)

Ethicists, researchers and policy makers have paid increasing attention to the ethical conduct of research, especially research involving human beings. Research performed with and by undergraduates poses a specific set of ethical challenges. These challenges are often overlooked by the research community because it is assumed that undergraduate student researchers do not have a significant impact on the research community and that their projects are not host to research posing important ethical issues. This paper identifies several features characteristic of research (...) in undergraduate environments. The paper pays special attention to selective small liberal arts colleges, an important segment of higher education in the US, and advocates integrating instruction in research ethics wherever undergraduates are engaged in research. (shrink)

This article's polemical thrust begins with Georges Bataille's 1956 critique of Tristes Tropiques, where Lévi-Strauss omits the Palaeolithic while extolling the Neolithic advent of agriculture and sedentism. Whereas Lévi-Strauss describes his own thinking as Neolithic, he characterizes it in ways that resemble the behaviour of hunter-gatherers and nomads. I trace this contradiction to current scholarship willing to challenge the long-standing narrative bias that either ignores the Palaeolithic and/or derides it in favour of the Neolithic, now subject to refutations of its (...) alleged advantages. Further theoretical backbone is provided by Ibn Khaldun and Bataille on the centrality of luxury. Thus, Palaeolithic cave art's social dimension as the expression of a privileged few is contrasted with the view of scholars who see it as the product of an egalitarian society indifferent to material gain. Bataille remains a key reference due to his exceptional commitment to prehistory, a relatively underexploited facet of his work. (shrink)

Atomic states are rigorously characterized by the total orbital angular momentum and the total spin angular momentum, but chemists persist in the use of electron configurations based on one-electron quantum numbers and simplified rules for predicting ground state configurations. This practice is defended against two lines of criticism, and its use in teaching chemistry is encouraged with the claim that the inductive approach of Mendeleev and the deductive approach initiated by Schrödinger compose the consummate example of that interaction of empirical (...) and rational epistemologies that defines how chemists think. (shrink)