Symmetric informationally complete quantum measurements, or SICs, are mathematically intriguing structures, which in practice have turned out to exhibit even more symmetry than their definition requires. Recently, Zhu classified all the SICs whose symmetry groups act doubly transitively. I show that lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups.

Nicholas Rescher examines the controversial social issue of the welfare state, and offers philosophical thoughts on the limits and liabilities of government and society. Questioning some of the principal assumptions of democratic theory and classical liberalism, Rescher theorizes that the current system is not a be-all end-all, but rather a necessity with limited scope that will ultimately fail to achieve its objectives. He further purports that the welfare state must be a transitional phase to a more affluent postindustrial society-a satisfying (...) life, rather than an adequate one. (shrink)

We report the identification of a recurrent, 520-kb 16p12.1 microdeletion associated with childhood developmental delay. The microdeletion was detected in 20 of 11,873 cases compared with 2 of 8,540 controls and replicated in a second series of 22 of 9,254 cases compared with 6 of 6,299 controls. Most deletions were inherited, with carrier parents likely to manifest neuropsychiatric phenotypes compared to non-carrier parents. Probands were more likely to carry an additional large copy-number variant when compared to matched controls. The clinical (...) features of individuals with two mutations were distinct from and/or more severe than those of individuals carrying only the co-occurring mutation. Our data support a two-hit model in which the 16p12.1 microdeletion both predisposes to neuropsychiatric phenotypes as a single event and exacerbates neurodevelopmental phenotypes in association with other large deletions or duplications. Analysis of other microdeletions with variable expressivity indicates that this two-hit model might be more generally applicable to neuropsychiatric disease. © 2010 Nature America, Inc. All rights reserved. (shrink)

During much of the past century, it was widely believed that phonemes--the human speech sounds that constitute words--have no inherent semantic meaning, and that the relationship between a combination of phonemes (a word) and its referent is simply arbitrary. Although recent work has challenged this picture by revealing psychological associations between certain phonemes and particular semantic contents, the precise mechanisms underlying these associations have not been fully elucidated. Here we provide novel evidence that certain phonemes have an inherent, non-arbitrary emotional (...) quality. Moreover, we show that the perceived emotional valence of certain phoneme combinations depends on a specific acoustic feature--namely, the dynamic shift within the phonemes' first two frequency components. These data suggest a phoneme-relevant acoustic property influencing the communication of emotion in humans, and provide further evidence against previously held assumptions regarding the structure of human language. This finding has potential applications for a variety of social, educational, clinical, and marketing contexts. (shrink)

Sociopolitical attitudes are often the root cause of conflicts between individuals, groups, and even nations, but little is known about the origin of individual differences in sociopolitical orientation. We test a combination of economic and evolutionary ideas about the degree to which the mating market, sex, age, and income affect sociopolitical orientation. We collected data online through Amazon’s Mechanical Turk from 1108 US participants who were between 18 and 60, fluent in English, and single. While ostensibly testing a new online (...) dating website, participants created an online dating profile and described people they would like to date. We manipulated the participants’ popularity in the mating market and the size of the market and then measured participants’ sociopolitical attitudes. The sociopolitical attitudes were reduced to five dimensions via Principal Components Analysis. Both manipulations affected attitudes toward wealth redistribution but were largely not significant predictors of the other dimensions. Men reported more unrestricted sociosexual attitudes, and more support for benevolent sexism and traditional family values, than women did, and women supported wealth redistribution more than men did. There was no sex difference in accepting nonconforming behaviors. Younger people and people with lower incomes were more liberal than older people and people with higher incomes, respectively, regardless of sex. Overall, effects were largely not interactive, suggesting that individual differences in sociopolitical orientation may reflect strategic self-interest and be more straightforward than previously predicted. (shrink)

In a morally fragmented society there is no good reason for ethics committees to assume any particular point of view, yet failure to do so compromises their ability to function in either a case‐review or an educational capacity. A casuist methodology might enable committees to fulfill both roles.

Judicial reasoning in termination of treatment decisions has neglected valid state interests in the preservation of life and the ethical integrity of medicine. Courts must balance these interests against individual liberty, rather than assuming that patient autonomy is absolute.

Incorporating theoretic insights from ageing biology could advance the “staying alive” hypothesis. Higher male extrinsic mortality can weaken selection against ageing-related diseases and self-preservation, leading to high male intrinsic mortality. This may incidentally result in female-biased longevity-promoting traits, a possibility that will require rigorous testing in order to disentangle from the adaptive self-preservation hypothesis presented in the target article.

Despite a large and multifaceted effort to understand the vast landscape of phenotypic data, their current form inhibits productive data analysis. The lack of a community-wide, consensus-based, human- and machine-interpretable language for describing phenotypes and their genomic and environmental contexts is perhaps the most pressing scientific bottleneck to integration across many key fields in biology, including genomics, systems biology, development, medicine, evolution, ecology, and systematics. Here we survey the current phenomics landscape, including data resources and handling, and the progress that (...) has been made to accurately capture relevant data descriptions for phenotypes. We present an example of the kind of integration across domains that computable phenotypes would enable, and we call upon the broader biology community, publishers, and relevant funding agencies to support efforts to surmount today's data barriers and facilitate analytical reproducibility. (shrink)

The Protein Ontology (PRO) provides a formal, logically-based classification of specific protein classes including structured representations of protein isoforms, variants and modified forms. Initially focused on proteins found in human, mouse and Escherichia coli, PRO now includes representations of protein complexes. The PRO Consortium works in concert with the developers of other biomedical ontologies and protein knowledge bases to provide the ability to formally organize and integrate representations of precise protein forms so as to enhance accessibility to results of protein (...) research. PRO (http://pir.georgetown.edu/pro) is part of the Open Biomedical Ontologies (OBO) Foundry. (shrink)

An ideal vision model accounts for behavior and neurophysiology in both naturalistic conditions and designed lab experiments. Unlike psychological theories, artificial neural networks (ANNs) actually perform visual tasks and generate testable predictions for arbitrary inputs. These advantages enable ANNs to engage the entire spectrum of the evidence. Failures of particular models drive progress in a vibrant ANN research program of human vision.

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...) by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...) better thought of as an early stage of a dialogue than as a definitive treatise. (shrink)

It is widely agreed by philosophers that the so-called “Frege-Russell definition of natural number” is actually an assertion concerning the nature of the numbers and that it cannot be regarded as a definition in the ordinary mathematical sense. On the basis of the reasoning in this paper it is clear that the Frege-Russell definition contradicts the following three principles (taken together): (1) each number is the same entity in each possible world, (2) each number exists in each possible world, (3) (...) some entities existing in the actual world do not exist in every possible world. Since these principles seem to be true, the paper is a refutation of the Frege-Russell definition. The paper does more. It shows that the contradictory of the Frege-Russell definition follows even when principles 2 and 3 are replaced by one considerably weaker principle. The ideas contained in the paper are related to two earlier objections to the definition. The first, sometimes attributed to the mathematician, C. S. Keyser, is that existence of the numbers as defined implies the existence of infinitely many particulars in each possible world. The second is, in effect, an idea which is said to have led Whitehead to reject the definition of number to which he had subscribed in Principia Mathematica. Whitehead is supposed to have said that he could not believe that the number two changes every “time twins are born”. The mathematician H. Jeffreys expressed similar ideas [Philos. of Sci. 5 (1938), 434–451]. One of the merits of the author’s work is that it refutes the Frege-Russell definition without the need to take sides on controversial points presupposed by the Keyser and Whitehead objections. The objections made by the author are therefore not to be identified with the Keyser and Whitehead objections. Even if the author’s work is to be regarded as a refinement and integration of previous ideas, it is nevertheless a contribution—not only because the basic points are well worth repeating but also because the refinements are logically significant improvements and because the author has stated them clearly and concisely in the idiom of contemporary philosophy. (shrink)

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...) many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...) that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Sophocles’s Enemy Sisters: Antigone and IsmeneWm. Blake Tyrrell (bio) and Larry J. BennettAt the core of the Oedipus myth, as Sophocles presents it, is the proposition that all masculine relationships are based on reciprocal acts of violence. Laius, taking his cue from the oracle, violently rejects Oedipus out of fear that his son will seize his throne and invade his conjugal bed. Oedipus, taking his cue from the (...) oracle, does away with Laius, violently rebuffs the sphinx, then takes their places—as king and “scourge of the city,” respectively. Again, Oedipus, taking his cue from the oracle, plots the death of that unknown figure who may be seeking to usurp his own position. Oedipus, Creon, and Tiresias, each taking his cue from the oracle, seek one another’s downfall.All these acts of violence gradually wear away the differences that exist not only in the same family but throughout the community.—René Girard, Violence and the SacredRené Girard does not include feminine relationships in his assessment of the Oedipus myth, yet the same redundancy that characterizes the males marks the females.1 Jocasta conjoins in one person multiple and redundant social roles: she is the mother and wife of the same person, for which she [End Page 1] hangs herself, leaving for Oedipus “many pains that a mother’s furies fulfilled” (Homer Odyssey 11.279–80). Her daughters, their father’s sisters, manifest kinship redundancy in two persons. Incest produces circularly, reverting to a sibling of the parent rather than moving forward with a descendant. The absence of linear progression from one generation to the next creates a sameness and equilibrium that thwart separation and individuality. Oedipus’s brothers/sons fail in their adult roles, because neither can overcome the other’s right to the throne of Thebes and the mastery of its royal household. They are enemy brothers locked in reciprocal violence.2 Antigone and Ismene have escaped notice not only as enemy sisters but even as products of the same incest. Audiences for Sophocles’s Antigone have viewed them as “normal” women and cooperated with his characters in emphasizing the differences between them. They have assumed from Antigone’s betrothal to Haemon and resistance to Creon that she is the elder, more mature sister.3 They tend to accept without question that Antigone engages in burial rituals with Polyneices’s corpse (241–58) and returns to it (442–35).4 Bernard M. W. Knox’s critically powerful concept of the “Sophoclean hero” has bolstered this view of Antigone while reducing Ismene to a foil, and abetted the tendency of modern producers of the play to cast an older or more famous actress in the role of Antigone.5 Naturalistic readings like that of C. M. Bowra—“seeing that Ismene is her only close relative in the world, Antigone is remarkably cold to her”6—have masked the source and hence the vehemence of Antigone’s fury.That the reciprocity of the violence between Ismene and Antigone has gone unnoticed is understandable in view of the familiarity of the conflict between their brothers. Males in Greek society pursued difference by striving to excel as aristoi (best) in competition for prestige, wealth, and power.7 Whenever Eteocles and Polyneices came together, each asserted a right to Oedipus’s household and throne that was equally matched, and violence ensued from the equilibrium. On the other hand, Greek women were not supposed to compete with one another for distinction. They wove wool for clothes, maintained the household, and cared for the children, the sick, and the dead, activities that required cooperation away from public view.8 Proximity to other women was the norm and desideratum. Moreover, lawgivers like Solon based their funeral legislation on the premise that every woman wanted to participate in mourning.9 For the sake of public tranquillity, legislators tried to limit the numbers of women participants by imposing restrictions according to degrees of kinship, for instance, to children of fifth cousins. In this context, women were interchangeable, and the places they held during birth, coming of age in wedding ceremonies, and death, [End Page 2] were open to more than one woman. Closeness and... (shrink)

Open peer commentary on the article “Designing Constructionist E-Books: New Mediations for Creative Mathematical Thinking?” by Chronis Kynigos. Upshot: As a mathematics teacher educator and “digital tourist,” I focus my response to the many questions posed by Kynigos from three perspectives. First, I outline the theories he uses to frame the reporting of the research into the design of constructionist e-books. Second, I compare his theoretical tools with design-based research as an organising framework for a research project of this nature. (...) Third, I propose the possible contribution of further theory-testing to the work. (shrink)

Corcoran, J. 2007. Syntactics, American Philosophy: an Encyclopedia. 2007. Eds. John Lachs and Robert Talisse. New York: Routledge. pp.745-6. -/- Syntactics, semantics, and pragmatics are the three levels of investigation into semiotics, or the comprehensive study of systems of communication, as described in 1938 by the American philosopher Charles Morris (1903-1979). Syntactics studies signs themselves and their interrelations in abstraction from their meanings and from their uses and users. Semantics studies signs in relation to their meanings, but still in (...) abstraction from their uses and users. Pragmatics studies signs as meaningful entities used in various ways by humans. Taking current written English as the system of communication under investigation, it is a matter of syntactics that the two four-character strings ‘tact’ and ‘tics’ both occur in the ten-character string ‘syntactics’. It is a matter of semantics that the ten-character string ‘syntactics’ has only one sense and, in that sense, it denotes a branch of semiotics. It is a matter of pragmatics that the ten-character string ‘syntactics’ was not used as an English word before 1937 and that it is sometimes confused with the much older six-character string ‘syntax’. Syntactics is the simplest and most abstract branch of semiotics. At the same time, it is the most basic. Pragmatics presupposes semantics and syntactics; semantics presupposes syntactics. The basic terms of syntactics include the following: ‘character’ as alphabetic letters, numeric digits, and punctuation marks; ‘string’ as sign composed of a concatenation of characters; ‘occur’ as ‘t’ and ‘c’ both occur twice in ‘syntactics’. However, perhaps the most basic terms of syntactics are ‘type’ and ‘token’ in the senses introduced by Charles Sanders Peirce (1839-1914), America’s greatest logician, who could be considered the grandfather of syntactics, if not the father. These are explained below. (shrink)

The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact fallacy if (...) they think that a proposition has different consequences were it true than it would have if false. C. I. Lewis said that confusing logical consequence with material consequence leads to this fallacy. See Corcoran’s 1973 “Meanings of implication” [available on Academia. edu]. -/- The premise-fact confusion occurs in a written passage that implies the premise-fact fallacy or that suggests that the writer isn’t clear about the issues involved in the premise-fact fallacy. Here are some examples. -/- E1: If Abe is Ben and Ben swims, then it would follow that Abe swims. -/- Comment: The truth is that from “Abe is Ben and Ben swims”, the proposition “Abe swims” follows. Whether in fact Abe is Ben and Ben swims is irrelevant to whether “Abe swims” follows from “Abe is Ben and Ben swims”. -/- E1 suggests that maybe “Abe swims” wouldn’t follow from “Abe is Ben and Ben swims” if the latter were false. -/- E2: The truth of “Abe is Ben and Ben swims” implies that Abe swims. -/- E3: Indirect deduction requires assuming something false. -/- Comment: If the premises of an indirect deduction are true the conclusion is true and thus the “reductio” assumption is false. But deduction, whether direct or indirect, does not require true premises. In fact, indirect deduction is often used to determine that the premises are not all true. -/- Anyway, the one-page paper accompanying this abstract reports one of dozens of premise-fact errors in PRIOR ANALYTICS. In the session, people can add their own examples and comment on them. For example, is the one at 25b32 the first? What is the next premise-fact error after 25b32? Which translators or commentators discuss this? -/- . (shrink)