This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic of belief change (...) is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine. -/- . (shrink)

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of generalizing (...) Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems. (shrink)

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of generalizing (...) Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems. (shrink)

Under the presupposition that human time perception is distorted in intertemporal choice, this study constructs a time scale in the framework of axiomatic measurement. First, the conditions (homogeneity of degree one or two) to identify the form of a time scale are proposed so that one can determine whether the hyperbolic or exponential is a more suitable function for modeling people’s discounting. Homogeneity of degree one implies that subjective time delay is measured by a power scale and its discount function (...) becomes a power-exponential type, whereas homogeneity of degree two implies that subjective time delay is measured by a log scale and its discount function becomes a hyperbolic type. Second, a method is shown for constructing a model that can reflect subadditive and superadditive discounting. A non-commutative and non-associative concatenation operation is provided to generate a time string consisting of subdivided durations that incorporates the effect of repeated delay with a subdivided duration. The discounting model is yielded by substituting these strings in an exponential model equipped with a generalized time scale, and the determination of subadditivity or superadditivity depends on whether the discount function value of a product by the non-commutative and non-associative operation is, respectively, smaller or greater than that of a product by an operation of the usual extensive structure. (shrink)

The nonadditive properties of mass make it desirable to abandon mass as a basis unit in physics and to replace it by a unit of the dimension of the quantum of action [h]. The ensuing four-unit system of action, charge, length, and time [h, q, l, t] interacts in a much more elucidating fashion with experiment and with the fundamental structure of physics. All space-time differential forms expressing fundamental laws of physics are forms of physical dimensions, h, h/q, or q. (...) Their occurrence as periods (residues) of period integrals of forms makes h and q topological invariants in space-time and stresses in general the global nature of quantization. The coordinate dimensions [l] and [t] only come into play for the form-coefficients, the metric tensor, and their tensorial relatives. One thus obtains a very natural guidance for implementing the principle of general covariance, when coordinate-based descriptions are necessary. The consequences for the general theory of relativity are discussed. (shrink)

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable (...) by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

Memory exhibits episodic superposition, an analog of the quantum superposition of physical states: Before a cue for a presented or unpresented item is administered on a memory test, the item has the simultaneous potential to occupy all members of a mutually exclusive set of episodic states, though it occupies only one of those states after the cue is administered. This phenomenon can be modeled with a nonadditive probability model called overdistribution (OD), which implements fuzzy-trace theory's distinction between verbatim and gist (...) representations. We show that it can also be modeled based on quantum probability theory. A quantum episodic memory (QEM) model is developed, which is derived from quantum probability theory but also implements the process conceptions of global matching memory models. OD and QEM have different strengths, and the current challenge is to identify contrasting empirical predictions that can be used to pit them against each other. (shrink)

Many different arguments have been put forward in order to assign the best place for a given element within Mendeleev's Table: its spectroscopy, its chemical activity, the crystalline structure of its solid state, etc. We here propose another criterion; the nature of the few body corrections to the pairwise additive energy. This argument is used here to address a question often brought forward by Eric Scerri in Foundations of Chemistry, namely the rightful place of helium; either above the column of (...) the alkaline earths (beryllium, etc.) or rather above the noble gas elements. (shrink)

Every so often an experiment trying to give reliable evidence for a metallic hydrogen solid is reported. Such evidence is, however, not too convincing. As Eric Scerri has recently reiterated, “the jury is still out on that issue” . This search stems from the common spectroscopy shared by the hydrogen atom and all the alkali metal atoms, and perhaps is guided by a desire to place hydrogen atop the alkali metals, in Mendeleiev’s Table, reinforced by the fact pointed out by (...) Scerri that there is no other obvious place for hydrogen in said Table. But H2 is a light gas at room temperature, while Li, Na, K and the other alkali elements form solid metal crystals. At very low temperatures, of course, hydrogen solidifies, but it is formed by H2 molecules . Our purpose here is to use a new argument to break this impasse: “should H be grouped with the alkali metals with which it shares a common spectroscopy, but which solidifies in a completely different fashion?” This argument has been proposed before in a couple of papers in this journal to establish a similar question for He and the alkaline earths , as is discussed in “Precedents” section. (shrink)

Denis Walsh has written a striking new defense in this journal of the statisticalist (i.e., noncausalist) position regarding the forces of evolution. I defend the causalist view against his new objections. I argue that the heart of the issue lies in the nature of nonadditive causation. Detailed consideration of that turns out to defuse Walsh’s ‘description‐dependence’ critique of causalism. Nevertheless, the critique does suggest a basis for reconciliation between the two competing views. *Received December 2009; revised December 2009. †To contact (...) the author, please write to: Department of Philosophy, 599 Lucas Hall, One University Boulevard, University of Missouri, St. Louis, MO 63121; e‐mail: [email protected]. (shrink)

It has been proposed that natural selection occurs on a hierarchy of levels, of which the organismic level is neither the top nor the bottom. This hypothesis leads to the following practical problem: in general, how does one tell if a given phenomenon is a result of selection on level X or level Y. How does one tell what the units of selection actually are?It is convenient to assume that a unit of selection may be defined as a type of (...) entity for which there exists, among all entities on the same level as that entity, an additive component of variance for some specific component F of fitness which does not appear as an additive component of variance in any decomposition of this F among entities at any lower level. But such a definition implicitly assumes that if f(x, y) depends nonadditively on its arguments, there must be interaction between the quantities which x and y represent. This assumption is incorrect. And one cannot avoid this error by speaking of transformability to additivity instead of merely additivity. (shrink)

In this paper I consider recent feminist critiques of the whiteness of philosophy’s secularism. Building on the distinction in disability studies between accommodation and access, I argue that, in order to effectively address philosophy’s whiteness and heteronormativity, critiques of philosophy’s secularism must be accountable to religion’s historical and contemporary role in perpetuating harm against queer people. While it is absolutely crucial to critique and work to undo the whiteness of mainstream philosophy, it is equally important to do so in a (...) way that does not further marginalize queer people. I build on Gloria Anzaldùa’sdistinction between spirituality and religion, Sara Ahmed’s discussion of willfulness, and the distinction between accommodation and accessin disability studies to suggest a nonadditive concept of pluralism that moves toward the transformation of philosophy. (shrink)

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the (...) system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations. (shrink)

The derivation of heritability from human twin studies involves serious methodological flaws. Heritability is consistently overestimated because of biological confounds of twinning, consistent and often gross underestimation of the environmental variance, and nonadditive genetic influences that can hugely exaggerate heritability values. Despite this bad research design, behaviour geneticists continue to publish results implying that their heritability results are valid.

Emergent properties have been described by Mill, Lewes, Broad, Morgan and others, as novel, nonadditive, nonpredictable and nondeducible within a hierarchical context. I have developed a more definitive concept of a hierarchy that can be used to inspect the phenomenon of emergence in a new and detailed manner. A hierarchy is held together by descending constraints and new features can arise when an upper level entity restrains its components in new combinations that are not expected when viewing these components alone. (...) Examples of emergent features are matching anticodons and amino acids by aminoacetyl-tRNA synthetase enzymes appearing early among the first forms of life, negative feedback in end-product inhibition first occurring in microbes, memory in animals and apical cells in plants. Until recently, life was considered only in terms of physics and chemistry, but now it is known to have a third aspect of information that along with the descendant constraints in its hierarchical organization makes emergentism possible within a reductionist’s framework. (shrink)

We propose a theory that relates perceived evidence to numerical probability judgment. The most successful prior account of this relation is Support Theory, advanced in Tversky and Koehler. Support Theory, however, implies additive probability estimates for binary partitions. In contrast, superadditivity has been documented in Macchi, Osherson, and Krantz, and both sub- and superadditivity appear in the experiments reported here. Nonadditivity suggests asymmetry in the processing of focal and nonfocal hypotheses, even within binary partitions. We extend Support Theory by (...) revising its basic equation to allow such asymmetry, and compare the two equations’ ability to predict numerical assessments of probability from scaled estimates of evidence for and against a given proposition. Both between- and within-subject experimental designs are employed for this purpose. We find that the revised equation is more accurate than the original Support Theory equation. The implications of asymmetric processing on qualitative assessments of chance are also briefly discussed. (shrink)

The Choquet expected utility model deals with nonadditive probabilities (or capacities). Their dependence on the information the decision-maker has about the possibility of the events is taken into account. Two kinds of information are examined: interval information (for instance, the percentage of white balls in an urn is between 60% and 100%) and comparative information (for instance, the information that there are more white balls than black ones). Some implications are shown with regard to the core of the capacity and (...) to two additive measures which can be derived from capacities: the Shapley value and the nucleolus. Interval information bounds prove to be satisfied by all probabilities in the core, but they are not necessarily satisfied by the nucleolus (when the core is empty) and the Shapley value. We must introduce the constrained nucleolus in order for these bounds to be satisfied, while the Shapley value does not seem to be adjustable. On the contrary, comparative information inequalities prove to be not necessarily satisfied by all probabilities in the core and we must introduce the constrained core in order for these inequalities be satisfied. However, both the nucleolus and the Shapley value satisfy the comparative information inequalities, and the Shapley value does it more strictly than the nucleolus. (shrink)

This paper critically examines Richard Kraut’s attack on the notion of absolute value, and lays out some of the conceptual work required to defend such a notion. The view under attack claims that absolute goodness is a property that provides a reason to value what has it. Kraut’s overall challenge is that absolute goodness cannot play this role. Kraut’s own view is that goodness-for, instead, plays the reason-providing role. My targets are Kraut’s double-counting objection, and his ethical objection against absolute (...) value. After explaining the double-counting objection, and discussing the idea of non-additive reasons, I examine and reject Kraut’s reasons for holding that nonadditivity can rescue relative value but not absolute value. I proceed then to explore a different reply to the double-counting objection by introducing a distinction between normative reasons for action and reasons that explain why a certain consideration is a reason for action. Such a distinction (hinted at by Kraut) would either help both Kraut and the friend of absolute value, or neither of them. I defend the distinction from the objection that it would make absolute value just a ‘shadow’. Finally, I reply to Kraut’s ethical objection that being motivated by absolute value is depersonalizing, on two grounds: 1) if thinking in terms of absolute value depersonalizes relationships, then we have absolute-value-given reasons not to think in those terms; 2) the distinction between normative and explanatory reasons explains why even a motivation centred on absolute value need not be depersonalizing. (shrink)