This paper offers a new approach to an old debate about superaddition in Locke. Did Locke claim that some objects have powers that are unrelated to their natures or real essences? The question has split commentators. Some (Wilson, Stuart, Langton) claim the answer is yes and others (Ayers, Downing, Ott) claim the answer is no. This paper argues that both of these positions may be mistaken. I show that Locke embraced a robust epistemic humility. This epistemic humility includes ignorance (...) of the real essences of bodies, of the causal processes underlying the production of natural phenomena, and of God’s method of creation. I show how this epistemic humility offers strong support for an agnostic response to the question of superaddition. Locke did not intend to claim that bodies either do or do not have properties unrelated to their real essences. Instead, his primary goal in discussing the topic was to emphasize the strict limits to human knowledge. (shrink)

Far from being a product of Locke’s philosophical genius, the theory of the divine superaddition of thought to matter is rooted in the discussions about Descartes’ conception of the soul as res cogitans which took place in France and in the Netherlands in the years 1640-1680, from Mersenne to Regius and Bayle. Locke’s historical and theoretical relationship with these sources can be clearly documented, as well as the influence of the superaddition theory in the eighteenth century, mostly in (...) the realm of free-thinking, from Collins to Bolingbroke and above all Voltaire. In the light of this intellectual genealogy, the accusations of materialism, or even Spinozism, frequently levelled against Locke acquire a new significance and are worth exploring again. (shrink)

Trinity College, Hartford, CT 06511, USA.

One of the deepest and most abiding of Pierre Bayle's philosophical preoccupations concerns the possibility of rational theology, or more specifically, the extent to which unaided reason is competent to secure the fundamental tenets of orthodox Christianity. Doubtless the most familiar aspect of this intellectual ‘obsession’ is his tenacious criticism of traditional Solutions to the problem of evil. Yet these discussions represent only one facet of Bayle's engagement with the complex issues involved in the question of rational theology. Throughout the (...) Historical and Critical Dictionary and in subsequent works, three issues in particular figure prominently in Bayle's discussions: the existence of a transcendent, immaterial God, the immortality of the soul, and mind-body dualism. These topics are, of course, interrelated, and Bayle rarely treats them in complete isolation. Although his official position is explicitly fideistic, there is reason to believe that Bayle was a reluctant skeptic, who was naturally sympathetic with the metaphysical dogmatism of Descartes and Malebranche. (shrink)

Locke claimed that God superadded various powers to matter, including motion, the perfections of peach trees and elephants, gravity, and that he could superadd thought. Various interpreters have discussed the question whether Locke's claims about superaddition are in tension with his commitment to mechanistic explanation. This literature assumes that for Locke mechanistic explanation involves deducibility. We argue that this is an inaccurate interpretation and that mechanistic explanation involves a different type of intelligibility for Locke.

This chapter discusses reasons why we have no prospect of knowing whether or not matter thinks. It focuses on the mechanist hypothesis, its purported explanatory scope, and John Locke's commitment to it. The chapter then demonstrates God's immateriality and its implications for the possibility that God has given perception and thought to some material things. It addresses the notion of divine superaddition elaborated in letters to Stillingfleet and considers how thinking, extension, solidity, and motion are connected in case they (...) do coexist in the same substance. The whole difference between Locke and his opponents on the epistemic possibility of thinking matter comes down to this. He maintains, and they deny, that we know the fixed nature of substances of various kinds, a constituent of a substance that determines the powers it necessarily has and those it necessarily lacks. (shrink)

We revisit the characterization of the Shapley value by van den Brink (Int J Game Theory, 2001, 30:309–319) via efficiency, the Null player axiom, and some fairness axiom. In particular, we show that this characterization also works within certain classes of TU games, including the classes of superadditive and of convex games. Further, we advocate some differential version of the marginality axiom (Young, Int J Game Theory, 1985, 14: 65–72), which turns out to be equivalent to the van den Brink (...) fairness axiom on large classes of games. (shrink)

This paper investigates Locke’s views about materialism, by looking at the discussion in Essay IV.x. There Locke---after giving a cosmological argument for the existence of God---argues that God could not be material, and that matter alone could never produce thought. In discussing the chapter, I pay particular attention to some comparisons between Locke’s position and those of two other seventeenth-century philosophers, René Descartes and Ralph Cudworth. -/- Making use of those comparisons, I argue for two main claims. The first is (...) that the important argument of Essay IV.x.10 is fundamentally an argument about the causation of perfections. Indeed, Locke gives multiple such arguments in the chapter. My second main claim is that my proposed reading of IV.x is not merely consistent with what Locke says elsewhere about superaddition, but also provides reasons to favor a particular understanding of what superaddition is. (shrink)

In the past, experts have disagreed about whether Samuel Clarke accepted the idea that gravity is a power superadded to matter by God. Most scholars now agree that Clarke did not support superaddition. But the argumentation employed by Clarke to reject superaddition has not been studied before in detail. In this paper, I explicate Clarke's argumentation by relating it to an important discussion about the possibility of superadded gravity in the Clarke-Collins correspondence. I examine Clarke's responses to Collins (...) and draw on his other works to reconstruct Clarke's reasons for rejecting superadded gravity. (shrink)

In this paper, I argue that Locke is not in fact agnostic about the ultimate nature of the mind. In particular, he produces an argument, much like Jaegwon Kim's exclusion argument, to show that any materialist view that takes mental states to supervene on physical states is committed to epiphenomenalism. This result helps illuminate Locke's otherwise puzzling notion of 'superaddition.'.

Searching through semantic memory may involve the use of several retrieval cues. In a verbal fluency task, the set of available cues is limited and every candidate word is a target. Individuals exhibit clustering behavior as predicted by optimal foraging theory. In another semantic search task, the remote associates task, three cues are presented and a single target word has to be found. Whereas the task has been widely studied as a task of creativity or insight problem solving, in this (...) article, the RAT is treated as a semantic retrieval task and assessed from the perspective of information foraging theory. Experiments are presented that address the superadditive combination of cues and the anti-clustering behavior in the recall sequence. A new type of search behavior in the RAT is put forward that involves maximizing the difference in activation between target and distractors. This type of search is advantageous when the target is weak and cue patches are contaminated with strong competitors. (shrink)

Pierre Bayle shows that, in order to avoid devastating objections, materialism should postulate that the property of thinking does not emerge from certain material combinations but is present in matter from the start and everywhere—a hypothesis recently revived and labelled “panpsychism”. There are reasons for entertaining the idea that Bayle actually considers this enhanced materialism to be tenable, as it might use the same line of defence that Bayle outlined for Stratonism. However, this would lead to a view similar to (...) Locke’s superaddition theory, and I contend that such cannot be Bayle’s position because he embraces the Cartesian principle that each substance has only one principal attribute. This makes untenable, in his eyes, any system that conjoins thought with matter in the same simple substance. By contrast, this makes clear which kinds of metaphysics and epistemology panpsychists need to adopt to defend their view. (shrink)

A semimeasure is a generalization of a probability measure obtained by relaxing the additivity requirement to superadditivity. We introduce and study several randomness notions for left-c.e. semimeasures, a natural class of effectively approximable semimeasures induced by Turing functionals. Among the randomness notions we consider, the generalization of weak 2-randomness to left-c.e. semimeasures is the most compelling, as it best reflects Martin-Löf randomness with respect to a computable measure. Additionally, we analyze a question of Shen, a positive answer to which would (...) also have yielded a reasonable randomness notion for left-c.e. semimeasures. Unfortunately, though, we find a negative answer, except for some special cases. (shrink)

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that has been (...) proposed in previous work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL. (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)

Although it is beyond doubt that there were historical connections between Whitehead and some of the proponents of Gestalt psychology, it is difficult to determine on the available body of historical evidence whether they were substantive or just marginal. A detailed comparison of Whitehead's process metaphysics and the theories of Gestalt psychology is a task yet to be undertaken. Whitehead's process philosophy and Gestalt psychology share basic similarities in their major principles. This is substantiated by two of Ehrenfels'well-known gestalt qualities: (...) superadditivity, and figure-ground relation. Both approaches can profit from one another: while Whitehead's concept of consciousness and its interrelatedness with unconscious processes seems to be more elaborate, the Gestalt psychological approach, on the other hand, shows how these topics can be investigated by using experimental research designs. This is illustrated by an experiment on complex problem solving which demonstrates that unreportable hints can improve even such sophisticated processes as complex problem solving. Since this is what should be expected from a Whiteheadian point of view, the results empirically confirm the process position on perception and thinking. Finally, further interesting possibilities of undertaking future empirical process research are outlined. (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)

A great deal of research has demonstrated that learning is influenced by the learner’s prior background knowledge (e.g. Murphy, 2002; Keil, 1990), but little is known about the processes by which prior knowledge is deployed. We explore the role of explanation in deploying prior knowledge by examining the joint effects of eliciting explanations and providing prior knowledge in a task where each should aid learning. Three hypotheses are considered: that explanation and prior knowledge have independent and additive effects on learning, (...) that their joint effects on learning are subadditive, and that their effects are superadditive. A category learning experiment finds evidence for a superadditive effect: explaining drives the discovery of regularities, while prior knowledge constrains which regularities learners discover. This is consistent with an account of explanation’s effects on learning proposed in Williams & Lombrozo (in press). (shrink)

Sadr al-Sharīʿah (d. 747/1346) is one of the theologians representing the later period of the Māturīdī kalām. He based his system of thought on his criticisms of Avicenna, al-Rāzī, and Ṭūsī. His criticism of these names stems from his own understanding of being. He thinks differently from the theologians of the later period on issues such as the essence-existence division, the superaddition of existence to essence, and the acceptance of mental being, which are accepted by the majority of theologians (...) of the later period. His understanding of being in question also influenced his analysis of the idea of the wahdat al-wujūd. In the study, some aspects of the framework proposed by Muhammed Bedirhan will be given first. Then, in order to make sense of Sadr al-Sharīʿah’s criticism of wahdat al-wujūd, the major understandings of wahdat al-wujūd will be summarized briefly, and finally, Sadr al-Sharīʿah’s analysis of wahdat al-wujūd will be examined and clarified using Bedirhan’s framework. Although the framework has subheadings, it classifies criticisms into two categories: rationally-based and sharʻī-based objections. Rational objections are directed from the traditions of kalām and philosophy, while sharʻī-based objections come from Salafi thinkers, faqihs, and sufis. The framework is comprehensive in classifying criticisms against the theory of wahdat al-wujūd. This framework will clarify Sadr al-Sharīʿah’s approach, and the source of his criticisms should be identified. According to Bedirhan, the sufis’ theory is in conflict with the members of other schools in two aspects, practical and theoretical. While the first one considers sufism a religious state (ḥal), the second one is the point that shapes the view of other intellectual groups on sufism in terms of the fact that sufism is also a science. Bedirhan has based the theoretical conflict part of his framework on the triple classification of al-Jābiri: burhān, beyān and irfān. According to al-Jābiri’s classification, sufism, which is included under the title of irfān, deals with the previous two traditions mentioned. However, burhan and beyan traditions also offer their criticisms of the epistemological and ontological acceptances of the irfān tradition. Behind the criticism of the traditions of thought towards each other is the claim that the metaphysical theory of the opposite group is insufficient. According to the presented framework Sadr al-Sharīʿah’s criticisms can be considered within not only the kalām tradition but also the sufi tradition, because he is a sufi who accepts ittihād as one of the “sayr sulūk” degrees. Sadr al-Sharīʿah’s explains two proofs by which sufis defend their metaphysical theory, and also presents a counter-proof based on the verbal commonality of sense knowledge and being. He also aims to point out the weakness of the metaphysical theory of sufis with the view that the idea of ittihād is unique to a certain degree. By mentioning Sadr al-Sharīʿah’s criticisms and explanations of wahdat al- wujūd, the study identifies Sadr al-Sharīʿah’s stance on the rational and sharʻī-based objections. (shrink)

This paper explores the metaphysical system developed in Richard Bentley’s 1692 Boyle Lectures. The lectures are notable for their attempt to argue that developments in natural philosophy, including Newton’s Principia, could bolster natural theology. The paper explores Bentley’s matter theory focusing on his commitment to a particular form of mechanism and his rejection of occult qualities. It then examines his views on the nature of divine omnipotence. Finally, it turns to his understanding of gravitational attraction. While some recent commentators have (...) argued for a “superaddition” interpretation of gravitation in Bentley, this paper argues for an “occasionalist” interpretation. The argument proceeds on the basis of both textual considerations and considerations stemming from the systematic interpretation of Bentley’s metaphysics developed earlier in the paper. (shrink)

In this paper, I address the controversial issue around Locke’s account of a “superadded” power of thought. I first show that Locke uses the term “super­addition” in discussing the nominal distinction of natural kinds. This general observation applies to Locke’s account of thinking matter. Specifically, I attribute to him the following three theses: (1) the mind-body distinction is nominal; (2) there is no metaphysical repugnancy between them; and (3) their common ground—namely, substratum—can only be characterized in terms of its functional (...) role. Examining each thesis and their interconnections, this paper casts light upon the Lockean type of mind-body union in “a system of matter fitly disposed.”. (shrink)

I examine two strands in Locke's thought which seem to conflict with his corpuscularian sympathies: his repeated suggestion that natural philosophy is incapable of being made a science, and his claim that some of the properties of bodies--secondary qualities, powers of gravitation, cohesion and maybe even thought--are arbitrarily "superadded" by God. ;Locke often says that a body's properties flow from its real essence as the properties of a triangle flow from its definition. He is widely read as having thought that (...) if we had ideas of a body's real essence, we would be able to perceive a priori a necessary connection between that body's real essence and its observable properties. I argue that this leaves Locke's skepticism without any rationale, making it depend entirely upon our ignorance of corpuscular structures when in fact he never rules out the possibility of our acquiring ideas of corpuscular structures through improvements in microscopy. I argue that Locke's geometrical analogy is better understood as an endorsement of deductivism about scientific explanation. He thinks that knowledge of corpuscular structures is a necessary, but not a sufficient, condition for scientific knowledge of bodies. The deeper source of his skepticism is his view that we cannot have universal and certain knowledge of the laws of nature because they are contingent. ;I approach the subject of Locke's attitude toward mechanism by examining his superaddition doctrine. In contrast with M. R. Ayers, I attribute to Locke what I call strong voluntarism: the view that a body's powers to interact with other bodies are not fully determined by the essence of matter, and that they are at least partly determined by the will of God. I argue that Descartes and Boyle are also strong voluntarists, but that Locke's voluntarism differs in that he maintains that bodies have some powers which are not even partly explicable in terms of the motions of matter. Locke's position is thus incompatible with the mechanism of Descartes and Boyle. (shrink)

Jazz band is a 3 player superadditive game in characteristic function form. Three players have to divide the payoff they can get, while being in a grand coalition, provided their individual and duo coalitions payoffs are known. Assumptions of individual and collective rationality lead to the notion of the core of the game. We discuss offers that cannot readily be refused [OCRR] as the solutions of the game in case of an empty core, when duo coalitions are the best options (...) but only for two out of three players. The experiment shows that even in case of an empty core the most probable results are three-way coalitions and the share of the weakest player usually exceeds his OCRR. The Shapley value is introduced and its fairness is discussed as it lies at the side of the core while, on the other hand, the nucleolus lies exactly at the center of the core. We conclude that, in spite of that, the Shapley value is the best candidate for a fair sharing solution of the jazz band game and other similar games as, opposite to the other values, it is dependent both on individual and duo coalitions payoffs. (shrink)

Commentators almost universally agree that Locke denies the possibility of thinking matter in Book IV Chapter 10 of the Essay. Further, they argue that Locke must do this in order for his proof of God’s existence in the chapter to be successful. This paper disputes these claims and develops an interpretation according to which Locke allows for the possibility that a system of matter could think (even prior to any act of superaddition on God’s part). In addition, the paper (...) argues that this does not destroy Locke’s argument in the chapter, instead it helps to illuminate the nature of it. The paper proceeds in two main stages. First, Locke denies that matter can produce thought. A distinction between two senses of “production” shows that this claim is compatible with the existence of thinking matter. Second, Locke denies that God could be a system of randomly moving particles. Most commentators take this to mean that such a system could not think. But Locke is better interpreted as denying that such a system could have the wisdom and knowledge of God. (shrink)

New research on affective computing aiming to develop computer systems that recognize and respond to affective states can also contribute to the issues raised by Coan. Research on how humans interact with computers, and computer models that automatically recognize affective states from features in our physiology, behaviour, and language, may provide insights on how emotions that are experienced and expressed come to be. For example, there is empirical evidence that affect recognition techniques using several modalities are more accurate than those (...) using a single modality, but it is not clear if these improvements are caused by superadditivity (i.e., emergence) or redundancy. (shrink)

We revisit the Nowak (Int J Game Theory 26:137–141, 1997) characterization of the Banzhaf value via 2-efficiency, the Dummy player axiom, symmetry, and marginality. In particular, we provide a brief proof that also works within the classes of superadditive games and of simple games. Within the intersection of these classes, one even can drop marginality. Further, we show that marginality and symmetry can be replaced by van den Brink fairness/differential marginality. For this axiomatization, 2-efficiency can be relaxed into superadditivity on (...) the full domain of games. (shrink)

This paper shows that temperance is the highest order risk preference condition for which spreading N independent and unfair risks provides the highest level of welfare than any other possible allocations of risks. These results are also interpreted through the concept of N-superadditivity of the utility premium. This paper provides a novel application of temperance, not in terms of two risks as it is common, but in terms of N risks.

This paper analyzes the metaphysical system developed in Cheyne’s Philosophical Principles of Religion. Cheyne was an early proponent of Newtonianism and tackled several philosophical questions raised by Newton’s work. The most pressing of these concerned the causal origin of gravitational attraction. Cheyne rejected the occasionalist explanations offered by several of his contemporaries in favor of a model on which God delegated special causal powers to bodies. Additionally, he developed an innovative approach to divine conservation. This allowed him to argue that (...) Newton’s findings provided evidence for God’s existence and providence without the need for continuous divine intervention in the universe. (shrink)

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, studies, and characterizes a (...) natural method of associating coalitional interval games with strategic games. (shrink)