The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...) logic R of relevant implication. A further aim is the use of metavaluations in a new context, expanding the range of application of this novel technique, already used in the context of negation and arithmetic, thus providing an alternative to traditional model theoretic approaches. (shrink)

We give a simple and direct proof that super-consistency implies the cut-elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut-free calculus. As an application, we compare our work with the cut-elimination theorems in higher-order logic that involve V-complexes.

I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but (...) the more general case is also considered. (shrink)

What is the relation between the intention to A and doing A intentionally? It is natural to suppose that the latter entails the former. That is, it is natural to accept what Michael Bratman has called the ‘Simple View’ of the relation between acting intentionally and having an intention. Bratman is one noteworthy writer who has denied that the Simple View is true. In the present paper I do not defend this view. I contend that one well-known argument (...) that Bratman offers for thinking that the Simple View is false fails, in fact, to disprove it. If there are reasons for thinking that the Simple View is false, as I believe there are, they are not the ones that Bratman has offered. My discussion of Bratman also raises some more general questions about the principles governing the rational formation of intentions. I suggest that a special sort of example casts doubt on the tenability of a commonly accepted principle that Bratman, among others, utilizes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:424 CAN HUME'S USE OF A SIMPLE/COMPLEX DISTINCTION BE MADE CONSISTENT? There is little doubt that Hume equivocates on the distinction between simple and complex impressions and ideas. Sometimes he identifies properties such as colors and shapes as simples. This is what he does, in fact, when he first introduces the distinction: Simple perceptions or impressions and ideas are such as admit of no distinction nor (...) separation. The complex are the contrary to these, and may be distinguished into parts. Tho' a particular colour, taste, and smell are qualities all united together in this apple, 'tis easy to perceive they are not the same, but are at least distinguishable from each other. Later, however, Hume speaks of simples not as qualities (or, of course, as substances) but as objects, i.e., things with properties: it is not red and round that are the simples but the red, round spot. He says, for example: Before I leave this subject I shall employ the same principles to explain that distinction of reason, which is so much talk'd of, and is so little understood, in the schools. Of this kind is the distinction betwixt figure and the body figur'd; motion and the body mov'd. The difficulty of explaining this distinction arises from the principle above explain'd, that all ideas, which are different, are separable. For it follows from thence, that if the figure be different from the body, their ideas must be separable as well as distinguishable; if they be not different, their ideas can neither be separable nor distinguishable (T 2425 ). 425 A genuine inconsistency with regard to the simple/complex distinction would have far reaching implications for Hume's system. Even the question concerning his understanding of necessity may be affected. It has been argued, for example, that what Hume believes separates the philosophical relations that are necessary from those that are not is that the former are internal relations. The suggestion is that the doctrine of internal relations, which is inextricably tied to a specific characterization of a simple/complex distinction, provides the essential contrast Hume needs for his ultimate denial that the causal relation is necessary. The consequences are compounded if we also take Robinson to be right in his attempt to reconcile Hume's 'conflicting' statements about causation in terms of the distinction between the natural and philosophical relations. While it is pointless to deny the ambiguity just set out (and, of course, one must remain constantly watchful to determine how Hume is employing the simple/complex distinction in a particular case), I believe a reconciliation of the two positions is still possible and that there is no genuine contradiction in Hume's system over this issue. The principle shift occurs between the distinction presented in logical terms and its presentation in psychological terms. In the latter instance what Hume seems to be worried about is Platonism: a metaphysics that countenances the existence of unexemplif ied qualities. This is most evident in the passage above where Hume, in effect, makes the following argument: if it were the case that (1) what is distinguishable in thought is separable in reality; and (2) figure and body are 426 distinguishable in thought; then it would follow that (3) figure and body are separable in reality. However, (3), i.e., Platonism, is false. But then so must be (2). Hume never deviates from this conclusion and its implications for his model of thought throughout the Treatise. It is this argument, for example, which became the basis for Hume's accusation against Locke's theory of abstraction and the foundation of his own view. So far Hume has it that neither thought nor experience present us with colors and shapes in isolation. This is his psychological point. Yet that need not be seen as conclusive with regard to what is to count as a logical simple. Building on his notion of a distinction of reason, Hume says: Thus when a globe of white marble is presented, we receive only the impression of a white colour dispos 'd in a certain form, nor are we able to separate and distinguish the colour from the form. But observing afterwards... (shrink)

A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation”. It is shown that consistent prime theories built upon G3 can be understood as u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.

The Simple View (SV) holds that for someone to intentionally A, he must intend to A. Critics of SV point to intentional actions which, due to belief-conditions or consistency constraints, agents cannot intend. By recognizing species of intention which vary according to the agent's confidence in acting, I argue that the stringency of consistency constraints depends on the agent's confidence. A more sophisticated SV holds that the species of intending is related to the degree of intentionality of (...) the action. Finally, I show that where agents do what they believe impossible, without intending to do so, the action is not intentional. (shrink)

In addition to beliefs, people have attitudes of confidence called credences. Combinations of credences, like combinations of beliefs, can be inconsistent. It is common to use tools from probability theory to understand the normative relationships between a person’s credences. More precisely, it is common to think that something is a consistency norm on a person’s credal state if and only if it is a simple transformation of a truth of probability. Though it is common to challenge the right-to-left (...) direction of this biconditional, I argue in this paper that the left-to-right direction is false for standard versions of probability theory. That is, I make the case that there are consistency constraints on credal states that are not simple transformations of truths of standard versions of probability theory. I do so by drawing on a newly discovered type of credal attitude, a quantificational credence, and by showing how the consistency norms on this attitude can’t be represented as simple transformations of truths of standard versions of probability theory. I conclude by showing that a probability theory that could avoid the result would have to be strikingly different from the standard versions—so different that I suspect many would hesitate to call it a theory of probability at all. (shrink)

Human agents draw a variety of inferences effortlessly, spontaneously, and with remarkable efficiency – as though these inferences were a reflexive response of their cognitive apparatus. Furthermore, these inferences are drawn with reference to a large body of background knowledge. This remarkable human ability seems paradoxical given the complexity of reasoning reported by researchers in artificial intelligence. It also poses a challenge for cognitive science and computational neuroscience: How can a system of simple and slow neuronlike elements represent a (...) large body of systemic knowledge and perform a range of inferences with such speed? We describe a computational model that takes a step toward addressing the cognitive science challenge and resolving the artificial intelligence paradox. We show how a connectionist network can encode millions of facts and rules involving n-ary predicates and variables and perform a class of inferences in a few hundred milliseconds. Efficient reasoning requires the rapid representation and propagation of dynamic bindings. Our model (which we refer to as SHRUTI) achieves this by representing (1) dynamic bindings as the synchronous firing of appropriate nodes, (2) rules as interconnection patterns that direct the propagation of rhythmic activity, and (3) long-term facts as temporal pattern-matching subnetworks. The model is consistent with recent neurophysiological evidence that synchronous activity occurs in the brain and may play a representational role in neural information processing. The model also makes specific psychologically significant predictions about the nature of reflexive reasoning. It identifies constraints on the form of rules that may participate in such reasoning and relates the capacity of the working memory underlying reflexive reasoning to biological parameters such as the lowest frequency at which nodes can sustain synchronous oscillations and the coarseness of synchronization. (shrink)

This paper offers an elementary proof that formal arithmetic is consistent. The system that will be proved consistent is a first-order theory R♯, based as usual on the Peano postulates and the recursion equations for + and ×. However, the reasoning will apply to any axiomatizable extension of R♯ got by adding classical arithmetical truths. Moreover, it will continue to apply through a large range of variation of the un- derlying logic of R♯, while on a simple and straightforward (...) translation, the classical first-order theory P♯ of Peano arithmetic turns out to be an exact subsystem of R♯. Since the reasoning is elementary, it is formalizable within R♯ itself; i.e., we can actually demonstrate within R♯ (or within P♯, if we care) a statement that, in a natural fashion, asserts the consistency of R♯ itself. The reader is unlikely to have missed the significance of the remarks just made. In plain English, this paper repeals Goedel’s famous second theorem. (That’s the one that asserts that sufficiently strong systems are inadequate to demonstrate their own consistency.) That theorem (or at least the significance usually claimed for it) was a mis- take—a subtle and understandable mistake, perhaps, but a mistake nonetheless. Accordingly, this paper reinstates the formal program which is often taken to have been blasted away by Goedel’s theorems— namely, the Hilbert program of demonstrating, by methods that everybody can recognize as effective and finitary, that intuitive mathematics is reliable. Indeed, the present consistency proof for arithmetic will be recognized as correct by anyone who can count to 3. (So much, indeed, for the claim that the reliability of arithmetic rests on transfinite induction up to ε0, and for the incredible mythology that underlies it.). (shrink)

What are the necessary and jointly sufficient conditions for an object's being a simple (an object without proper parts)? According to one prominent view, The Pointy View of Simples, an object is a simple if and only if the region occupied by that object contains exactly one point in space. According to another prominent view, MaxCon, an object is a simple if and only if it is maximally continuous. In this paper, I argue that both of these (...) views are inconsistent with the possibility of discrete space. I then go on to formulate analogues to these two views that are consistent with this possibility, and argue that if we are willing to grant the possibility of discrete space, we should endorse the analogue to The Pointy View of Simples over the analogue to MaxCon. (shrink)

Accounts of personal identity over time are supposed to fall into two broad categories: 'complex views' saying that our persistence consists in something else, and 'simple views' saying that it doesn' t. But it is impossible to characterize this distinction in any satisfactory way. The debate has been systematically misdescribed. After arguing for this claim, the paper says something about how the debate might be better characterized.

This essay deals with the problem of the status of colours, traditionally considered as the paradigmatic case of secondary qualities: do colours exist only as aspects of experience or are they real properties of objects, existing independently of human and animal perception? Recently, John Campbell has argued in favour of the simple view of colours, according to which colours are real properties of objects. I discuss the place of Campbell's position in a debated which was started by John Mackie (...) and continued by John McDowell, and defend it from a criticism due to Michael Smith. I conclude that the simple view is a philosophically credible position. Subsequently, I consider an alleged contradiction between the simple view and semantic externalism pointed out by Jim Edwards. I suggest that a supporter of the simple view may consistently maintain semantic externalism, if she also accepts epistemological externalism about the canonical warrant of perceptual judgements. (shrink)

This chapter investigates the extent to which claims of massive modular organization of the mind (espoused by some members of the evolutionary psychology research program) are consistent with the main elements of the simple heuristics research program. A number of potential sources of conflict between the two programs are investigated and defused. However, the simple heuristics program turns out to undermine one of the main arguments offered in support of massive modularity, at least as the latter is generally (...) understood by philosophers. So one result of the argument will be to force us to re-examine the way in which the notion of modularity in cognitive science should best be characterized, if the thesis of massive modularity isn’t to be abandoned altogether. What is at stake in this discussion, is whether there is a well-motivated notion of ‘module’ such that we have good reason to think that the human mind must be massively modular in its organization. I shall be arguing (in the end) that there is. (shrink)

This article discusses three important models of concept combination—Smith and colleagues' Selective Modification model, Hampton's Composite Prototype model, and Costello and Keane's C3 model. Smith and colleagues' famous model of concept combination combines a model for producing complex concepts out of simple concepts with a prototype model of concept representation and a metric for computing the typicality of objects with respect to those concepts. The model of concept combination proposed by Smith and colleagues applies only to modifier–head complex concepts. (...) Hampton's model of concept combination includes, along with a qualitative description of the process resulting in complex concepts, a model of concepts, a model of categorization, and a model of typicality judgement. For Hampton, concept combination consists in the inheritance of typical properties from the combined concepts by the complex concept. (shrink)

The notion of an extended simple region (henceforth ESR) has recently been marshalled in the service of arguments for a variety of conclusions. Exactly how to understand the idea of extendedness as it applies to simple regions, however, has been largely ignored, or, perhaps better, assumed. In this paper we first (§1) outline what we take to be the standard way that philosophers are thinking about extendedness, namely as an intrinsic property of regions. We then introduce an alternative (...) picture (§2), according to which extendedness is extrinsic. In §3 we argue that it matters which way of thinking about extendedness is the right one, since how ESRs behave is sensitive to what extendedness consists in, and various arguments that appeal to ESRs turn out to be unsound if extendedness is extrinsic rather than intrinsic. (shrink)

In this paper, following an idea of Christophe Chalons, I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence φ holding in some forcing extension $V\P$ and all subsequent extensions V\P*\Qdot holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme $\implies\necessaryφ$, and is equivalent to the modal theory S5. In this article, (...) I prove that the Maximality Principle is relatively consistent with \ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in φ, is equiconsistent with the scheme asserting that $Vδ\elesub V$ for an inaccessible cardinal δ, which in turn is equiconsistent with the scheme asserting that $\ORD$ is Mahlo. The strongest principle along these lines is $\necessary\MPtilde$, which asserts that $\MPtilde$ holds in V and all forcing extensions. From this, it follows that 0# exists, that x# exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain. (shrink)

Husserl’s Logical Investigations has undergone explicitly conceptualist and non-conceptualist interpretations. For Richard Cobb-Stevens, he has extended understanding into the domain of sensuous intuition, leaving no simple perceptions that are actually separated from higher-level understanding. According to Kevin Mulligan, Husserl does in fact sunder nominal and propositional seeing from the simple or straightforward—and yet interpretative—seeing of particulars. To see simply is not to exercise an individual meaning or a general concept. Arguing that Logical Investigations provides evidence for both views, (...) I endeavour to show that the account of perceptual consciousness in Husserl’s subsequent work is far more clear and consistent. It is one of growing beyond the situation portrayed by Mulligan and into the one explicated by Cobb-Stevens. Though they are notionally separable, pre-conceptual syntheses at the passive and noematic levels are inevitably interwoven with conceptual and categorial articulations in a developed consciousness. (shrink)

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. (...) 11 EUCh. These competing rights are denoted by ( \(i_1\) ) _right to privacy _ and ( \(i_2\) ) _access to information_; mathematically, their indices are respectively assigned by \(u_1\in [0,1]\) and \(u_2\in [0,1]\) subject to the constraint \(u_1+u_2=1\). This constraint allows us to use one single index _u_ to resolve the conflict through balancing. The outcome will be concluded by comparing the index _u_ with a prior given threshold \(u_0\). For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome _u_ by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for _u_, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data. (shrink)

This essay deals with the problem of the status of colours, traditionally considered as the paradigmatic case of secondary qualities: do colours exist only as aspects of experience or are they real properties of objects, existing independently of human and animal perception? Recently, John Campbell has argued in favour of the simple view of colours, according to which colours are real properties of objects. I discuss the place of Campbell's position in a debated which was started by John Mackie (...) and continued by John McDowell, and defend it from a criticism due to Michael Smith. I conclude that the simple view is a philosophically credible position. Subsequently, I consider an alleged contradiction between the simple view and semantic externalism pointed out by Jim Edwards. I suggest that a supporter of the simple view may consistently maintain semantic externalism, if she also accepts epistemological externalism about the canonical warrant of perceptual judgements. (shrink)

In this paper, following an idea of Christophe Chalons. I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence varphi holding in some forcing extension $V^P$ and all subsequent extensions $V^{P\ast Q}$ holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme $(\lozenge \square \varphi) \Rightarrow \square \varphi$ , and is equivalent to (...) the modal theory S5. In this article. I prove that the Maximality Principle is relatively consistent with ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in φ, is equiconsistent with the scheme asserting that $V_\delta \prec V$ for an inaccessible cardinal δ, which in turn is equiconsistent with the scheme asserting that ORD is Mahlo. The strongest principle along these lines is $\square MP\!_{\!\!\!\!\!\!_{\!\!_\sim}}$ , which asserts that $MP\!_{\!\!\!\!\!\!_{\!\!_\sim}}$ holds in V and all forcing extensions. From this, it follows that $0^\#$ exists, that $x^\#$ exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain. (shrink)

As a stress test of experimenter demand effects, we run an experiment where subjects can physically destroy coupons awarded to them. About one subject out of three does. Giving money back to the experimenter is possible in a separate task but is more consistent with an experimenter demand effect than an explanation based on altruism towards the experimenter. A measure of sensitivity to social pressure helps predict destruction when social information is provided.

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare that way (...) with other two ways based on Łukasiewicz’s three-valued logic and branching temporal logic. (shrink)

Minimally inconsistent LP (MiLP) is a nonmonotonic paraconsistent logic based on Graham Priest's logic of paradox (LP). Unlike LP, MiLP purports to recover, in consistent situations, all of classical reasoning. The present paper conducts a proof-theoretic analysis of MiLP. I highlight certain properties of this logic, introduce a simple sequent system for it, and establish soundness and completeness results. In addition, I show how to use my proof system in response to a criticism of this logic put forward by (...) JC Beall. (shrink)

This essay deals with the problem of the status of colours, traditionally considered as the paradigmatic case of secondary qualities: do colours exist only as aspects of experience or are they real properties of objects, existing independently of human and animal perception? Recently, John Campbell has argued in favour of the simple view of colours, according to which colours are real properties of objects. I discuss the place of Campbell's position in a debated which was started by John Mackie (...) and continued by John McDowell, and defend it from a criticism due to Michael Smith. I conclude that the simple view is a philosophically credible position. Subsequently, I consider an alleged contradiction between the simple view and semantic externalism pointed out by Jim Edwards. I suggest that a supporter of the simple view may consistently maintain semantic externalism, if she also accepts epistemological externalism about the canonical warrant of perceptual judgements. (shrink)

ArgumentIt seems theoretically convenient to construe knowledge practices in financial markets and organizations as “applied economics.” Alternatively or additionally, one might argue that practitioners draw on economic knowledge in order to systematically orient their actions towards profit-maximization; models, then, are understood as devices that make calculative rationality possible. However, empirical studies do not entirely confirm these theoretical positions: Practitioners’ actual calculations are often not “framed” by models; organizations and institutions influence the choice and adoption of models; and different professional groups (...) in financial markets have diverging attitudes towards model calculations. In order to account for this diversity, this article proposes the concept ofcultures of economic and financial expertise; the concept focuses on the patterns of knowledge practices and knowledge-related self-definitions of groups within financial organizations and markets; it also facilitates an analysis of the relations between and, more specifically, the hierarchies among different practices and identities. The article then goes on to explore the process of foreign exchange forecasting in a particular bank. The description immediately reveals that two groups are involved in this process: economists and analysts. These groups maintain quite different practices and self-descriptions in relation to models: While the economists in the bank use the models as organizational resources for consistent forecasting procedures and observe data with the help of simple model structures, analysts approach model forecasts from the perspective of critics: They see limits in the variable-centered, as opposed to a “thematic” approach and they disregard a model's imposed temporality. Nevertheless, analysts use model forecasts as anchors for developing their own “paths” and stories about possible future expectation changes in the markets. The specific division of labor between economists and analysts, and specifically the dominant role of analysts in the forecasting process, fit into a larger picture: The rise of institutional investors in the foreign exchange markets and their demand for genuine market knowledge for speculative investment projects has contributed to the rise and dominance of analysts’ culture. (shrink)

This essay defends an analysis of malapropisms consistent with the Simple Picture of communication, namely the view that speakers communicate that P by employing expressions associated with P by the regularities appropriate for the linguistic community to which they belong. My analysis, grounded on the distinction between traces, shapes, and forms, is consistent with an intuitive assessment of the contents conveyed by instances of malapropisms, and with a standard, ‘fully articulated’ approach to semantic interpretation.

Bird argues that scientific progress consists in increasing knowledge. Dellsén objects that increasing knowledge is neither necessary nor sufficient for scientific progress, and argues that scientific progress rather consists in increasing understanding. Dellsén also contends that unlike Bird’s view, his view can account for the scientific practices of using idealizations and of choosing simple theories over complex ones. I argue that Dellsén’s criticisms against Bird’s view fail, and that increasing understanding cannot account for scientific progress, if acceptance, as opposed (...) to belief, is required for scientific understanding. (shrink)

Within the field of human‐computer interaction, the study of the interaction between people and computers has revealed many phenomena. For example, highly interactive devices, such as the Apple Macintosh, are often easier to learn and use than keyboard‐based devices such as Unix. Similarly, consistent interfaces are easier to learn and use than inconsistent ones. This article describes an integrated cognitive model designed to exhibit a range of these phenomena while learning task‐action mappings: action sequences for achieving simple goals, such (...) as opening a file in a word processor. The model, called TAL, is of a user who is familiar with the basic operations of a keyboard and mouse, but unfamiliar with the particular menu structures, words, and actions required to use the device. The model is constructed in Soar and employs a single set of architectural mechanisms. It exhibits behavior that captures human preference for consistent, interactive, and meaningful task‐action mappings. (shrink)

In this note we present an axiomatization of the classical two-valued propositional calculus, for which proofs of decidability, consistency, completeness, and independence, are almost trivial (given an understanding of truth tables).

Let $V_\propto$ be a fixed, fully effective, infinite dimensional vector space. Let $\mathscr{L}(V_\propto)$ be the lattice consisting of the recursively enumerable (r.e.) subspaces of $V_\propto$ , under the operations of intersection and weak sum (see § 1 for precise definitions). In this article we examine the algebraic properties of $\mathscr{L}(V_\propto)$ . Early research on recursively enumerable algebraic structures was done by Rabin [14], Frolich and Shepherdson [5], Dekker [3], Hamilton [7], and Guhl [6]. Our results are based upon the more (...) recent work concerning vector spaces of Metakides and Nerode [12], Crossley and Nerode [2], Remmel [15], [16], and Kalantari [8]. In the main theorem below, we extend a result of Lachlan from the lattice E of r.e. sets to $\mathscr{L}(V_\propto)$ . We define hyperhypersimple vector spaces, discuss some of their properties and show if $A, B \in \mathscr{L}(V_\propto)$ , and A is a hyperhypersimple subspace of B then there is a recursive space C such that A + C = B. It will be proven that if $V \in \mathscr{L}(V_\propto)$ and the lattice of superspaces of V is a complemented modular lattice then V is hyperhypersimple. The final section contains a summary of related results concerning maximality and simplicity. (shrink)

Within the field of human‐computer interaction, the study of the interaction between people and computers has revealed many phenomena. For example, highly interactive devices, such as the Apple Macintosh, are often easier to learn and use than keyboard‐based devices such as Unix. Similarly, consistent interfaces are easier to learn and use than inconsistent ones. This article describes an integrated cognitive model designed to exhibit a range of these phenomena while learning task‐action mappings: action sequences for achieving simple goals, such (...) as opening a file in a word processor. The model, called TAL, is of a user who is familiar with the basic operations of a keyboard and mouse, but unfamiliar with the particular menu structures, words, and actions required to use the device. The model is constructed in Soar and employs a single set of architectural mechanisms. It exhibits behavior that captures human preference for consistent, interactive, and meaningful task‐action mappings. (shrink)

Locke seems to hold that we have knowledge of the existence of external objects through sensation. Two problems face Locke's account. The first problem concerns the logical form of knowledge of real existence. Locke defines knowledge as the perception of the agreement or disagreement between ideas. However, perceiving agreements between ideas seems to yield knowledge only of analytic truths, not propositions about existence. The second problem concerns the epistemic status of sensitive knowledge: How could the senses yield certain knowledge? This (...) essay argues that the key to solving both problems is Locke's claim that simple ideas are all real, adequate, and true. This explains why, on Locke's view, we have certain knowledge through the senses. It also explains how sensitive knowledge can consist in perceiving an agreement between ideas: perceived agreements among simple ideas of sensation are guaranteed to track relations that obtain among really existing things. (shrink)

Experts have been claimed to perceive risks in a different way than the general public. It is likely that experts often see risks in their own field of expertise as smaller than the public does, but that does not imply that their risk perception is also driven by other factors. Topical experts and general risk assessors are two quite different types of experts. Still, common assertions as to the simple structure of expert risk perception, said to be related only (...) to technical or statistical risk estimates, builds on a meager database consisting of 15 general risk assessors. Results from a study reported here show that the factors explaining experts’ risk perception are similar to those of a comparable group of nontopical experts with a similar level of technological literacy and to the general public, and that the level of explained variance is quite comparable for experts and the general public. (shrink)

The paper re-expresses arguments against the normative validity of expected utility theory in Robin Pope (1983, 1991a, 1991b, 1985, 1995, 2000, 2001, 2005, 2006, 2007). These concern the neglect of the evolving stages of knowledge ahead (stages of what the future will bring). Such evolution is fundamental to an experience of risk, yet not consistently incorporated even in axiomatised temporal versions of expected utility. Its neglect entails a disregard of emotional and financial effects on well-being before a particular risk is (...) resolved. These arguments are complemented with an analysis of the essential uniqueness property in the context of temporal and atemporal expected utility theory and a proof of the absence of a limit property natural in an axiomatised approach to temporal expected utility theory. Problems of the time structure of risk are investigated in a simple temporal framework restricted to a subclass of temporal lotteries in the sense of David Kreps and Evan Porteus (1978). This subclass is narrow but wide enough to discuss basic issues. It will be shown that there are serious objections against the modification of expected utility theory axiomatised by Kreps and Porteus (1978, 1979). By contrast the umbrella theory proffered by Pope that she has now termed SKAT, the Stages of Knowledge Ahead Theory, offers an epistemically consistent framework within which to construct particular models to deal with particular decision situations. A model by Caplin and Leahy (2001) will also be discussed and contrasted with the modelling within SKAT (Pope, Leopold and Leitner 2007). (shrink)

Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency and the corresponding classes (...) of Boolean algebras. (shrink)

A repulsive core force is derived which, assuming π mesons are the field particles, gives binding energies in good agreement with binding energies per nucleon of heavy nuclei. The physical model consists of a field of relatively short range, in which emission of a π meson by a nucleon and subsequent absorption by a neighboring nucleon is equivalent to a potential well. The binding energy at the equilibrium spacing of the nucleons is the self-energy of the π mesons, which is (...) calculated by analogy with classical electric fields. (shrink)

Este artículo investiga la coherencia entre la propuesta de una organización modular masiva de la mente y el enfoque de las heurísticas simples. Se discute una serie de potenciales conflictos entre los dos programas, pero finalmente son desestimados. De todos modos, el programa de las heurísticas simples sí termina socavando uno de los muchos argumentos propuestos para apoyar la modularidad masiva, al menos en el modo en que esta última es comprendida por los filósofos. Así que un resultado de la (...) argumentación será forzarnos a reexaminar la mejor manera de caracterizar la noción de modularidad en la ciencia cognitiva, para que la tesis de la modularidad masiva no deba ser abandonada completamente. Lo que está en juego en esta discusión es si existe una noción de "módulo" que esté bien motivada, de modo que tengamos una buena razón para pensar que la mente humana deba ser masivamente modular en su organización. Argumentaré que tal noción existe. This chapter investigates the extent to which claims of massive modular organization of the mind are consistent with the main elements of the simple heuristics research program. A number of potential sources of conflict between the two programs are investigated and defused. However, the simple heuristics program turns out to undermine one of the main arguments offered in support of massive modularity, at least as the latter is generally understood by philosophers. So one result of the argument will be to force us to re-examine the way in which the notion of modularity in cognitive science should best be characterized, if the thesis of massive modularity isn't to be abandoned altogether. What is at stake in this discussion, is whether there is a well-motivated notion of "module" such that we have good reason to think that the human mind must be massively modular in its organization. I shall be arguing that there is. (shrink)

Hume’s division of perceptions into simple and complex has been criticized for being vague and perfunctory. Often the division is considered to be a rather weak part of his system, yet there is no agreement on its particular shortcomings and no consensus that it is totally impracticable. At the same time, the division between simple and complex perceptions has not attracted strong interest or attention from commentators. Most accounts consist of short paraphrases, some of which suggest a connection (...) with Locke. The few attempts at a systematic explanation include the accounts of Baier, Frasca-Spada, Garrett, Pears, and Waxman. (shrink)

Wittgenstein's views on mathematics are radically original. He criticizes most of the traditional philosophies of mathematics. His views have been subject to harsh criticisms. In this dissertation, I attempt to defend Wittgenstein's philosophy of mathematics from two objections: the objectivity objection and the consistency objection. The first claims that Wittgenstein's account of mathematics is not sufficient for the objectivity of mathematics; the second claims that it is only a partial account of mathematics because it cannot explain the semantic properties (...) of mathematical systems. ;The first chapter outlines Wittgenstein's Philosophy of Mathematics by stressing the differences and similarities with more traditional accounts. The second chapter discusses the objectivity objection. I distinguish epistemic from non-epistemic objectivity and discuss their relation with the issue of realism and anti-realism. I conclude first that either notion of objectivity is insufficient for disparaging anti-realist accounts of mathematics and, second, that Wittgenstein's account is sufficient for both. The third chapter is a detailed discussion of the consistency objection. Some unsuccessful replies are discussed. In the fourth chapter, I reformulate the objection by means of a rather simple axiomatic system that I call theory T. This allows us to see more clearly why the replies considered before are not successful and, furthermore, which view Wittgenstein is actually required to hold in order to reject the objection. In the fifth chapter, I offer a brief outline of Wittgenstein's account of logic and, finally, show how it provides the required answer to the consistency objection. (shrink)

The doctrine on predicative judgment sustained by Frege and Husserl reopens a discussion already present in the philosophical tradition: Does predicative judgment consist in a “composition” of concepts made by the understanding, or in an “assent” to a propositional content? For Frege, the “thought”, i. e., the sense of the proposition, as expresion of the judgment, presents such unity that it cannot be explained by a “composition” of previous elements; Husserl on the contrary, sustains that, although the propositional content of (...) judgments in composed judgments do present a unity, in the case of the simple predicative judgment this unity arises due to a “synthesis”. Thus, for Frege the act of judging consists in “recognizing the truth-value of a thought”, which agrees with the doctrine of an “assent” to a propositional content. For Husserl, on the contrary, the basic act of judging consists in a “synthesis” of basic representations, which is very close to Aristotle’s doctrine. (shrink)

R.A.Fisher introduced the fiducial argument as a means for obtaining something from nothing. He thought that on some occasions it was legitimate to obtain a posterior probability distribution over a range of simple statistical hypotheses without commitment to a prior distribution [4].H.Jeffreys thought he could tame Fisher by casting his argument in a Bayesian mold through a derivation of the fiducial posterior from a suitably constructed ignorance prior via Bayes’ theorem and conditionalization on the data of experimentation. According to (...) Jeffreys, Fisher was using something to obtain something after all ([7],pp.381-383).D.V.Lindley furthered the process of taming by specifying allegedly necessary and sufficient conditions for the consistency of fiducial reasoning in contexts of one parameter estimation with Bayesian requirements [14]. I. Hacking exploited Lindley’s result to supply his own ingenious method for taming Fisher([5],ch. 9).T.Seidenfeld has recently demonstrated that Lindley’s conditions are insufficient for consistency and that reconstructions like Jeffreys’ or Hacking’s lead to contradiction ([15], PP. 721-727). (shrink)

There are indications that simple reaction time might have slowed in Western countries, based on both cohort- and multi-study comparisons. A possible limitation of the latter method in particular is measurement error stemming from methods variance, which results from the fact that instruments and experimental conditions change over time and between studies. We therefore set out to measure the simple auditory reaction time (SRT) of 7,081 individuals (2,997 males and 4,084 females) born in Sweden 1959-1985 (subjects were aged (...) between 27 and 54 years at time of measurement). Depending on cut-offs and adjustment for ageing related slowing on SRT, the data suggest that SRT has increased between 3 and 16 ms in the 27 birth years covered in the present sample. The slowing is unlikely to be explained by attrition, as evaluated by comparing the general intelligence × birth-year interactions and standard deviations for both male participants and dropouts, utilizing military conscript cognitive ability data. The present result is consistent with previous studies employing alternative methods, and may result from several synergistic factors, such as possible recent micro-evolutionary trends favouring lower g in Sweden and the effects of industrially produced neurotoxic substances on peripheral nerve conduction velocity. (shrink)

Some researchers on binary choice inference have argued that people make inferences based on simple heuristics, such as recognition, fluency, or familiarity. Others have argued that people make inferences based on available knowledge. To examine the boundary between heuristic and knowledge usage, we examine binary choice inference processes in terms of attribute substitution in heuristic use (Kahneman & Frederick, 2005). In this framework, it is predicted that people will rely on heuristic or knowledge‐based inference depending on the subjective difficulty (...) of the inference task. We conducted competitive tests of binary choice inference models representing simple heuristics (fluency and familiarity heuristics) and knowledge‐based inference models. We found that a simple heuristic model (especially a familiarity heuristic model) explained inference patterns for subjectively difficult inference tasks, and that a knowledge‐based inference model explained subjectively easy inference tasks. These results were consistent with the predictions of the attribute substitution framework. Issues on usage of simple heuristics and psychological processes are discussed. (shrink)