I argue that extended simples are possible. The argument given here parallels an argument given elsewhere for the claim that the shape properties of material objects are extrinsic, not intrinsic as is commonly supposed. In the final section of the paper, I show that if the shape properties of material objects are extrinsic, the most popular argument against extended simples fails.

Both extended simples and unextended complexes have been extensively discussed and widely used in metaphysics and philosophy of physics. However, the characterizations of such notions are not entirely satisfactory inasmuch as they rely on a mereological notion of extension that is too simplistic. According to such a mereological notion, being extended boils down to having a mereologically complex exact location. In this paper, I make a detailed plea to supplement this notion of extension with a different one (...) that is phrased in terms of measure theory. This proposal has significant philosophical payoffs. I provide new characterizations of both extended simples and unextended complexes, that help re-evaluating the question of whether such entities are metaphysically possible. Finally, I advance several suggestions as to how different notions of extension relate, first, to one another and, second, to mereological structure. (shrink)

The problem of qualitative heterogeneity is to explain how an extended simple can enjoy qualitative variation across its spatial or temporal axes, given that it lacks both spatial and temporal parts. I discuss how friends of extended simples should address the problem of qualitative heterogeneity. I present a series of arguments designed to show that rather than appealing to fundamental distributional properties one should appeal to tiny and short-lived tropes. Along the way, issues relevant to debates about (...) material composition, persistence over time and existence monism are discussed.  . (shrink)

The idea that there could be spatially extended mereological simples has recently been defended by a number of metaphysicians (Markosian 1998, 2004; Simons 2004; Parsons (2000) also takes the idea seriously). Peter Simons (2004) goes further, arguing not only that spatially extended mereological simples (henceforth just extended simples) are possible, but that it is more plausible that our world is composed of such simples, than that it is composed of either point-sized simples, (...) or of atomless gunk. The difficulty for these views lies in explaining why it is that the various sub-volumes of space occupied by such simples, are not occupied by proper parts of those simples. Intuitively at least, many of us find compelling the idea that spatially extended objects have proper parts at every sub-volume of the region they occupy. It seems that the defender of extended simples must reject a seemingly plausible claim, what Simons calls the geometric correspondence principle (GCP): that any (spatially) extended object has parts that correspond to the parts of the region that it occupies (Simons 2004: 371). We disagree. We think that GCP is a plausible principle. We also think it is plausible that our world is composed of extended simples. We reconcile these two notions by two means. On the one hand we pay closer attention to the physics of our world. On the other hand, we consider what happens when our concept of something—in this case space—contains elements not all of which are realized in anything, but instead key components are realized in different features of the world. (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)

Extended simples are physical objects that, while spatially extended, possess no actual proper parts. The theory that physical reality bottoms out at extended simples is one of the principal competing views concerning the fundamental composition of matter, the others being atomism and the theory of gunk. Among advocates of extended simples, Markosian’s ‘MaxCon’ version of the theory (Aust J Philos 76:213–226, 1998, Monist 87:405–428, 2004) has justly achieved particular prominence. On the assumption of (...) causal realism (i.e., on the assumption that a Humean account of causation is false), I argue here that the reality of MaxCon simples would entail the reality of irreducible, intrinsic dispositional properties. The existence of dispositional properties in turn has important implications for another central debate in metaphysics, namely that between two major competing views concerning the ontology of laws: dispositionalism versus nomological necessitarianism. (shrink)

In this paper, I will offer an analogy between the Trinity and extended simples that supports a Latin approach to the Trinity. The theoretical tools developed to discuss and debate extended simples in the literature of contemporary analytic metaphysics, I argue, can help us make useful conceptual distinctions in attempts to understand what it could be for God to be Triune. Furthermore, the analogy between extended simples and the Trinity might surprise some who find (...) one of these at least plausibly possible and the other incoherent. (shrink)

I argue that the assumptions that physically basic things are either mereologically atomic, or that they are continuous and there are no atoms, both face difficult conceptual problems. Both views tend to presuppose a largely unquestioned assumption, that things have parts corresponding to the geometric parts of the regions they occupy. To avoid these problems I propose a third view, that physically simple things occupy a finite volume without themselves having parts. This view is examined enough to tease out some (...) of its consequences and show that it withstands the obvious questions it faces. I conclude by mentioning some precedents for this view in Democritus, Kant, and Whitehead, with close variants in Boscovich, Harré, and Markosian. (shrink)

Perhaps the most commonly discussed argument against the possibility of extended simples is the argument from heterogeneity. The argument states that, if extended simples are possible, then extended simples which exhibit intrinsic qualitative variation across space (or spacetime) are also possible [Premise 1]. But, the argument goes, it is impossible for an extended simple to exhibit intrinsic qualitative variation across space (or spacetime) [Premise 2]. Thus, extended simples are impossible. I argue (...) that there is a serious problem with the argument from heterogeneity: the best arguments in support of the first premise undermine support for the second. Thus, there appears to be no good reason to accept both premises. (shrink)

There are four main theories concerning the ultimate constitution of matter: atomism version 1, atomism version 2, the theory of gunk, and the theory of extended simples. These four theories are usually seen as diametrically opposed. Here I take a stab at ecumenism, and argue that atomism version 1 and the theory of extended simples can be reconciled and rendered compatible by reference to the reality of dispositions.

Is it possible that there are extended simples—material objects extended in space or spacetime that have no proper parts? The most commonly cited argument for this possibility is based on a version of the Humean principle: namely (and with some qualifications), any pattern of instantiation of a fundamental relation is possible. In this paper, we make the Humean argument fully explicit, and criticise it from three aspects—the Disjunction problem, the Pluralist problem, and the Accidentality problem. First, the (...) original argument only shows a disjunctive thesis: either extended simples are possible, or unextended complexes are possible. In order to reach the desired conclusion, some additional premise is needed. Yet, even though we agree that the Disjunction problem can be met, we argue that the Humean argument fails to establish the possibility of extended simples, for two reasons: the first comes from compositional pluralism, and the second is about the definition of accidental properties. We contend that the latter two problems put the proponents of the Humean argument in serious difficulty. Thus, metaphysicians who hold that there are extended simples should find better arguments for this view. (shrink)

It is sometimes claimed that string theory posits a fundamental ontology including extended mereological simples, either in the form of minimum-sized regions of space or of the strings themselves. But there is very little in the actual theory to support this claim, and much that suggests it is false. Extant string theories treat space as a continuum, and strings do not behave like simples.

A substantivalist dualist who believes in spacetime and material objects is committed to a relation of occupation or location. This chapter explores different candidate descriptions of this relation and investigates some of the philosophical difficulties which arise for the resulting conceptions. One reason to focus on the metaphysics of occupation relations is that some of them seem to make room for the possibility of extended mereological simples. The chapter critically evaluates several philosophical attempts to promote the cause of (...) extended simples. Four problems are then advanced to yield the conclusion that extended mereological simples are conceptually possible yet metaphysically impossible: the problem of spatial intrinsics, the problem of shapes, the problem of parsimony, and the problem of diachoric identity. (shrink)

Let us say that an extended object is “composed wholly of simples” just in case it is an aggregate of absolutely unextended parts spread throughout an extended region—that is, just in case there is a set S such that: every member is a point-sized part of the object, and for every x, x is part of the object if and only if it has a part in common with some member of S. Could a truly extended (...) substance be composed entirely of unextended parts? Reflection upon the fact that it must be at least possible for extended objects to touch one another suggests that the answer to this question is: No. (shrink)

A material simple is a material object that has no proper parts. Some philosophers have argued for the possibility of extended simples. Some have even argued for the possibility of heterogeneous simples or simples that have intrinsic variations across their surfaces. There is a puzzle, though, that is meant to show that extended, heterogeneous simples are impossible. Although several plausible responses have been given to this puzzle, I wish to reopen the case against (...) class='Hi'>extended, heterogeneous simples. In this paper, I briefly canvass responses to this puzzle which may be made in defense of extended, heterogeneous simples. I then present a new version of this puzzle which targets simples that occupy atomic yet extended regions of space. It seems that none of the traditional responses can be used to successfully save this particular kind of extended simple from the new puzzle. I also consider some non-traditional defenses of heterogeneous extended simples and argue that they too are unsuccessful. Finally, I will argue that a substantial case can be made against the possibility of extended heterogeneous simples of any kind. (shrink)

Substitution and simple sentences -- Simple sentences and semantics -- Simple sentences and implicatures -- The enlightenment problem and a common assumption -- Abandoning (EOI) -- Beyond matching propositions -- App. A : extending the account -- App. B : belief reporting.

An object is a simple if and only if it has no proper parts. An object is gunk if and only if every proper part of that object itself has a proper part. In my dissertation, I address the following questions. The concepts of simples and gunk presuppose the concept of parthood. What is the status of this concept? his question itself divides into the following: does the concept of parthood have universal applicability, so that, just as every object (...) is self-identical, every object has parts? Finally, is the concept of parthood univocal, or are there different notions of parthood, each of which is defined on distinct ontological categories? I argue that the concept of parthood has univocal. I also argue that there is some evidence that the concept of parthood has universal applicability. I address the Simple Question, which is “under what circumstances is it true of some object that it has no proper parts?” I argue against several popular answers to the Simple Question, such as the view that simples are all and only point-sized objects, and the view that simples are maximally continuous material objects. I defend the Brutal View, which holds that there is no true, finitely expressible, and informative answer to the Simple Question. In short, there is no criterion for being a simple. Along the way, I address the question of whether extended simples, i.e., simples that are extended in space, are possible. I argue that one popular argument against the possibility of extended simples is unsound. I address the question of whether both simples and gunk are possible. I argue that it is metaphysically possible that material objects be composed of gunk. (shrink)

This unique textbook, in contrast to a standard logic text, provides the reader with a logic that can be used in practice to express and reason about mathematical ideas. The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The (...) book illustrates using Alonzo how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge. For this second edition, more than 400 additions, corrections, and improvements have been made, including a new chapter on inductive sets and types. Topics and features:!-- [if!supportLists]--·!--[endif]--Offers the first book-length introduction to simple type theory as a predicate logic!-- [if!supportLists]--·!--[endif]--Provides the reader with a logic that is close to mathematical practice!-- [if!supportLists]--·!--[endif]--Includes a module system for building libraries of mathematical knowledge!-- [if!supportLists]--·!--[endif]--Employs two semantics, one for mathematics and one for logic!-- [if!supportLists]--·!--[endif]--Emphasizes the model-theoretic view of predicate logic!-- [if!supportLists]--·!--[endif]--Presents several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of mathematics and computing at the graduate or upper-undergraduate level, this book is well suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas. William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada. (shrink)

Extended simple regions have been the focus of recent developments in philosophical logic, metaphysics, and philosophy of physics. However, only a handful of works provides a rigorous characterization of an extended simple region. In particular, a recent paper in this journal defends a definition based on an extrinsic notion of least distance. Call it the Least Distance proposal. This paper provides the first assessment of it. It argues that Least Distance faces difficulties and drawbacks. The paper then goes (...) on to suggest a different proposal, the Diameter proposal that is able to handle such drawbacks and difficulties. (shrink)

A number of philosophers have argued in favour of extended simples on the grounds that they are needed by fundamental physics. The arguments typically appeal to theories of quantum gravity. To date, the argument in favour of extended simples has ignored the fact that the very existence of spacetime is put under pressure by quantum gravity. We thus consider the case for extended simples in the context of different views on the existence of spacetime. (...) We show that the case for extended simples based on physics is far more complex than has been previously thought. We present and then map this complexity, in order to present a much more textured picture of the argument for extended simples. (shrink)

I give reasons to suggest that the various ‘homogeneous substance’ objections to perdurance theory should not be regarded as raising serious difficulties. The main strategy is to show that there are equally exotic possibilities involving extended mereological simples that may turn the tables on the endurance theorist, insofar as she will have difficulties with these cases analogous to those she raises for the perdurantist. I conclude that such exotic cases are less useful that we might suppose in adjudicating (...) between these competing doctrines of persistence. (shrink)

Mainstream epistemology has typically taken for granted a traditional picture of the metaphysics of mind, according to which cognitive processes (e.g. memory storage and retrieval) play out entirely within the bounds of the skull and skin. But this simple ‘intracranial’ picture is falling in- creasingly out of step with contemporary thinking in the philosophy of mind and cognitive science. Likewise, though, proponents of active exter- nalist approaches to the mind—e.g. the hypothesis of extended cognitition (HEC)—have proceeded by and large (...) without asking what epistemological ramifications should arise once cognition is understood as criss-crossing the bounds of brain and world. This paper aims to motivate a puzzle that arises only once these two strands of thinking are brought in contact with one another. In particular, we want to first highlight a kind of con- dition of epistemological adequacy that should be accepted by proponents of extended cognition; once this condition is motivated, the remainder of the paper demonstrates how attempts to satisfy this condition seem to inevitably devolve into a novel kind of epistemic circularity. At the end of the day, proponents of extended cognition have a novel epistemological puzzle on their hands. (shrink)

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)

This paper continues earlier work and extends it to an intuitionistic setting. Kripke frames are used to semantically define a family of intuitionistic-like logics for which the “local” part of the truth definition is supplied by many-valued logics whose semantics are algebraically simple and natural. A uniform tableau system is given and soundness and completeness are proved. The tableau connection entails that the semantic family collectively determines just four logics, intuitionistic logic itself, and intuitionistic-like versions of FDE, K3, and LP. (...) These, apparently, are new logics, and are of natural interest. For instance, all have the disjunction property, and standard double negation embeddings are applicable. In addition, intuitionistic analogues of ST (strict-tolerant logic) and TS (tolerant-strict) logics are defined, and shown to have the same relationships to intuitionistic logic that the usual ST and TS have to classical logic. (shrink)

Extended simples are fruitfully discussed in metaphysics. They are entities which are located in a complex region of space but do not themselves have parts. In this paper, I will discuss unextended complexes: entities which are not located at a complex region of space but do themselves have parts. In particular, I focus on one type of unextended complex: pointy complexes. Four areas are indicated where pointy complexes might prove philosophically useful. Unextended complexes are therefore philosophically fruitful, in (...) much the same way as extended simples. (shrink)

In [1], we established Gentzenizations for a good range of relevant logics with distribution, but, in the process, we added inversion rules, which involved extra structural connectives, and also added the sentential constantt. Instead of eliminating them, we used conservative extension results to relate them back to the original logics. In [4], we eliminated the inversion rules andtand established a much simpler Gentzenization for the weak sentential relevant logicDW, and also for its quantificational extensionDWQ, but a restriction to normal formulae (...) (defined below) was required to enable these results to be proved. This method was quite general and hope was expressed about extending it to other relevant logics.In this paper, we develop an innovative method, which makes essential use of this restriction to normality, to establish two simple Gentzenizations for the normal formulae of the slightly weaker logic B, and then extend the method to other sentential contraction-less logics. To obtain the first of these Gentzenizations, for the logicsBandDW, we remove the two branching rules (F&) and (T∨), together with the structural connective ‘,’, to simplify the elimination of the inversion rules andt. We then eliminate the rules (T&) and (F∨), thus reducing the Gentzen system to one containing only ˜ and → and their four associated rules, and reduce the remaining types of structures to four simple finite types. Subsequently, we re-introduce (T&) and (F∨), and also (F&) and (T∨), to obtain the second Gentzenization, which contains ‘,’ but no structural rules. (shrink)

We provide a constructive, direct, and simple proof of the completeness of the cut-free part of the hypersequential calculus for G¨odel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). We then extend the results and proofs to derivations from assumptions, showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions.

The advance of science and human knowledge is impeded by misunderstandings of various statistics, insufficient reporting of findings, and the use of numerous standardized and non-standardized presentations of essentially identical information. Communication with journalists and the public is hindered by the failure to present statistics that are easy for non-scientists to interpret as well as by use of the word significant, which in scientific English does not carry the meaning of "important" or "large." This article promotes a new standard method (...) for reporting two-group and two-variable statistics that can enhance the presentation of relevant information, increase understanding of findings, and replace the current presentations of two-group ANOVA, t-tests, correlations, chi-squares, and z-tests of proportions. A brief call to highly restrict the publication of risk ratios, odds ratios, and relative increase in risk percentages is also made, since these statistics appear to provide no useful scientific information regarding the magnitude of findings. (shrink)

In the movie, Memento, the hero, Leonard, suffers from a form of anterograde amnesia that results in an inability to lay down new memories. Nonetheless, he sets out on a quest to find his wife’s killer, aided by the use of notes, annotated polaroids, and body tattoos. Using these resources he attempts to build up a stock of new beliefs and to thus piece together the puzzle of his wife’s death. At one point in the movie, a character exasperated by (...) Leonard’s lack of biological recall, shouts: “YOU know? What do YOU know. YOU don’t know anything. In 10 minutes time YOU won’t even know you had this conversation” Leonard, however, believes that he does, day by day, come to know new things. But only courtesy of those photos, tattoos, tricks and ploys. Who is right?These are the kinds of question addressed at length in the paper ‘The Extended Mind’. Is the mind contained in the head? Or does the notion of thought allow mental processes to inhere in extended systems of body, brain and aspects of the local environment? The answer, we claimed, was that mental states, including states of believing, could be grounded in physical traces that remained firmly outside the head. As long as a few simple conditions were met, Leonard’s notes and tattoos could indeed count as new additions to his store of long-term knowledge and dispositional belief. In the present treatment I revisit this argument, defending our strong conclusion against a variety of subsequent observations and objections. In particular, I look at objections that rely on a contrast between the intrinsic content of neural symbols and the merely derived content of external inscriptions, at objections concerning the demarcation of scientific domains via natural kinds, and at objections concerning the ultimate locus of agentive control and the nature of perception versus introspection. I also mention a possible alternative interpretation of the argument as a reductio of the very idea of the mind as an object of scientific study. This is an interesting proposal. (shrink)

Dividing chains have been used as conditions to isolate adequate subclasses of simple theories. In the first part of this paper we present an introduction to the area. We give an overview on fundamental notions and present proofs of some of the basic and well-known facts related to dividing chains in simple theories. In the second part we discuss various characterizations of the subclass of low theories. Our main theorem generalizes and slightly extends a well-known fact about the connection between (...) dividing chains and Morley sequences (in our case: independent sequences). Moreover, we are able to give a proof that is shorter than the original one. This result motivates us to introduce a special property of formulas concerning independent dividing chains: For any dividing chain there exists an independent dividing chain of the same length. We study this property in the context of low, short and ω -categorical simple theories, outline some examples and define subclasses of low and short theories, which imply this property. The results give rise to further studies of the relationships between some subclasses of simple theories. (shrink)

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)

Philosophers of language have long recognized that in opaque contexts, such as those involving propositional attitude reports, substitution of co-referring names may not preserve truth value. For example, the name ‘Clark Kent’ cannot be substituted for ‘Superman’ in a context like:1. Lois believes that Superman can flywithout a change in truth value. In an earlier paper, Jennifer Saul demonstrated that substitution failure could also occur in ‘simple sentences’ where none of the ordinary opacity-producing conditions existed, such as:2. Superman leaps more (...) tall buildings than Clark Kent does.Accounts focusing on opacity were unable to explain our ‘anti-substitution intuitions’ in such cases.In Simple Sentences, Substitution, and Intuitions, Saul extends her earlier work. She provides a comprehensive presentation and criticism of recent accounts of simple sentence substitution failure, and proposes a new approach drawing on psychological evidence about cognitive processing. Saul's purpose is not merely to solve the substitution puzzle cases, but to make …. (shrink)

Should people be assisted to die or be given euthanasia when they are suffering from terminal medical conditions? Should they be assisted to die when they are suffering but do not have a ‘diagnosable medical illness?’ What about assisted dying for psychiatric conditions? And is there a difference morally between assisted suicide, voluntary active euthanasia and voluntary passive euthanasia?These are deep questions directly addressed or in the background of the productive discussion between Varelius and Young.1 ,2 Their focus is whether (...) doctors should assist people to die who are ‘tired of life’ and experiencing ‘existential suffering’. An example was Edward Brongersma, an 86-year-old man, who was tired of life but with no serious medical condition, who was assisted by Dr Philip Sutorius to commit suicide in 1998. In the Netherlands, where euthanasia is legal, the Dutch Supreme Court ruled in 2002 that this was wrong because "edical expertise, by its nature, does not extend to questions and complaints that do not have a sick- ness or ailment—mental or physical—as their source.3"Sutorius was convicted, but not punished.Robert Young, considering this case, concurs, concluding, "a physician may justifiably consider that an individual who is ‘tired of life’ should consult a non-medical, professional counsellor, and if that produces no change in outlook, choose suicide. Outside Switzerland, an individual who makes that choice has to then be determined enough to do so unassisted .2"I will argue that there is, within current medical ethics and human rights, a method of assisted suicide which could fall within the limits of the law. But first I will review some recent cases involving requests for dying. I will then discuss an alternative which some may argue addresses these cases, and those of …. (shrink)

According to a widely shared interpretation, research employing spontaneous-response false belief tasks demonstrates that infants as young as 15 months attribute (false) beliefs. In contrast with this conclusion, I advance an alternative reading of the empirical data. I argue that infants constantly form and update their expectations about others’ behaviour and that this ability extends in the course of development to reflect an appreciation of what others can and cannot see. These basic capacities account for infants’ performance in spontaneous-response false (...) belief tasks without the need to assume the existence of a cognitive module specific for mental state attribution. My proposal suggests a plausible explanatory strategy for the problem of the representational format of the information processed in spontaneous-response false belief tasks. (shrink)

We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon hypothesis and (...) explanatory power of recent neuroimaging studies as well as provides<br>evidence. (shrink)

This paper extends the defense of a simple theory of indicative conditionals previously proposed by the author, in which the truth conditions are material, and Grice-style assertability conditions are given to explain the paradoxes of material implication. The paper discusses various apparent counter-examples to the material account in which conditionals are not asserted, and so the original theory cannot be applied; it is argued that, nevertheless, the material theory can be defended.

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism can be (...) applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena. (shrink)

What experimental game theorists may have demonstrated is not that people are systematically irrational but that human rationality is heavily scaffolded. Remove the scaffolding, and we do not do very well. People are able to get on because they “offload” an enormous amount of practical reasoning onto their environment. As a result, when they are put in novel or unfamiliar environments, they perform very poorly, even on apparently simple tasks. -/- This observation is supported by recent empirically informed shifts in (...) philosophy of mind toward a view of cognition as (to cite the current slogan) “embodied, embedded, enactive, extended.” Andy Clark and others have made a very plausible case for the idea that a proper assessment of human cognitive competence must include environmental components. To limit our attention to what lies within the skin-skull boundary is, in effect, to miss the big story on human rationality. Insofar as we are rational, it is often because of our ingenuity at developing “work-arounds” to the glitches in the fast-and-frugal heuristic problem-solving capabilities that natural selection has equipped us with. And these work-arounds often involve a detour through the environment (so-called offloading of cognitive burdens). -/- When it comes to practical rationality, things are no different. Yet in many discussions of “the will,” there is still a tendency to put too much emphasis on what goes on inside the agent’s head. Our objective in this chapter is to articulate this conception of “the extended will” more clearly, using the strategies that people employ to overcome procrastination for the central set of examples. Procrastination, in our view, constitutes a particular type of self-control problem, one that is particularly amenable to philosophical reflection, not only because of the high volume of psychological research on the subject but also because of the large quantity of “self-help” literature in circulationa literature that provides an invaluable perspective on the everyday strategies that people use in order to defeat (or, better yet, circumvent) this type of self-defeating behavior pattern. In general, what we find is that the internalist bias that permeates discussions of the will gives rise to a set of practical recommendations that overemphasize changing the way one thinks about a task, while ignoring the much richer set of strategies that are available in the realm of environmental scaffolding. In the concluding section, we highlight some of the policy implications of this, particularly regarding social trends involving the dismantling of support structures. (shrink)

We propose a simple notion of "extender" for coding large elementary embeddings of models of set theory. As an application we present a self-contained proof of the theorem by D. Martin and J. Steel that infinitely many Woodin cardinals imply the determinacy of every projective set.

In this study, an extended paradefinite logic with classical negation (EPLC), which has the connectives of conflation, paraconsistent negation, classical negation, and classical implication, is introduced as a Gentzen-type sequent calculus. The logic EPLC is regarded as a modification of Arieli, Avron, and Zamansky’s ideal four-valued paradefinite logic (4CC) and as an extension of De and Omori’s extended Belnap–Dunn logic with classical negation (BD+) and Avron’s self-extensional four-valued paradefinite logic (SE4). The completeness, cut-elimination, and decidability theorems for EPLC (...) are proved and EPLC is shown to be embeddable into classical logic. The strong equivalence substitution property and the admissibilities of the rules of negative symmetry, contraposition, and involution are shown for EPLC. Some alternative simple Gentzen-type sequent calculi, which are theorem-equivalent to EPLC, are obtained via these characteristic properties. (shrink)

In this paper we study three-valued simple games as a natural extension of simple games. We analyze to which extent well-known results on the core and the Shapley value for simple games can be extended to this new setting. To describe the core of a three-valued simple game we introduce vital players, in analogy to veto players for simple games. Moreover, it is seen that the transfer property of Dubey can still be used to characterize the Shapley value for (...) three-valued simple games. We illustrate three-valued simple games and the corresponding Shapley value in a parliamentary bicameral system. (shrink)

Let T1 and T2 be two simple complete theories in disjoint languages. We prove that there is a simple complete theory which extends T1 ∪ T2 if T2 has a certain condition.

This paper evaluates and criticises the developmental systems conception of evolution and develops instead an extension of the gene's eye conception of evolution. We argue (i) Dawkin's attempt to segregate developmental and evolutionary issues about genes is unsatisfactory. On plausible views of development it is arbitrary to single out genes as the units of selection. (ii) The genotype does not carry information about the phenotype in any way that distinguishes the role of the genes in development from that other factors. (...) (iii) There is no simple and general causal criterion which distinguishes the role of genes in development and evolution. (iv) There is, however, an important sense in which genes but not every other developmental factor represent the phenotype. (v) The idea that genes represent features of the phenotype forces us to recognise that genes are not the only, or almost the only, replicators. Many mechanisms of replication are involved in both development and evolution. (vi) A conception of evolutionary history which recognises both genetic and non-genetic replicators, lineages of replicators and interactors has advantages over both the radical rejection of the replicator/interactor distinction and the conservative restriction of replication to genetic replication. (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)

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)

What is Leibniz’s argument for simple substances? I propose that it is an extension of his prior argument for incorporeal forms as principles of unity for individual corporeal substances. The extension involves seeing the hylomorphic analysis of corporeal substances as implying a resolution of matter into forms, and this seems to demand that forms, which are themselves simple, be the only elements of things. The argument for simples thus presupposes the existence of corporeal substances as a key premise. Yet (...) a theory of simple substances as the elements of things threatens to preclude the existence of corporeal substances for Leibniz, and the extension of the argument for forms into an argument for simples is not cogent. If nothing else rides on the simplicity of individual substances, then perhaps instead of being its most fundamental tenet, the doctrine of simples—the monadology—is something that over-extends and destabilizes Leibniz’s metaphysics. (shrink)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...) are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

An SR model is presented that shows how an objective (noncontextual and local) interpretation of quantum mechanics can be constructed, which contradicts some well-established beliefs following from the standard interpretation of the theory and from known no-go theorems. The SR model is not a hidden variables theory in the standard sense, but it can be considered a hidden parameters theory which satisfies constraints that are weaker than those usually imposed on standard hidden variables theories. The SR model is also (...) class='Hi'>extended in a natural way that shows how a broader theory embodying quantum mechanics can be envisaged which is realistic in a semantic sense, hence compatible with various “realistic” perspectives. (shrink)

The first part of this paper investigates the purpose, methodological approach, and fundamental thesis of Du Châtelet’s theory of simple beings. The paper shows that ‘simple beings’ in Du Châtelet is a theory concerned with the understanding of extended bodies. The second part of the paper shows that her theory of simple beings, while it has important roots in both Leibniz and Wolff, is remarkably different from theirs. Thus, contrary to a common thread in the literature, Du Châtelet’s theory (...) of simple beings does not commit her to an ontology that can be equated with that of Leibniz or Wolff. Instead, her theory of simple beings is faculty-centred and draws a fundamental and novel distinction between the phenomenal realm of the senses and ‘real’ substances, which can only be grasped through the understanding. (shrink)

Physical boundaries and the earliest topologists. Topology has a relatively short history; but its 19th century roots are embedded in philosophical problems about the nature of extended substances and their boundaries which go back to Zeno and Aristotle. Although it seems that there have always been philosophers interested in these matters, questions about the boundaries of three-dimensional objects were closest to center stage during the later medieval and modern periods. Are the boundaries of an object actually existing, less-than-three-dimensional parts (...) of the object—that is, are solids bounded by two-dimensional surfaces, surfaces by one-dimensional “edges” or “physical lines”, edges by dimensionless “simples”? If not, how does a perfectly spherical object manage to touch a perfectly flat object—what part of the sphere is in immediate contact with the plane, if the sphere has no unextended parts? But if such parts be admitted, are we not then saddled with “actual infinities” of simples, lines, and surfaces spread throughout each continuous object—the boundaries of all the object’s internal parts? Does it help to say that these internal boundaries exist only “potentially”? (shrink)