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)

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.

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 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)

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 has justly achieved particular prominence. On the assumption of causal realism, 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)

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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

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.

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)

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.

Mainstream epistemology has typically taken for granted a traditional picture of the metaphysics of mind, according to which cognitive processes 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 —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)

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)

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)

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)

This meta-study of animal semantics is anchored in two claims, seemingly creating a fuzzy mismatch, that animal utterances generally appear to be simple in structure and content variation and that animals’ communicative understanding seems disproportionally more advanced. A set of excerpted, new studies is chosen as basis to discuss whether the semantics of animal uttering and understanding can be fused into one. Studies are prioritised due to their relatively complex designs, giving priority to dynamics between syntax, semantics, pragmatics, and between (...) utterers and receivers in context. A communicational framework based on utterance theory is applied as a lens for inspection of how these aspects relate to the assumed mismatch. Inspection and discussions of the studies bring several features to surface of which five are stressed in the following. Firstly, both syntactic structures and possible semantic content are seen as lean, although richer than earlier believed, and research continues to reveal new complexities in utterances. Secondly, there is a clear willingness to broaden the perception of animals’ semantic capacity to comprehend communication both by arguing theoretically and by generating empirical research in new contexts. Thirdly, the ambition to make sense of these tendencies is still often motivated by an evolutionary search for early building blocks for verbal language, with the pro et cons that such a position can have. Fourthly, the ‘allowed’ scientific frame for studying semantic capacity among animals is extended to new fields and contexts challenging the only-in-the-wild norm. Fifthly, the dilemma of integrating uttering and understanding as aspects of an after all functional communicational system, calls for new epistemological concepts to make sense of the claimed mismatch. Affordances, abduction, life-genre, and lifeworld are suggested. (shrink)

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)

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)

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 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)

This article provides an analysis of theories of metaphor, tracing how far those which have dominated Western thought until the past few decades are reflective of the definitions within which writers from Classical Greece were working. It is shown how, during the Middle Ages and beyond, in particular since the seventeenth century, definitions of metaphor which emphasised ‘literal’ and ‘figurative’ levels of meaning have led to serious misconceptions concerning its nature and function in the attempts of human beings to conceptualise (...) and make sense of their experiences. A discussion of these misconceptions is provided in some detail and traditional definitions are shown to have distorted the deeper insights held by classical writers, such as Aristotle, Demetrius and Longinus. The article continues with descriptive analyses of the mistaken nature of definitions of metaphor which confine it to creative, poetic forms of discussion. It is shown that conventional speech utterances comprise simple metaphors to a large extent and how these provide an immensely important base from which education could help pupils extend and enrich both their thought and language. This could be done by teaching them ways of interpreting the novel, poetic metaphors of others and how to create their own. (shrink)

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second-order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them (unconstrained evolution). The problem of the 3-d computational simulation of even a single isolated vacuum black hole has proven to be remarkably difficult. Recently, we have become aware of two publications that (...) describe very long term evolution, at least for single isolated black holes. An essential feature in each of these results is constraint subtraction. Additionally, each of these approaches is based on what we call “modern,” hyperbolic formulations of the Einstein equations. It is generally assumed, based on computational experience, that the use of such modern formulations is essential for long-term black hole stability. We report here on comparable lifetime results based on the much simpler (“traditional”) ${\dot g} - {\dot K}$ formulation. With specific subtraction of constraints, with a simple analytic gauge, with very simple boundary conditions, and for moderately large domains with moderately fine resolution, we find computational evolutions of isolated non-spinning black holes for times exceeding 1000 GM/c2. We have also carried out a series of constrained 3-d evolutions of single isolated black holes. We find that constraint solution can produce substantially stabilized long-term single hole evolutions. However, we have found that for large domains, neither constraint-subtracted nor constrained ${\dot g} - {\dot K}$ evolutions carried out in Cartesian coordinates admit arbitrarily long-lived simulations. The failure appears to arise from features at the inner excision boundary; the behavior does generally improve with resolution. (shrink)

Hegselmann and Krause have developed a simple yet powerful computational model for studying the opinion dynamics in societies of epistemically interacting truth-seeking agents. We present various extensions of this model and show their relevance to the investigation of socio-epistemic questions, with an emphasis on normative questions.

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)

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)

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)

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.

Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...) which produced richness of local computability-theoretic structure. To this extent, he was not just interested in causal structure as an abstraction, but in the way in which this structure emerges in natural contexts. Post’s programme was the genesis of a more far reaching research project. In this article we will firstly review the history of Post’s programme, and look at two interesting developments of Post’s approach. The first of these developments concerns the extension of the core programme, initially restricted to the Turing structure of the computably enumerable sets of natural numbers, to the Ershov hierarchy of sets. The second looks at how new types of information coming from the recent growth of research into randomness, and the revealing of unexpected new computability-theoretic infrastructure. We will conclude by viewing Post’s programme from a more general perspective. We will look at how algorithmic structure does not just emerge mathematically from information, but how that emergent structure can model the emergence of very basic aspects of the real world. (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)

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)

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)

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)

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)

This article explores the question of what character relations must have before the orthodox law of obligations will describe them as ‘causal’ relations. The article does not purport to identify the metaphysical nature of ‘causation’. Instead it provides a non-reductive account of what is essential before the law has described the relation between a specific factor and the existence of a particular indivisible phenomenon as ‘causal’. Section 1 presents a simple test for this relation—an ‘extended but-for test’—that can be (...) deployed in a straightforward way without engaging with theoretically complex and often problematic accounts of causation based on the notion of sufficient sets, such as Wright’s NESS account. Section 2 demonstrates how important principles relating to the separateness of a legal entity and to legal responsibility can resolve theoretical puzzles and in turn illuminate why the orthodox law of obligations does not choose to describe as ‘causal’ a relation wider than the one identified in this article. (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)

Two critiques of simple adaptationism are distinguished: anti-adaptationism and extended adaptationism. Adaptationists and anti-adaptationists share the presumption that an evolutionary explanation should identify the dominant simple cause of the evolutionary outcome to be explained. A consideration of extended-adaptationist models such as coevolution, niche construction and extended phenotypes reveals the inappropriateness of this presumption in explaining the evolution of certain important kinds of features—those that play particular roles in the regulation of organic processes, especially behavior. These biological or (...) behavioral ‘levers’ are distinctively available for adaptation and exaptation by their possessors and for co-optation by other organisms. As a result they are likely to result from a distinctive and complex type of evolutionary process that conforms neither to simple adaptationist nor to anti-adaptationist styles of explanation. Many of the human features whose evolutionary explanation is most controversial belong to this category, including the female orgasm. (shrink)

As quantum information science approaches the goal of constructing quantum computers, understanding loss of information through decoherence becomes increasingly important. The information about a system that can be obtained from its environment can facilitate quantum control and error correction. Moreover, observers gain most of their information indirectly, by monitoring (primarily photon) environments of the “objects of interest.” Exactly how this information is inscribed in the environment is essential for the emergence of “the classical” from the quantum substrate. In this paper, (...) we examine how many-qubit (or many-spin) environments can store information about a single system. The information lost to the environment can be stored redundantly, or it can be encoded in entangled modes of the environment. We go on to show that randomly chosen states of the environment almost always encode the information so that an observer must capture a majority of the environment to deduce the system’s state. Conversely, in the states produced by a typical decoherence process, information about a particular observable of the system is stored redundantly. This selective proliferation of “the fittest information” (known as Quantum Darwinism) plays a key role in choosing the preferred, effectively classical observables of macroscopic systems. The developing appreciation that the environment functions not just as a garbage dump, but as a communication channel, is extending our understanding of the environment’s role in the quantum-classical transition beyond the traditional paradigm of decoherence. (shrink)

Theories of possible worlds abound. Since the introduction of modal logic, the term of a possible world, and the very nature of an entity denoted by the term, have stood on the top of metaphysical inquiries. A possible world, roughly speaking, is a complete way things could have been. On the face of it, whatever is possible takes place in some possible world, and whatever is not possible, does not. The aim of the present book is to argue that even (...) impossible things happen. By taking David Lewis’s Modal Realism (henceforth as “MR”) seriously, I claim that besides infinitely many concrete ways things could have been, there exist ways things could not have been. I call them concrete impossible worlds. In Chapter I, I outline Lewis’s well-defined conception of philosophical analysis. I present its structure, aims, methodology and criteria for success. Besides the virtues of the Lewisian conception, I point out several limitations the theory has and offer very simple solution: the admission of concrete impossible worlds. In Chapter II, I present a version of an epistemological objection against MR and a positive account in favour of Modal Fictionalism (henceforth as “MF”). I then present the puzzle in this matter and attempt to generalise my point. 9 Introduction Chapter III demonstrates how flexible Lewis’s theory is. I consider a putative impossibility of there being island universes – spatiotemporally disjoint spacetimes – and show what a proponent of modal realism can do in order to account for it. I present three possible moves: a revision of our pre-theoretical opinions, a modification of our definitions and, finally, an ex- tension of our metaphysical commitments. I consider two ersatz theories of impossible worlds in Chapter IV. In particular, I scrutinize Franz Berto’s and Edwin Mares’s (hybrid) theories of MR. Although I admit that the theories radically extend the scope of applications of MR without extending its metaphysical commitments, the approaches do have some limits. Finally, in Chapter V, I present Extended Modal Realism (henceforth EMR), a theory according to which the best way to go in order to account for impossible phenomena is to ex- tend our metaphysical base by genuine impossibilia. I try to (at least) weaken, if not meet, the crucial objections to the proposal. Namely, I challenge the proclaimed universality of classical logic and, subsequently, motivate certain kind of paraconsistent approach to modal reality. Although the consequences are very hard to swallow, I argue that it is because of the fact that we are unsure of our pre-theoretical opinions concerning the impossible. (shrink)

In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These expressions allow, inter alia, to consider different points of view of social entities (humanistic coefficient). In the article, we perform a metalogical analysis of this logic. Finally, we present some simple examples of its application.