This paper explores the value of skepticism towards the Approximate Number System (ANS). I sketch some of the main arguments levied against ANS-based interpretations of numerical cognition data and argue that there are empirical and conceptual reasons to reject wholesale replacement of the ANS with an Analog Magnitude System (AMS). To simplify the discussion, I focus for the most part on a recent critical review representative of this new wave of revisionist skepticism (Leibovich, T., Katzin, N., Harel, M., & Henik, (...) A., 2017). I start with a brief review of some of the reasons offered to deny that experiments studying our numerical abilities reveal the presence of a system dedicated to representing quantities of discrete objects, before turning briefly to empirical responses to these worries. I then offer a few reflections on why even if the empirical rebuttal were to fail, there are conceptual reasons to doubt that we are only equipped with an AMS. While some of these reasons involve methodological implications of AMS-based theories, other conceptual reasons to doubt AMS skepticism revolve around how ANS-skepticism seems to go against the history of the relation between the continuous and the discrete, and how one cannot be derived from the other. I then end with a potential reply to my worries involving an appeal to the Object-File System (OFS) as a source of discrete content in our numerical abilities and find it wanting. (shrink)

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also (...) argue that discrete representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. (...) This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics. (shrink)

There have been few studies of the Law Lords, and no study of them by a political scientist for more than ten years. This book concentrates on the arguments the Law Lords use in justifying their decisions, and is concerned as much with the legal methodology as with the substance of their decisions. Very close attention is paid to the different approaches and styles of judicial argument, but the book is not restricted to this traditional analytic approach. One chapter applies (...) the statistical techniques Americans call 'jurimetrics' and have successfully used on the US Supreme Court. The main theme is that the Law Lords enjoy and fully utilise far more discretion in their judgements than is normally admitted, and that much depends on exactly which judges happen to hear a case. the second part of the book shows the impact this extreme discretion has had in shaping both public law and areas of civil law. (shrink)

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schrödinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete (...) and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism. (shrink)

In this paper, I present a discrete solution for the paradox of Achilles and the tortoise. I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete. I then answer two objections that could be made against this solution. First, I argue that the discrete solution is not an ad hoc solution. It is embedded in a discrete formulation of classical mechanics. Second, I show that (...) the discrete solution cannot be falsified experimentally. (shrink)

We present two discrete dualities for double Stone algebras. Each of these dualities involves a different class of frames and a different definition of a complex algebra. We discuss relationships between these classes of frames and show that one of them is a weakening of the other. We propose a logic based on double Stone algebras.

Democratic institutions and practice depend on trust, in two ways. Citizens must trust each other to abide by shared rules and norms that together govern a political community; it is a feature of democratic states that they direct their resources not to enforcement of rule abidingness, but rather towards providing collective and public goods. Instead, states rely on the semi-voluntary compliance of citizens with these shared norms and laws. Citizens must also trust their political representatives, who via their election are (...) granted discretion to make decisions that will have significant impact on the lives of those they represent. Yet, according to many scholars across many disciplines, this trust is at risk of being undermined, if it hasn’t yet been so. The possible reasons for weakened and broken trust are many, ranging from escalating wealth inequalities, to increasing cultural and ethnic diversity, to political incompetence of both voters and political representatives, to corruption among political representatives. In this article, I examine the trust that underpins the discretion accorded to elected representatives, to identify when the improper use of this discretion may reasonably be thought to be a source of distrust. In particular, I argue that where discretion is used arbitrarily, it may threaten to undermine the trust relations between citizens and their representatives, and therefore the efficient and effective running of democratic states. (shrink)

In this essay, I argue against a way of approaching the issue of Judicial discretion that finds its clearest exposition and highest development in recent works by Ronald Dworkin. This approach is too narrow. It ignores a kind of Judicial discretion whose existence has been maintained by jurists with discretionist sympathies, and which is philosophically significant. The kind of discretion it ignores raises the issue of the justification of adjudication as clearly as does the kind of discretion that it recognizes. (...) Moreover, discussion of the kind of discretion ignored is in some respects the natural starting place for a discussion of judicial discretion in general. (shrink)

The present study provides evidence that valence focus and arousal focus are important processes in determining whether a dimensional or a discrete emotion model best captures how people label their affective states. Individuals high in valence focus and low in arousal focus fit a dimensional model better in that they reported more co-occurrences among like-valenced affective states, whereas those lower in valence focus and higher in arousal focus fit a discrete model better in that they reported fewer co-occurrences (...) between like-valenced affective states. Taken together, these findings suggest that one static, nomothetic theory may not accurately describe the subjective affective experience of all individuals. (shrink)

This paper argues that liberal tenats that justify intervention to promote the welfare of an incompetent do not suffice as a basis for analyzing parent-child relationships, and that this inadequacy is the basis for many of the problems that arise when thinking about the state's role in resolving family conflicts, particularly when monitoring parental discretion in medical decision-making on behalf of a child. The state may be limited by the best interest criterion when dealing with children, but parents are not. (...) The state's relation with the child is formal while the parental relation is intimate, having its own goals and purposes. While the liberal canons insist on the incompetent one's best interest, parents are permitted to compromise the child's interests for ends related to these familial goals and purposes. Parents decisions should be supervened, in general, only if it can be shown that no responsible mode of thinking warrants such treatment of a child. Keywords: proxy medical consent, children's rights, state's protection of children, parental authority and the state's intervention, paternalism, liberalism, parental values CiteULike Connotea Del.icio.us What's this? (shrink)

We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with a particular emphasis on the set $D'$ comprised of differences between successive elements. In particular, if the burden of the structure is at most n, then the result of applying the operation $D \mapsto D'\ n$ times must be a finite set (Theorem 1.1). In the case when the structure is densely ordered and has burden (...) $2$, we show that any definable unary discrete set must be definable in some elementary extension of the structure $\langle \mathbb{R}; <, +, \mathbb{Z} \rangle $ (Theorem 1.3). (shrink)

Philip Pettit’s conception of freedom as nondomination is modally robust in that it requires not simply reducing the probability of uncontrolled interference by others but entirely eliminating that possibility. In this article, I consider whether freedom as nondomination provides an attractive analysis of official discretion, particularly in the context of the criminal law, an area of recurring interest for Pettit. I argue that not only does the modally robust character of freedom as nondomination have some rather unattractive implications in the (...) criminal law, but that it sits poorly with Pettit’s more general ambitions to provide a consequentialist framework for the evaluation of social institutions. Drawing on recent work by Niko Kolodny, I develop an ‘anti-deference’ interpretation of nondomination and contrast it to Pettit’s modally robust conception. (shrink)

In this field questions arise which are certainly difficult; but as I listened last time to members of the group, I felt that the main difficulty perhaps lay in determining precisely what questions we are trying to answer. I have the conviction that if we could only say clearly what the questions are, the answers to them might not appear so elusive. So I have begun with a simple list of questions about discretion which in one form or another were, (...) as it seemed to me, expressed by the group last time. I may indeed have omitted something and inserted something useless: if so, no doubt I shall be informed of this later. The central questions then seem to me to be the following: 1. What is discretion, or what is the exercise of discretion? 2. Under what conditions and why do we in fact accept or tolerate discretion in a legal system? 3. Must we accept discretion or tolerate discretion, and if so, why? 4. What values does the use of discretion menace, and what values does it maintain or promote? 5. What can be done to maximize the beneficial operation of the use of discretion and to minimize any harm that it does? (shrink)

A book on the notion of fundamental length, covering issues in the philosophy of math, metaphysics, and the history and the philosophy of modern physics, from classical electrodynamics to current theories of quantum gravity. Published (2014) in Cambridge University Press.

Prosecutors in the US legal system have great power to interfere at their discretion in the lives of citizens, and face relatively few checks on the exercise of this discretion. The vast scope of the criminal law provides a pretext for prosecuting nearly anyone. Meanwhile, other features of the legal system, such as the way plea bargains are structured and the doctrine of prosecutorial immunity, further increase prosecutorial power. And existing institutional restraints on prosecutorial abuses, such as democratic accountability, the (...) grand jury system, and the possibility of a selective prosecution defense, are mostly ineffectual. I draw on republican political theory, including insights from Philip Pettit and Elizabeth Anderson, to argue that this state of affairs gives prosecutors dominating, and therefore unjust, power over vast swathes of the public. I then survey some potential institutional changes which might help ameliorate the problem. (shrink)

Elected prosecutors have pledged not to enforce abortion laws, in response to state-level abortion bans. For their pledges to be meaningful, prosecutors must exercise their discretion in cases of individuals who face legal risk, including people who help others self-manage their abortions. With a harm-reduction approach to improving abortion access, prosecutors should aim to reduce abortion helpers’ involvement with the criminal justice system.

The theoretical core of positivism is thought to consist of three theses about the nature of law. The separability thesis denies the existence of necessary moral constraints on the content of law. The pedigree thesis articulates necessary and sufficient conditions for legal validity having to do with how or by whom law is promulgated. The discretion thesis asserts that judges decide hard cases by making new law. While it is often assumed that these theses form a coherent theoretical whole, such (...) an assumption is false. Construed as a claim about all possible legal systems, the discretion thesis is inconsistent with the pedigree thesis. Construed as a claim that is true in some, but not all, possible legal systems, the discretion thesis makes a fundamentally different kind of claim than those made by the pedigree and separability theses and hence should not be thought of as part of positivism's theory of law. (shrink)

The discretionary powers of welfare state professionals are in tension with the requirements of the democratic Rechtsstaat. Extensive use of discretion can threaten the principles of the rule of law and relinquish democratic control over the implementation of laws and policies. These two tensions are in principle ineradicable. But does this also mean that they are impossible to come to grips with? Are there measures that may ease these tensions? We introduce an understanding of discretion that adds an epistemic dimension (...) (discretion as a mode of reasoning) to the common structural understanding of discretion (an area of judgment and decision). Accordingly we distinguish between structural and epistemic measures of accountability. The aim of the former is to constrain discretionary spaces or the behaviour within them while the aim of the latter is to improve the quality of discretionary reasoning. The focus in this article is on epistemic measures that are internally related to the main characteristic of accountability, namely justified use of discretionary power. (shrink)

Automated decision-making takes up an increasingly significant place in the administrative state. This article presents a conception of discretion that is helpful for evaluating the proper place of algorithms in public decision-making. I argue that the algorithm itself is not a site of discretion. The threat is that automated decision-making alters the relationships between traditional actors in a way that can cut down discretion and human commitment. Algorithmic decision-makers can serve to fetter the discretion that the legislature and the populace (...) expect to be exercised. We must strive to maintain discretion, moral agency, deliberative ideals, and human commitment through the system that surrounds the use of an algorithm and to develop a new expertise that can retain and exercise the expected discretion. Backing this argument are traditional legal constraints, public expectations, and administrative law principles, tied together through the organizing principle of discretion. (shrink)

Discrete supposition occurs whenever a discrete term, such as ‘Socrates‘, is the subject of a given proposition. I propose to examine this apparently simple notion. I shall draw attention to the incongruity, within a general theory of the semantic variation of terms in a propositional context, of the notion of discrete supposition, in which a term usually has a single semantic correlate. The incongruity comes to the fore in those treatises that attempt to describe discrete supposition (...) as a sort of personal supposition, although the same term cannot be in simple supposition in another propositional context, because it has no significate distinct from its suppositum. This shows a fundamental link between common signification, simple supposition and predicability, three notions that rely on the existence of a significate distinct and independent from the suppositum of the term. The connection is to be seen especially in William of Sherwood’s Introductiones, the only author of a terminist Summa who recognizes the existence of simple supposition for discrete terms. (shrink)

In various guises (usually referred to as the “basic emotion” or “discrete emotion” approach), scientists and philosophers have long argued that certain categories of emotion are natural kinds. In a recent paper, Colombetti (2009) proposed yet another natural kind account, and in so doing, characterized and critiqued psychological constructionist approaches to emotion, including our own Conceptual Act Model. In this commentary, we briefly address three topics raised by Columbetti. First, we correct several common misperceptions about the discrete emotion (...) approach to emotion. Second, we discuss misconceptions of our Conceptual Act Model. Finally, we briefly comment on Columbetti's Dynamical Discrete Emotion model. (shrink)

How might we locate originality as emerging from within the “discrete” work of commentary? Because many women have engaged with philosophy informs that preclude their work from being seen as properly “original,” this question is a feminist issue. Via the work of selected contemporary French women philosophers, the author shows how commentary can reconfigure the philosophical tradition in innovative ways, as well as in ways that change what counts as philosophical innovation.

Causal connectionists need to provide an account of causal linkage and of causal direction. This chapter distinguishes between two kinds of causal connection, namely, discrete and continuous. Causal connectionists have a number of options for explaining the linkage between causes and effects in the case of discrete causation. The chapter provides some popular options. If some causation is discrete, and the exercise of causal powers provides a direction to discrete causation, then the causal direction of processes (...) can be derived from the causal direction of discrete interaction. David Hume famously made the claim about the knowledge of causation in his Enquiry Concerning Human Understanding. Hume offers, in defense of his principle, a set of thought‐experiments that seem to show that we can always imagine any event's having a different result from the one we in fact observe. Causal processes like locomotion may provide counterexamples to Hume's Epistemic Principle. (shrink)

The present study provides evidence that valence focus and arousal focus are important processes in determining whether a dimensional or a discrete emotion model best captures how people label their affective states. Individuals high in valence focus and low in arousal focus fit a dimensional model better in that they reported more co-occurrences among like-valenced affective states, whereas those lower in valence focus and higher in arousal focus fit a discrete model better in that they reported fewer co-occurrences (...) between like-valenced affective states. Taken together, these findings suggest that one static, nomothetic theory may not accurately describe the subjective affective experience of all individuals. (shrink)

H.L.A. Hart’s lost and found essay ‘Discretion’ has provided new insight into the issue of how legal systems can cope with indeterminacy in the law. The so-called ‘open texture’ of law calls for the exercise of judicial discretion, which, I argue, renders judges susceptible to the problem of dirty hands. To show this, I frame the problem as being open to an array of appropriate emotional responses, namely, various senses of guilt. With these responses in mind, I revise an example (...) from Michael Walzer’s original analysis in a way that highlights purely personal sacrifices in solutions to dirty hands situations. I then turn to an account of moral emotions in legal decision-making and show how judges—in failing to advance all interests—might be left with a unique sense of guilt. With an application of this account to Hart’s legal positivism, it can be seen that a judge’s hands are often dirtied in resolving borderline cases. If discretion leaves judges in situations where they must do wrong in order to do right, Hart’s endorsement of a closure view of wrongdoing will lead to difficulties in how he can explain the presence of moral remainders in jurisprudence. (shrink)

Recent discussions in the philosophy of science have devoted considerable attention to the analysis of conceptual issues relating to the methodology of explanation and prediction in the sciences. Part of this literature has been devoted to clarifying the very ideas of explanation and prediction. But the discussion has also ranged over various related topics, including the status of laws to be used for explanatory and predictive purposes, the logical interrelationships between explanatory and predictive reasonings, the differences in the strategy of (...) explanatory argumentation in different branches of science, the nature and possibility of teleological explanation, etc. The aim of the present article is to examine the issues involved in such questions from the specialized perspective afforded by one particular kind of physical systems--namely, systems, here to be characterized as discrete state systems, whose behavior has been studied extensively in the scientific literature under the general heading of Markov chains. These systems have been chosen as our focus because their behavior over time can be analyzed at once with great ease and with extraordinary precision. (shrink)

Leibniz argues against Descartes’s conception of material substance based on considerations of unity. I examine a key premise of Leibniz’s argument, what I call the Plurality Thesis—the claim that matter (i.e., extension alone) is a plurality of parts. More specifically, I engage an objection to the Plurality Thesis stemming from what I call Material Monism—the claim that the physical world is a single material substance. I argue that Leibniz can productively engage this objection based on his view that matter is (...) discrete. The discreteness of matter provides two aspects of support for the Plurality Thesis. First, it indicates that the parts of matter do not share boundaries and are, therefore, independent in an important sense. Second, it indicates that the parts of matter are determinate and are, therefore, ontologically prior to the wholes they compose. (shrink)

Examining the role of dispositions (potentials and propensities) in both physics and psychology reveals that they are commonly derivative dispositions, so called because they derive from other dispositions. Furthermore, when they act, they produce further propensities. Together, therefore, they appear to form discrete degrees within a structure of multiple generative levels. It is then constructively hypothesized that minds and physical nature are themselves discrete degrees within some more universal structure. This gives rise to an effective dualism of mind (...) and nature, but one according to which they are still constantly related by causal connections. I suggest a few of the unified principles of operation of this more complicated but universal structure. (shrink)

Discrete Mathematics is designed to serve as a textbook for undergraduate engineering students of computer science and postgraduate students of computer applications. The book would also prove useful to post graduate students of mathematics. It seeks to provide a thorough understanding of the subject and present its practical applications to computer science.

Prior has conjectured that the tense-logical system Gli obtained by adding to a complete basis for the classical propositional calculus the primitive symbolG, the definitionsDf. F:Fα=NGNαDf. L:Lα=KαGα,and the postulatesis complete for the logic of linear, infinite, transitive, discrete future time. In this paper it is demonstrated that that conjecture is correct and it is shown that Gli has the finite model property: see [4]. The techniques used are in part suggested by those used in Bull [2] and [3]:Gli can (...) be shown to be complete for the logic of linear, infinite, transitive, discrete future time in the sense that every formula of Gli which is true of such time can be proved as a theorem of Gli. For this purpose the notion of truth needs to be formalized. This formalization is effected by the construction of a model for linear, infinite, transitive, discrete future time. (shrink)

Fix an integer $r \ge 3$. We consider metric spaces on n points such that the distance between any two points lies in $\left\{ {1, \ldots,r} \right\}$. Our main result describes their approximate structure for large n. As a consequence, we show that the number of these metric spaces is $\left\lceil {{{r + 1} \over 2}} \right\rceil ^{\left + o\left}.$Related results in the continuous setting have recently been proved by Kozma, Meyerovitch, Peled, and Samotij [34]. When r is even, our (...) structural characterization is more precise and implies that almost all such metric spaces have all distances at least $r/2$. As an easy consequence, when r is even, we improve the error term above from $o\left$ to $o\left$, and also show a labeled first-order 0-1 law in the language ${\cal L}_r $, consisting of r binary relations, one for each element of $[r]$. In particular, we show the almost sure theory T is the theory of the Fraïssé limit of the class of all finite simple complete edge-colored graphs with edge colors in $\left\{ {r/2, \ldots,r} \right\}$.Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws. (shrink)

This project explores the "contradiction" that critics contend lies at the heart of the Supreme Court's capital sentencing jurisprudence. The doctrine of "guided discretion," represents the Court's attempt to achieve both consistency and individuation in capital sentencing. Guided discretion rejects the unbridled sentencing discretion of an earlier era that resulted in sentencing decisions that were "arbitrary and capricious." At the same time, guided discretion requires juries to give individualized consideration to the facts and circumstances of individual defendants. Critics contend that (...) consistency and individuation are mutually exclusive, and that "guided discretion" is a contradiction in terms. ;The analysis first attempts to isolate the moral dimension of the capital punishment debate, arguing that such analytical clarity is essential to any defensible view of capital punishment. Second, it sets forth and defends the coherence approach to moral and legal justification, according to which the specific moral and legal principles relevant to capital sentencing are evaluated for their compatibility with the principles of the legal system more generally. Third, the analysis canvasses the traditional justifications for punishment, as well as the development of the Court's capital sentencing jurisprudence, and identifies retribution and deterrence as the most promising rationales for the death penalty. Fourth, the claim of contradiction is considered in the context of legal liberalism, which, contrary to critics, has ample resources to accommodate the doctrinal balancing act that guided discretion entails. Moreover, examination of a typical capital sentencing statute establishes that the doctrine of guided discretion is compatible with at least some forms of retributivism and with traditional principles of deterrence. Finally, the analysis recognizes the limits of philosophical consistency. The capital sentencing process presents daunting practical challenges that a theoretical defense of guided discretion cannot fully address. Substantial reforms are needed before the theoretical coherence of guided discretion can be translated into a constitutionally defensible capital sentencing process. (shrink)

Three classes of decidable discrete linear orders with varying degrees of effectiveness are investigated. We consider how a classical order type may lie in relation to these three classes, and we characterize by their order types elements of these classes that have effective nontrivial self-embeddings.

Rousseau's understanding of legislation as the expression of the general will implies a constitutional principle of legislative supremacy. In turn, this should translate to a narrow, mechanical account of adjudication, lest creative judicial interpretation subvert the primacy of legislative power. Yet in his constitutional writings, Rousseau recommends open-textured and vague legislative codes, which he openly admits will require judicial development. Thus he apparently trusts a great deal in judicial discretion. Ostensibly, then, he overlooks the problem of how legislative indeterminacy—and correspondingly, (...) judicial discretion—may undermine the authority of the general will. However, I argue that Rousseau aims to check judicial subversion of legislative supremacy simply by extending his broader social politics—and specifically, his peculiar concept of republican virtue—to the domain of law. His main concern is that the law should not develop as a mystifying expert practice; therefore, he necessarily rejects any understanding of judicial virtue as lying in principled discourse. Instead, he envisages that judicial power will be checked by a more generic sense of republican virtue. In turn this echoes his apprehension of social differentiation and social complexity as sources of domination and hierarchy. (shrink)

Managers often have discretion in interpreting their ethical requirements, and they should seek democratic guidance in doing so. The undemocratic nature of managerial ethical discretion is shown to be a recurring problem in business ethics. Joseph Heath’s market failures approach (MFA) is introduced as a theory better positioned to deal with this problem than other views. However, due to epistemic uncertainty and conceptual indeterminacy, the MFA is shown to allow a much wider range of managerial discretion than initially appears. The (...) paper explores how this range can be narrowed down with democratic input, comparing models based on formal state institutions and on the informal public sphere. A case study from the pharmaceutical industry illustrates the merits of the informal public sphere approach. (shrink)

We define a first-order extension LK(CP) of the cutting planes proof system CP as the first-order sequent calculus LK whose atomic formulas are CP-inequalities ∑ i a i · x i ≥ b (x i 's variables, a i 's and b constants). We prove an interpolation theorem for LK(CP) yielding as a corollary a conditional lower bound for LK(CP)-proofs. For a subsystem R(CP) of LK(CP), essentially resolution working with clauses formed by CP- inequalities, we prove a monotone interpolation theorem (...) obtaining thus an unconditional lower bound (depending on the maximum size of coefficients in proofs and on the maximum number of CP-inequalities in clauses). We also give an interpolation theorem for polynomial calculus working with sparse polynomials. The proof relies on a universal interpolation theorem for semantic derivations [16, Theorem 5.1]. LK(CP) can be viewed as a two-sorted first-order theory of Z considered itself as a discretely ordered Z-module. One sort of variables are module elements, another sort are scalars. The quantification is allowed only over the former sort. We shall give a construction of a theory LK(M) for any discretely ordered module M (e.g., LK(Z) extends LK(CP)). The interpolation theorem generalizes to these theories obtained from discretely ordered Z-modules. We shall also discuss a connection to quantifier elimination for such theories. We formulate a communication complexity problem whose (suitable) solution would allow to improve the monotone interpolation theorem and the lower bound for R(CP). (shrink)