In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs (...) is incoherent. This response was first given by Wittgenstein but has been best developed by Sullivan. While I agree with Wittgenstein and Sullivan's common conclusion, I believe that even the most compelling of Sullivan's arguments is importantly mistaken and that Wittgenstein's remarks are too opaque to be left as the end of the matter. In this article I uncover the fault in Sullivan's argument and present an alternative criticism of PFEs which is Wittgensteinian in spirit without being too mystifying. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 161 7 In, respectively, PaciWsm in Britain and Semi-Detached Idealists: the British Peace Movement and International Relations (Oxford: Oxford U. P., 2000). 8 See Monk 2: Chap. 13. FUNCTIONS OR PROPOSITIONAL FUNCTIONS? Alexander Paul Bozzo Philosophy / Marquette U. Milwaukee, wi 53233, usa [email protected] Michael Potter and Tom Ricketts, eds. The Cambridge Companion to Frege. Cambridge, (...) uk: Cambridge U. P., 2010. Pp. vii, 630. isbn 978-0-521-62479-4 (pb). £57.00; £21.99 (pb). us$38.99 (pb). February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd 162 Reviews 1 Frege: Philosophy of Mathematics (Cambridge, ma: Harvard U. P., 1991), p. 111. The paragraph contains an expression of Frege’s Context Principle and the need for Hume’s Principle as a criterion of identity in the deWnition of number. 2 There are in fact Wve stated goals. The others are: (iii) to serve as a reference work for students and non-specialists, (iv) to provide a route into the study of Frege historically and to any relevant contemporary concerns in the philosophies of logic, language, mathematics, and mind, and (v) to provide, for new readers, the most convenient detailed guide to Frege currently available. Gottlob Frege is widely recognized as one of the chief progenitors of mathematical logic and philosophy of languagez—zindeed, the importance attributed to Frege’s innovations is such that Michael Dummett, when reXecting on§62 of Frege’s Die Grundlagen der Arithmetik, feels compelled to remark that the paragraph therein is “arguably the most pregnant philosophical paragraph ever written.”1 Whether or not one agrees with Dummett on this point, the magnitude of Frege’s inXuence on the current philosophical landscape is incontestable. Frege revolutionized the then dominant Aristotelian conception of logic, introducing a formal language now recognized as the predicate calculus. Central to this end were Frege’s insights on quantiWcation, the notation that expressed it, the logicist project, and the extension of mathematical notions like function and argument to natural language. The long-awaited Cambridge Companion to Frege is a compendium of Fregean scholarship that rigorously explores these and similar topics; editors Thomas Ricketts and Michael Potter have compiled a comprehensive collection of fourteen essays that individually provide focused appraisals of a number of Frege’s most substantial insights. On the advice of this journal’s editor, I have limited my review to the connections (or rather dissimilarities ) that exist between Frege and Russell, relying exclusively on Peter Hylton ’s contribution to the collection, “Frege and Russell”. Following a brief consideration of the volume as a whole, I move immediately into a detailed explication of Hylton’s analysis. The volume includes among its goals the following two aims: (i) to provide, for advanced students and specialists, a conspectus of recent interpretation of Frege, and (ii) to dispel the intimidation felt by readers who confront a diUcult thinker.2 I single out these ambitions because they most clearly represent the volume’s strengths and shortcomings. Enthusiasts of Frege will not be disappointed by the multitude of rigorously and technically written essays, essays that contribute substantially and originally to the collective understanding of Frege and his work. For instance, Thomas Ricketts provides a thoughtful and thorough analysis—an analysis that moves well beyond mere explication—of Frege’s concept/object distinction, in particular its relevance for Frege’s Context Principle and logicism more generally. Similarly, Richard Heck addresses a number of central yet largely unexplored issues pertaining to the overall signiWcance of February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 163 3 I strongly encourage that non-specialists augment The Cambridge Companion to Frege with Joan Weiner’s Frege Explained: from Arithmetic to Analytic Philosophy (Chicago : Open Court, 2004), one of the best available introductory texts on Frege. 4 The essay in fact was available as early as 2005 in Hylton’s Propositions, Functions, and Analysis: Selected Essays on Russell’s Philosophy (New York, ny: Oxford U. P., 2005). The editors of The Cambridge Companion to Frege partially... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 161 7 In, respectively, PaciWsm in Britain and Semi-Detached Idealists: the British Peace Movement and International Relations (Oxford: Oxford U. P., 2000). 8 See Monk 2: Chap. 13. FUNCTIONS OR PROPOSITIONAL FUNCTIONS? Alexander Paul Bozzo Philosophy / Marquette U. Milwaukee, wi 53233, usa [email protected] Michael Potter and Tom Ricketts, eds. The Cambridge Companion to Frege. Cambridge, (...) uk: Cambridge U. P., 2010. Pp. vii, 630. isbn 978-0-521-62479-4 (pb). £57.00; £21.99 (pb). us$38.99 (pb). February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd 162 Reviews 1 Frege: Philosophy of Mathematics (Cambridge, ma: Harvard U. P., 1991), p. 111. The paragraph contains an expression of Frege’s Context Principle and the need for Hume’s Principle as a criterion of identity in the deWnition of number. 2 There are in fact Wve stated goals. The others are: (iii) to serve as a reference work for students and non-specialists, (iv) to provide a route into the study of Frege historically and to any relevant contemporary concerns in the philosophies of logic, language, mathematics, and mind, and (v) to provide, for new readers, the most convenient detailed guide to Frege currently available. Gottlob Frege is widely recognized as one of the chief progenitors of mathematical logic and philosophy of languagez—zindeed, the importance attributed to Frege’s innovations is such that Michael Dummett, when reXecting on§62 of Frege’s Die Grundlagen der Arithmetik, feels compelled to remark that the paragraph therein is “arguably the most pregnant philosophical paragraph ever written.”1 Whether or not one agrees with Dummett on this point, the magnitude of Frege’s inXuence on the current philosophical landscape is incontestable. Frege revolutionized the then dominant Aristotelian conception of logic, introducing a formal language now recognized as the predicate calculus. Central to this end were Frege’s insights on quantiWcation, the notation that expressed it, the logicist project, and the extension of mathematical notions like function and argument to natural language. The long-awaited Cambridge Companion to Frege is a compendium of Fregean scholarship that rigorously explores these and similar topics; editors Thomas Ricketts and Michael Potter have compiled a comprehensive collection of fourteen essays that individually provide focused appraisals of a number of Frege’s most substantial insights. On the advice of this journal’s editor, I have limited my review to the connections (or rather dissimilarities ) that exist between Frege and Russell, relying exclusively on Peter Hylton ’s contribution to the collection, “Frege and Russell”. Following a brief consideration of the volume as a whole, I move immediately into a detailed explication of Hylton’s analysis. The volume includes among its goals the following two aims: (i) to provide, for advanced students and specialists, a conspectus of recent interpretation of Frege, and (ii) to dispel the intimidation felt by readers who confront a diUcult thinker.2 I single out these ambitions because they most clearly represent the volume’s strengths and shortcomings. Enthusiasts of Frege will not be disappointed by the multitude of rigorously and technically written essays, essays that contribute substantially and originally to the collective understanding of Frege and his work. For instance, Thomas Ricketts provides a thoughtful and thorough analysis—an analysis that moves well beyond mere explication—of Frege’s concept/object distinction, in particular its relevance for Frege’s Context Principle and logicism more generally. Similarly, Richard Heck addresses a number of central yet largely unexplored issues pertaining to the overall signiWcance of February 19, 2011 (11:48 am) E:\CPBR\RUSSJOUR\TYPE3002\russell 30,2 040 red.wpd Reviews 163 3 I strongly encourage that non-specialists augment The Cambridge Companion to Frege with Joan Weiner’s Frege Explained: from Arithmetic to Analytic Philosophy (Chicago : Open Court, 2004), one of the best available introductory texts on Frege. 4 The essay in fact was available as early as 2005 in Hylton’s Propositions, Functions, and Analysis: Selected Essays on Russell’s Philosophy (New York, ny: Oxford U. P., 2005). The editors of The Cambridge Companion to Frege partially... (shrink)

Wittgenstein's Tractatus carefully distinguished the concept all from\nthe notion of a truth-function, and thereby from the quantifiers.\nI argue that Wittgenstein's rationale for this distinction is lost\nunless propositional functions are understood within the context\nof his picture theory of the proposition. Using a model Tractatus\nlanguage, I show how there are two distinct forms of generality implicit\nin quantified Tractatus propositions. Although the explanation given\nin the Tractatus for this distinction is ultimately flawed, the distinction\nitself is a genuine one, and the forms of (...) generality that Wittgenstein\nindicated can be seen in the quantified sentences of contemporary\nlogic. (shrink)

This article examines Wilfrid Sellars's views on the epistemic status of philosophical propositions. It suggests that according to Sellars philosophical propositions are normative and practically oriented. They do not form a theory for the description of reality; their function is, rather, that of motivating actions which aim at changing reality. The article argues that the role of philosophical propositions can be illuminated if they are understood as a special kind of (proposed) “material” rules of inference, provided that the latter are (...) construed as being firmly entrenched in practice. To this end, a distinction between “theoretical” and “practical” anomalies is drawn to better elucidate—and in some cases criticize and further expand—Sellars's position on the relation between the theoretical and practical dimensions of philosophical activity. In this connection, the Weberian notion of the “disenchantment of the world” is used to throw light on the relation between these two dimensions. (shrink)

Abstract: Groundwork is lain for answering questions as to how to situate Husserl’s theory of functions in relation to Frege’s. I examine Husserl’s ideas about analyticity and mathematics, logic and mathematics, formalization, calculating with concepts and propositions, the foundations of arithmetic, extensions to show that, although he knew, studied and lauded Frege’s ideas about functions and concepts, each man approached the issues from different angles. Seduced by the siren of transcendental phenomenology Husserl did not pursue the issues, implications, (...) and consequences of his ideas about functions. I ask whether so doing could provide new insight into, or even solutions to, the problems involving functions that beset Frege, Russell and have beset their successors. (shrink)

Contemporary epistemology has assumed that knowledge is represented in sentences or propositions. However, a variety of extensions and alternatives to this view have been proposed in other areas of investigation. We review some of these proposals, focusing on (1) Ryle's notion of knowing how and Hanson's and Kuhn's accounts of theory-laden perception in science; (2) extensions of simple propositional representations in cognitive models and artificial intelligence; (3) the debate concerning imagistic versus propositional representations in cognitive psychology; (4) recent (...) treatments of concepts and categorization which reject the notion of necessary and sufficient conditions; and (5) parallel distributed processing (connectionist) models of cognition. This last development is especially promising in providing a flexible, powerful means of representing information nonpropositionally, and carrying out at least simple forms of inference without rules. Central to several of the proposals is the notion that much of human cognition might consist in pattern recognition rather than manipulation of rules and propositions. (shrink)

This chapter contains sections titled: Recent Relativism Standard Semantics and Ordinary Truth Relativist Semantics and Ordinary Truth Issues of Commensurability References.

Although ‘glue semantics’ is the most extensively developed theory of semantic composition for LFG, it is not very well integrated into the LFG projection architecture, due to the absence of a simple and well-explained correspondence between glue-proofs and f-structures. In this paper I will show that we can improve this situation with two steps: (1) Replace the current quantificational formulations of glue (either Girard’s system F, or first order linear logic) with strictly propositional linear logic (the quantifier, unit and (...) exponential free version of either MILL or ILL, depending on whether or not tensors are used). (2) Reverse the direction of the standard σ-projection from f-structure to meaning, giving one going from the (atomic nodes of) the glue-proof to the f-structure, rather than from the f-structure to a ‘semantic projection’ which is itself somehow related to the glue-proof. As a side effect, the standard semantic projection of LFG glue semantics can be dispensed with. A result is that LFG sentence structures acquire a level composed of strictly binary trees, constructed out of nodes representing function application and lambda abstraction, with a significant resemblance to external and internal merge in the Minimalist Program. This increased resemblance between frameworks might assist in making useful comparisons. (shrink)

Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does (...) not appear in the _Principles_. I distinguish the functions and predicates versions, give a novel reading of the _Principles_, section 85, as a paradox dealing with what Russell calls _assertions_, and show that Russell's logical notation in 1902 had no way of even formulating the functions version. The propositional functions version had its origins in the summer of 1903, soon after Russell's notation had changed in such a way as to make a formulation possible. (shrink)

We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is (...) generated as a property of non-determinacy of games. Over-defined values are produced by adding a weak, contradictory negation or, alternatively, by relaxing the assumption that games are strictly competitive. In general, particular forms of extensive imperfect information games give rise to a generalised propositional logic where various forms of informational dependencies and independencies of connectives can be studied. (shrink)

In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in question. (...) With the focus on exclusive disjunction we comparatively study the proposed systems. Finally, we discuss Segerberg’s systems for connectiveless and negation fragments and compare them with our systems. (shrink)

The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of papers (...) which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

The propositional calculus AoC, “Algebra of Classes”,and the extended propositional calculus EAC, “Extended Algebra ofClasses” are introduced in this paper. They are extensions, by additionalpropositional functions which are not invariant under the biconditional,of the corresponding classical propositional systems. Theirorigin lies in an analysis, motivated by Cantor’s concept of the cardinalnumbers, of A. P. Morse’s impredicative, polysynthetic set theory.

Peter Geach has said that Russell's use of ‘propositional function’ is ‘hopelessly confused and inconsistent’. Geach is right, and attempts to say what exactly a Russellian propositional function is, or is supposed to be, are bound to end in frustration. Nevertheless, it may be worthwhile to pursue an account of propositional functions that accommodates a good deal of what Russell says about them and that can provide some of what he expected of them.

Russell argued, famously, that definite descriptions are not logical constituents of the sentences in which they appear. In neither of the following should we suppose that the definite description picks anything out: The King of France is bald The Prince of Wales is bald Since France is a republic, nothing could be picked out by the first; and if the semantic structures of each are the same, it cannot be the function of the second to pick anything out either. On (...) the alternative semantics developed in his 1905 article 'On Denoting', definite descriptions do not have meaning in isolation; they have meaning only in the context of a whole sentence. Andrew Botterell and Robert Stainton have pointed out that this conclusion appears to be at odds with the phenomenon of unembedded definite descriptions, in which definite descriptions are uttered, meaningfully, without accompanying predicates. For example, it is possible to utter 'The last temptation' on its own and in doing so express a proposition. Since definite descriptions can be used in this way, how can it be right to claim, with Russell, that they lack meaning in isolation? The present paper seeks to show how a Russellian semantics for definite descriptions is entirely compatible with the phenomenon of unembedded definite descriptions. In particular, Botterell and Stainton are wrong to think that generalized quantifier semantics is better able to cope with the phenomenon than a more authentically Russellian syncategorematic semantics. (shrink)

We give a sound and complete axiomatization of a probabilistic extension of intuitionistic logic. Reasoning with probability operators is also intuitionistic (in contradistinction to other works on this topic), i.e., measure functions used for modeling probability operators are partial functions. Finally, we present a decision procedure for our logic, which is a combination of linear programming and an intuitionistic tableaux method.

Theories that seek to explain the status of psychological states experienced in fictional contexts either claim that those states are special propositional attitudes specific to fictional contexts (make-believe attitudes), or else define them as normal propositional attitudes by stretching the concept of a propositional attitude to include ‘objectless’ states that do not imply constraints such as truth or satisfaction. I argue that the first theory is either vacuous or false, and that the second, by defining the reality (...) of the states in question only nominally, risks having a result similar to the first. Then I put forward an explanation of how propositional attitudes function in fictional contexts which meets the following requirements: (i) does not postulate the existence of attitudes specific to or definitive of fictionality; (ii) does not imply that we transgress our knowledge of the ontological claims of fictions for some attitudes (for example, fear) but not others (belief); (iii) explains how we can adopt normal propositional attitudes towards fictions; (iv) allows explanation of how attitudes adopted during fictional response connect or are relevant to our broader systems of belief and volition. (shrink)

In this work we define contingency logic with arbitrary announcement. In contingency logic, the primitive modality contingency formalises that a proposition may be true but also may be false, so that if it is non-contingent then it is necessarily true or necessarily false. To this logic one can add dynamic operators to describe change of contingency. Our logic has operators for public announcement and operators for arbitrary public announcement, as in the dynamic epistemic logic called arbitrary public announcement logic. However, (...) our language primitive is the more suitable notion of public announcement whether, instead of the public announcement that. We compare the expressive power of our logic and its various fragments to related dynamic epistemic logics. We further present an axiomatisation and show its completeness by adapting a method to demonstrate completeness of arbitrary public announcement logic. Various extensions are also shown to be complete with respect to the corresponding frame classes. (shrink)

This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function (...) for A. (shrink)

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are (...) discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games. (shrink)

Scott Soames has recently argued that traditional accounts of propositions as n-tuples or sets of objects and properties or functions from worlds to extensions cannot adequately explain how these abstract entities come to represent the world. Soames’ new cognitive theory solves this problem by taking propositions to be derived from agents representing the world to be a certain way. Agents represent the world to be a certain way, for example, when they engage in the cognitive act of predicating, or (...) cognizing, an act that takes place during cognitive events, such as perceiving, believing, judging and asserting. On the cognitive theory, propositions just are act types involving the act of predicating and certain other mental operations. This theory, Soames argues, solves not only the problem of how propositions come to represent but also a number of other difficulties for traditional theories, including the problem of de se propositions and the problems of accounting for how agents are capable of grasping propositions and how they come to stand in the relation of expression to sentences. I argue here that Soames’ particular version of the cognitive theory makes two problematic assumptions about cognitive operations and the contents of proper names. I then briefly examine what can count as evidence for the nature of the constituents of the cognitive operation types that produce propositions and argue that the common nature of cognitive operations and what they operate on ought to be determined empirically in cross-disciplinary work. I conclude by offering a semantics for cognitive act types that accommodates one type of empirical evidence. (shrink)

In this paper I describe the birth of Russell’s notion of a propositional function on 3 May 1902 and its immediate context and implications. In particular, I consider its significance in relation to the development of his views on analysis.

Since 2008 I have been closely following the conceptual/performance/video work of Daniel Peltz. Gently rendered through media installation, ethnographic, and performance strategies, Peltz’s work reverently and warmly engages the inner workings of social systems, leaving elegant rips and tears in any given socio/cultural quilt. He engages readymades (of social and media constructions) and uses what are identified as interruptionist/interventionist strategies to disrupt parts of an existing social system, thus allowing for something other to emerge. Like the stereoscope that requires two (...) identical images to create an illusion of a three-dimensional image, Peltz sometimes visualizes two separate elements to create an object or moment that requires space and depth to focus on its varied layers. They say your brain has to process and make meaningful sense out of all that visual information before it can accept the illusion. I say your brain has to do a similar thing when looking and seeing the divine, magical, and faithful (social) art making of Daniel Peltz. Daniel Peltz is Associate Professor of Film/Animation/Video at RISD. He divides his time between Rhode Island and Sweden and is currently at work on an exhibition at Botkyrka Konsthall, Stockholm opening February 2013 and a new project to be included in the IASKA: Spaced Biennial (Australia) in 2014. This interview took place on Skype and is part one of a two-part interview. Feliz Lucia Molina: Are you in Providence, RI? Daniel Peltz: I’m at my house in Providence. I’ve been back for six days teaching winter session at RISD and doing this workshop series—these investors’ drum circles with a group of wealth managers. a client of the firm, 2013, photo Shirin Adhami FLM: The wealth managers were all drumming together? DP: They were all drumming in response to the performance of their retirement portfolios. FLM: Is this part of the “Unrealized Gain/Loss” piece? DP: Yes, it’s part of a show I’m working on in Sweden. I can show you because it was just today. I’ll show you some of this. Lets see—share screen [click, click, click]. This is the room. I’ve been using the camera system that’s already installed in the conference rooms to record them. So the video is being recorded directly by the wealth management office’s tech staff. These are the people I worked with in the last workshop. This conference table is less wondrous. They’ve been learning to drum in response to their retirement portfolios. I started by bringing in my little bit of wealth for them to propose a management strategy, I came to the follow-up meeting with a counter proposal, which was this workshop. So they agreed to do this series of workshops instead of managing my wealth. FLM: Does everybody in the room manage your wealth? That’s kind of a lot of people. DP: That woman in the back there and Craig —they handle new client business. So when you come there with your wealth, they sit down with you and suggest to you how they would manage it. They’re very nice, responsible people. FLM: And where is this? DP: This is in Providence and the one I was showing you is in Waltham, where I was today. Then I’m going to Newport for the last one on Friday. So I will have done four of them. This is the group in Waltham that I just played with today. I played directly with the two groups in Providence and I’m working with an ethnomusicologist at Brown, Asha Tamarisa, who is facilitating the last two. She’s helped develop the workshop in terms of figuring out how to train a group to do this and thinking about the compositional challenges of working in response to retirement portfolio data. FLM: Screensharing helps me to figure out tiny bits here and there about the project. DP: I might even be able to play you a little of the audio I’ve also been working with a group of professional percussionists on what will become a quarterly public investors’ drum circle event. Their stuff was really nice, but I want you to hear what we sounded like in the workshops. They’ve all been recorded by the a/v system in the offices. We use a simple structure where the drummer investors interpret the sensation of gain or loss as embellishments to a base heartbeat rhythm. The group holds the heartbeat and, as each person experiences gain or loss, they embellish that rhythm. "Screensharing helps me to figure out tiny bits here and there about the project" FLM: Is the process all very spontaneous? DP: Its actually quite structured. We produce a custom stock ticker that shows the performance of their collective portfolios. In advance of the workshop each participant submits assets in their retirement portfolio. Then we make a stock ticker that shows the real-time performance of their assets so that they can respond to almost live data. FLM: Are they reading the stock ticker projected up on the screen in the room? Do people drum in correspondence to the visual live data of the performance of their assets? DP: Exactly. They’re looking at the stock ticker as opposed to each other, so it’s a slightly shifted drum circle. They’re looking at the ticker but they’re listening to each other—that’s what we’re practicing. For example, NVO—the price is 172.08 but it’s down -1.16 and as that moves across the screen, the person who’s retirement is invested in that asset starts to embellish when that arrow first appears, based on their experience of loss. They stop when it exits the screen and return to the heartbeat. You could have one ticker for each retirement portfolio, but the way the workshop is constructed is that we just isolate one asset from each person’s portfolio so that everyone in the group is represented in a single ticker. So they’re drumming and looking at the ticker, but they’re hearing each other experience gain and loss. We’ve removed direct visual engagement from the social structure of a drum circle but the oral engagement is still there. FLM: So they had their own sound interpretation of gain and loss? DP: Yeah and that part is quite spontaneous as you were saying. In some of the preparatory exercises we’ve been working to give the participants more strategies for interpreting the sensations of gain and loss. We’re trying to develop their capacity to embellish a heartbeat or base rhythm but I’m not invested in having a melodious result. I’m quite curious about what this kind of structure will result in without any desire for a particular result. FLM: For context, can you talk about the project you did a couple years ago in Bali, “Unrealized Gain/Loss” in relation to this current wealth management project? DP: The workshops I’ve been doing use a similar strategy to the other components in this project. It started in Indonesia on my sabbatical and I was really trying to understand where I was physically and where I was being on sabbatical—this kind of strange jubilee structure where every seventh year you’re supposed to renew your self. And it was around the time of the global financial crisis. I was on sabbatical for the global financial crisis. I remember watching my father, in particular, respond to the financial crisis by monitoring his retirement portfolio and trying to make sense of it. I realized on a visit to their home that he checked his retirement portfolio every single day and I was really struck by that because in some way our parents are mysteries to us as children, especially their moods. We know how important their moods are but we don’t know what governs them. And somehow it was like I’d figured it out, it’s the performance of the DOW! So I think there was something in that. Then I was in Indonesia and I had been drawn there by an interest in their highly ritualized Hindu culture, where so much of life is driven by a ceremonial calendar. I was interested in Bali as this predominantly Hindu pocket within a predominantly Islamic country and life there being organized by this ritual calendar functioning as a kind of resistance to the dominant global religion of free-market capitalism. So I started to explore that correlation between the ways in which this culture that I was living in was sort of “living for the afterlife” and this idea within certain segments of American society of “living for the afterwork life”. The idea that your wellbeing in the “afterwork life” is tied to forces that are unseen and largely beyond your control has strong similarities to many religious understandings of the universe. So I started to explore that and the crafts and materials that were around me were primarily Batik and percussion. Percussion is a huge part of daily life in Bali. These gamelan troupes were everywhere. And I also happened to be there for Nyepi, the day of silence, which is preceded by a very elaborate procession and construction of demonic statues. These were the things that were around me and I started studying Batik with one of the Batik artists there and also started a conversation with two master Batik artists, one who is American and her Indonesian husband. I developed these patterns that were based on symbols from the performance of my retirement portfolio and worked with the batik artists to produce two sarongs. d. peltz - 2012 In producing the designs, I treated the performance of my retirement portfolio since my arrival at RISD [7 years] as a significant interval and then I looked at the ways in which decisions are made within retirement portfolios as having an extension outwards from the individual assets that underlie the retirement portfolio, which are kind of like the base elements of the retirement world. Then there’s the allocation of your assets, which is a global way of understanding an individual according to typologies, which are often referred to in terms of risk—this notion of a ‘risk profile’. What type of ‘person’ you are is determined by your attitude towards risk, or potentiality, and I found that to be a really fascinating way of understanding the universe. I remember looking at the tabs in my retirement portfolio and finding this one for viewing ‘Unrealized Gain/Loss’ and that’s often how I work—is just going through the Cambridge Parking Code, for example, and finding this section of the code that was called ‘Crossing Non-Signalized Locations’ and just feeling “I can’t do any better than that,” you know? That’s what I was talking about in terms of ready-mades that exist in the social sphere. So I found that tab, actually, a long time ago, and I pulled it out of a journal when I was there [in Bali] working on these pieces and I wound up making these two sarongs and later on a series of porcelain vessels for holding one’s unrealized gains and losses. At the time, I knew that I wanted a performance to come out of them, but I wasn’t sure what it was. I was inspired very much by this sort of thing: Pulls out a TIAA-CREF brochure with a man in a suit seated at a table. This guy is probably an actor, and [the brochure] says “TIAA-Cref announces “Individual counseling sessions at the Rhode Island School of Design. Individual counseling sessions at no additional cost to you. You can discuss your personal financial situation with an experienced TIAA consultant on a confidential basis. We are available to help you discuss how to achieve your financial goals by investing in financial solutions such as mutual funds, brokerage, life insurance, and annuities...etc....What retirement benefits best fits your situation?” Often I encounter this and I think O.K., this is one way to prepare for the after-work life and it seems inadequate to me. But, I also find it really inspiring. I really like the visual language of it. I kind of want to be that man. I’d like to see if I could maybe buy his clothes. FLM: What it is about the man on the brochure that interests you? DP: He’s offering personalized objective advice and a detailed evaluation of everything you need to know and do. Who wouldn’t want that? But he’s also something of a contemporary priest or priestess, mediating between the unseen all-powerful universe of global capitalism and the common worker. So I started off developing Unrealized Gain/Loss directly from the charts that represent the performance of my retirement portfolio. Then I came home and I wanted to use those. I had this word in my journal “unrealized gain/loss vessel.” I had this notion of vessels that would contain unrealized gains and losses. That felt really important to me that they would have somewhere to go. I had been thinking a lot about altars and making offerings—that somehow this really fickle, massive, difficult-to-comprehend-universe of the financial world—that somehow it might be nice if you could making an offering to it. [In Bali] they made such beautiful elaborate offerings. So I studied offering making as well with one of the women there and she taught me some of the standard forms created by folding leaves and the significance of the floral arrangements. I started working in clay and then moved to porcelain and I made these unrealized gain/loss vessels. I made a few of them, they have holes on either side that you can’t get your fingers in. But something can go in there and something can go out of there. It’s a nice size for putting on an altar. Then I got this commission from Artists in Context who was interested in my doing something for this project “Artists Perspectives for the Nation” project. I proposed initiating these investors’ drum circles as a new public performance form. I’m interested in bringing together those two symbols—the symbol of the djembe and the drum circle. unrealized gain/loss vessel - d.peltz - 2012 FLM: I can imagine the public digital stock ticker performing like a soft fleeting stream of information, a kind of (meaningless) illusory comfort blanket. DP: In some way you have to understand its relevance outside of the obvious, right? Because the obvious is illogical. Nobody is actually using that data to day trade, for example. People aren’t sitting there with their computers watching the market data in Times Square or setting up an outdoor office and being like “OK it’s up 3 points or it’s up 1.56, trade! Ok now buy, Ok now sell!” That would be a kind of a nice performance, actually. But actual day traders would want more up to date data than that. To understand what that data is doing is really important. And that’s something I’ve realized—that I’m interested in a particular kind of data visualization, which is not about what data can tell people, but what data can tell people who are visualizing it. For example, in the Cambridge Project “Crossing Non-Signalized Locations” I was interested in the 10,000 excuses archive of data recording five years worth of excuses for why people thought they shouldn’t have received their parking ticket. I was not interested in making that excuse wall so that the public could see and understand this data. Inevitably the data will be seen by others but I was really interested in what the action of visualizing the data told those who were visualizing it. The parking attendants themselves were writing those excuses on the wall—I was interested in what that kind action of writing the excuses on the wall told them about the data. Similarly, I’m interested in designing a way to allow people to pass this data from the unseen universe of the market, through their own bodies, which happens through the merging of the drum and the stock ticker. I’m interested in those two also as symbols; the drum as this symbol of the earth, the body and a pagan counterculture, and the stock ticker referring to the ethereal world of global markets—bringing those two together and making them dependent. I’m often drawn to conceptual propositions that I become invested in testing in a sincere way—at first they often they sound humorous to others, but I have to remember that there is humor in them. I don’t sit around and laugh about these things. I stop finding them funny at all. I’m interested in the proposition that we could know something about the after-work life by drumming in response to our retirement portfolio. So then I become really interested in how to craft that into a viable performance form for myself and others. FLM: The aspect of using sound in “Unrealized Gain/Loss” as a way of embodying the information to the asset holder is really intriguing—using sound as a means of embodying the asset data. Was sound a medium that made sense to use immediately or were you considering other means of attempting to embody it? DP: Well I do use other mediums within the project like textile, ceramic, and batik patterns. I was first drawn to the history of Batik patterns as a socio-economic stratification system and the vessels as a way of embodying or manifesting this data of unrealized gain and loss. My first approach was to work with meditation actually—a meditation workshop with my colleagues. I was going to offer this “Unrealized Gain/Loss” workshop where you would explore the sensations of gain and loss by adapting the way yogi-nidra brings you into contact with your physical surroundings and stretches your perception. FLM: At Naropa University there are/were business & compassion workshops—a sort of mash-up of business and compassion and how compassion could be incorporated into a business model. This process and engagement of “embodying data” also has to do with “Participatory Democracy and the Future of Karaoke” you created at the DNC in Denver in 2008. DP: That kind of appropriation and instrumentalization of spiritual practice could be disturbing and thus compelling as a strategy. For various reasons, I’ve come to be drawn to both the form of a quarterly public performance and the established performance form of a drum circle. Its something I’ve seen myself do before, that is to mess up a really good functional social system like a drum circle or karaoke. I remember I was developing language for the karaoke project and started calling it “Participatory Democracy and the Future of Karaoke” and one of my assistants on the project, who’s an incredible artist, said, “but don’t you think the future of karaoke is guitar hero?” and I realized that maybe he thought I was trying to improve the form. I’m just trying to get people to have this shifted embodied experience, I need to craft the performance context so that they can do that. In the case of the karaoke project, for example, what did I need in order to be able to do this [a person to stand up in front of a bar and deliver a karaoke speech]? I realized that the body is very vulnerable so I built a podium so that the speaker can feel secure enough to do this, otherwise you couldn’t get to this state achieved by passing these speeches through the body. Then I was, like, well you need to be able to practice the lyrics because you don’t know all the “songs” by heart, which became an insert to the massive track books carried by most karaoke VJs. And then sometimes the crowd in the bar isn’t there with me, so I needed to extract the voice of the crowd cheering from the original venue and I needed the local audience to cheer if they wanted to. I’m interested in both where the form succeeds and fails. In particular, one of the most interesting things is this auditory gap between the space where you are, the reduced scale of applause in your own little bar, and this grand scale of applause at the convention center where the speech was originally delivered. FLM: How did the concept of “Participatory Democracy Karaoke” come about and why did you use karaoke as a means of engaging what was happening at the DNC in 2008? DP: I was looking at a lot of different readymade media infrastructures within the city at the time. I was interested in the emergency broadcast systems and I developed a proposal to repurpose that system and karaoke became an important symbol because it was this populist form that was already engaged in exploring the sensation of celebrity but also visualizing the gap between ourselves and those with more power and influence. So it had this readymade capacity to play with power and celebrity and I felt like the Obama presidential campaign, the first one in particular, had some very curious overlaps with this culture of celebrity. Obama of course rose to power partly based on his oratory abilities and I was interested in how karaoke as a vehicle was so adept at offering people all that was left of authentic expression in a political speech. Managing a politician and constructing their identity is such a developed practice that it becomes, kind of automatically, a metaphor for the way that our own identities are constructed. Of course the Obama campaign was very hip and savvy and deploying this notion of grassroots. It was really pioneering in its use of social media and this deployment of notions of populism. I was interested at that time in the capacity of karaoke to track speech patterns, precise tempos of anyone’s delivery, and that to me was a way of thinking about what might be left of the authentic self. I was interested in karaoke’s capacity to extract that authentic component and offer it to others. So not just to stand up and be them, but to [literally] pass their speech patterns through your own body. A long time ago, it started to strike me as odd that one would make media at all. It struck me as a kind of un-contemporary way of going about making art in an age of media overflow. That logic extended into my thinking on delivery devices and installation as well. Why would one buy a screen or even set one up when there are so many out there? And the way in which these media displays function in karaoke bars and bars in general is very interesting to me. I’m drawn to this passive consumption of media where your primary social interaction is with the bartender or a few other individuals but these screens are around you and your attention is shifting back and forth between these spaces. So much political rhetoric is spoken to a half-listening audience. I was interested in what was happening in the slippage and that karaoke was a kind of slippage amplifier. So if you put people in a bar and they are delivering a Kucinich speech and Kucinich comes up on a screen then your getting a sound bite of Kucinich and an image of Kucinich and your friend is talking to you— FLM: A kind of magic takes place in that incongruency between sound and image and the karaoke participant who’s relaying the speech-text at the same time. DP: Exactly and there’s some kind of truth in that experience of reality. FLM: Yeah, there’s something uncanny about seeing the body close-up like that as though it can’t lie to you in that moment or context. It’s a weird moment of luminous clarity. The work you’ve done and all of what you’re saying about karaoke is so very interesting to me. Growing up, my dad and uncles sang karaoke a lot (and still do) and being first-generation Filipino American is a different cultural subtext entirely. I’m also seeing it from the position of witnessing family members who are carriers of these stories and songs. And seeing them cherish these Tony Bennett, Frank Sinatra, Elvis Presley songs so much, I also see how their bodies are literal vessels of popular music that signifies something greater—it signifies their cultural and socioeconomic place in the world. The way that they cherish these American 1950s and 1960s pop songs is similar to having a certain kind of reverence for their spiritual faith or Catholicism. It’s a similar kind of care, focus, and attention exerted in karaoke and Catholicism—that these two structures and systems give something to focus on. Setsuko, Seiji and Hitoshi in Obama, Japan as Obama in Indiana — d. peltz — 2008 DP: Sure there something about the relationship we have to our candidate or the way we go about choosing a candidate, which is very similar to a deity or idol. I learned a lot about karaoke culture through this project. I’d never done karaoke. I’d never been interested in it as a form and then I travelled to Japan as part of the project when I made “Setsuko, Seiji and Hitoshi in Obama, Japan as Barack Obama in Indiana” and it was quite fascinating because my image of karaoke had always been this very public forum in a karaoke bar and then I discovered there’s this whole other world of karaoke where people even go on their own, they go and rent a room or cubicle and sing, or they go on a date—just the two of them go and sit in a room and do karaoke together. FLM: I’m interested in issues that take place within or as a result of specific karaoke culture(s). In the Philippines within the last several years there’s been occurring the “My Way Killings” phenomenon. Apparently baklas or gay men are employed by karaoke establishments to help “smooth over conflicts over karaoke singing”—these social forms of conduct, or lack thereof that arise out of the infrastructures of this social sport. In this one rural part of the Philippines there’s a village karaoke machine that the whole village shares—the Aeta indigenous people have an appointed “keeper” of the karaoke machine. I also see karaoke as a proxy to the confessional box in Catholicism where one goes to pour out their sins (minus the penance and redemption). The karaoke machine enables one to literally sing out whatever’s going on internally, but through highly saturated popular song lyrics. While karaoke is a public and social sport, it can also be a private one. Karaoke is a means of communion with each other. DP: Right, this preference for this kind of mediated communication. In Japan I was trying to organize people to work on this project and I was talking about throwing a party and they were like, well, we have to rent a karaoke machine because what else are we going to do? And I think its kind of serving that function of surrogacy—emotional surrogacy. FLM: And karaoke tools can be read as ritual tools—the magic mic that holds everything. There’s got to be some overlap at some point—between religious ceremony and devotion to the karaoke machine. DP: The way I designed the piece was so that it could slip right on top of the ready-made karaoke infrastructure. There was a flat-packed podium and it was made of a single sheet of plywood with no fasteners that slotted into itself. Those were sent out to a network of karaoke bars that I invited to become “karaoke convention centers.” The local VJs downloaded our custom-made, speech-extracted tracks that were designed to play on their existing equipment. In this sense the piece is a permanent installation. If you go to Denver today, some of the VJs still have the tracks in their library of offerings, the Ramones and Romney. It was this notion of re-purposing readymade infrastructure to create a distributable populist form. Obama was coming and the convention was in the Pepsi Center and 30,000 people were coming including 10,000 journalists. The impetus behind the larger art project that commissioned international artists to make works in Denver, was that local people weren’t going to have much access to this convention. It was like an invasion, the city was being descended upon, but if you lived a block away from the site, you had the same access as people in Zimbabwe&mash;30 second media bits excerpted from the speeches. So it seemed to me that the fundamental gesture was how do I take that signal, which was travelling out of the convention center, and create a local interruption? FLM: Is that what you mean by ‘intervention’? The term is frequently used to help describe your work. DP: It depends on the day. Around that karaoke project I had a conversation with Krzysztof Wodiczko and he was proposing that maybe rather than intervention, we should consider the word interruption. Because intervention is kind of an overused term in the field of art and it has militaristic and therapeutic associations outside of the art context. Fundamentally, the idea of intervening speaks to the readymade social world as your primary material. So it’s basically suggesting a kind of subtractive process, which gets back to this question: what is the role of the contemporary media artist in a world that’s so saturated with media? You can’t work additively in a saturated field. If you want to make a visible mark you have to work subtractively. That’s what intervention is about to me, just another way of saying “to work subtractively.” FLM: So the interventions or interruptions aren’t necessarily adding or subtracting, but are they putting orange cones there? What are they doing exactly? DP: I think you’re right about that, they’re not really subtracting. They’re adding to the scope of possibility. I’ve been thinking (with this exhibition I’m mounting next month) about the work as explorations and expansions of social possibility. Maybe it’s more insertion. I started calling the pieces ‘insertions’ that I was making in Rejmyre—a small town in Sweden where I’ve been working for six years now. My favorite site to install there is the tourist bureau. I started calling the video pieces that I made for the tourist bureau, video insertions. This idea that you’re inserting something into the readymade media infrastructure of the world resonates with me. Insertion leverages a context, creating a possibility that the inserted object might be naturalized in the process — that someone can encounter my video in Rejmyre as tourist information. And then all of a sudden tourist information can include some American guy prostrating through town and it can include really bad relationship advice. Maybe insertion is a better word. tourist information – d. peltz 2009-present  . (shrink)

Evidentiality has been extensively studied in linguistics for its function in coding the source of knowledge or for expressing the speaker’s attitude towards knowledge. However, few studies examine how evidential marking is sensitive and responsive to the unfolding talk and actions of the participants in social interaction. Analyzing audio and video data of naturally occurring conversations in Korean in a conversation analysis framework, this article demonstrates how the speaker often makes the choice of evidential marking or shifts the choice of (...) evidential marking according to the participant’s response, achieving certain interactional functions. The speaker makes a strategic choice to use the experiential evidential marking -telako or shifts from zero-evidential marking to overt experiential evidential marking -telako for the same proposition to achieve entitlement, objectivity, or detachment regarding his claim. This study shows that, in social interaction, the choice of the speaker’s evidential marking is relative and interactively organized rather than static and predetermined. (shrink)

Unbound anaphoric pronouns or ‘E-type pronouns’ have presented notorious problems for semantic theory, leading to the development of dynamic semantics, where the primary function of a sentence is not considered that of expressing a proposition that may act as the object of propositional attitudes, but rather that of changing the current information state. The older, ‘E-type’ account of unbound anaphora leaves the traditional notion of proposition intact and takes the unbound anaphor to be replaced by a full NP whose (...) semantics is assumed to be known (e.g. a definite description). In this paper, I argue that there are serious problems with any version of the E-type account as well as the (original form of the) dynamic account. I will explore a new account based on structured propositions, which can be considered a conservative extension of a traditional proposition-based semantics, but which at the same time incorporates some crucial insights of the dynamic account. (shrink)

Human consciousness, the result of breathing process as dealt with in the Upanishads, is translated into modern scientific terms and modeled as a mechanical oscillator of infrasonic frequency. The bio-mechanic oscillator is also proposed as the source of psychic energy. This is further advanced to get an insight of human consciousness (the being of mind) and functions of mind (the becoming of mind) in terms of psychic energy and reversible transformation of its virtual reflection. An alternative analytical insight of (...) human consciousness and mental functions to other theoretical approaches is developed based on Upanishadic insight and presented.That reversible transformation of virtual psychic energy reflection termed as maya, creating various consequential / parallel / simultaneous conscious-states, phases, cognitive and communicative states, modes of language acquisition and communication, and kinds of function of human mind is visualized. The concept is extended to delineate form, structure and functional mechanism of human mind and to know how it facilitates human mental acquisitions, retention, communications, including language abilities. This proposal is extensively discussed and the hardware and software of mind as envisaged in Indian philosophical systems are put forward.All this presentation is translated to neuro-biology in terms of brain wave modulation / demodulation terms. Also a preliminary proposition of physic-chemical nature of human thoughts and ideas is given. (shrink)

The general principle of epistemic closure stipulates that epistemic properties are transmissible through logical means. According to this principle, an epistemic operator, say ε, should satisfy any valid scheme of inference, such as: if ε(p entails q), then ε(p) entails ε(q). The principle of epistemic closure under known entailment (ECKE), a particular instance of epistemic closure, has received a good deal of attention since the last thirty years or so. ECKE states that: if one knows that p entails q, and (...) she knows that p, then she knows that q. It is widely accepted that ECKE constitutes an important piece of the skeptical argument, but the acceptance of an unrestricted version of ECKE is still a matter of debate. On the side of the defenders of ECKE, one finds Stine (1976), Brueckner (1985), Vogel (1990), and Feldman (1995). Others proposed a refutation or a limitation of the principle, like Dretske (1970), Nozick (1981), Hales (1995), Williams (1996), and Sosa (1999). As it turns out, the relevant alternatives view (RAV) elaborated by Dretske, which restricts the scope of ECKE, has been discussed extensively and acknowledged as one of the most important contributions. There is nonetheless a major unsolved difficulty pertaining to Dretske-RAV: the notion of relevant alternatives is defined in such a way that it is bounded by counterfactual possibilities. This ontological import leaves open the door to the skeptic. Some have tried to give more precision to this notion, like Stine (1976), who appealed to a Gricean approach to define relevant alternatives in conversational contexts. My proposal is in accordance with the gist of Dretske’s strategy, i.e. to restrict the validity of ECKE, and I claim that in order to escape the difficulties inherent to RAV one has to introduce a more robust notion, the notion of epistemic context. Epistemic contexts are a subclass of propositional contexts. In that perspective, the closure property is expressed in terms of a property of a relation between epistemic contexts. ECKE holds when and only when either the epistemic context of the premisses is the same as the epistemic context of the conclusion, or the epistemic context change between the premisses and the conclusion is permissible. Permissibility of epistemic context change is a function of consistency. By means of this epistemic context approach, I will show that: (1) epistemic contexts are defined by basic propositions (unchallenged justified beliefs), (2) ECKE holds only under very specific constraints, and (3) the skeptical argument involves a non-permissible change of epistemic context and, by the same token, cannot rely upon ECKE. (shrink)

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers and Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper, we will present a natural refinement of their definition that allows for stability results to hold within the wider class of [Formula: see text]-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem (...) class='Hi'>functions from the proofs. As a result, we obtain stability in particular for all intermediate structures between the semi-algebraic and the sub-analytic languages. (shrink)

In [1] Todorov has shown by means of axiomatic set theory that there exists a nonstandard function Δ: *ℝn → * ℂ such that for all continuous functions φ: ℝn → ℂ, equation image.Here *ℝ and *ℂ are the set of the nonstandard real numbers and the set of the nonstandard complex numbers, respectively, and *φ: *ℝn → *ℂ is the nonstandard extension of φ In the present note we want to prove an analogous theorem by predicative means (...) only. (shrink)

A large number of scholars have argued that a) Islamic architecture is hidden, in the sense that its interior is not articulated on the basis of its exterior; b) the form of Islamic buildings neither expresses nor embodies its function; and c) Islamic architecture is not tectonic or structural, but iconic in character. In this paper, we use Ernst Grube’s analysis of these three claims and focus our attention on the design of the congregational mosques. This paper presents informed arguments (...) against these claims. We begin the discussion with a clarification of the meaning of ‘form follows function’. A clear understanding of the relationship between these two concepts is indispensable for evaluating the claims that Grube makes in his analyses. Then we argue that the form of the congregational mosque embodies its function in a significant manner. Finally, the paper explains in some detail how the function of a mosque is the basis on which its formal structure is designed. The proposition that we defend in this paper is that Islamic architecture exists and expresses the spirit of Islamic culture. (shrink)

We show how mereotopological notions can be expressed by extending intuitionistic propositional logic with propositional quantification and a strong modal operator. We first prove completeness for the logics wrt Kripke models; then we trace the correspondence between Kripke models and topological spaces that have been enhanced with an explicit notion of expressible region. We show how some qualitative spatial notions can be expressed in topological terms. We use the semantical and topological results in order to show how in (...) some extensions of the logics it is possible to express connectedness, non-emptiness and a set of jointly exhaustive, pairwise disjoint, binary relations that play a significant role in qualitative spatial reasoning. (shrink)

A number of general points behind the story of this paper may be worth setting out separately, now that we have come to the end.There is perhaps one obvious omission to be addressed right away. Although the word “information” has occurred throughout this paper, it must have struck the reader that we have had nothing to say on what information is. In this respect, our theories may be like those in physics: which do not explain what “energy” is (a notion (...) which seems quite similar to “information” in several ways), but only give some basic laws about its behaviour and transmission.The eventual recommendation made here has been to use a broad type-theoretic framework for studying various more classical and more dynamic notions of proposition in their interaction. This is not quite the viewpoint advocated by many current authors in the area, who argue for a whole-sale switch from a ‘static’ to a ‘dynamic’ perspective on propositions. This is not the place, however, to survey the conceptual arguments for and against such a more radical move.This still leaves many questions about possible reductions from one perspective to another. For instance, it would seem that classical systems ought to serve as a ‘limiting case’, which should still be valid after procedural details of some cognitive process have been forgotten. There are various ways of implementing the desired correspondence: e.g. by considering extreme cases with ⫅ equal to identity, or, in the pure relational algebra framework by considering only pairs (x, x). What we shall want then are reductions of dynamic logics, in those special cases, to classical logic. But perhaps also, more sophisticated views are possible. How do we take a piece of ‘dynamic’ prose, remove control instructions and the like, and obtain a piece of ‘classical’ text, suitable for inference ‘in the light of eternity’?There is also a more technical side to the matter of ‘reduction’. By now, Logic has reached such a state of ‘inter-translatability’ that almost all known variant logics can be embedded into each other, via suitable translations. In particular, once an adequate semantic has been given for a new system, this usually induces an embedding into standard logic: as we know, e.g., for the case of Modal Logic. Like-wise, all systems of dynamic interpretation or inference proposed so far admit of direct embedding into an ordinary ‘static’ predicate logic having explicit transition predicates (cf. van Benthem 1988b). Thus, our moral is this. The issue is not whether the new systems of information structure or processing are essentially beyond the expressive resources of traditional logical systems: for, they are not. The issue is rather which interesting phenomena and questions will be put into the right focus by them.The next broad issue concerns the specific use of the perspective proposed here, vis-à-vis concrete proposals for information-oriented or dynamic semantics. The general strategy advocated here is to locate some suitable base calculus and then consider which ‘extras’ are peculiar to the proposal. For instance, this is the spirit in which modal S4 would be a base logic of information models, and intuitionistic logicthe special theory devoting itself to upward persistent propositions. Or, with the examples in Section 4.1, the underlying base logic is our relational algebra, whereas, say, ordinary updates then impose special properties, such as ‘idempotence’: $$xRy \Rightarrow yRy$$ Does this kind of application presuppose the existence of one distinguished base logic, of which all others are extensions? This would be attractive-and some form of relational algebra or linear logic might be a reasonable candidate. Nevertheless, the enterprise does not rest on this outcome. What matters is an increased sensitivity to the ‘landscape’ of dynamic logics, just as with the ‘Categorial Hierarchy’ in Categorial Grammar (cf. van Benthem 1989a, 1991) where the family of logics with their interconnections seems more important than any specific patriarch.Finally, perhaps the most important issue in the new framework is the possibility of new kinds of questions arising precisely because of its differences from standard logic. Notably, given the option of regarding propositions as programs, it will be of interest to consider systematically which major questions about programming languages now make sense inside logic too.EXAMPLE. Correctness. When do we have $$\left[\kern-0.15em\left[ \pi \right]\kern-0.15em\right](\left[\kern-0.15em\left[ A \right]\kern-0.15em\right]) \subseteq \left[\kern-0.15em\left[ B \right]\kern-0.15em\right]$$ for (s, t) propositions A, B and a dynamic (s, (s, t)) proposition π?Program Synthesis. Which dynamic proposition will take us from an information state satisfying A to one satisfying B? (This question needs refinement, lest there be trivial answers.)Determinism. Which propositions as programs are deterministic, in the sense of defining single-valued functions from states to states?Querying. What does it mean to ask for information in the present setting? (Again, individual types referring to e will be crucial here.)This is not merely an agenda for wishful thinking. Within Logic, there are various ways of introducing such concerns into semantics, especially, using tools from Automata Theory. (See van Benthem 1989c for further discussion of such computational perspectives in ‘cognitive programming’.)At least if one believes that ‘dynamics’ is of the essence in cognition (rather than a mere interfacing problem between the halls of eternal truth and the noisy streets of reality), the true test for the present enterprise is the development of a significant new research program not merely copying the questions of old. (shrink)

Let M be a first-order structure; we denote by DEF(M) the set of all first-order definable relations and functions within M. Let π be any one-to-one function from N into the set of prime integers. Let ∣ and $\bullet$ be respectively the divisibility relation and multiplication as function. We show that the sets DEF(N,π,∣) and $\mathrm{DEF}(\mathbb{N},\pi,\bullet)$ are equal. However there exists function π such that the set DEF(N,π,∣), or, equivalently, $\mathrm{DEF}(\mathbb{N},\pi,\bullet)$ is not equal to $\mathrm{DEF}(\mathbb{N},+,\bullet)$ . Nevertheless, in all (...) cases there is an $\{\pi,\bullet\}$ -definable and hence also {π,∣}-definable structure over N which is isomorphic to $\langle\mathbb{N},+,\bullet\rangle$ . Hence theories TH(N,π,∣) and $\mathrm{TH}(\mathbb{N},\pi,\bullet)$ are undecidable. The binary relation of equipotence between two positive integers saying that they have equal number of prime divisors is not definable within the divisibility lattice over positive integers. We prove it first by comparing the lower bound of the computational complexity of the additive theory of positive integers and of the upper bound of the computational complexity of the theory of the mentioned lattice. The last section provides a self-contained alternative proof of this latter result based on a decision method linked to an elimination of quantifiers via specific tables. (shrink)

Let E be a subset of. A linear extension operator is a linear map that sends a function on E to its extension on some superset of E. In this paper, we show that if E is a semi‐algebraic or subanalytic subset of, then there is a linear extension operator such that is semi‐algebraic (subanalytic) whenever f is semi‐algebraic (subanalytic).

Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $$\Gamma $$, then its $$\Gamma $$ -code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau’s theorem to Borel functions: If a Borel function on a Polish space happens to be a $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -function, then one can find its $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -code hyperarithmetically relative to its Borel code. More generally, we (...) prove extension-type, domination-type, and decomposition-type variants of Louveau’s theorem for Borel functions. (shrink)

We define a propositionally quantified intuitionistic logic Hπ + by a natural extension of Kripke's semantics for propositional intutionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π +, S4π +, S4.2π +, K4π +, Tπ +, Kπ + and Bπ +, studied by Fine.

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. (...) I use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia. The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)