Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

The history of the idea of predicate is the history of its emancipation. The lesson of this paper is that there are two more steps to take. The first is to recognize that predicates need not have a fixed degree, the second that they can combine with plural terms. We begin by articulating the notion of a multigrade predicate: one that takes variably many arguments. We counter objections to the very idea posed by Peirce, Dummett's Frege, and Strawson. We show (...) that the arguments of a multigrade predicate must be grouped into places, with perhaps several arguments occupying positions at a place. Variability may relate to places or positions. Russell's multiple judgement predicate turns out to be just one example of a family-'is necessarily true of', 'is said of', 'is instantiated by' and so on-of predicates with variably many places. Our main concern, however, is lists. Any adequate account of lists must include plural as well as singular terms. On one account, lists are mere strings of separate arguments, which occupy variably many positions within a place of a multigrade predicate. A quite different account takes the list itself to be a compound plural term. We compare these rival conceptions, and reach some surprising conclusions. As a coda, we deploy the conceptual apparatus developed in the paper to assess Morton's pioneer system of multigrade logic. (shrink)

The study has two objectives: to introduce grip force recording as a new technique for studying embodied numerical processing; and to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line, A Theory of Magnitude and Embodied Cognition account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip (...) force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research. (shrink)

Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...) if only because mathematicians take many-valued functions seriously. We assess the objection (by Russell, Frege and others) that many-valued functions are illegitimate because the corresponding terms are ambiguous. We also assess the various methods proposed for getting rid of them. Finding the objection ill-founded and the methods ineffective, we introduce a logical framework that admits plural reference, and use it to answer some earlier questions and to raise some more. (shrink)

We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour of (...) quantification; on the contrary, quantification is definable in terms of it. Predicates and functors (function signs) can take plural as well as singular terms as arguments, and both many-valued and single-valued functions are expressible. The system accommodates collective as well as distributive predicates, and the condition for a predicate to be distributive is definable within it; similarly for functors. An essential part of the project is to demonstrate the soundness and completeness of the calculus with respect to a semantics that does without set-theoretic domains and in which the use of settheoretic extensions of predicates and functors is replaced by the sui generis relations and functions for which the extensions were at best artificial surrogates. Our metalanguage is designed to solve the difficulties involved in talking plurally about individuals and about the semantic values of plural items. (shrink)

The combination of increased availability of large amounts of fine-grained human behavioral data and advances in machine learning is presiding over a growing reliance on algorithms to address complex societal problems. Algorithmic decision-making processes might lead to more objective and thus potentially fairer decisions than those made by humans who may be influenced by greed, prejudice, fatigue, or hunger. However, algorithmic decision-making has been criticized for its potential to enhance discrimination, information and power asymmetry, and opacity. In this paper, we (...) provide an overview of available technical solutions to enhance fairness, accountability, and transparency in algorithmic decision-making. We also highlight the criticality and urgency to engage multi-disciplinary teams of researchers, practitioners, policy-makers, and citizens to co-develop, deploy, and evaluate in the real-world algorithmic decision-making processes designed to maximize fairness and transparency. In doing so, we describe the Open Algortihms project as a step towards realizing the vision of a world where data and algorithms are used as lenses and levers in support of democracy and development. (shrink)

We all learn about the mistake of treating ‘nothing’ as if it were a term standing for something; but is it a mistake to treat it as an empty term, denoting nothing? We argue not, and we introduce ‘zilch’, defined as ‘the non-self-identical thing’, as a term which is empty as a matter of logical necessity. We contrast its behaviour with that of the quantifier ‘nothing’, and illustrate its uses. We use the same idea to vindicate Locke’s, Descartes’ and Hume’s (...) handling of ‘nothing’, and we show how Heidegger’s ‘das Nichts nichtet’ comes out as logically true. (shrink)

Alex Oliver; XI*—A Few More Remarks on Logical Form, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 247–272, https://doi.org/10.

Yah boo sucks to the grammer wot we lernt in skool! Grammar (and the bad old traditional logic) says that quantifier phrases such as 'nobody', 'everyone', 'all women', 'some men' and 'a man' are in the same category as names such as 'Milly', 'Molly' and 'Mandy'. So, prior to their first corrective lessons, students are awfully muddled, the first and fundamental problem being the Woozle hunt for somebody called 'nobody'. Hoorah for modern logic and logic teachers! The story used to (...) justify our current logics is entirely fictional. The claims about names and quantifier phrases in English are wildly false. Two of the heroes of modern logic, Russell and Hilbert, make the very mistakes which are falsely blamed on traditional logic. The villain, Meinong, turns out to have been working a different patch. Ideas ascribed to traditional grammar are modern inventions. Neither logicians nor grammarians can be trusted to tell the history of either grammar or logic. (shrink)

When we say a certain rose is red, we seem to be attributing a property, redness, to it. But are there really such properties? If so, what are they like, how do we know about them, and how are they related to the objects which have them and the linguistic devices which we use to talk about them? This collection presents these ancient problems in a modern light. In particular, it makes accessible for the first time the most important contributions (...) to the contemporary controversy about the nature of properties. Those new to the subject will find the clearly-written introduction, by two experts in the field, an invaluable guide to the intricacies of this debate. The volume illustrates very well the aims and methods of modern metaphysics and show how a thorough understanding of the metaphysics of properties is crucial to most of analytic philosophy. (shrink)

In "Frege: Philosophy of Mathematics" Dummett recommends the following thesis, (PNP): the correct analysis of any sentence containing a plural noun phrase will show that the phrase is functioning predictively. According to Dummett, (PNP), applied to numerical predications such as the leaves are 1,000' is the key premise in Frege's argument against Mill's theory of numbers. But Frege never subscribed to (PNP) and he rejected such numerical predications, and point out how Frege's own semantic theory for plural noun phrases obscures (...) his idea of a relation. (shrink)

Dummctt argues that classical quantification is illegitimate when the domain is given as the objects which fall under an indefinitely extensible concept, since in such cases the objects are not the required definite totality. The chief problem in understanding this complex argument is the crucial but unexplained phrase 'definite totality' and the associated claim that it follows from the intuitive notion of set that the objects over which a classical quantifier ranges form a set. 'Definite totality' is best understood as (...) disguised plural talk like Cantor's 'consistent multiplicity', although this does not help in understanding how a totality could be anything other than definite. Moreover, contrary to his claims, Dummett's own notion of set is not intuitive and he does not demystify the set-theoretic paradoxes. In conclusion, it is argued that Dummett's context principle is responsible for the incoherent projection of the haziness of a conception of some objects onto reality. (shrink)

Dummctt argues that classical quantification is illegitimate when the domain is given as the objects which fall under an indefinitely extensible concept, since in such cases the objects are not the required definite totality. The chief problem in understanding this complex argument is the crucial but unexplained phrase 'definite totality' and the associated claim that it follows from the intuitive notion of set that the objects over which a classical quantifier ranges form a set. 'Definite totality' is best understood as (...) disguised plural talk like Cantor's 'consistent multiplicity', although this does not help in understanding how a totality could be anything other than definite. Moreover, contrary to his claims, Dummett's own notion of set is not intuitive and he does not demystify the set-theoretic paradoxes. In conclusion, it is argued that Dummett's context principle is responsible for the incoherent projection of the haziness of a conception of some objects onto reality. (shrink)

Almost all set theorists pay at least lip service to Cantor’s definition of a set as a collection of many things into one whole; but empty and singleton sets do not fit with it. Adapting Dana Scott’s axiomatization of the cumulative theory of types, we present a ‘Cantorian’ system which excludes these anomalous sets. We investigate the consequences of their omission, examining their claim to a place on grounds of convenience, and asking whether their absence is an obstacle to the (...) theory’s ability to represent ordered pairs or to support the arithmetization of analysis or the development of the theory of cardinals and ordinals. (shrink)

The fundamental thesis of David Lewis's "Parts of Classes" is that the nonempty subsets of a set are mereological parts of it. This paper shows that Lewis's considerations in favor of this thesis are unpersuasive. First, common speech provides no support. Second, the formal analogy between mereology and the Boolean algebra of sets can be explained without accepting the thesis. Third, it is very doubtful that the thesis is fruitful. Certainly, Lewis's claim that it helps us understand set theory is (...) unwarranted. (shrink)

Alex Oliver; Discussions: Classes and Goodman's Nominalism, Proceedings of the Aristotelian Society, Volume 93, Issue 1, 1 June 1993, Pages 179–192, https://doi.

Alex Oliver; Discussions: Classes and Goodman's Nominalism, Proceedings of the Aristotelian Society, Volume 93, Issue 1, 1 June 1993, Pages 179–192, https://doi.

Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.

1. ExpositionRichard Sharvy's ‘A more general theory of definite descriptions’ was published in 1980. Its aim was to replace Russell's paradigm by " a general theory of definite descriptions, of which definite mass descriptions, definite plural descriptions, and Russellian definite singular count descriptions are species. … We have an account of the generic ‘the’ along these same lines. " By now his theory has attained the status of a new paradigm. Even a casual trawl of the literature throws up over (...) a score of citations and endorsements, and no rebuttals of its central contention that the primary use of ‘the’ is to indicate totality . We shall argue that it is wrong for mass description, wrong for singular description, wrong for plural description and wrong for generic ‘the’. Sharvy would have approved: his obituary says that his car displayed the slogan ‘Subvert the Dominant Paradigm’.He follows Russell in treating descriptions as incomplete symbols, but nothing in his paper turns on this aspect of it, and we can bypass the issue by considering them in the context of complete sentences. Where Russell translates F into the predicate calculus as Formula Sharvy translates it as Formula Here ≤ is supposed to stand for some or other species of part of relation. His other governing idea is of a predicate's being cumulative. G is cumulative if any number of things that satisfy G have a sum, i.e. a least upper bound with respect to ≤ which also satisfies G. The meanings of ≤, sum and cumulativity vary according to the different kinds of description, which we take in the order in which Sharvy presents them. Meanwhile, we note that he originally defined ‘sum’ to mean simply the l.u.b. , but subsequently redefined …. (shrink)

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. He has illuminated Aristotle’s syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection, and has worked to debunk the theory of descriptions. This volume brings together new articles by an international roster of leading logicians and philosophers in order to honour Smiley’s work. Their essays will be of significant interest to those working across the logical spectrum—in philosophy of (...) language, philosophical and mathematical logic, and philosophy of mathematics. (shrink)

In this chapter, we investigate the idea of trade marks as property. Three questions need to be answered. The first is a conceptual matter: are trade marks capable of being property or are they ruled out as a matter of conceptual necessity? The second is conceptual-cum-descriptive: is the current law's treatment of trade marks treatment of them as property? The third is normative: if the current law does in fact treat them as property, is it right to do so? The (...) questions need to be tackled in turn. (shrink)

Offers a comprehensive and accessible exploration of the scope and importance of Gottlob Frege's work.

The rapid dynamics of COVID-19 calls for quick and effective tracking of virus transmission chains and early detection of outbreaks, especially in the “phase 2” of the pandemic, when lockdown and other restriction measures are progressively withdrawn, in order to avoid or minimize contagion resurgence. For this purpose, contact-tracing apps are being proposed for large scale adoption by many countries. A centralized approach, where data sensed by the app are all sent to a nation-wide server, raises concerns about citizens’ privacy (...) and needlessly strong digital surveillance, thus alerting us to the need to minimize personal data collection and avoiding location tracking. We advocate the conceptual advantage of a decentralized approach, where both contact and location data are collected exclusively in individual citizens’ “personal data stores”, to be shared separately and selectively, voluntarily, only when the citizen has tested positive for COVID-19, and with a privacy preserving level of granularity. This approach better protects the personal sphere of citizens and affords multiple benefits: it allows for detailed information gathering for infected people in a privacy-preserving fashion; and, in turn this enables both contact tracing, and, the early detection of outbreak hotspots on more finely-granulated geographic scale. The decentralized approach is also scalable to large populations, in that only the data of positive patients need be handled at a central level. Our recommendation is two-fold. First to extend existing decentralized architectures with a light touch, in order to manage the collection of location data locally on the device, and allow the user to share spatio-temporal aggregates—if and when they want and for specific aims—with health authorities, for instance. Second, we favour a longer-term pursuit of realizing a Personal Data Store vision, giving users the opportunity to contribute to collective good in the measure they want, enhancing self-awareness, and cultivating collective efforts for rebuilding society. (shrink)

Guilt and shame are self-conscious emotions with implications for mental health, social and occupational functioning, and the effectiveness of sports practice. To date, the assessment and role of athlete-specific guilt and shame has been under-researched. Reporting data from 174 junior elite cricketers, the present study utilized exploratory factor analysis in validating the Athletic Perceptions of Performance Scale, assessing three distinct and statistically reliable factors: athletic shame-proneness, guilt-proneness, and no-concern. Conditional process analysis indicated that APPS shame-proneness mediated the relationship between general (...) and athlete-specific distress. While APPS domains of guilt-proneness and no-concern were not significant mediators, they exhibited correlations in the expected direction with indices of psychological distress and well-being. The APPS may assist coaches and support staff identify players who may benefit from targeted interventions to reduce the likelihood of experiencing shame-prone states. (shrink)

Two objections are raised against Oliver and Smiley’s analysis of the collective–distributive opposition in their 2016 book: They take it as a basic premise that the collective reading of ‘baked a cake’ corresponds to a predicate different from its distributive reading, and the same applies to all predicate expressions that admit both a collective and a distributive interpretation. At the same time, however, they argue that inflectional forms of the same lexeme reveal a univocity that should be preserved in (...) a formal representation of English. These two assumptions sit uneasily. In developing their analysis, Oliver and Smiley come to the conclusion that even a singular predication such as ‘Tom baked a cake’ must be regarded as ambiguous between a collective and a distributive reading. This is so artificial that it hardly makes sense, and yet there seems to be no way out of the difficulty unless we are prepared to give up the basic premise just mentioned. (shrink)

Many research fields concerned with the processing of information contained in human faces would benefit from face stimulus sets in which specific facial characteristics are systematically varied while other important picture characteristics are kept constant. Specifically, a face database in which displayed expressions, gaze direction, and head orientation are parametrically varied in a complete factorial design would be highly useful in many research domains. Furthermore, these stimuli should be standardised in several important, technical aspects. The present article presents the freely (...) available Radboud Faces Database offering such a stimulus set, containing both Caucasian adult and children images. This face database is described both procedurally and in terms of content, and a validation study concerning its most important characteristics is presented. In the validation study, all frontal images were rated with respect to the shown facial expression, intensity of expression, clarity of expression, genuineness of expression, attractiveness, and valence. The results show very high recognition of the intended facial expressions. (shrink)