Weakly Aggregative Modal Logic: Characterization and Interpolation

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation

Is Dialetheism an Idealism? The Russellian Fallacy and the Dialetheist’s Dilemma

International audienceIn his famous work on vagueness, Russell named 'fallacy of verbalism' the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories - the non-adjunctive and relevant approaches -, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of their underlying semantics. The meaning of 'intuitive reading' is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense - therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency - and this could be a welcome result for a dialetheist

MacColl’s elusive pluralism

MacColl a été récemment l’objet de trois intéressantes thèses. D’abord, il serait le probable père du pluralisme en logique. Ensuite, son pluralisme porterait un instrumentalisme sous-jacent. Enfin, les deux thèses précédentes expliqueraient l’oubli dans lequel il serait tombé après 1909. Bien qu’il soit à la fois pluraliste et instrumentaliste à certains égards, je suggèrerai qu’il est difficile de trouver dans les écrits de MacColl un pluralisme qui puisse satisfaire les trois thèses précédentes en apparaissant pour la première fois chez MacColl, en trouvant ses sources dans un instrumentalisme adapté à la logique, et en étant l’explication à l’oubli dans lequel était tombé son auteur.MacColl is the recent subject of three interesting theses. One is that he is the probable originator of pluralism in logic. The other is that his pluralism expresses an underlying instrumentalism. The third is that the first two help explain his post-1909 neglect. Although there are respects in which he is both a pluralist and an instrumentalist, I will suggest that it is difficult to find in MacColl’s writings a pluralism which honours the threefold attribution of having been originated by him, having been rooted in an instrumentalism adapted to logic, and being the occasion of his neglect

Reasoning with Inconsistent Information

In this thesis we are concerned with developing formal and representational mechanisms for reasoning with inconsistent information. Strictly speaking there are two conceptually distinct senses in which we are interested in reasoning with inconsistent information. In one sense, we are interested in using logical deduction to draw inferences in a symbolic system. More specifically, we are interested in mechanisms that can continue to perform deduction in a reasonable manner despite the threat of inconsistencies as a direct result of errors or misrepresentations. So in this sense we are interested in inconsistency-tolerant or paraconsistent deduction. … ¶ In this thesis we adopt a novel framework to unify both logic-as-deduction and logic-as-representation approaches to reasoning with inconsistent information. …

Dialetheism and the Impossibility of the World

This paper first offers a standard modal extension of dialetheic logics that respect the normal semantics for negation and conjunction in an attempt to adequately model absolutism, the thesis that there are true contradictions at metaphysically possible worlds. It is shown, however, that the modal extension has unsavoury consequences for both absolutism and dialetheism. While the logic commits the absolutist to dialetheism, it commits the dialetheist to the impossibility of the actual world. A new modal logic AV is then proposed which avoids these unsavoury consequences by invalidating the interdefinability rules for the modal operators with the use of two valuation relations. However, while using AV carries no significant cost for the absolutist, the same isn’t true for the dialetheist. Although using AV allows her to avoid the consequence that the actual world is an impossible world, it does so only on the condition that the dialetheist admits that she cannot give a dialetheic solution to all self-referential semantic paradoxes. Thus, unless there are any further available modal logics that don’t commit her to the impossibility of the actual world, the dialetheist is faced with a dilemma. Either admit that the actual world is an impossible world, or admit that her research programme cannot give a comprehensive solution to the self-referential paradoxes

Demystifying Emergence:A New Exploration Through Scientific Case Studies

In this thesis I argue that a modified version of Jessica Wilson’s subset view, what I call the Holistically Defined Modal view, is the most promising nonreductive physicalist account to accommodate not only mental causation but also other kinds of higher-level causation. In this thesis I do not endeavour to demonstrate nonreductive physicalism’s superiority against competitors, such as reductive physicalism or strong emergence. Rather, my goal is to investigate how nonreductive physicalism should be spelled out assessing what I consider the most interesting and successful candidates for the best nonreductive physicalist account. The three candidates are Jessica Wilson’s subset view, Sydney Shoemaker’s mereological version of the subset view, and Carl Gillett’s mutualism.In Chapter 1, I first provide historical context to the concept of emergence, and I explain its interpretation within this thesis to disambiguate it from alternative definitions or uses. I then introduce Jaegwon Kim’s Causal Exclusion Argument, which is one of the most potentially damning and recurrent objections against nonreductive physicalism. In Chapter 2, I present the subset view as well as Wilson’s response to Kim’s argument. The subset view proposes that for higher-level properties to be causally efficacious in a significant way it is sufficient that they have a distinct set of powers (or causal profile) vis-à-vis their realisers. In this chapter I also defend the subset view against Sara Bernstein’s version of Kim’s objection.In Chapter 3 I present Shoemaker’s version of the subset view and conclude that Wilson’s account is superior to it. In Chapter 4 I introduce Gillett’s account, as well as Gillett’s Problem of Qualitative Distinctness against the subset view. Gillett claims that science explains the behaviour of special science entities in terms of the joint behaviour of their constituents. From this claim he builds an argument to show that special science properties of composites are realised by the properties of its constituents, which leads him to conclude that properties at different levels do not share any powers ––i.e., they are qualitatively distinct. That claim is a direct threat to the subset view, which requires power sharing, and according to Gillett it makes it an untenable view.To assess Gillett’s objection, I focus on whether realisation is a many-to-one relation – what I refer to as realisationM-O – or a one-to-one relation – realisationO-O. Gillett argues that it must be many-to-one, given that this is the only way to preserve qualitative distinctness between realiser and realisee. Wilson’s way to deal with the apparent many-to-one nature of realisation of special science properties is to provide an ontologically lightweight structural property that bridges the many properties of constituents and the higher-level realised property of the composite. She refers to this kind of properties as “middleman properties”. In the last section of Chapter 4 I argue that Wilson has not provided a successful response to Gillett’s threat, and that the existence of middleman properties is not properly justified. The chapter, therefore, is inconclusive as to whether realisation has a one-to-one or many-to-one structure. Chapter 5 serves as a linking chapter, emphasizing the importance of case studies in elucidating the nature of realisation and discussing their treatment in Wilson’s and Gillett’s works. Chapters 6 and 7 present two scientific case studies and assess whether any of the two kinds of realisation, realisationM-O or realisationO-O, can account for them.In Chapter 6, I explain how statistical mechanics derives and defines entropy, which is a property of thermodynamic systems from the properties of the particles composing the systems. In Chapter 7, I explain how one of the most influential scientific theories of consciousness, the Global Neuronal Workspace Theory, explains how conscious states arise from brain states.This thesis concludes that the realisation relation that accounts for both the realisation of entropy and conscious properties is realisationO-O, whereas realisationM-O can, at best, only partially account for them. Hence, realisationO-O is the most general account of realisation. This conclusion is based on one main finding: in both case studies there are scientific grounds to accept the genuine existence of middleman properties. However, the case studies also unveil that Wilson’s definition of “middleman property” –and thus her view– needs to be substantially modified. In Chapters 6 and 7 I present and discuss the modified version of the subset view: the Holistically Defined Modal view –the HDM view. According to this view, a realiser is a holistically defined modal property. I define both the modal aspect and the holistic aspect of the view in a broad sense, that also encompasses cases where a narrow definition applies. The holistic aspect of the view entails that the realiser is defined in terms of properties and states of the system, where those properties and states of the system might or might not be further defined in terms of compositional principles and Boolean operations on its constituents. The modal aspect of the view entails that the realiser has a modal aspect, namely, it considers possible states the system could be in. In a broad sense, there are cases where the only possible states of the system considered are actual states, which nonetheless are possible states of the system. The Entropy Case Study is an example of a realiser that is a holistically defined modal property in a narrow sense for both aspects, whereas the Neuronal Global Workspace presents an example of a realiser that is holistically defined in a narrow sense and is modal in a broad sense.<br/

Glosarium Matematika

273 p.; 24 cm