1,321 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Strategies for defending the Principle of Identity of Indiscernibles: a critical survey and a new approach

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    The Principle of Identity of Indiscernibles (PII) is the focus of much controversy in the history of Metaphysics and in contemporary Physics. Many questions rover the debate about its truth or falsehood, for example, to which objects the principle applies? Which properties can be counted as discerning properties? Is the principle necessary? In other words, which version of the principle is the correct and is this version true? This thesis aims to answer this questions in order to show that PII is a necessarily true principle of metaphysics. To accomplish this task, the reader will find, in this thesis, an encyclopaedical introduction to the history of PII and to the reasons it matters so much, followed by a presentation of the most famous arguments against it and the defences used against these arguments. Then, the reader finds in-depth discussion of the minutiae involved in postulating the principle as to make clear what is in fact being attacked and defended. With these preliminaries solved, a deeper analysis of these defences is presented aiming to discover which is the most appropriate example to use against the attacks to the principle. This analysis allowed a classification of these defences in four families with different strategies within them. Finally, with these defensive strategies at hand we are able to confront alleged counterexamples to PII in Mathematics with the intention to test these defences

    To have done with theory? Baudrillard, or the literal confrontation with reality

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    Baudrillard, Eluding the temptation to reinterpret Jean Baudrillard once more, this work started from the ambition to consider his thought in its irreducibility, that is, in a radically literal way. Literalness is a recurring though overlooked term in Baudrillard’s oeuvre, and it is drawn from the direct concatenation of words in poetry or puns and other language games. It does not indicate a realist positivism but a principle that considers the metamorphoses and mutual alteration of things in their singularity without reducing them to a general equivalent (i.e. the meaning of words in a poem, which destroys its appearances). Reapplying the idea to Baudrillard and finding other singular routes through his “passwords” is a way to short-circuit its reductio ad realitatem and reaffirm its challenge to the hegemony of global integration. Even in the literature dedicated to it, this exercise has been rarer than the ‘hermeneutical’ one, where Baudrillard’s oeuvre was taken as a discourse to be interpreted and explained (finding an equivalent for its singularity). In plain polemic with any ideal of conformity between theory and reality (from which our present conformisms arguably derive, too), Baudrillard conceived thought not as something to be verified but as a series of hypotheses to be repeatedly radicalised – he often described it as a “spiral”, a form which challenges the codification of things, including its own. Coherent with this, the thesis does not consider Baudrillard’s work either a reflection or a prediction of reality but, instead, an out-and-out act, a precious singular object which, interrogated, ‘thinks’ us and our current events ‘back’. In the second part, Baudrillard’s hypotheses are taken further and measured in their capacity to challenge the reality of current events and phenomena. The thesis confronts the ‘hypocritical’ position of critical thinking, which accepts the present principle of reality. It questions the interminability of our condition, where death seems thinkable only as a senseless interruption of the apparatus. It also confronts the solidarity between orthodox and alternative realities of the COVID pandemic and the Ukrainian invasion, searching for what is irreducible to the perfect osmosis of “virtual and factual”. Drawing equally from the convulsions of globalisation and the psychopathologies of academics, from DeLillo’s fiction and Baudrillard’s lesser-studied influences, this study evaluates the irreversibility of our system against the increasingly silent challenges of radical thought. It looks for what an increasingly pessimistic late Baudrillard called ‘rogue singularities’: forms which, often outside the conventional realms one would expect to find them, constitute potential sources of the fragility of global power. ‘To have done with theory’ does not mean abandoning radical thought and, together with it, the singularity of humanity. It means, as the thesis concludes, the courage to leave conventional ideas of theory and listen to less audible voices which, at the heart of this “enormous conspiracy”, whisper — as a mysterious lady in Mariupol did to Putin — “It’s all not true! It’s all for show!”

    Erasure in dependently typed programming

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    It is important to reduce the cost of correctness in programming. Dependent types and related techniques, such as type-driven programming, offer ways to do so. Some parts of dependently typed programs constitute evidence of their typecorrectness and, once checked, are unnecessary for execution. These parts can easily become asymptotically larger than the remaining runtime-useful computation, which can cause linear-time algorithms run in exponential time, or worse. It would be unnacceptable, and contradict our goal of reducing the cost of correctness, to make programs run slower by only describing them more precisely. Current systems cannot erase such computation satisfactorily. By modelling erasure indirectly through type universes or irrelevance, they impose the limitations of these means to erasure. Some useless computation then cannot be erased and idiomatic programs remain asymptotically sub-optimal. This dissertation explains why we need erasure, that it is different from other concepts like irrelevance, and proposes two ways of erasing non-computational data. One is an untyped flow-based useless variable elimination, adapted for dependently typed languages, currently implemented in the Idris 1 compiler. The other is the main contribution of the dissertation: a dependently typed core calculus with erasure annotations, full dependent pattern matching, and an algorithm that infers erasure annotations from unannotated (or partially annotated) programs. I show that erasure in well-typed programs is sound in that it commutes with single-step reduction. Assuming the Church-Rosser property of reduction, I show that properties such as Subject Reduction hold, which extends the soundness result to multi-step reduction. I also show that the presented erasure inference is sound and complete with respect to the typing rules; that this approach can be extended with various forms of erasure polymorphism; that it works well with monadic I/O and foreign functions; and that it is effective in that it not only removes the runtime overhead caused by dependent typing in the presented examples, but can also shorten compilation times."This work was supported by the University of St Andrews (School of Computer Science)." -- Acknowledgement

    Indeterminacy and the law of the excluded middle

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    This thesis is an investigation into indeterminacy in the foundations of mathematics and its possible consequences for the applicability of the law of the excluded middle (LEM). It characterises different ways in which the natural numbers as well as the sets may be understood to be indeterminate, and asks in what sense this would cease to support applicability of LEM to reasoning with them. The first part of the thesis reviews the indeterminacy phenomena on which the argument is based and argues for a distinction between two notions of indeterminacy: a) indeterminacy as applied to domains and b) indefiniteness as applied to concepts. It then addresses possible attempts to secure determinacy in both cases. The second part of the thesis discusses the advantages that an argument from indeterminacy has over traditional intuitionistic arguments against LEM, and it provides the framework in which conditions for the applicability of LEM can be explicated in the setting of indeterminacy. The final part of the thesis then applies these findings to concrete cases of indeterminacy. With respect to indeterminacy of domains, I note some problems for establishing a rejection of LEM based on the indeterminacy of the height of the set theoretic hierarchy. I show that a coherent argument can be made for the rejection of LEM based on the indeterminacy of its width, and assess its philosophical commitments. A final chapter addresses the notion of indefiniteness of our concepts of set and number and asks how this might affect the applicability of LEM

    Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic

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    Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    The book of Qohelet. A digital scholarly edition of the hebrew text

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    The objective of the present dissertation is a born-digital critical edition of the Hebrew Old Testament book of Qohelet. The edition is based on an extensive collation of variant readings from indirect sources – the Septuagint, the Peshitta, the works of St. Jerome (the Vulgate and the Commentary), and the Targum – as well as from direct sources such as the Qumran fragments and Hebrew medieval manuscripts. The ultimate goal of the edition is (a) to reproduce the earliest textual form, the Archetype, that can be reconstructed on the basis of the available evidence; and (b) to propose a rehabilitation of the Original of the Author by resorting, when necessary, to conjectural emendation. We date the Archetype to the II century BCE, corresponding to the date of Hebrew fragments from Qumran, while we place the Original between the V and III centuries BCE. Unlike previous critical editions of Qohelet, ours follows the so-called eclectic model, which involves the reconstitution of a critical text and the preparation of an apparatus of secondary variants. Our edition includes, moreover, new data, taken both from primary literature, such as the recently published Göttingen Septuagint, and from up-to-date studies and critical commentaries on the text of Qohelet. The work is made up of five main parts: an introduction, which sets forth the rationale of the edition and the methodology adopted; the collation, where the variants are listed in their original language; the commentary, where they are extensively discussed; the critical text accompanied by the apparatus, which presents a selection of authentic Hebrew variants taken from the collation; and finally, a translation of the critical text. The edition uses the mark-up language of the Text Encoding Initiative (TEI). It is realized in pdf, via LaTeX, and will be available in digital form, via the TEI-Publisher editor
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