Dialectica Interpretation with Marked Counterexamples

Goedel's functional "Dialectica" interpretation can be used to extract functional programs from non-constructive proofs in arithmetic by employing two sorts of higher-order witnessing terms: positive realisers and negative counterexamples. In the original interpretation decidability of atoms is required to compute the correct counterexample from a set of candidates. When combined with recursion, this choice needs to be made for every step in the extracted program, however, in some special cases the decision on negative witnesses can be calculated only once. We present a variant of the interpretation in which the time complexity of extracted programs can be improved by marking the chosen witness and thus avoiding recomputation. The achieved effect is similar to using an abortive control operator to interpret computational content of non-constructive principles.Comment: In Proceedings CL&C 2010, arXiv:1101.520

Analysis of methods for extraction of programs from non-constructive proofs

The present thesis compares two computational interpretations of non-constructive proofs: refined A-translation and Gödel's functional "Dialectica" interpretation. The behaviour of the extraction methods is evaluated in the light of several case studies, where the resulting programs are analysed and compared. It is argued that the two interpretations correspond to specific backtracking implementations and that programs obtained via the refined A-translation tend to be simpler, faster and more readable than programs obtained via Gödel's interpretation. Three layers of optimisation are suggested in order to produce faster and more readable programs. First, it is shown that syntactic repetition of subterms can be reduced by using let-constructions instead of meta substitutions abd thus obtaining a near linear size bound of extracted terms. The second improvement allows declaring syntactically computational parts of the proof as irrelevant and that this can be used to remove redundant parameters, possibly improving the efficiency of the program. Finally, a special case of induction is identified, for which a more efficient recursive extracted term can be defined. It is shown the outcome of case distinctions can be memoised, which can result in exponential improvement of the average time complexity of the extracted program

Causation in contemporary analytical philosophy

Contemporary analytic philosophy is in the midst of a vigorous debate on the nature of causation. Each of the main proposals discussed in this chapter faces important problems: the deductive-nomological model, the counterfactual theory, the manipulability theory, the probabilistic theory and the transference theory. After having explored possible solutions to these problems, I conclude that one version of the transference approach is most promising. However, as I show in the last section, it is necessary to supplement this transference approach with the notion of lawful dependency. This gives rise to the notion of causal responsibility

What Do the Folk Think about Composition and Does it Matter?

Rose and Schaffer (forthcoming) argue that teleological thinking has a substantial influence on folk intuitions about composition. They take this to show (i) that we should not rely on folk intuitions about composition and (ii) that we therefore should not reject theories of composition on the basis of intuitions about composition. We cast doubt on the teleological interpretation of folk judgments about composition; we show how their debunking argument can be resisted, even on the assumption that folk intuitions have a teleological source; and we argue that, even if folk intuitions about composition carry no weight, theories of composition can still be rejected on the basis of the intuitions of metaphysicians

Colour Resemblance and Colour Realism

One prominent ambition of theories of colour is to pay full justice to how colours are subjectively given to us; and another to reconcile this first-personal perspective on colours with the third-personal one of the natural sciences. The goal of this article is to question whether we can satisfy the second ambition on the assumption that the first should and can be met. I aim to defend a negative answer to this question by arguing that the various kinds of experienced colour resemblances – notably similarities in hue distance, sameness in superdeterminables, and colour resemblances between surfaces, volumes and illuminants – cannot be accounted for in terms of the mental representa-tion of the scientifically studied properties, which colours are best identified with in response to the second ambition

Frege on Referentiality and Julius Caesar in Grundgesetze Section 10

This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It is argued that, in Frege’s standards of reducing arithmetic to logic, his solution to the indeterminacy does not give rise to any sort of Caesar problem in the book

Normative Modeling

By now we are familiar with scientific models of descriptive domains. But might we also model clusters of normative truths? In this piece I first identify elements central to all modeling efforts: modeling frameworks, interpretations, and domains of applicability. Then I consider some advantages and disadvantages of normative modeling

Augustinus ja märkide ning signifikatsiooni uurimine

Doktoritöö eesmärgiks on avada mõningaid aspekte, mis iseloomustavad suhet Aurelius Augustinuse (354¬–430 AD) ja märkide ning tähenduse uurimise vahel. Uurimusega püütakse näidata, miks on Augustinuse enam kui 1500 aasta tagused ideed tänapäevastes humanitaarteadustes asetleidvate arutelude jaoks endiselt olulised ja aktuaalsed. Augustinusega tegeledes ei saa temast rääkida üksnes kui teoloogist või üksnes kui filosoofist, sest sageli on need mõlemad pooled temas korraga esindatud. Enne Hippo linna piiskopiks saamist oli Augustinus edukas retoorikaõpetaja Kartaagos, Roomas ja Milaanos. Vaimustus sõnade ja igasuguste märkide vastu nagu ka sügav huvi dialektika ja kommunikatsiooni vastu saatsid teda läbi kogu elu. Käesolevas doktoritöös väidetakse, et Augustinuse mõtlemises võib selgelt näha märgiteooriale omaseid põhijooni, millele ta on pühendanud mitmeid teoseid, kus märgiteoreetilised probleemid on asetatud laiemasse teoloogilisse ja eksegeetilisse konteksti. Uurimuse eesmärgiks on Augustinuse kirjutiste analüüsi ja tõlgendamise kaudu anda lugejale ülevaade tema märgi ja signifikatsiooni teooriatest ja nende mõjust semiootikale. Doktoritöö (1) avab ja kirjeldab Augustinuse õpetust märkidest nii nagu see kajastub tema kirjutistes alates teosest “Dialectica” ja lõpetades teosega “De doctrina christiana”; (2) esitab Augustinuse semiootilise terminoloogia ja selgitab mõningaid selle eripärasid; (3) tõlgendab Augustinuse arusaamat märkidest märgiteooria algse sõnastamise ja loomise kontekstis; (4) selgitab valetamise (vale kui ebaõige signifikatsioon) käsitlust ja toob esile selle tähenduse semiootika teooriale; (5) sünteesib Augustinuse märgiteooria peamised tunnusjooned ja toob välja nende olulisuse üldise märgiteooria jaoks. Püstitatud eesmärkidest lähtudes on uurimus jagatud neljaks peatükiks, mis keskenduvad vastavalt Augustinuse teostele “De dialectica” (387), “De magistro” (389), “De doctrina christiana” (396¬–427) ja “De mendacio” (395). Lisaks neile peamistele allikatele leiavad uurimistöös kasutamist ja kajastamist ka mitmed teised teemasse puutuvad Augustinuse kirjutised. Doktoritöös analüüsitavaid teoseid siduvateks teemadeks on asjade ja märkide eristus, intentsionaalsuse idee, arusaam sõnadest kui märkidest, objekt-keele ja meta-keele eristamine, mis kõik iseloomustavad Augustinuse semiootika põhijooni.This study attempts to unravel some aspects of the relation between Augustine of Hippo (354¬–430 AD) and the study of signs and signification. This dissertation will attempt to show why, after more than fifteen hundred years, Augustine’s ideas are still as significant to the contemporary debate within the humanities. With an author such as Augustine one should be careful when drawing a line between the theologian and the philosopher because these two souls in fact often coexist. Before becoming Bishop of Hippo, Augustine was a successful teacher of rhetoric at Carthage, Rome and Milan. His fascination for words and signs of all kinds, his profound interest in dialectics and communication were indeed lifelong concerns. The present study argues that the rudiments of a theory of signs can be discerned with the clarity of Augustine, who explicitly devoted numerous works to the subject, albeit generally framed within a broader theological and exegetical context. The aim of this dissertation is to present an account of the theories of the sign and signification on the basis of the interpretation of Augustine’s works, with a view to its implications to the domain of semiotics. This study (1) unravels and describes the Augustinian doctrine of signs from the Dialectica to the De doctrina christiana; (2) expounds Augustine’s semiotic terminology and clarifies some obscure or misunderstood knots; (3) interprets Augustine’s approach to signs within the context of where the theory was originally formulated and grafted; (4) offers an account of the subject of lies (understood as a false signification) in light of its relevance to a theory of semiotics; (5) synthesizes the main features of Augustine’s sign theory and emphasizes the significance for a general theory of signs. In light of these objectives, the four chapters around which the study is articulated takes a closer look at the De dialectica (387), the De magistro (389), the De doctrina christiana (396¬–427), and the De mendacio (395), respectively. Although the inquiry is primarily confined to the abovementioned works, it does take into account numerous additional Augustinian and contemporary sources that encourage the elucidation, interpretation, and expansion of the subject. The distinction of things and signs, the concept of intentionality, the understanding of words as signs, the distinction between object language and metalanguage are the trait d’union of the works scrutinized and illustrate some of the key features of the Augustinian semiotics