Impossible events and the knowability paradox

This note disambiguates the predicate ‘is an unknowable event’ and shows how Transparent Intensional Logic interprets the sentences “Agent a is calculating the final decimal of π” and “Agent a has calculated the final decimal of π”. The knowability paradox is used to set the stage

Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study

The following is a critical and historical account of Aristotelian Essentialism informed by recent work on Aristotle’s modal syllogistic. The semantics of the modal syllogistic are interpreted in a way that is motivated by Aristotle, and also make his validity claims in the Prior Analytics consistent to a higher degree than previously developed interpretative models. In Chapter One, ancient and contemporary objections to the Aristotelian modal syllogistic are discussed. A resolution to apparent inconsistencies in Aristotle’s modal syllogistic is proposed and developed out of recent work by Patterson, Rini, and Malink. In particular, I argue that the semantics of negation is distinct in modal context from those of assertoric negative claims. Given my interpretive model of Aristotle’s semantics, in Chapter Two, I provide proofs for each of the mixed apodictic syllogisms, and propose a method of using Venn Diagrams to visualize the validity claims Aristotle makes in the Prior Analytics. Chapter Three explores how Aristotle’s syllogistic fits within Aristotle’s philosophy of science and demonstration, particularly within the context of the Posterior Analytics. Consideration is given to the Aristotelian understanding of the relationship among necessity, explanation, definition, and essence. Chapter Four applies Aristotelian modal logic in contemporary contexts. I contrast Aristotelian modality and essentialism with contemporary modalism based upon the semantics of possible worlds, e.g. Kripke and Putnam. I also develop an account of how Aristotelian modal logic can ground a sortal dependent theory of identity, as discussed by Wiggins

Inferring knowledge from textual data by natural deduction

In this paper, we introduce the system for inferring implicit computable knowledge from textual data by natural deduction. Our background system is Transparent Intensional Logic (TIL) with its procedural semantics that assigns abstract procedures known as TIL constructions to terms of natural language as their context-invariant meanings. The input data for our method are produced by the so-called Normal Translation Algorithm (NTA). The algorithm processes natural-language texts and produces TIL constructions. In this way we have obtained a large corpus of TIL meaning procedures. These procedures are furthermore processed by our algorithms for type checking and context recognition, so that the rules of natural deduction for inferring computable knowledge can be afterwards applied.Web of Science241482

Aristotle and the Problem of Concepts

By a "concept" , I mean a unitary thought (of the sort normally represented by a word) that applies to a plurality of differing objects, and by "The Problem of Concepts" I mean the pervasive philosophical questions of how such thoughts are to be explained and by what standards they are to be evaluated. Aristotle is generally held to have been a Moderate Realist, who held that a concept is a putative grasp of a mind-independent universal object that exist somehow in or derivatively on the many particular objects to which the concept applies. I argue that Aristotle rejected the posit of such universal objects and instead understood universality as a feature of thought, which has a basis in reality and a function in cognition. With some notable exceptions, concepts are based on relations of difference in "the more and the less" between their instances and on the causal relations between the various parts and characteristics of each instance. A concept's function is to serve as a term in deductions which enable us to represent the necessity of causal connections. I go on, then, to explore the manner in which, on Aristotle's view, concepts compose propositions and bodies of knowledge and the way in which they are formed

Theory of Judgment in Edmund Husserl's Logical Investigations

Tutkielma käsittelee fenomenologisen perinteen perustajan Edmund Husserlin kognitiivisen tai tiedollisen arvostelman teoriaa vuosina 1900-1901 julkaistuissa Loogisissa tutkimuksissa ja muissa samalta Husserlin ajattelun kaudelta peräisin olevissa kirjoituksissa. Tavoitteena on esittää tarkasti ja selvässä muodossa Husserlin teorian filosofiset pääpiirteet, teorian keskeisiin väitteisiin johtavat analyysit ja niitä ohjaavat teoreettiset pyrkimykset sekä asettaa Husserlin teoria laajempaan filosofiseen kontekstiin. Työssä on kolme päälukua, joista ensimmäinen on historiallinen katsaus erilaisiin arvostelman luonnetta koskeviin käsityksiin Platonista Brentanoon. Luvun keskeisin tulos on jaottelu kahden arvostelmaa koskevan teoriaperheen tai käsityksen välillä, joihin tässä työssä viitataan platonis-aristoteelisenä ja apprehensio-myöntämis-käsityksenä, ja joiden keskeisin erottava tekijä liittyy predikaation ja myöntämisen tai kieltämisen väliseen suhteeseen yleensä perustapauksena pidetyssä kategorisessa, "S on p" -muotoisessa arvostelmassa. Platonis-aristoteelisen käsityksen mukaan myöntäminen ja kieltäminen ovat predikaation muotoja, kun taas kilpailevan käsityksen mukaan arvostelma edellyttää erillistä apprehensio- tai käsittämisaktia, johon predikoiminen sisältyy, ja arvostelmassa tällaisen käsittämisen kohteeseen suhtaudutaan hyväksyvästi tai hylkäävästi sen päälle rakentuvassa asenteessa. Luvun viimeisissä osioissa käsitellään lisäksi 1800-luvun arvostelmateorioiden keskeisiä kiistakysymyksiä ja erityisesti niiden filosofien teorioita, jotka vaikuttivat suoraan Husserlin omien käsitysten muotoutumiseen, ja joista keskeisimmät ovat Bolzano, Lotze ja Brentano. Toisessa luvussa tarkastellaan Loogisten tutkimusten laajempaa filosofista projektia, joka liittyi sen selventämiseen, mikä on logiikan peruskäsitteiden rooli tiedossa, sekä arvostelman analyysien asemaa tässä projektissa. Huomion keskipisteenä on jännite kahden Husserlin ajattelua luonnehtivan perussitoumuksen välillä, joista ensimmäinen on käsitys logiikan objektiivisuudesta ja riippumattomuudesta psykologisista ilmiöistä ja toinen taas ajatus, että filosofisten peruskäsitteiden analyysissä tietoisuuden ilmiöiden kuvailemisella on olennainen rooli. Luvussa osoitetaan, että keskeinen ajatus näiden käsitysten yhteensovittamisen kannalta Loogisissa tutkimuksissa on Husserlin teoria merkityksistä ideaalisina aktilajeina, joiden instansseja yksittäiset intentionaaliset aktit kuten arvostelmat ovat. Luvun lopussa tarkastellaan lisäksi Husserlin intentionaalisuusteorian yleisiä piirteitä erityisesti suhteessa Brentanon aiempaan teoriaan. Kolmas luku on työn temaattinen ydin, jossa keskitytään nimenomaisesti Husserlin analyyseihin arvostelman luonteesta, rakenteesta ja suhteista objekteihin maailmassa. Luvussa tarkastellaan neljää toisiinsa läheisesti kytkeytyvää Husserlin teorian piirrettä, joita arvioidaan suhteessa Brentanon teoriaan ja ensimmäisessä luvussa esitettyyn historialliseen jaotteluun. Ensimmäinen näistä on väite, ettei arvostelmaan sisälly erotettavissa olevaa kokemusta, jossa sen kohde ainoastaan käsitettäisiin. Toinen on, ettei suoraviivainen arvostelman tekeminen ole sellaista myöntämistä, joka edellyttää edeltävää harkintaa ja kohdistuu harkinnan kohteena olevaan väitteeseen. Kolmas väite on, ettei Brentanon kuvailema pelkkä jonkin kohteen tietoinen esittäminen tai mieltäminen ole perustavampi tai rakenteellisesti yksinkertaisempi intentionaalinen aktityyppi kuin arvostelma, vaan jälkimmäisen "modifikaatio". Neljäs Husserlin teorian pääpiirre on monitahoinen käsitys arvostelmista "propositionaalisina akteina", jotka instantioivat ideaalisia propositioita ja suuntautuvat intentionaalisesti asiaintiloihin maailmassa tavalla, joka Husserlin yksinkertaisimpana pitämässä tapauksessa rakentuu havaintokokemuksen pohjalle jäsentämällä havainnon sisällön subjekti-predikaatti-muodossa. Tutkielman keskeinen johtopäätös ensimmäisessä luvussa esitetyn jaottelun näkökulmasta on, että Husserlin arvostelmateoriaa voidaan oiketutetusti pitää kriittisesti uudelleenmuotoiltuna versiona platonis-aristoteelisestä käsityksestä, jossa kuitenkin huomioidaan apprehensio-myöntämis-käsityksen keskeiset käsitteelliset erottelut ja sisällytetään teoriaan erityistapauksina ne ilmiöt, joihin jälkimmäinen käsitys keskittyi. Erityisesti Husserlin teoriaa voidaan pitää sellaisen aristoteelisen perinteen jatkajana, jossa predikaation kaltaisten ajattelun loogisten rakenteiden ajatellaan olevan läheisessä suhteessa havaintokokemukseen ja tavallaan kasvavan tällaisen kokemuksen rakenteista

Towards a classification of continuity and on the emergence of generality

This dissertation has for its primary task the investigation, articulation, and comparison of a variety of concepts of continuity, as developed throughout the history of philosophy and a part of mathematics. It also motivates and aims to better understand some of the conceptual and historical connections between characterizations of the continuous, on the one hand, and ideas and commitments about what makes for generality (and universality), on the other. Many thinkers of the past have acknowledged the need for advanced science and philosophy to pass through the “labyrinth of the continuum” and to develop a sufficiently rich and precise model or description of the continuous; but it has been far less widely appreciated how the resulting description informs our ideas and commitments regarding how (and whether) things become general (or how we think about universality). The introduction provides some motivation for the project and gives some overview of the chapters. The first two chapters are devoted to Aristotle, as Aristotle’s Physics is arguably the foundational book on continuity. The first two chapters show that Aristotle\u27s efforts to understand and formulate a rich and demanding concept of the continuous reached across many of his investigations; in particular, these two chapters aim to better situate certain structural similarities and conceptual overlaps between his Posterior Analytics and his Physics, further revealing connections between the structure of demonstration or proof (the subject of logic and the sciences) and the structure of bodies in motion (the subject of physics and study of nature). This chapter also contributes to the larger narrative about continuity, where Aristotle emerges as one of the more articulate and influential early proponents of an account that aligns continuity with closeness or relations of nearness. Chapter 3 is devoted to Duns Scotus and Nicolas Oresme, and more generally, to the Medieval debate surrounding the “latitude of forms” or the “intension and remission of forms,” in which concerted efforts were made to re-focus attention onto the type of continuous motions mostly ignored by the tradition that followed in the wake of Aristotelian physics. In this context, the traditional appropriation of Aristotle’s thoughts on unity, contrariety, genera, forms, quantity and quality, and continuity is challenged in a number of important ways, reclaiming some of the largely overlooked insights of Aristotle into the intimate connections between continua and genera. By realizing certain of Scotus’s ideas concerning the intension and remission of qualities, Oresme initiates a radical transformation in the concept of continuity, and this chapter argues that Oresme’s efforts are best understood as an early attempt at freeing the concept of continuity from its ancient connection to closeness. Chapters 4 and 5 are devoted to unpacking and re-interpreting Spinoza’s powerful theory of what makes for the ‘oneness’ of a body in general and how ‘ones’ can compose to form ever more composite ‘ones’ (all the way up to Nature as a whole). Much of Spinoza reads like an elaboration on Oresme’s new model of continuity; however, the legacy of the Cartesian emphasis on local motion makes it difficult for Spinoza to give up on closeness altogether. Chapter 4 is dedicated to a closer look at some subtleties and arguments surrounding Descartes’ definition of local motion and ‘one body’, and Chapter 5 builds on this to develop Spinoza’s ideas about how the concept of ‘one body’ scales, in which context a number of far-reaching connections between continuity and generality are also unpacked. Chapter 6 leaves the realm of philosophy and is dedicated to the contributions to the continuitygenerality connection from one field of contemporary mathematics: sheaf theory (and, more generally, category theory). The aim of this chapter is to present something like a “tour” of the main philosophical contributions made by the idea of a sheaf to the specification of the concept of continuity (with particular regard for its connections to universality). The concluding chapter steps back and discusses a number of distinct characterizations of continuity in more abstract and synthetic terms, while touching on some of the corresponding representations of generality to which each such model gives rise. This chapter ends with a brief discussion of some of the arguments that have been deployed in the past to claim that continuity (or discreteness) is “better.

The arrival of mimesis and methexis in the enquiries of Jean-Luc Nancy

This thesis advances from the conjecture that Jean-Luc Nancy's work demands to be interpreted according to the logic it describes. For Nancy unity is irreducible from exposure, because a distinct entity cannot be abstracted from its boundary conditions. It is my contention, therefore, that Nancy's work must be treated accordingly, as a syntactic unity that can only be understood in its exposure to other syntactic unities. Two interrelated claims are therefore made. First: that the current literature on Nancy’s work fails to identify that an inheritance from Plato and from Greek philosophy more widely is a key to the specificity of Nancy’s thinking, and second that only by retrieving this connection can Nancy’s contribution to contemporary ontological debates be made out. The thesis attempts to take a preliminary step in this direction by positioning Nancy’s work within a contemporary philosophical scene definitively characterised by its exposure to Ancient Greek philosophy. This investigation places a conceptual focus on the Platonic terms μίμησις and μέθεξις, terms which bear a rich history of implications in philosophies of immanence, transcendence, production, and art. I argue that in showing that there is never μίμησις without μέθεξις, and vice versa, Nancy shows that there is never immanence without transcendence, and vice versa. Furthermore, I argue that this mutuality places sensibility at the core of Nancy’s thought, and determines the artwork to be a privileged site at which the reciprocity of immanence and transcendence is presented. In this much, I suggest Nancy’s work offers an alternative to the demand for some mutually exclusive decision between immanence and transcendence

The Function Argument in the Eudemian Ethics

This paper reconstructs the function argument of Aristotle’s Eudemian Ethics 2.1. The argument seeks to define happiness through the method of division; shows that the highest good is better than all four of the goods of the soul, not only two, as commentators have thought; and unlike the Nicomachean argument, makes the highest good definitionally independent of the human function