27 research outputs found
Choice sequences and knowledge states: extending the notion of finite information to produce a clearer foundation for intuitionistic analysis
There are currently four major formal foundational systems for intuitionistic analysis: LS, CS (both in Troelstra 1977), FIM (Kleene and Vesley 1965) and the derivable FIRM-INT (Moschovakis 2016). All of these systems rely on different universes of choice sequences and different conceptions of what a choice sequence is. There is a strong common ground between these systems as they use the same very restrictive notion of finite information when dealing with these choice sequences { the notion of restricting ourselves to initial segments.
This text extends the notion of a choice sequence given in Fletcher (1998) and uses it to construct a generalised system capable of expressing results about intensional properties of choice sequences. This is achieved by constructing a language capable of representing intensional first order restrictions on choice sequences (the language of knowledge states) and their relations to other sequences. This extended system allows us to formulate a notion of lawlessness that evades a series of paradoxes highlighted in Fletcher (1998), allows us to prove a generalised form of open data and offers additional clarity to other key areas of the theory. When a certain set of restrictions are applied to this extended theory (extensionality and a second order restriction on knowledge states) we obtain a system suitable for the foundation of analysis
Indeterministic finite-precision physics and intuitionistic mathematics
In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In this thesis, we discuss some motivations for dropping this assumption, which we believe partly arises from the usual point-based approach to the mathematical continuum. We focus on the case of classical mechanics specifically, but the ideas could be extended to other theories as well. We analyse the alternative theory of classical mechanics presented by Gisin and Del Santo, which suggests that physical quantities can equivalently be thought of as being only determined up to finite precision at each point in time, and that doing so naturally leads to indeterminism. Next, we investigate whether we can use intuitionistic mathematics to mathematically express the idea of finite precision of quantities, arriving at the cautious conclusion that, as far as we can see, such attempts are thwarted by conceptual contradictions. Finally, we outline another approach to formalising finite-precision quantities in classical mechanics, which is inspired by the intuitionistic approach to the continuum but uses classical mathematics
Randomness? What randomness?
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics (like Bohmian mechanics or 't Hooft's Cellular Automaton interpretation) are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low (or even zero) probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements (and of the safety of quantum cryptography) should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness (or algorithmic randomness) that in various guises was investigated by Solomonoff, Kolmogorov, Chaitin, Martin-Lo"f, Schnorr, and others, and treat Bell's (1964) Theorem and the Free Will Theorem with their implications for randomness
An interpretation of the structure of the world based on Whiteheadâs notion of dipolarity: a new ontological and physical framework for theories of quantum gravity
The main aim of the thesis is to explore the structure of the world from a Whiteheadian process theoretic perspective and suggest it as a framework for an algebraic approach to Quantum Gravity. In particular, throughout the thesis, the analysis focuses on the notion of dipolarity that appears in Whiteheadâs philosophy. The thesis begins with an exploration of Whiteheadâs process of becoming which is followed by a presentation of sheaf theory as the mathematical basis. Based on the analysis of Whiteheadâs philosophy in combination with physical theories, the features of the structure of the world are explored. The process of becoming is translated as a transformation from determinable dispositions to determinate manifestations. In virtue of dispositions, the structure of the world acquires a causal status. The introduction of causality in terms of becoming is accompanied by the introduction of relata in the structure of the world. There is then a comparison between our Neo-Whiteheadian thesis and both structuralism and constructivism. In particular, the comparison with constructivism is justified by the fact that we adopt a view about the generation of abstract notions out of concrete instances or manifestations of determinable dispositions, where manifested quantities are related mereologically. On the other hand, the comparison with structuralism is motivated by the holistic character of the process of becoming. The thesis ends with exploring laws and the process notion of dipolarity
Constructive Perspectives on Inductive Logic
Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences.
One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds.
This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced.
The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.TyössÀ tutkitaan havaintoja koskevien vÀitelauseiden totuutta tilanteissa, joissa havaintojen mÀÀrÀllÀ ei ainakaan tiedetysti ole ylÀrajaa.
Filosofian ja matematiikan alaan kuuluvassa konstruktiivisessa semantiikassa eli merkitysteoriassa lauseiden merkitys mÀÀrĂ€ytyy niiden todennettavuusehtojen perusteella. ĂĂ€rettömĂ€n havaintomaailman tapauksessa todennettavuusehto on hankalasti muotoiltavissa, koska tĂ€llaista maailmaa koskevia yleistyksiĂ€ ei yleisessĂ€ tapauksessa voi todentaa.
TÀmÀ on yhteydessÀ myös induktion ongelmaan, joka koskee pÀÀttelyÀ menneisyyden havainnoista tulevaisuuteen. Induktiivinen pÀÀttely ei sÀilytÀ totuutta siinÀ mielessÀ, ettÀ tosista oletuksista tehtÀvÀ johtopÀÀtös ei ole tosi loogisella vÀlttÀmÀttömyydellÀ, vaan korkeintaan todennÀköisesti tosi.
TyössÀ esitetÀÀn Rudolf Carnapin (1891-1970) induktiivisen logiikan sovelluksena, kuinka ÀÀrettömiÀ havaintomaailmoja koskevien lauseiden totuus voidaan muotoilla konstruktiivisten periaatteiden mukaisesti. Kukin ÀÀretön havaintoprosessi on vapaalakinen jono perÀkkÀisiÀ havaintoja, joiden muodostaman kokonaisuuden ominaisuuksia ei voida tietÀÀ prosessin ÀÀrellisissÀ vaiheissa. Voidaan kuitenkin tietÀÀ, vastaako prosessin annettu ÀÀrellinen vaihe jonkin ennalta mÀÀritellyn havaintojonon ÀÀrellistÀ vaihetta. NÀin voidaan mÀÀrittÀÀ lauseen konstruktiivinen todennÀköisyys ÀÀrettömille havaintojonoille: se on niiden ennalta mÀÀrÀttyjen havaintojonojen ÀÀrellisten vaiheiden todennÀköisyyksien raja-arvo, jotka toteuttavat lauseen kussakin ÀÀrellisessÀ vaiheessaan tietystÀ vaiheesta alkaen. TÀmÀn todennÀköisyyskÀsitteen ominaisuuksia tutkitaan suhteessa Carnapin esittÀmÀÀn asymptoottisen todennÀköisyyden kÀsitteeseen.
LisÀksi työssÀ tutkitaan mahdollisuutta mÀÀrittÀÀ todennÀköisyys ÀÀrettömyydessÀ erÀÀnlaisten havaintojonojen joukkojen eli ympÀristöjen avulla. TÀmÀn todetaan olevan ristiriidassa sen kanssa, ettÀ havaintojonoja koskevat lauseet olisivat konstruktiivisesti tosia ÀÀrettömyydessÀ.
Induktiivisessa logiikassa lauseiden todennÀköisyys mÀÀrÀytyy ns. induktiivisen menetelmÀn avulla laskettujen todennÀköisyyksien mukaan. Ongelma on, ettÀ annettuun tilanteeseen parhaiten soveltuvaa induktiivsta menetelmÀÀ ei tiedetÀ. EtenkÀÀn ei tiedetÀ, onko sellainen induktiivinen menetelmÀ kaikkein paras, joka ei anna lainkaan painoarvoa havaitulle evidenssille esimerkiksi siten ettÀ sata havaittua mustaa korppia lisÀisi 101. mustan korpin todennÀköisyyttÀ.
TyössÀ kÀsitellÀÀn myös oikean induktiivisten menetelmÀn valitsemisen ongelmaa ja pÀÀdytÀÀn siihen, ettÀ toisen kertaluvun todennÀköisyydet eivÀt tarjoa tÀhÀn ratkaisua. Sen sijaan induktiivisen menetelmÀn itsensÀ pÀivitys annetun evidenssin nojalla tuottaa tietyin reunaehdoin annettua menetelmÀÀ paremman induktiivisen menetelmÀn.
Toisin kuin Carnapin alkuperÀisessÀ jÀrjestelmÀssÀ, induktiivisen menetelmÀn pÀivitys ja konstruktiivinen semantiikka yhdessÀ mahdollistavat nollasta poikkeavat todennÀköisyydet empiirisille yleistyksille (kuten kaikki korpit ovat mustia )
Nature and Reason: A Study on Natural Law and Environmental Ethics
A study on nature and reason as normative concepts in natural law thought and environmental ethics. The Protestant reformer, Philipp Melanchthon, and the pre-enlightenment thinker, Christian Wolff, are read as representatives of a normative understanding of nature. With regard to reason as the source of normative, the study focuses on the reformer, Martin Luther, and the Enlightenment thinker, Immanuel Kant. The study shows how there is a remarkable parallel to contemporary environmental ethics in the underlying mode of normative thought. This is demonstrated both with respect to nature as norm (Holmes Rolston III, J. Baird Callicott, and Paul W. Taylor) and reason as a source of normativity (Bryan G. Norton, Mark Sagoff, and Robin Attfield). The study is concluded with an attempt to reshape nature and reason as normative concepts
PĂ”hiseadus kui sĂŒsteem
VĂ€itekirja eesmĂ€rk on kinnitada ideed, et pĂ”hiseadus on sĂŒsteem, ja tuua esile sĂŒsteemse lĂ€henemise eelised. Autor leiab, et iga uus kriitiline kĂ€sitlus vĂ”ib heita valgust mĂ”nele pĂ”hiseadusliku sĂŒsteemi vÀÀrtuslikule seosele ja aidata laiendada olemasolevate argumentide ringi. Sissejuhatavas artiklis analĂŒĂŒsib autor kahte pĂ”himĂ”istet â pĂ”hiseaduse ja sĂŒsteemi mĂ”istet. Esimeses peatĂŒkis kaitseb autor pĂ”hiseaduse sĂŒsteemsuse keskseid teoreetilisi aluseid. JĂ€rgnevates peatĂŒkkides nĂ€itab autor, et idee pĂ”hiseadusest kui sĂŒsteemist vĂ”imaldab meil jĂ”uda pĂ”hiseaduse konsistentse ja koherentse dogmaatikani ning leida seelĂ€bi paremaid lahendusi praktilistele pĂ”hiseaduslikele juhtumitele.The aim of the thesis is to confirm the idea that the constitution is a system and to demonstrate the advantages of the systematic approach. The author considers that every new critical approach might bring a new valuable connection of the constitutional system to light and help to broaden the scope of available arguments. In the introductory article the author analyses two fundamental concepts â the concept of constitution and the concept of system. In the first chapter the author will defend central theoretical foundations of the systematicity of the constitution. In the following chapters the author demonstrates that the idea of the constitution being a system enables us to achieve consistent and coherent doctrine of constitutional law and therefore better solutions for practical constitutional cases.https://www.ester.ee/record=b526929
Lost in technology: Towards a critique of repugnant rights
Modern law is founded on an idea of justice that is made felt through rights and entitlements legal subjects enjoy. As such, for law and its idea of justice, rights are inherently good and therefore abundant. On encounter with injustice, it has become commonplace to inquire what laws and rights have been flouted, as if injustice would disappear in encounter with rights that encode justice. But what if no number of laws and rights â even with faultless execution â is up for the task of upholding what we deem just? In this dissertation, I look at the heart of this question, and find the lawâs answer not simply wanting but repugnant.
The research is animated by interaction of three topoi: personhood, technology, and international law. The first part concerns how these concepts are perceived in law and by those working with laws. As part of the unearthing of the conceptual ground rules, a trilemma between effectiveness, responsiveness, and coherence familiar from regulatory research and international law rears its head. I show how setting the priority on effective and responsive solutions has amounted to derogation of justice and diminishment of lawâs foundational entity, a natural person. I explore whether these outcomes could be avoided within liberal international law and answer my own question on the negative. I title this systematic outcome a theory of repugnant rights.
The latter part of the dissertation concerns technology, its regulation, and tendency to produce repugnant outcomes in international law. I focus on bio- and information technologies and their legal coding as tools to dismantle legal protection provided by our quality of being human. I will show how intricate legal norms break and remake us in ways that blur the boundaries between persons and things. Once something falls beyond or below the category of a person, its legal status can be warped, twisted, and turned â all while remaining at armâs length from the person it was once legally part of. Technological intervention to such things allows for effective circumvention of legal shelter provided by human rights, as I show through example of regulation of surrogacy and data storage.
To come to terms with the repugnancy, I seek shelter from anger as a transitory category that would enable us to move across the present impasse with rights. I suggest that at the very least international lawyers ought to be angry at quotidian horrors international law upholds. And through such anger overcome the misery and repugnancy of international law.---
Moderni oikeus pohjaa ajatukseen oikeudenmukaisuudesta, joka ilmenee oikeussubjektien nauttimien ja kĂ€yttĂ€mien oikeuksien vĂ€lityksellĂ€. NĂ€in ymmĂ€rrettynĂ€ oikeuden ja sen omaaman oikeudenmukaisuuden kĂ€sityksen kannalta oikeudet ovat itseisarvoisesti hyviĂ€, mikĂ€ selittÀÀ niiden suuren mÀÀrĂ€n. Kun kohtaamme epĂ€oikeudenmukaisuutta tapaamme kysyĂ€, mitĂ€ lakeja ja oikeuksia on loukattu, ikÀÀn kuin epĂ€oikeudenmukaisuus kaikkoaisi sen kohdatessa oikeuden sisĂ€ltĂ€mĂ€n oikeudenmukaisuuden idean. Mutta entĂ€ jos mikÀÀn mÀÀrĂ€ lakeja ja oikeuksia â edes tĂ€ydellisesti tĂ€ytĂ€ntöönpantuna â ei riitĂ€ puolustamaan oikeudenmukaisena pitĂ€mÀÀmme? VĂ€itöskirjassani kurkistan tĂ€mĂ€n kysymyksen ytimeen ja löydĂ€n vastauksen, joka ei ole ainoastaan riittĂ€mĂ€tön vaan myös vastenmielinen.
VÀitöksessÀni operoin oikeushenkilön, teknologian ja kansainvÀlisen oikeuden rajapinnoilla. VÀitökseni ensimmÀinen osa koskee sitÀ, kuinka oikeuden ja lakien parissa työskentelevÀt mieltÀvÀt nÀmÀ kÀsitteet. NÀiden kÀsitteiden tarkastelun yhteydessÀ havaitsen sÀÀntelytutkimuksesta ja kansainvÀlisestÀ oikeudesta tutun tehokkuuden, responsiivisuuden ja johdonmukaisuuden vÀlisen trilemman. Osoitan, miten tehokkaiden ja responsiivisten ratkaisujen asettaminen etusijalle on merkinnyt lipeÀmistÀ oikeudenmukaisuudesta ja samalla oikeuden keskeisen subjektin, luonnollisen henkilön, merkityksen pienentymistÀ. Tutkin, voitaisiinko tÀmÀ trilemma vÀlttÀÀ liberaalin kansainvÀlisen oikeuden puitteissa, ja vastaan omaan kysymykseeni kielteisesti. NimeÀn tÀmÀn tuloksen vastenmielisten oikeuksien teoriaksi.
VÀitöskirjan jÀlkimmÀinen osa kÀsittelee teknologiaa, sen sÀÀtelyÀ ja sen taipumusta tuottaa vastenmielisiÀ lopputuloksia kansainvÀlisessÀ oikeudessa. Tarkastelen lÀhemmin bio- ja informaatioteknologioita ja niiden oikeudellista sÀÀntelyÀ, sekÀ sitÀ millaisia vÀlineitÀ ne tarjoavat ihmisyyden tarjoaman oikeudellisen suojan purkamiseen. Osoitan kuinka monimutkaiset oikeudelliset normit rikkovat ja muokkaavat meitÀ tavoilla, jotka hÀmÀrtÀvÀt ihmisten ja asioiden vÀlisiÀ rajoja. Kun jokin ei ole enÀÀ henkilö, sen oikeudellista asemaa voidaan vÀÀristÀÀ, vÀÀntÀÀ ja kÀÀntÀÀ. Teknologinen puuttuminen tÀllaisiin esineisiin ja asioihin mahdollistaa ihmisoikeuksien tarjoaman laillisen suojan tehokkaan kiertÀmisen, kuten osoitan sijaissynnytyksen ja datan tallennuksen sÀÀntelyn kautta.
Vastauksena oikeuden vastenmielisyydelle haen suojaa vihasta. Viha tarjoaa sellaisen tilapÀisen kategorian, jonka avulla voimme vÀlttÀÀ havaitsemani oikeuksien umpikujan. Katson, ettÀ kansainvÀlisen oikeuden harjoittajien olisi vÀhintÀÀnkin oltava vihaisia kohdatessaan kansainvÀlisen oikeuden synnyttÀmiÀ ja mahdollistamia jokapÀivÀisiÀ kauhuja. Turvautumalla vihaan, jonka voimme myöhemmin asettaa sivuun, voisimme selÀttÀÀ kansainvÀlisen oikeuden surkeuden ja sen vastenmielisyyden