In clear and lively prose that avoids jargon, the author carefully and systematically examines the many kinds of subtly nuanced words or word-pairs of everyday discourse such as 'and'-'but', 'before'-'ere', 'Chinese'-'Chink', and 'sweat'-'perspiration', that have proven resistant to truth-conditional explanations of meaning. / https://dc.etsu.edu/etsu_books/1108/thumbnail.jpg

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This thesis addresses an issue in the philosophy of Mathematics which is little discussed, and indeed little recognised. This issue is the phenomenon of a ‘change of setting’. Changes of setting are events which involve a change in a scientific framework which is fruitful for answering questions which were, under an old framework, intractable. The formulation of the new setting usually involves a conceptual re-orientation to the subject matter. In the natural sciences, such re-orientations are arguably unremarkable, inasmuch as it is possible that within the former setting for one’s thinking one was merely in error, and under the new orientation one is merely getting closer to the truth of the matter. However, when the subject matter is pure mathematics, a problem arises in that mathematical truth is (in appearance) timelessly immutable. The conceptions that had been settled upon previously seem not the sort of thing that could be vitiated. Yet within a change of setting that is just what seems to happen. Changes of setting, in particular in their effects on the truth of individual propositions, pose a problem for how to understand mathematical truth. Thus this thesis aims to give a philosophical analysis of the phenomenon of changes of setting, in the spirit of the investigations performed in Wilson (1992) and Manders (1987) and (1989). It does so in three stages, each of which occupies a chapter of the thesis: 1. An analysis of the relationship between mathematical truth and settingchanges, in terms of how the former must be viewed to allow for the latter. This results in a conception of truth in the mathematical sciences which gives a large role to the notion that a mathematical setting must ‘explain itself’ in terms of the problems it is intended to address. 2. In light of (1), I begin an analysis of the change of setting engendered in mathematical logic by Gottlob Frege. In particular, this chapter will address the question of whether Frege’s innovation constitutes a change of setting, by asking the question of whether he is seeking to answer questions which were present in the frameworks which preceded his innovations. I argue that the answer is yes, in that he is addressing the Kantian question of whether alternative systems of arithmetic are possible. This question arises because it had been shown earlier in the 19th century that Kant’s conclusion, that Euclid’s is the only possible description of space, was incorrect. 3. I conclude with an in-depth look at a specific aspect of the logical system constructed in Frege’s Grundgesetze der Arithmetik. The purpose of this chapter is to find evidence for the conclusions of chapter two in Frege’s technical work (as opposed to the philosophical). This is necessitated by chapter one’s conclusions regarding the epistemic interdependence of formal systems and informal views of those frameworks. The overall goal is to give a contemporary account of the possibility of setting-changes; it will turn out that an epistemic grasp of a mathematical system requires that one understand it within a broader, somewhat historical context.

In order to understand the implications of Frege's Grundlagen der Arithmetik, we must bear in mind that Frege saw logic as an overarching discipline, necessary for all scientific enquiry. This consideration allows us to make sense of his logicism, the idea that arithmetic is embedded in logic, and his platonism, the commitment to the mind-independent nature of arithmetic objects, such as numbers. In 1902, Russell generated a paradox from Basic Law (V), found in the first volume of Grundgesetze, which suggested that Frege's entire logical system was inconsistent. Recent work by Boolos and Wright, have fenced off the damage and shown that the bulk of Frege's work is consistent. I shall argue, however, that their proposed solutions prove unsatisfactory with respect to Frege's view of logic and especially his logicism.

The problem which spurred this thesis has three components. First, there are entities which we may call stuff – alluded to by uncountable nouns; these entities seem to have a duality for behaving like both (i) an object or a discrete middle size substance – which are supposed to be non-repetitive and independent, and as well as (ii) a concept or a universal – which are repetitive but dependent (on some independent substances). Second, a dichotomy persists between the two aspects of the duality: what is non-repeatable cannot be repeatable and, conversely what is repeatable cannot be non-repeatable. Third, there is a background of how we conventionally do logic, and our present trend of doing – or rather, doing away with – metaphysics. The thesis then came up with four chapters. Chapter 1 deals with the question – how can, or how do we deal with stuff predication following the conventional guidelines? – where by stuff predication I mean any predication involving stuff. I also tried there to find out some clues from Frege’s works. Chapter 2 dives into some related issues pertaining to language, grammar and the notion of constitution. Chapter 3 examines critically two types of theories or views (one of them has been recently championed by Michael Dummett and P.F. Strawson; the other by David Armstrong) arguing how repetitive entities differ from the non-repetitive ones. My counter argument is that those arguments are either fallacious or not even complete. Chapter 4 takes an Aristotelian perspective following the lead of E.J. Lowe. The thesis has a pessimistic tone at the end: the conventional method is quite inadequate as it misses some subtleties pertaining to stuff, nor could Lowe’s Aristotle take us too far. Nevertheless, one cannot – I hope – miss some deeper insights glimpsing into this work. Particularly, Chapter 3 opens up some new venues to think about: our thoughts about our own arguments and proofs may need some revamping.

Univ., Habil.-Schr.--Augsburg, 2004.

Thesis (Ph. D.)--University of Chicago, Committee on the History of Culture, March 2000. / Includes bibliographical references. Also available on the Internet.

El Enigma de Frege es considerado como uno de los principales problemas al que se enfrenta el millianismo. Como se sabe, el millianismo sostiene que el significado de un nombre propio es simplemente su referente. Dicho brevemente, el problema consiste en explicar por qué dos oraciones de identidad que contienen nombres propios co-referenciales (por ejemplo, “Mark Twain es Samuel Clemens” y “Mark Twain es Mark Twain”) parecen tener distinto valor informativo, esto es, por qué una de las oraciones parece ser trivial mientras que la otra parece ser informativa. El propósito del presente trabajo es mostrar que el millianismo puede responder de manera plausible al Enigma de Frege haciendo uso de la distinción entre la proposición semánticamente expresada por una oración y la(s) proposición(es) pragmáticamente impartida(s) por el uso o la emisión de una oración. El trabajo consta de tres capítulos. En el primer capítulo planteo el Enigma de Frege, explico cuáles son los principios presupuestos al plantear el problema y expongo qué respuesta le dio Frege al Enigma de Frege. En el segundo capítulo expongo los argumentos anti-descriptivistas de Kripke que pusieron en duda la respuesta que dio Frege al Enigma de Frege. En el tercer capítulo expongo un intento milliano por responder al Enigma de Frege que consiste en distinguir entre la proposición semánticamente expresada por una oración y la(s) proposición(es) pragmáticamente impartida(s) por el uso o la emisión de una oración, y, finalmente, evalúo si haciendo uso de esta distinción el millianismo responde de manera plausible al Enigma de Frege. / Tesis

Esta dissertação tem como objetivo compreender como a distinção entre conceito e objeto opera no sistema fregeano de modo a autorizar ou não alguma concepção de inexpressabilidade como característica fundamental da lógica. O problema de fundo é determinar em que sentido distinções entre categorias lógicas, especificamente a distinção entre conceito e objeto, envolvem algum tipo de inexpressabilidade. A questão é abordada com foco no problema do estatuto da proposição “O conceito cavalo não é um conceito”. Tratamos do problema através da apresentação de duas alternativas que envolvem um esforço de formalização da proposição. A primeira alternativa insere-se numa tradição de comentários que aproxima as considerações de Frege sobre essa proposição a certas ideias do Tractatus de Wittgenstein, atribuindo à proposição o estatuto de contrassenso. A segunda alternativa problematiza, pelo menos em parte, a primeira, ao trazer razões para a consideração da afirmação como uma proposição com sentido. Refletindo sobre as duas alternativas, consideramos que há mais de uma maneira de conceber a ideia de inexpressabilidade da lógica presente nas obras de Frege. / This work aims to understand how the distinction between concept and object works in the fregean system in such a way as to authorize some conception of inexpressibility as a fundamental feature of logic. The background problem is to ascertain how distinctions between logical categories, specifically the distinction between concept and object, involve some kind of inexpressibility. Our approach to the question focuses on the problem of the status of the proposition ‘The concept horse is not a concept’. Two alternatives are shown here that involve an effort of formalization of this proposition. The first alternative is part of a tradition of Frege’s exegesis that approximates Frege’s considerations about this proposition to certain ideas of Wittgenstein's Tractatus, assigning to the proposition the status of nonsense. The second alternative probematizes the first one at least in part by bringing reasons to considerate the statement as a proposition with sense. Reflecting on the two alternatives, we believe that there is more than one way of conceiving the idea of inexpressibility of logic in the works of Frege.

Orientador: Prof. Dr. Renato Rodrigues Kinouchi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Filosofia, 2017. / Figura central no programa logicista de fundamentação da aritmética, Gottlob Frege (1848-1925) elencou uma série de objeções àquilo que, dentro da história da filosofia, veio a ser denominado de "psicologismo", entendendo por este qualquer postura epistemológica que outorga à psicologia a tarefa de fundamentação das ciências, notadamente das ciências da lógica e da matemática. A dissertação abordará as críticas feitas por Frege àquilo que ele denominou de "métodos psicológicos de reflexão" no campo da teoria do significado, notadamente sua crítica à tese psicologista de que os significados são representações mentais (Vorstellungen). Recorrendo sobretudo às obras Fundamentos da aritmética (1884) e à Lógica de 1897, o trabalho analisará tais críticas tendo por enfoque as influências exercidas no pensamento fregeano pela consolidação da psicologia científica e as inter-relações por ele detectadas entre questões postas pela nova ciência da psicologia e certos problemas de epistemologia. Em última instância, buscar-se-á elucidar se a necessidade de Frege em postular a existência de um terceiro reino (drittes Reich) de entidades objetivas não-reais, para explicar a possibilidade do conhecimento objetivo, foi ou não uma necessidade motivada por problemas próprios ao contexto científico de sua época. / As the central figure in the logicist program in the foundations of mathematics, Gottlob Frege (1848-1925) brought forth a series of objections to what, in the history of philosophy, would be called "psychologism". This term denotes any epistemological position that gives to psychology the task of laying the foundations of the sciences, especially the sciences of logic and mathematics. The present dissertation examines the criticisms made by Frege to what he called the "psychological methods of reasoning", in the context of the theory of meaning, particularly his criticism to the psychologist thesis that meanings are mental representations (Vorstellungen). Based especially on the Foundations of arithmetic (1884) and on his Logic of 1897, the monograph analyzes such criticisms, focusing on the influences exerted on Frege¿s thought by the consolidation of scientific psychology, and on the interrelations that he detected between the questions posed by the new science of psychology and certain problems of epistemology. In the end, we will try to clarify whether the need for Frege to postulate the existence of a third realm (drittes Reich) of non-real objective entities, to explain the possibility of objective knowledge, was or not a need motivated by the problems pertaining to the scientific context of his time.