Wir schlagen eine praxisorientierte Explikation der philosophischen Position des Mathematischen Pluralismus vor. Dieser Position zufolge existieren mehr als ein legitimes mathematisches System. Wir interpretieren 'legitim' als 'geeignet zur Realisierung wissenschaftlicher Ziele' und wenden die resultierende pluralistische Position auf die Mathematische Ökonomie an. Wir präsentieren ein begriffliches Rahmenwerk, in dem pluralistische Thesen formuliert und evaluiert werden können, stellen ein informelles System der Konstruktiven Mathematik als Alternative zur Klassischen Mathematik vor, und zeigen, dass verschiedene ökonomische Theoreme nicht konstruktiv beweisbar sind. Auf dieser Basis argumentieren wir, dass Pluralismus relativ zu Zielen mit Bezug zu Erklärung und Simplizität in der Ökonomie vorliegt. / We propose a practice-oriented explication of the philosophical position known as mathematical pluralism. According to this position there exist more than one legitimate mathematical system. We interpret 'legitimate' as 'suitable for realizing scientific goals' and apply the resultant pluralist position to mathematical economics. We present a conceptual framework within which pluralist theses can be formulated and evaluated, introduce an informal system of constructive mathematics as an alternative to classical mathematics, and point out that central theorems of economic equilibrium theory are not constructively provable. On this basis, we argue that pluralism obtains with respect to goals related to explanation and simplicity in economics.

This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense.

MARTINS, Francisco Gomes. A lógica das entidades intencionais. 2012. 130f. – Dissertação (Mestrado) – Universidade Federal do Ceará, Programa de Pós-graduação em Filosofia, Fortaleza (CE), 2012. / Submitted by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2013-11-12T12:03:43Z No. of bitstreams: 1 2012-DIS-FGMARTINS.pdf: 986022 bytes, checksum: dc59d2215a6ff9289414db0edc6b00d1 (MD5) / Approved for entry into archive by Márcia Araújo(marcia_m_bezerra@yahoo.com.br) on 2013-11-12T14:25:13Z (GMT) No. of bitstreams: 1 2012-DIS-FGMARTINS.pdf: 986022 bytes, checksum: dc59d2215a6ff9289414db0edc6b00d1 (MD5) / Made available in DSpace on 2013-11-12T14:25:13Z (GMT). No. of bitstreams: 1 2012-DIS-FGMARTINS.pdf: 986022 bytes, checksum: dc59d2215a6ff9289414db0edc6b00d1 (MD5) Previous issue date: 2012 / A feature of the distinction between extensionalism and intensionalism, which has been widely taken as a criterion to separate the two positions, is that within an extensionalist logic, substitution is possible salva veritate (that is, without thereby changing the truth-value of the statement concerned) with respect to identical instances of some basic logical form – and in an intensionalist logic it is not. The different logical forms with respect to which such substitution might take place accounts for some of the variety of different extensionalisms on offer in the current philosophical landscape. So our starting-point is Frege’s puzzle. This question is frequently accepted as one of the foundations of modern semantics. To explain why a true sentence of the form “a = b” can be informative, unlike a sentence of the form “a = a”, Frege introduced an entity standing between an expression and the object denoted (bezeichnet) by the expression. He named this entity Sinn (sense) and explained the informative character of the true “a=b”-shaped sentences by saying that ‘a’ and ‘b’ denote one and the same object but differ in expressing (ausdrücken) distinct senses. The problem, though, is that Frege never defined sense. The conception of senses as procedures that is developed here has much in common with a number of other accounts that represent meanings, also, as structured objects of various kinds, though not necessarily as procedures. In the modern literature, this idea goes back to Rudolph Carnap’s (1947) notion of intensional isomorphism. Church in (1954) constructs an example of expressions that are intensionally isomorphic according to Carnap’s definition (i.e., expressions that share the same structure and whose parts are necessarily equivalent), but which fail to satisfy the principle of substitutability. The problem Church tackled is made possible by Carnap’s principle of tolerance (which itself is plausible). We are free to introduce into a language syntactically simple expressions which denote the same intension in different ways and thus fail to be synonymous. Tichý’s objectualist take on ‘operation-processes’ may be seen in part as linguistic structures transposed into an objectual key; operations, procedures, structures are not fundamentally and inherently syntactic items, but fully-fledged, non-linguistic entities, namely, constructions. / Um grave problema presente quando aplicamos semântica composicional, que atribui simples valores de verdade a frases, é que quando essas seqüências estão presentes em alguns contextos específicos, a substituição de certas expressões com a mesma referência pode cambiar o valor de verdade da frase maior ou então impedir que inferências válidas sejam realizadas. Por exemplo, da afirmação "Pedro acredita que Alexandre o Grande foi aluno de Aristóteles", não se pode inferir corretamente neste contexto de crença que a substituição de "Alexandre o grande" por "o vencedor da batalha de Arbela" seja válida porque eventualmente Pedro pode não saber que "Alexandre o Grande é o vencedor da batalha de Arbela" e por isso a verdade das premissas não garante a verdade da conclusão: "Pedro acredita que o vencedor da batalha de Arbela foi aluno de Aristóteles". A conclusão não se segue pois ela não depende da relação de identidade efetiva entre “Alexandre o Grande” e “O vencedor da Arbela”, e sim depende, de maneira contingente, do conjunto de crenças de Pedro; ou ainda, segundo Frege, depende do sentido que Pedro associa a descrição “Alexandre o Grande”. Em contextos intensionais a verdade da conclusão (após substituição) depende de uma maneira específica da maneira de conceber o nome em questão, por isso a substituição entre nomes cujo referente é o mesmo, mas que diferem em sentido, não funciona em todos os casos. O fato é que Frege nunca estabeleceu critérios de identidade para o sentido (Sinn), apenas reservou-se a declarar simplesmente que o sentido é o "modo de apresentação" da referência. Pretendemos apresentar critérios de identidade para o sentido em geral, e em contextos intensionais, em particular. Os sucessores de Frege, dentre eles o lógico Alonzo Church e o filósofo Rudolf Carnap foram os primeiros a estabelecer que duas expressões têm o mesmo sentido se e somente se são sinonimamente isomorfas e intensionalmente isomorfas, respectivamente. Tais critérios devem ser entendidos à luz dos pressupostos lógicos de Church em sua Lógica do Sentido e da Denotação (LSD) e das idéias de Carnap – muitas delas constituintes do programa filosófico do Positivismo lógico, em seu livro Meaning and Necessity. Mais recentemente, Pavel Tichý estabeleceu de maneira mais exata o que é o sentido e sua identidade através do Procedural isomorphism o qual constitui um dos fundamentos da Lógica Intensional Transparente (TIL).

No description available.

Die Dissertation leistet drei Beiträge zur Forschung: (1) Sie entwickelt ein neuartiges vierstufiges Modell wissenschaftlicher Theorien. Dieses Modell kombiniert logisch-empiristische Ansätze (Carnap, Popper, Frege) mit Konzepten von Metaphern & Narrativen (Wittgenstein, Burke, Morgan), erlaubt so deutlich präzisiere Beschreibungen wissenschaftlicher Theorien bereit und löst/mildert Widersprüche in logisch-empiristischen Modellen. (Realismus vs. Empirismus, analytische vs. synthetische Aussagen, Unterdeterminiertheit/ Holismus, wissenschaftliche Erklärungen, Demarkation) (2) Mit diesem Modell gelingt ein Reihenvergleich sechs biologischer Theorien von Lamarck (1809), über Cuvier (1811), Geoffroy St. Hilaire (1835), Chambers (1844-60), Owen (1848-68), Wallace (1855/8) zu Darwin (1859-1872). Dieser Vergleich offenbart eine interessante Asymmetrie: Vergleicht man Darwin mit je einem Vorgänger, so bestehen zahlreiche wichtige Unterschiede. Vergleicht man ihn mit fünf Vorgängern, verschwinden diese fast völlig: Darwins originärer Beitrag zur Revolution in der Biologie des 19.Jh ist klein und seine Antwort nur eine aus einer kontinuierlichen Serie auf die empirischen Herausforderungen durch Paläontologie & Biogeographie seit Ende des 18. Jh. (3) Eine gestufte Rezeptionsanalyse zeigt, warum wir dennoch von einer Darwinschen Revolution sprechen. Zuerst zeigt eine quantitative Analyse der fast 2.000 biologischen Artikel in Britannien zwischen 1858 und 1876, dass Darwinsche Konzepte zwar wichtige Neuerungen brachten, jedoch nicht singulär herausragen. Verlässt man die Biologie und schaut sich die Rezeption bei anderen Wissenschaftlern und gebildeten Laien an, wechselt das Bild: Je weiter man aus der Biologie heraustritt, desto weniger Ebenen biologischen Wissens kennen die Rezipienten und desto sichtbarer wird Darwins Beitrag. Schließlich findet sich sein Beitrag in den abstraktesten Ebenen des biologischen Wissens: in Narrativ und Weltbild – den Ebenen die Laien rezipieren. / The dissertation makes three contributions to research: (1) It develops a novel 4-level-model of scientific theories which combines logical-empirical ideas (Carnap, Popper, Frege) with concepts of metaphors & narratives (Wittgenstein, Burke, Morgan), providing a new powerful toolbox for the analysis & comparison of scientific theories and overcoming/softening contradictions in logical-empirical models. (realism vs. empiricism, analytic vs. synthetic statements, holism, theory-laden observations, scientific explanations, demarcation) (2) Based on this model, the dissertation compares six biological theories from Lamarck (1809), via Cuvier (1811), Geoffroy St. Hilaire (1835), Chambers (1844-60), Owen (1848-68), Wallace (1855/8) to Darwin (1859-1872) and reveals an interesting asymmetry: Compared to any one of his predecessors, Darwins theory appears very original, however, compared to all five predecessor theories, many of these differences disappear and it remains but a small original contribution by Darwin. Thus, Darwin’s is but one in a continuous series of responses to the challenges posed to biology by paleontology and biogeography since the end of the 18th century. (3) A 3-level reception analysis, finally, demonstrates why we speak of a Darwinian revolution nevertheless. (i) A quantitative analysis of nearly 2.000 biological articles reveals that Darwinian concepts where indeed an important theoretical innovation – but definitely not the most important of the time. (ii) When leaving the circle of biology and moving to scientists from other disciplines or educated laymen, the landscape changes. The further outside the biological community, the shallower the audience’s knowledge – and the more visible Darwin’s original contribution. After all, most of Darwin’s contribution can be found in the narrative and worldview of 19th century biology: the only level of knowledge which laymen receive.