This thesis defends the Quine-Putnam indispensability argument for mathematical realism and introduces a new indispensability argument for a substantial conception of truth. Chapters 1 and 2 formulate the main components of the Quine-Putnam argument, namely that virtually all scientific laws quantify over mathematical entities and thus logically presuppose the existence thereof. Chapter 2 contains a detailed discussion of the logical structure of some scientific theories that incorporate or apply mathematics. Chapter 3 then reconstructs the central assumptions of Quine's argument, concluding (provocatively) that "science entails platonism". Chapter 4 contains a brief discussion of some major theories of truth, including deflationary views (redundancy, disquotation). Chapter 5 introduces a new argument against such deflationary views, based on certain logical properties of truth theories. Chapter 6 contains a further discussion of mathematical truth. In particular, non-standard conceptions of mathematical truth such as "if-thenism" and "hermeneuticism". Chapter 7 introduces the programmes of reconstrual and reconstruction proposed by recent nominalism. Chapters 8 discusses modal nominalism, concluding that modalism is implausible as an interpretation of mathematics (if taken seriously, it suffers from exactly those epistemological problems allegedly suffered by realism). Chapter 9 discusses Field's deflationism, whose central motivating idea is that mathematics is (pace Quine and Putnam) dispensable in applications. This turns on a conservativeness claim which, as Shapiro pointed out in 1983, must be incorrect (using Godel's Theorems). I conclude in Chapter 10 that nominalistic views of mathematics and deflationist views of truth are both inadequate to the overall explanatory needs of science.

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.

´Scientific revolution´, as a concept, is both ´philosophically general´ and ´historically unique´. Both dual-sense of the term alludes to the occurrence of great changes in science. The former defines the changes in science as a continual process while the latter designate them, particularly, as the ´upheaval´ which took place during the early modern period. This research aims to demonstrate how the historicists´ critique of the justification of the traditional claims of science on the basis of the scientific processes and norms of the 16th and 17th centuries, illustrates the historical/local determinacy of the science claims. It argues that their identification of the contextual and historical character of scientific processes warrants a reconsideration of our notion of the universality of science. It affirms that the universality of science has to be sought in the role of such sources like scientific instruments, practical training and the acquisition of methodological routines / "Revolución científica", como concepto, se refiere a la vez a algo «filosóficamente general» e « históricamente único". Ambos sentidos del término aluden a la ocurrencia de grandes cambios en la ciencia. El primero define los cambios en la ciencia como un proceso continuo, mientras que el último los designa, en particular, como la "transformación", que tuvo lugar durante la Edad Moderna. Esta investigación tiene como objetivo demostrar cómo la crítica de los historicistas a la justificación de las características tradicionales de la ciencia sobre la base de los procesos y normas científicos de los siglos XVI y XVII, ilustra la determinación histórica y local de los atributos de la ciencia. Se argumenta que la identificación del carácter contextual e histórico de los procesos científicos justifica una reconsideración de nuestra noción de la universalidad de la ciencia. Se afirma que la universalidad de la ciencia se ha de buscar en el papel de tales fuentes como instrumentos científicos, la formación práctica y la adquisición de rutinas metodológicas