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Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity, or numerosity, or symmetry. Let us start with an example, as Aristotelians always prefer, an example that introduces the essential themes of the Aristotelian view of mathematics. A typical mathematical truth is (...) |
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I argue against theories that attempt to reduce scientific representation to similarity or isomorphism. These reductive theories aim to radically naturalize the notion of representation, since they treat scientist's purposes and intentions as non-essential to representation. I distinguish between the means and the constituents of representation, and I argue that similarity and isomorphism are common but not universal means of representation. I then present four other arguments to show that similarity and isomorphism are not the constituents of scientific representation. I (...) |
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The objective of this paper is twofold. First, I present a framework called historical coherentism (Chang, 2004; Tal, 2016; Van fraassen 2008) and argue that it is the best epistemological framework available to tackle the problem of coordination, an epistemic conundrum that arises with every attempt to provide empirical content to scientific theories, models or statements. Second, I argue that the problem of coordination, which has so far been theorized only in the context of measurement practices (Reichenbach, 1927; Chang, 2001; (...) |
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Axiomatic measurement theories are commonly interpreted as claiming that, in order to quantify an empirical domain, the qualitative structure of data about that domain must be mapped to a numerical structure. Such mapping is supposed to be established independently, i.e., without presupposing that the domain can be quantified. This interpretation is based on two myths: that it is possible to independently infer the qualitative structure of objects from empirical data, and that the adequacy of numerical representations can only be justified (...) |
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Recent philosophy of measurement has emphasized the existence of both diachronic and synchronic “loops,” or feedback processes, in the epistemic achievements of measurement. A widespread response has been to conclude that measurement outcomes do not convey interest-independent facts about the world, and that only a coherentist epistemology of measurement is viable. In contrast, I argue that a form of measurement realism is consistent with these results. The insight is that antecedent structure in measuring spaces constrains our empirical procedures such that (...) |
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Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...) |
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In the late 1970s and early 1980s a number of philosophers, notably Churchland, Field, Stalnaker, Dennett, and Davidson, began to argue that propositional attitude predicates (such as believes that it’s sunny outside) are a species of measure predicate, analogous in important ways to numerical predicates by which we attribute physical magnitudes (such as mass, length, and temperature). Other philosophers, including myself, have subsequently developed the idea in greater detail. In this paper I sketch the general outlines of measurement‐theoretic accounts of (...) |
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Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we draw some limitations for measurement procedures: procedures that verify if a quantity is measured cannot work in every case. |
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In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics, on the possibility of quantitative psychology, and on the meaning of temperature measurement. Late nineteenth-century scrutinisers of the foundations of mathematics made little of Helmholtz’s essay. Yet it inspired two mathematicians with an eye on physics, and a few philosopher-physicists. The aim of the present paper is to situate Helmholtz’s contribution (...) |
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