In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...) to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism. (shrink)

The debate over whether we should believe that mathematical objects exist quickly leads to the question of how to determine what we should believe. Indispensabilists claim that we should believe in the existence of mathematical objects because of their ineliminable roles in scientific theory. Eleatics argue that only objects with causal properties exist. Mark Colyvan’s recent defenses of Quine’s indispensability argument against some contemporary eleatics attempt to provide reasons to favor the indispensabilist’s criterion. I show that Colyvan’s argument is not (...) decisive against the eleatic and sketch a way to capture the important intuitions behind both views. (shrink)

Formalism shares with nominalism a distaste for _abstracta_. But an honest exposition of the former position risks introducing _abstracta_ as the stuff of syntax. This article describes the dangers, and offers a new escape route from platonism for the formalist. It is explained how the needed role of derivations in mathematical practice can be explained, not by a commitment to the derivations themselves, but by the commitment of the mathematician to a practice which is in accord with a theory of (...) derivations. (shrink)

The Eleatic Principle or causal criterion is a causal test that entities must pass in order to gain admission to some philosophers’ ontology.1 This principle justifies belief in only those entities to which causal power can be attributed, that is, to those entities which can bring about changes in the world. The idea of such a test is rather important in modern ontology, since it is neither without intuitive appeal nor without influential supporters. Its supporters have included David Armstrong (1978, (...) Vol 2, 5), Brian Ellis (1990, 22) and Hartry Field2 (1989, 68) to name but a few. (shrink)

The meaning of scientific propositions is not always expressible in terms of observable phenomena. Such propositions involve generalizations, and also terms that are theoretical constructs. I study here how to assess the meaning of scientific propositions, that is, the specific import of theoretical terms. Empiricists have expressed a concern that scientific propositions, and theoretical terms, should always be, to some degree, related to observable consequences. We can see that the former empiricist criterion of meaning only implies for theoretical terms not (...) to be definable in terms of observable, but that their use put a constraint on the observable consequences of a theory. To that effect, Ramsey's method of formal elimination of theoretical terms can be an interesting tool. It has faced important logical objections, which have mostly been addressed with respect to the problem of the ontological commitment of the second-order quantification they imply. I show here that these criticisms can be overcome, and that there can be a successful Ramsey elimination of theoretical terms with first order sentences, making Ramsey's method a relevant tool to assess the empirical meaning of scientific propositions. (shrink)

In this paper, I examine Azzouni's tracking requirement and its use as a normative constraint on theories about objects which we take as real. I focus on what he calls ‘thick epistemic access’ and argue that there is a logical–conceptual sense in which thick access to the real presupposes thin access to it. Then, I move on to advance an alternative—Sellarsian—way to ontic commitment and show that (a) it is better than Azzouni's, and (b) it can accommodate thick epistemic access (...) as a bonus. Finally, I try to defend the Quinean theoretical virtues against some of Azzouni's objections. Introduction Theoretical irrealism vs holistic realism On the epistemic authority of observation The myth of the levels Quinean virtues Conclusion. (shrink)

According to Jody Azzouni’s “deflationary nominalism,” the singular terms of mathematical language applied or unapplied to science refer to nothing at all. What does exist, Azzouni claims, must satisfy the quaternary condition he calls “thick epistemic access” (TEA). In this paper I argue that TEA surreptitiously reifies some mathematical entities. The mathematical entity that I take TEA to reify is the Fourier harmonic, an infinite-duration monochromatic sinusoid applied throughout engineering and physics. I defend the reality of the harmonic, in Azzouni’s (...) account, not by satisfying all four TEA conditions with respect to it, but by showing that the harmonic renders satisfiable the TEA condition called “grounding,” specifically in Azzouni’s (Talking about nothing: numbers, hallucinations, and fictions. New York: Oxford University Press, 2010) example of a human visually perceiving a vase. The harmonic thereby plays what Azzouni calls an “epistemic role,” and merits inclusion in the deflationary nominalist ontology. Against the “coding” objection of Azzouni and Bueno (Br J Philos Sci 67:781–816, 2016), which would nominalize the harmonic to nonexistent status, I reply that in the context of grounding, the coding objection begs the question. (shrink)

Philosophers such as Plato, Aristotle, Kant, Brentano, Moore, and Chisholm suggest marks of intrinsic value. Contemporary philosophers such as Christine Korsgaard have insightful discussions of intrinsic value. But how do we verify that some specific thing really is intrinsically valuable? I propose a natural way to test for intrinsic value: first, strip the candidate bare of all considerations of good consequences; and, second, see if what remains is still a good thing. I argue that we, as ordinary human beings, have (...) an astonishingly difficult time completing this test for plausible candidates. More precisely, for us as we are, it seems that the conditions for completing the first step of the test militate against the conditions for completing the second step. I conclude, then, that we have a good reason to think that we cannot verify whether or not particular things are intrinsically good. I explore some implications and I consider a number of important objections. (shrink)

Structural realists claim that structure is preserved across instances of radical theory change, and that this preservation provides an argument in favor of realism about structure. In this paper, I use the shift from Newtonian gravity to Einstein’s general relativity as a case study for structural preservation, and I demonstrate that two prominent views of structural preservation fail to provide a solid basis for realism about structure. The case study demonstrates that (i) structural realists must be epistemically precise about the (...) concrete structure that is being preserved, and (ii) they must provide a metaphysical account of how structure is preserved through re-interpretation in light of a new theory. Regarding (i), I describe a means of epistemic access to the unobservable that I call “thick detection” of structure, which isolates the structure that will be preserved. Regarding (ii), I argue that thickly detectable structure is preserved across theory change through a process of extracting the old structure from the new structure, much like what has been done with geometrized versions of Newtonian gravity. With these two responses in hand, the structural realist can adequately account for the preservation of structure and can provide a strong argument in favor of structural realism. (shrink)

This article elaborates the epistemic indispensability argument, which fully embraces the epistemic contribution of mathematics to science, but rejects the contention that such a contribution is a reason for granting reality to mathematicalia. Section 1 introduces the distinction between ontological and epistemic readings of the indispensability argument. Section 2 outlines some of the main flaws of the first premise of the ontological reading. Section 3 advances the epistemic indispensability argument in view of both applied and pure mathematics. And Sect. 4 (...) makes a case for the epistemic approach, which firstly calls into question the appeal to inference to the best explanation in the defense of the indispensability claim; secondly, distinguishes between mathematical and physical posits; and thirdly, argues that even though some may think that inference to the best explanation works in the postulation of physical posits, no similar considerations are available for postulating mathematicalia. (shrink)

Normal 0 21 false false false PT-BR X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} No presente artigo expomos alguns aspectos das concepções gödelianas acerca da percepção. Procuramos mostrar aqui que a comparação realizada por Gödel entre percepção sensível e racional, bem como suas concepções sobre esta última, correspondem a (...) uma análise do conceito de percepção. Em uma primeira seção, expomos a analogia gödeliana entre percepção sensível e racional, salientando que ambas são comparadas tendo em vista seu status de relação de acesso a entes. A partir disto, argumentamos, na segunda seção, que subjazendo à analogia há uma análise do conceito de percepção como o conceito geral ou formal de uma relação de acesso, do qual a percepção sensível e a racional são casos particulares. Tal análise, como defendemos, acaba por ser mais adequada ao uso comum que fazemos deste conceito do que pareceria à primeira vista. (shrink)

The detection of extrasolar planets presents a good case in which to clarify the distinction between observation and inference from evidence. By asking whether these planets have been observed or inferred from evidence, and by using the scientific details to answer the question, we will get a clearer understanding of the epistemic difference between these two forms of information. The issue of scientific realism pivots on this distinction, and the results of this case will help to articulate the epistemically important (...) factors in assessing theoretical claims.Keywords: Planetary systems; Scientific realism; Observation; Scientific method. (shrink)

In his recent 2018 book, Resisting Scientific Realism, K. Brad Wray provides a detailed, full-fledged defense of anti-realism about science. In this paper, I argue against the two main claims that constitute Wray’s positive and novel argument for his position, viz., his suggested Darwinian-selectionist explanation of the success of science and his skepticism about unobservables based on radical theory change. My goal is not wholly negative though. Instead, I aim to identify the type of work that an anti-realist like Wray (...) would need to undertake in order to further substantiate their position, viz., taking a stance on inductive inference and support, and the type of realist and anti-realist positions that seem viable. (shrink)

I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science.

In this articleIconsider what it would take to combine a certain kind of mathematicalPlatonism with serious presentism.Iargue that a Platonist moved to accept the existence of mathematical objects on the basis of an indispensability argument faces a significant challenge if she wishes to accept presentism. This is because, on the one hand, the indispensability argument can be reformulated as a new argument for the existence of past entities and, on the other hand, if one accepts the indispensability argument for mathematical (...) objects then it is hard to resist the analogous argument for the existence of the past. (shrink)