Kitcher, Ideal Agents, and Fictionalism

To Be is to Be the Object of a Possible Act of Choice

“…Sarah Hoffman [9] observes that, since the ideal agent does not exist, Kitcher's philosophy would be better understood as a form of fictionalism. We think, however, that a fictional aspect, together with the naturalistic one, is already implicit in Kitcher's perspective, since any idealization is fictional in the obvious sense that idealized entities do not exist and idealized actions are not performable by real human beings.…”

What anti-realism in philosophy of mathematics must offer

“…There are anti-realistic approaches that resort to some general concepts that apply to mathematics as a whole, such as nominalistic (or empirical) adequacy, to account for the usefulness of mathematics (Melia 2000;Hoffman 2004). These concepts may be of some interest, but they say nothing about such genuine relationships between the mathematical and the physical, and nothing about scientists' reasons for the applicability of a particular mathematical theory to a particular type of natural phenomena based on such relationships.…”

“…Similarly, some anti-realists appear to be claiming that there is no more explanation for the applicability of a mathematical theory for a type of natural phenomena (e.g., the applicability of Riemann space theory to space-time), and that scientists' explanation for it (i.e., by assuming the literal existence of Riemann spaces and a real isomorphism between Riemann spaces and space-time) is just wrong. For instance, Hoffman (2004) takes her fictionalist view to be a completion of van Fraassen's views. I will not try to contest such claims here, but I would like to point out that anti-realists will certainly be in a better position to meet the realist challenge if antirealists can offer a literally truthful explanation of such genuine relationships between the mathematical and the physical, as well as an explanation of the applicability of mathematics based on such relationships.…”

“…They hold the opposite intuition that mathematical entities are unlike robustly real physical objects, and that scientists seem to treat mathematical entities differently. Therefore, for instance, some anti-realistic philosophers contend that scientific confirmation cannot reach mathematics (Maddy 1997(Maddy , 2005aSober 1993;Leng 2002); some argue that we are entitled to "take back" the assertions on the existence of mathematical entities in the sciences (Melia 2000), or to treat mathematical entities as fictions (Field 1980;Hoffman 2004), or to interpret mathematical assertions non-literally (Yablo 2001(Yablo , 2002Chihara 2005;Hellman 2005). The debate sometimes boils down to the question: Who has the burden of proof (Rosen and Burgess 2005)?…”

“…I am only trying to say that current anti-realistic philosophies have not offered (and some of them have not even tried to offer) the most essential thing that an anti-realistic philosophy of mathematics must offer. For instance, sometimes they simply label the phenomena to be explained by names such as "empirical adequacy" (Hoffman 2004) or "nominalistic adequacy" (Melia 2000), without really offering (or trying to offer) a "realistic" explanation for the phenomena and resolving the genuine puzzles (i.e., explaining why mathematics is empirically or nominalistically adequate if not true). Sometimes, they do try to offer an explanation (e.g., Field 1980), but in those explanations, they commit to something that is equally suspicious from the nominalistic point of view (i.e., infinity and continuity of space-time, etc.).…”