6

Mark Balaguer is a philosopher who advances the position there is one form of mathematical Platonism, that every consistent mathematical object exists, and one form of anti Platonism, ficitonalism. Also that there is no fact of the matter about which is correct/true.

Platonism is usually identified as realism regarding mathematical objects, although there might be other forms of realism in math. Fictionalism is usually one of many anti-realist positions about mathematical objects.

I’m wondering if we can use much of Balaguer’s argument about that status of mathematical objects to have the same conclusion of realism and anti realism about all kinds of objects. Namely, that there is no fact of the matter toward realism vs anti realism writ large.

I don’t feel like I can give a comprehensive and/or succinct reason why or why not, so I come here for your wisdom.

Improve this question
4
  • 1
    Not directly. Balaguer's argument is an inference to the best explanation rooted in the Benacerraf's dilemma: if mathematical truths are platonic we cannot know them since platonic entities are causally inert; if mathematical truths are not platonic then they lack objects to be truths about. Balaguer's "full-blooded platonism" resolves the problem of access, we do not need causal interaction to know if everything (consistent) platonically exists. But there is no such problem for non-platonic entities.
    – Conifold
    Commented May 3 at 21:13
  • @Conifold if there is a (realist) position that only universals (or tropes?) exist (and they’d have to be abstract), and an anti realist position where we lack objects for there to be truths about (a pessimistic view of science/anti realism in science perhaps) then could we do it directly?
    – J Kusin
    Commented May 4 at 17:05
  • Balaguer's point is, basically, that for objects we can only know without interaction there is no way (for us) to distinguish between platonism and fictionalism. But this is the case for platonic objects not just because they are abstract, but also because they are non-contingent, that is what allows knowledge of them 'sight unseen', 'by reason alone'. Even if one could somehow reduce the concrete world to universals, I do not see how they would account for perception and contingent knowledge on his model. To argue that realism/anti-realism are indistinguishable, one has to address those.
    – Conifold
    Commented May 5 at 1:05
  • @Conifold the contingency of non-mathematical abstract universals does put the kibosh on this idea then, thank you. At least I’m not prepared to take it further
    – J Kusin
    Commented May 5 at 1:42

0

Reset to default

You must log in to answer this question.