Friday, 26 October 2012

Suppes on neuroscience as foundations of mathematics

(I posted this originally at NewAPPS, which is where I usually post my thoughts on philosophical methodology, but on this topic in particular I look forward to the opinions of readers of M-Phi as well.)

Between today and tomorrow, the workshop ‘Groundedness in Semantics and Beyond’ is taking place at MCMP in Munich, co-organized with the the ERC project Plurals, Predicates, and Paradox led by Øystein Linnebo. The workshop’s program seems excellent across the board, but the opening talk is what really caught my attention: Patrick Suppes on ‘A neuroscience perspective on the foundations of mathematics’. The abstract:
I mainly ask and partially answer three questions. First, what is a number? Second, how does the brain process numbers? Third, what are the brain processes by which mathematicians discover new theorems about numbers? Of course, these three questions generalize immediately to mathematical objects and processes of a more general nature. Typical examples are abstract groups, high dimensional spaces or probability structures. But my emphasis is not on these mathematical structures as such, but how we think about them. For the grounding of mathematics, I argue that understanding how we think about mathematics and discover new results is as important as foundations of mathematics in the traditional sense.
I cannot stress enough how fantastic it is that someone like Suppes, who has done so much groundbreaking foundational work in the traditional sense, now turns his attention to this more ‘human’ aspect of mathematics. (And also how amazing it is that he is over 90 years old and rocking!)

To be sure, focus on mathematical practices as an alternative approach to the philosophy of mathematics has been gaining popularity in recent years (see for example P. Mancosu’s Philosophy of Mathematical Practice), but emphasis on the philosophical importance specifically of empirical findings from the psychology and cognitive science of mathematics is still quite rare (exceptions: Marcus Giaquinto, Helen de Cruz, Dirk Schlimm, among others). And yet, work on the cognitive science of numbers such as e.g. S. Dehaene’s seems to lend itself quite easily to philosophical theorizing. The point is not that this approach should supplant more traditional approaches, but rather that a number of philosophical questions cannot be adequately addressed unless we adopt such an integrative methodology (or so I have claimed several times at NewAPPS, here for example).

For those of us who couldn’t be in Munich this morning (myself included), we can now look forward to the video podcast of the talk which is bound to become available at the MCMP iTunes channel in due course. But for now, here is a picture of Suppes in action, courtesy of Olivier Roy.

3 comments:

  1. Any thoughts about how Suppes is thinking of this and

    Hofweber, T. (2005). Number determiners, numbers, and arithmetic. The Philosophical Review, 114(2):179–225

    ?

    ReplyDelete
    Replies
    1. I'll take a look at the paper. I saw Hofweber speaking once many years ago on this, so I don't remember the details.

      Delete
  2. Love to see Dehaene and Suppes making the rounds!

    ReplyDelete