### Scientific Platonism without Metaphysical Presuppositions talk by Peter Punin

#### by Lev Burov

**Update:** Peter asked to share these presentation notes with those who are interested to ask follow-up questions.

Time: today, Dec 1, at the usual place and time.

Title: Scientific Platonism without Metaphysical Presuppositions

Subtitle: A Way to Go Beyond Dogmatic Materialism

Reference paper available at http://philsci-archive.pitt.edu/11465/

Abstract: Belonging to metaphysics, scientific Platonism nevertheless can be defended without metaphysical presuppositions. Comparing the complexity and intrinsic plausibility of the hypotheses Platonism and its negations respectively require to remain consistent, we realize that the conception of an immaterial truth beyond matter is easier to support than materialism.

My question how does the platonic math reality interface with the human mind? The implications of the question is that that must be a joining and reduction of subject object distinction. Leads to phenomenology /existential analysis as well as cognitive science etc. Thanks for the

presentation.

Carl, thanks! this is a great question; see my comment to Matt below.

In the talk it was emphasized that mathematical entities exist independent of the human mind. Someone else then asked something along the lines of “how do we ‘download’ this mathematical knowledge into our brains”.

I want to consider how Socrates may have answered this based on his concept of ‘knowledge as remembering’ discussed in Plato’s Phaedo. Socrates argues that (paraphrasing to keep this question reasonably short…) when we see two similar things (sticks, rocks…) they remind us of equality, even though no matter how similar two material things are they will ultimately fall short of being truly equal. But if the only things we observe are material things, how can we be ‘reminded’ of equality by them (that is how do we already have knowledge of equality)? Socrates answer is that at one point we knew true equality before we were born but upon doing so, forgot it, and so invokes the notion of a soul that existed and had wisdom before we were born.

It is not a stretch to include mathematics in this. For example every attempt to construct a perfect physical right triangle will fail yet we are reminded of right triangles in countless geometry/physics problems.

This is how it seems Socrates might have answered how we ‘download’ mathematics (we were all great mathematicians before we were born!). At the same time this argument probably will make many modern scientific ‘skeptics’ cringe. So is there any modern day alternative to how we come to have knowledge of mathematics?

Matt, this great question was asked by Carl, see his comment right above yours. Thank you for your stressing it; I highly appreciate your recollection of Phaedo in this respect. I am still waiting to collect all the questions people may want to ask Peter, but did not formulate them yet. I think I will send them to him at the end of the week.

Hi everyone,

Peter has sent to me his updated presentation notes. I’ve updated this page with a link to download them.

Hi Everyone,

Perhaps it would be good for me to clarify the question I had asked earlier. In my question, I supposed the existence of a universe where Euclidean geometry is not useful. The speaker pointed out that Euclidian geometry is a subset of Riemann geometries, which he claims have some existence outside of physical reality.

I would say that there is an even larger set of geometries that obey the basic rules of arithmetic (i.e. 1 + 1 = 2). However, one could imagine a mathematical system in which addition was not a useful operation. Perhaps another operation, f(x,y) = x + y + g(x,y) is more relevant to the laws of nature in another universe. We could let g(2,2) = 1 and g(x,y) ~= 0 for values far away from 2,2.

So, in some sense, we could have a universe in which 2 + 2 = 5. Perhaps there could be other values as well as (2,2) where g(x,y) deviated significantly from zero. Or we could imagine a universe in which counting numbers are not even a relevant quanity. Nimbers (or grundy numbers) are an alternative to counting numbers, and perhaps there could be a universe in which they are the fundamental building blocks of the mathematics that is relevant to physics.

The point is that, if mathematical axioms are themselves neither true nor false, we can still imagine physical systems in which they’re not useful. A hard-nosed philosopher could insist that 2 + 2 =4 is still true in this other universe, their laws of physics just don’t use addition the way ours do. But this just seems to be relabeling the same thing in different language. If you’re going to talk about abstract math as it interfaces with actual science, like physics or biology, you can’t ignore what is applicable to that actual science, and is therefore “true” or not, in a more pragmatic sense.

Thanks, Kevin, for this good and well-formulated question. It’s interesting what Peter will answer.

My question to Peter follows.

Dear Peter, in your consideration I do not see any place given to the mathematical beauty. Does it mean that you see it unrelated to the problem of mathematical ontology? Would you agree that in the Platonic World various mathematical structures/ideas exist independently of their beauty, that their beauty is something totally human? Do you think that the ‘mathematical democracy’ of Tegmark, which Lev and I refuted for the physical multiverse, can be accepted for the Platonic world, instead of the ‘mathematical aristocracy’ of the beautiful systems?

Hi Peter (and Alexey). I am not deeply knowledgeable in your particular topic, but despite I am fearing to look a Lack of all trades, let me ask a question that would help me clarify what you actually have in mind in your paper. You “collide” Platonism and anti-Platonism, not so widespread opposition nowadays. Are not you, in fact, discussing the positivist (or logical empiricist, if you wish) and post-positivist positions, because the former implies anti-Platonism, and the latter – Platonism, but also many other important things in between (for example the Kantian transcendental apperception to “bind” Platonic forms to our consciousness to form theories)? In other words, is not your Platonism-anti-Platonism opposition in fact empiricism-post-positivism one (widely discussed in past decades, with plenty of arguments and ended up by the victory of the latter)? Just to understand.

Let me follow-up on Matthew Andorf comments above. I am assuming the implication here is that mathematical entities exist in some kind of undefined “ether” (if you will). If mathematical entities exist independent of the human mind in some type of ether, wouldn’t this existence require some sort of specification and set of requirements for this media? Substrates for the concept of DNA exist in the neurons of our brains, in the scientific literature, and many other places. If you subtracted our neurons, scientific literature, & other locations, where specifically do the mathematical entities exist? (May be it’s in some undefined space between the multiple universes. :))

If we based our conclusions on the starting point of mathematical entities exist independent of the human mind, how can this starting point be falsified and a better replacement be found? Also, how are the beauties of mathematical entities connected to this undefined ether and to the entities themselves? And what exactly is mathematical beauty

Hi everyone. Thanks for all your great questions. They have been sent over to Peter, and he responded:

Thanks for sending the questions. Since they are good questions, the answers will take a bit of time.

Hi again everyone,

Peter has answered our questions. You can download the answers here, https://fermisocietyofphilosophy.wordpress.com/2017/01/08/peter-punins-answers-to-presentation-questions/