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Comment by Fede_V | Hacker News Reader

Thanks for the interesting post - however, I respectfully disagree with the example you've picked out.

How can you do intelligent philosophy about probability if you don't have a good detailed understanding of what probability is?

To make a concrete example: the best philosophers of logic (Kripke, Ruth Barcan Marcus, Quine, etc) were also superb logicians with an excellent understand of logic itself. Regardless of how you feel about his atheism, Richard Dawkins is in my mind the best philosopher of biology currently alive, and his first two books (Selfish Gene and Extended Phenotypes) are masterworks. Certain concepts in physics are much clearer when formulated in math - and you can only really explain them clearly once you are firmly grounded in the math. Speaking for myself, I've never met someone who I would describe as having a fantastic understand of QM yet skipped the formal mathematical training to deeply understand the equations.

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> How can you do intelligent philosophy about probability if you don't have a good detailed understanding of what probability is?

There is more than one way to answer the question of 'what probability is'; you are advocating for an inductive approach where the general category is arrived at through exposure to particular instances; another approach is to work within a more general framework which expresses different types of probability theories as configurations of more general types. Granted, one must start inductively in order to get the general framework I speak of—but such frameworks are now in place, so it is not necessary for everyone who wants to compare theories of probability to proceed inductively. Then again, if your expertise is philosophy of probability you should do it anyway—but that brings me to the other point I wanted to make, which is: in my original post I was not referring to philosophers of probability, since that would be their expertise; instead I was referring to ancillary knowledge and whether someone acquires foundational or 'philosophical' (i.e. meta) knowledge of these ancillary fields.

As for whether there can be value to knowing about something like QM without knowing the math behind it, consider Feynman's preface to Q.E.D (the edition he wrote for the layman [well, transcription of lectures technically]). In it he describes the six years of training required in order to actually perform the mystical rites of physics, but knowing what the rites are about and what purpose they serve etc. is also valuable, which is why he wrote the book/gave the lectures (sorry, trying to give a rough quick summary, but the analogy he presents in the preface is the best explanation I've seen).

But that's exactly my point. Feynman was only able to give such a clear explanation because he really understood QM inside out.

If you want to describe yourself as someone who can read and appreciate Feynman's books - that's completely fine with me. However, I hope we can agree that reading Feynman's books (the ones for laymen at least) is not enough to call yourself a polymath.

> However, I hope we can agree that reading Feynman's books (the ones for laymen at least) is not enough to call yourself a polymath

Of course not. However, first off, the reason I brought up the specific book of Feynman's wasn't because I believe reading it gives you anything special—I was just referencing an argument that Feynman makes in the preface.

Secondly, I'm addressing what I see as an impossibility in what it appears to me that you're advocating for:

> I've never met someone who I would describe as having a fantastic understand of QM yet skipped the formal mathematical training to deeply understand the equations.

That quote sums up what I'm talking about. Another way of stating it, at the level of generality of the greater question at hand here: "no one who is not an expert in field X understands field X as deeply as someone who is an expert in field X" —since people generally already know that, the more useful question is, "If I'm going to learn some things about field X, even though I'm an expert from field Y and not field X—which things from field X should I focus on?"

I think part of our disagreement here comes from what one pictures the person with knowledge of many fields doing with that knowledge. Are they working professionally as a philosopher and then on the weekends as a physicist? If so, they have to be an expert equally in both. Or, is there something that can be added to their philosophy work by having fairly in depth knowledge of say, physics, linguistics, psychology, history, and literature? If you are going for this second thing, the way you pick up knowledge from the ancillary fields is different from if you're going for the first thing.

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