Comment by jondeval | Hacker News Reader

Comment by jondeval | Hacker News Reader

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> That's a rather naive view of truth.

I'm a puzzled by the confidence here. I would assume pg is at least minimally familiar with some of the key philosophical themes and schools of thought around this topic.

> For intuitionistic mathematics ... truth is a mental construct of a proof in a language, and only shared by communicating that construct to other minds.

Even assuming you are fully and accurately representing the intuitionist view, you must be aware that there are competing schools of thought with strong pedigrees, like mathematical platonism, that are grounded in a more realist view of mathematical objects.

PG didn't go so far as to stake out that position here in the essay, but his thought experiment leverages a view of mathematical truth that hues closer to this (platonist) camp.

> The question is whether we can communicate our mathematics to non-humans ...

That is an interesting question, but pg did not ask that question in the essay, and its answer doesn't seem relevant to the point he was trying to make.

It's Graham's confidence that I (and I think OP) find puzzling. He doesn't say "According to Platonist ideas...", or "In my opinion...". Just "mathematical truths are true by definition". There's a brashness and lack of nuance there that makes me want to stop reading.

Some of that is a stylistic judgement call on the part of pg. He wants to move quickly to his central idea, not enter into a nuanced discussion of the philosophy of mathematics.

I think pg is educated, at least the broad outline, of the age-old controversies in this topic and I'm grateful as a reader that he spares me the details and assumes some preliminary context.

He’s clearly not, is the thing, unless he has acquired that education in the last year or two.

His style of pop philosophy is useful in startups because it does not require context. It is ungrounded in actual philosophy, and would struggle to find an audience outside of this group.

I appreciate what you're saying; it's only the first paragraph and he wants to nail some initial things down that he sees as straightforward context or examples.

But it is not straightforward to me. Or, in my impression, most philosophers. I'm reluctant to agree that aliens will assign any importance or even understand concepts like geometry or calculus. So to me, it is not preliminary context but it is a critical part of the discussion.

> I would assume pg is at least minimally familiar with some of the key philosophical themes and schools of thought around this topic.

But even a brief foray into discussions by actual philosophers will show that to not be true. What Paul Graham is doing is providing small subcultural insights tailored to an audience with a passing interest in philosophy.

> his thought experiment leverages a view of mathematical truth that hues closer to this (platonist) camp

I think the word in that idiom is 'hews', which means to adhere strictly to a standard, probably from the sense of the word meaning to strike or cut or beat - often used to talk about cutting a tree into shape.

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