> That's not the same as seeing the absence of knowledge produced by anyone else.
But that's not what you asked, and it's not what I claimed. I didn't say that philosophy is entirely devoid of value, only that a lot of it is.
> our ethical beliefs are not biologically determined
What difference does that make? A lot of your physical characteristics aren't biologically determined. That doesn't put them beyond the reach of scientific inquiry.
> "the integers are closed under addition" is still something one can know without making any observations of the world
Really? How do you know what the word "integer" means without making any observations of the world? How can you even become aware of the existence of the word "integer", let alone what it is that that word denotes, without making any observations of the world?
> Further, by arguing that the importance of mathematical knowledge is only its relationship to making predictions about physical reality, you are once again begging the question.
Am I? What is it that made you decide to write "the integers are closed under addition" if not some prediction on the effect that writing those words rather than some other words (like, say, "pandas are partial to purple parkas") would have on physical reality?
> But that's not what you asked, and it's not what I claimed. I didn't say that philosophy is entirely devoid of value, only that a lot of it is.
You claimed you can empirically observe "that the most effective method for expanding human knowledge is science", which I think requires you to observe the efficacy of all methods of expanding human knowledge.
Regarding ethics, empirically gathering what people's ethical opinions are is surveying. This is distinct from knowledge about ethical systems. For example, preference utilitarianism sets the stage for social choice theory, in which theorems tell us about the properties and weaknesses of systems for groups of agents to collectively make choices (Arrow's theorem, Harsanyi's theorem etc).
> Really? How do you know what the word "integer" means without making any observations of the world?
I know the English word "integer" through interaction with the world; this does not mean that true properties of addition are "empirical" truths proceeding from science.
> requires you to observe the efficacy of all methods of expanding human knowledge
I should have hedged with "all known methods". It's possible that someone might invent a more effective method (but I believe there is actually good reason to believe that this is not possible, but that's a tangent).
> preference utilitarianism sets the stage for social choice theory, in which theorems tell us about the properties and weaknesses of systems for groups of agents to collectively make choices (Arrow's theorem, Harsanyi's theorem etc).
Sure. So?
Arrow's theorem is a great example. It's a theorem. It's math. It's not what is generally done under the rubric of "philosophy".
> this does not mean that true properties of addition are "empirical" truths proceeding from science
Yes it does. What is the "true" value of (say) 11 + 27? It could be 38, but it could also be 1 (mod 12) or 13 (mod 24) any of which might be the "true" value depending on the application.
But that's not what you asked, and it's not what I claimed. I didn't say that philosophy is entirely devoid of value, only that a lot of it is.
> our ethical beliefs are not biologically determined
What difference does that make? A lot of your physical characteristics aren't biologically determined. That doesn't put them beyond the reach of scientific inquiry.
> "the integers are closed under addition" is still something one can know without making any observations of the world
Really? How do you know what the word "integer" means without making any observations of the world? How can you even become aware of the existence of the word "integer", let alone what it is that that word denotes, without making any observations of the world?
> Further, by arguing that the importance of mathematical knowledge is only its relationship to making predictions about physical reality, you are once again begging the question.
Am I? What is it that made you decide to write "the integers are closed under addition" if not some prediction on the effect that writing those words rather than some other words (like, say, "pandas are partial to purple parkas") would have on physical reality?