> Is it directly observable whether a belief is "knowledge", such that the efficacy of a method can be known by "empirical observation"?
Yes.
> How would one know?
Just look around you. You have computers, GPS, mRNA vaccines, etc. etc. etc. Those things were not produced by philosophers.
> I think ethics are pretty important,
I agree.
> but aren't about something that's objectively true in the world.
What can I say? You are simply wrong about that. Ethics are instincts produced by evolution. Like all instincts, they exist because they have survival value: genes that build brains with instincts about ethics reproduce better (in certain environmental niches) than genes that don't. Ethics are every bit as amenable to scientific inquiry as any other natural phenomenon.
> we don't validate that e.g. arithmetic works the way we know it does by doing "experiments" and "empirical observations" of operations with large cardinality sets of physical objects
Of course we do, because there are different ways of doing arithmetic. Some of them are better models of the world than others, and so those are the ones that we tend to think of as "the way" of doing arithmetic. But the only thing that makes standard arithmetic special is that it corresponds to the way that (parts of) the world work.
> You are simply wrong about that. Ethics are instincts produced by evolution. Like all instincts, they exist because they have survival value
That sounds like a rather cheap version of evolution (and - not wanting to offend you, but in my view you sound rather too convinced that you have figured it all out for your own good).
The way you map moral values on survival smells like Skinner's cheap way to explain language in terms of behavioral stimulus-response pairs: not an adequate explanation. Beware that for every Skinner, there may a Chomsky around the corner to give his views a run for his money.
I would also clarify: We have instincts about ethics. This does not imply that ethics are instincts, any more than having instincts about geometry implies that geometry is instincts or having instincts about physical quantities implies that measure theory is instincts.
> Just look around you. You have computers, GPS, mRNA vaccines, etc. etc. etc. Those things were not produced by philosophers.
You're clearly not getting this. Yes, you can see the products of scientific progress. That's not the same as seeing the absence of knowledge produced by anyone else. And one would expect that truths revealed about the physical world we live in should of course be the ones that give rise to physical artifacts you can point at.
> Ethics are instincts produced by evolution.
... and yet, our ethical beliefs are not biologically determined, but change as a function of culture, and at least in part through the work of philosophers. Our beliefs about the importance of freedom, equality, fairness (or what those mean) change dramatically over decades, far too quick for genetics to have any contribution to the change.
Re arithmetic, "the integers are closed under addition" is still something one can know without making any observations of the world, even if standard addition were somehow not useful in making predictions about the physical 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.
> 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.
Yes.
> How would one know?
Just look around you. You have computers, GPS, mRNA vaccines, etc. etc. etc. Those things were not produced by philosophers.
> I think ethics are pretty important,
I agree.
> but aren't about something that's objectively true in the world.
What can I say? You are simply wrong about that. Ethics are instincts produced by evolution. Like all instincts, they exist because they have survival value: genes that build brains with instincts about ethics reproduce better (in certain environmental niches) than genes that don't. Ethics are every bit as amenable to scientific inquiry as any other natural phenomenon.
> we don't validate that e.g. arithmetic works the way we know it does by doing "experiments" and "empirical observations" of operations with large cardinality sets of physical objects
Of course we do, because there are different ways of doing arithmetic. Some of them are better models of the world than others, and so those are the ones that we tend to think of as "the way" of doing arithmetic. But the only thing that makes standard arithmetic special is that it corresponds to the way that (parts of) the world work.