You can call someone's reasoning circular all you want but at the end of the day there's what you've accomplished, and the score is philospher 0 engineer 1.
True, it's basically indisputable that engineers are better at engineering than philosophers are. But that seems orthogonal to the issues raised in the problem of induction.
My thrust was more that people are out doing stuff in the world, and for the most part philosophers don't do anything other than say things about what people are already doing. Engineering was an empirical science long before it was a deductive and analytic one.
Philosophers make arguments for/against claims, I don't see why that doesn't count as doing something. I mean, maybe you're complaining that they're not building rockets or feeding the poor, but philosophers are far from the only ones who don't do these things.
Making arguments for/against claims can be a noble pursuit, and mathematicians have done it to great benefit for humanity. I suspect the sum total of the benefit from philosophers' claims is much lower.
Maybe so, but I don't see why every discipline needs to be evaluated purely on "benefit for humanity" in the sense of scientific or technological progress, if that's what you're implying. There's more to humanity than just scientific/technological progress.
But Popper wasn't saying that empiricism could be justified empirically, was he?
In his own words, in the section on the problem of induction in The Logic of Scientific Discovery:
"My own view is that the various difficulties of inductive logic here
sketched are insurmountable. So also, I fear, are those inherent in the
doctrine, so widely current today, that inductive inference, although
not ‘strictly valid’, can attain some degree of ‘reliability’ or of ‘probability’."
He then goes on to provide the (now contentious) falsification-based view of science after conceding that inductivism can't work.
Because the only reason you have to believe anything at all is that you perceive things. And the things that you perceive probably lead you to believe things like that you are a human being, that you exist in a particular subset of three-dimensional space, that there are other humans that exist in other subsets of that same three-dimensional space, that these other humans move around and do things that can reasonably be described as "saying things" and "writing things", and that the things that these other humans say and write correspond to circumstances in this three-dimensional space that you occupy so that it makes sense, at least in some circumstances, to label these sayings and writings with labels like "true" and "false" to indicate whether the way they correspond with circumstances is a positive or negative correlation, and if you get these labels right it can help you survive and flourish. Likewise, if you get them wrong (and that includes denying what I have just told you) it will greatly diminish your prospects of survival, and evolution will take care of the rest. In short, it isn't circular because if you try to pick a fight with reality, reality will win.
I see where you're coming from, but none of this really means that justifying inductive reasoning through inductive reasoning isn't circular.
Hume himself thinks that inductive reasoning is grounded in "custom or habit", and thinks it's rational to proceed this way---a solution you'd probably agree with.