This is an accurate description of what has come to be considered the 'scientific' attitude in modern times and, to the best of my knowledge, owes its genesis to Bertrand Russell, who's epistemology was founded on the tenet of scientific verifiability.
Hmmm, I don't think logical positivism has quite that long of a reach these days, but it is certainly influential. Anyway, Russell had a significant influence upon the logical positivists (so did Wittgenstein, even more than Russell), but the real father of logical positivism was a fellow by the name of Moritz Schlick.
Schlick is interesting for a couple of reasons, actually - one, he was pretty much the founding father of positivism, as I said. Two, he was actually a physicist, who started his career studying under Max Planck, and fell into philosophy later. Three, one of the most common critiques of positivism is that it renders ethics to be meaningless. Schlick happened to be quite interested in ethics and ethical systems, and he spent a great deal of time and effort reconciling ethical systems to a positivist framework - I'll leave it to you to look his work up and judge for yourself how successful he was, but it is well worth the effort regardless of how you come to see it.
Finally, more personally, if you're familiar with the life and work of Dietrich von Hildebrand - and what good Christian isn't? ;) - then you should know that, despite the possible implications of positivism, Schlick was practically von Hildebrand's only friend when they were at Vienna together.
Food for thought ;)
The problem, of course, is that such an arbitrary intellectual fiat has no rational basis itself, beyond satisfying the materialist's desire to cram the entire universe into a one-dimensional scientific model.
I don't know that it's entirely accurate to describe positivists as materialists - there's a difference between asserting that only the verifiable exists and asserting that only the verifiable is meaningful in a logical sense. If we take atheism, the denial that God exists, to be a materialist position, we have to recognize that positivism rejects atheism as a meaningful statement. IOW, in a positivist framework, the statement "God exists" is taken to be meaningless, and therefore any position you take on the issue is also meaningless - theism, atheism, and agnosticism are all equally meaningless in a positivist framework.
If we believe Russell and like-minded followers, we should be obliged to throw out all philosophy prior to around the time of Newton...
A little bit later than that - the positivists weren't particularly enamored of Kant, for example.
It is an intellectual trap that attempts to take the success of empirical science and impose it on all questions whatsoever -- and it leaves humanity all the poorer for the effort.
Not necessarily. Whether you subscribe to the positivist view of verifiability or not, it did lead directly to Popper's ideas on falsifiability, which have greatly enriched humanity, I think ;)