Quite simply: positivism is the view that anything that can't be proven either empircally or mathematically is just meaningless, unverifiable conjecture.
I am one: even though I studied philosophy academically, I am basically a positivist.
Why? After studying the history of philosophy, I simply noticed that for any major issue, the debates do not terminate at any point; they therefore do not culminate with one viewpoint being 'mainly right,' 'certain,' 'better,' 'absolutely correct,' etc. The debates just rage on without ever being resolved in any way. My natural conclusion is that philosophy is just conjecture that (at least for the time being) cannot be resolved. I therefore accept positivism.
The exception: positivists did not accept ethics or ethical viewpoints in any way, deeming them to be 'unverifiable.' I do not agree, as there are basic ethical rights, issues, etc. about which almost everyone agrees. Is murder wrong? Is torture wrong? Do most (if not all) of us deserve basic freedoms? There is certainly something odd about someone not agreeing with the majority on any of those issues.
*However,* when you start getting into the more complex issues - Do animals have rights? Is euthanasia right? Is abortion wrong? - we are now once again posing a metaphysical question, and just like other metaphysical questions, the debates rage on - with good arguments for both sides. Therefore, metaphysical questions are just hypothethical and there is no single answer to them.
What is your viewpoint then? Are you a positivist?