***I'm struggling to erect the supports of this question because of lack of knowledge, I hope that it makes sense and is useful and appropriate for this site.
I'm hoping there's a form of logical empiricism that tries to understand epistemology writ large, not just sentences or propositions, which seems to be its main focus. Maybe they'd count that leap as metaphysics which they abhor so I don't know if I can even get past point 1.
I believe to fit the mold of logical empiricism, knowledge must either be "ideas" not based on experience or matters of fact based purely on experience (like Hume, before the focus on propositions and sentence)
My impression is logical empiricism fell partly because the impossibility of conclusively determining truth through experience. Truths that modern science regularly employ (e.g. spacetime is continuous or discrete) don't come about from finite experiential procedures, and aren't just ideas either - there's a fact of the matter
But then comes Chomsky who provides us tremendous innate ideas through inborn language capacity, not born out through experience.
Chomsky and others to support this ‘nativist’ view that what makes language acquisition possible is the fact that much of our linguistic knowledge is unlearned; it is innate or inborn, part of the initial state of the language faculty
acquiring mastery of a language is not a matter of being trained what to say. It's simply false, says Chomsky, that “a careful arrangement of contingencies of reinforcement by the verbal community is a necessary condition of language learning.” (1959:39) First, children learning language do not appear to be being ‘conditioned’ at all!
it is unclear that conditioning could even in principle give rise to a set of dispositions rich enough to generate the full range of a person's linguistic behavior https://plato.stanford.edu/entries/innateness-language/
Call innate language "ideas" and suddenly only small bits of factual experience are required to explain language.
Language to Chomsky is cognitive as opposed to behaviorist. He is also internalist about language, believing in I-language: "it denotes a mental or psychological entity", "your I-language is a state of your mind/brain. Meaning is internal—indeed, on Chomsky’s conception https://plato.stanford.edu/entries/linguistics/
With 5 & 6, only small bits of factual/empirical experience explain a large portion of our minds/brains/knowledge.
One interpretation of the above is tiny bits empirical stimuli triggering a wealth of ideas/mental states/knowledge due to the nature of innate language capacity.
So maybe logical positivist epistemology does not require lengthy impossible procedures. The tradeoff is we are to be trapped by language or at least language makes up most of our knowledge being the much larger portion of the ideas/fact fork. But possibly that does not trap knowledge very much if at all. We "just" have to recast knowledge and mental states as largely linguistic affairs. Linguistic brain states would be the unlockable ideas by relatively minor empirical stimuli. Facts would be which empirical experiences happen and which ideas they unlock.
Answers/responses could be about is there anything blatantly wrong with this? Do any philosophers want to resurrect logical empiricism and would this be a way in? This isn't a thesis I'm trying to get responses on, it's long because its background and context (by a layman) for I think answerable philosophical questions.