I think there's some credit due to logical positivists with the advent of computer science and formal systems like programming languages. — Shawn

I'm hardly an expert on Logical Positivism (LP), but I think I see the connection you are making between their emphasis on pure mathematical Logic in the search for true knowledge. You could say that Shannon's distillation of communication down to True (1) or False (0) statements owes some debt to Logical Positivism. Hence, computer programming is about as close to Pure Logic as humans have come. I don't know if their digital logic led directly to digital computers, but the historical turn toward Yes or No purity in logic probably should include their contribution to clarity in language.

The radical philosophy of LP may have been a reaction to what they saw as irrelevant excursions into metaphysics, based on Intuition rather than Reason. Ironically, their quest for perfection in reasoning met the same fate as Russell's attempt to ground mathematics in the certainty of pure Logic. His Holy Grail was dashed by Godel's proof of inevitable Incompleteness and Heisenberg's principle of Uncertainty. Likewise, Logical Positivism failed in its attempt to mathematicize philosophical reasoning. That may be because modern Philosophy, post-enlightenment, has relinquished the purity of Physics to scientists, and is now primarily concerned with messy Meta-Physics. :smile:

Logical Positivism :
Essentially, logical positivism is empiricism pushed to the extreme, absolutely as far as it can go. It is antimetaphysical, anti-idealist, and convinced that science alone can provide knowledge.
https://www.sciencedirect.com/topics/social-sciences/logical-positivism

Why Metaphysics Needs Logic and Mathematics Doesn't :
https://www.jstor.org/stable/40321072?seq=1

The logical positivists wanted to mathematize knowledge and make math into logic. Traditionalist say they have it backwards. Paul Cowen however in the 60's proved that there IS and is NOT an infinity between countable and uncountable sets. Both his proofs made sense. There is something about this area of knowledge by which we can come up with contrary results. It's probably an area were no proof is possible, as Godel talked about. There are infinite things we can prove and infinite things we cant. Can the infinite unprovable things be known by intuition? Idn. Mathematicians now have to ask "is this even provable" so they prefer to ignore Godel.

Godel's proof, as I saw it explained, is like having a card that says " this is not the answer, turn over" on both sides. It leads to a spurious infinity. Intuitively it makes sense to me that this can happen in mathematics but the logicists and positivists weren't into those kinds of ideas

Totally. It's no mistake nowadays that analytic philosophy has proffered from logical positivism and figures such as Quine and Carnap as well as Schlick and other logical positivists.

I'm not quite sure Quine was a logical positivist or something that came after its advent.