How did logical empiricism draw on the ideas of David Hume and Ernst Mach?

Logical empiricism, a school of thought developed by the Vienna Circle, drew heavily on the empiricist traditions of David Hume and Ernst Mach to establish a "scientific world view" grounded in experience.12

• Hume’s Influence: Logical empiricists adopted Hume’s fundamental empiricist orientation, which holds that all knowledge concerning the world must derive from immediate experience. They utilized his reductive approach to analyze concepts like causality and the self, viewing them not as necessary connections or substantial entities, but as products of mental habit or constant conjunctions in experience.132
• Mach’s Influence: Mach’s "critical positivism" provided a framework for rejecting speculative metaphysics and theology as meaningless. He argued that all factual knowledge is a conceptual organization of sensory data, leading logical empiricists to adopt a strict verifiability principle. Mach’s critique of absolute space and time, as well as his view of scientific theories as useful instruments for predicting observable phenomena, directly informed the logical empiricist focus on conceptual analysis and the reduction of scientific terms to observational statements.145