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Why did logical positivists want philosophy to develop a logic of science?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Philosophy of science Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

Logical positivists sought to develop a "logic of science" to establish a rigorous foundation for philosophy that mirrored the clarity and success of the natural sciences. Inspired by advancements in formal logic by thinkers like Gottlob Frege and Bertrand Russell, the Vienna Circle aimed to distinguish between the inconclusive, often circular debates of traditional philosophy and the firm, verifiable accomplishments of scientific inquiry.1

By applying the tools of mathematical logic to the scientific method, they intended to:

Eliminate Meaningless Discourse: They used criteria of "cognitive significance" to demonstrate that traditional philosophical questions—particularly those in metaphysics, ethics, and religion—were meaningless because they lacked empirical verifiability.123
Clarify Scientific Inquiry: They believed that an explicit, logical understanding of method would resolve debates, clear away conceptual confusions, and provide a unified framework for all areas of knowledge.13
Formalize Knowledge: They viewed philosophy’s correct task as formulating a logic of the sciences, which would allow fruitful inquiries to proceed free from the "encumbrances" of speculative, non-empirical philosophy.1