Russell, Frege, Wittgenstein, and others were all members of the Vienna Circle. Their work influenced many philosophers including Carnap, von Wright, Quine, and Davidson. Logical positivists wanted to establish a foundation for scientific knowledge. They thought that philosophy could not tell us what we should think about the world, but it could help us understand our language and the concepts we use to talk about the world. So they worked out a system of logic that would allow science to function. They believed that the best way to approach philosophy is through logic and that every statement must be tested against its own standards. If it passes the test, then it is true.
To speak clearly and objectively about scientific concepts and theories, we need to understand what they mean and whether they hold up to scrutiny. We need to establish what is meaningful and what isn’t. Logical positivism states that all statements should meet certain criteria before they can be considered true. Anything that doesn’t fit those criteria is meaningless.