I am convinced that we now find ourselves at an altogether decisive turning point in philosophy. And that we are objectively justified in considering that an end has come to the fruitless conflict of systems.
Bertrand Russell and Gottlob Frege have opened up important stretches in the last decades, but Ludwig Wittgenstein (in his Tractatus-Logico-Philosophicus, 1922) is the first to have pushed forward to the decisive turning point.Moritz Schlick, 1930
Its philosophy of logic and mathematics was what most characteristically distinguished logical empiricism from previous forms of empiricism or positivism. This is the aspect that gave it the name logical empiricism, and gave it the hope of succeeding where the nineteenth-century attempts at a scientific empiricism by such figures as Comte, Mill, and Mach had failed. The inability of these thinkers to supply a plausible account of mathematics had undermined the claim of empiricism to be the philosophical approach most adequate to modern science. It was generally agreed that Mill's empiricist account of arithmetic had not succeeded.