Logical positivism, also known as logical empiricism, neo-positivism, and empirio-criticism, was a philosophical school originating in the 1920's. Its adherents attempted to rid philosophy of metaphysics by dismissing metaphysical statements as literally meaningless. Logical positivism is perhaps best known today for its defense of the verifiability criterion of meaning.
Most influential in the early development of the movement were a group of German and Austrian intellectuals meeting at the University of Vienna. This group of people became known as the Vienna Circle. Its members included, at one time or another, Moritz Schlick, Rudolf Carnap, Otto Neurath, and Hans Hahn. There was a similarly inclined group of intellectuals meeting in Berlin that comprised such figures as Hans Reichenbach, Carl Gustave Hempel, and David Hilbert.
Verifiability Criterion of Meaning
Logical positivists, in the tradition of Hume, Kant, and several other thinkers, divided propositions into two groups, namely, the analytic and the synthetic. They called "analytic" those propositions belonging to pure logic. They considered such statements to be tautological, and therefore not to say anything significant about the world. That is not to say, however, that the logical positivists considered analytical propositions to be useless; rather, analytic statements were considered to be useful in relating ideas to one another and in understanding the workings of language.
Logical positivists called "synthetic" those propositions that make significant statements about the world. In general, any proposition that is not a tautology would be considered synthetic.
Within synthetic propositions, logical positivists distinguished between those that were meaningful and those that were meaningless. It is in the articulation of this demarcation that the verifiability criterion of meaning makes its appearance. While different logical positivist thinkers formulated the criterion differently, and its precise formulation continues to be problematic, the essential point is that a synthetic proposition is meaningful to a person only if insofar as the person is aware of what (theoretically possible, thought not necessarily practical) observations would verify or falsify the proposition. This was interpreted to mean that the only meaningful sentences were those that could be "translated" into reports of direct observation, with the result that logical positivists believed that anyone uttering sentences that could not be so translated was simply babbling nonsense.
It is important to note here that most logical positivists did not contend that such "babbling" was without any communicative value; rather, it can perhaps less abrasively be described as cognitively meaningless, factually empty, devoid of truth-aptitude. In other words, while sentences that did not meet the criterion did not express truths or falsehoods, they could still be expressive of the emotions of the speaker.
Theology and ethics
Applying the criterion to philosophy, logical positivists labeled as metaphysics any inquiry that depended on meaningless propositions. In particular, they believed that theology and ethics are essentially metaphysical fields of inquiry. To them, ethical statements (such as "Killing is wrong") and theological statements (e.g. "God exists" or "The soul is immortal") could not be verified or falsified by any conceivable observation, so they were neither true nor false, instead being cognitively meaningless.
Logical positivists, then, should not be characterized as denying the existence of God or gods, thought they certainly did not affirm it. They should not even be called agnostic. They considered as equally meaningless all of the characteristic theses of theists, atheists, and agnostics, namely, "There is a god or there are gods", "There are no gods at all", and "There is not enough evidence to determine whether or not there are any gods".
Most logical positivists believed that ethical propositions are expressions of emotion, attempts to evoke certain emotions in others, or attempts to induce certain behavior in others. For example, to many logical positivists, including A. J. Ayer, sentences such as "Killing is wrong" mean roughly the same as "Killing, yuck!", "Boo to killing!", or "Let us all feel bad about the thought of killing". Such a position regarding ethical statements, called emotivism, is not an ethical position, but a meta-ethical one. It is a subspecies of moral non-cognitivism.
Logical positivism today
(1) Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/vienna-circle/
(2) Ayer, Alfred J. Language, Truth, and Logic, 3rd ed. New York, Dover Publications, 1952.