Logical positivism is more subtle than it looks.
Consequently, my debates with dualists (e.g., here and here) degenerate into, shall we say, less-than-generous characterizations of materialism and logical positivism. Here are a few misconceptions.
Parody 1: The materialist believes everything is physical.
Incorrect. She claims that only the intelligible parts of the universe are logical and governed by natural laws. The materialist can admit that there might well be unintelligible (inconsistent, random, inexplicable) parts, but she will insist that we cannot know anything about such parts.
Parody 1B: The radical empiricist believes everything is physical or everything is ideal.
If mental sensation and physical sensation are two sides of the same coin, then it does not follow that the coin has two heads or two tails. Saying they are the same kind of thing actually says that mentality and physicality are joined in some other aspect, specifically by their experiential nature, their regularity and their consistency. It says that, like physical phenomena, intelligible mental phenomena are consistent and governed by rules. A priori, it does not declare that the mind is reducible to laws of physics, nor that the mind must be wholly explicable.
Parody 2: The logical positivist says that statements are meaningless unless physically verifiable, e.g., in a lab.
I, too, would laugh at such a claim. However, the actual claim is that thoughts (expressed as propositions) are semantically meaningful when they are models of past or potential experience. Physicality is not a requirement.
A thought that purports to be a mental model must specify what experiences (mental or physical) are implied and denied by the model. If there are no such experiences, then the thought is not a model at all, but just a thought. Such non-model thoughts have either precluded the existence of the modeled thing by their definition (they are confusions), or they were never intended as models in the first place (they are art).
Physical or mental existence (essence, as some would put it) is a correlation between mental and physical patterns of sensation, i.e., it is actual correlation of a mental model with an experience. A unicorn is a meaningful concept because I know what experiences I would interpret as a unicorn. However, I only know that unicorns exist when I correlate my model with implied experiences.
Thus, logical positivism analyzes mental models for consistency. If a mental model is found to preclude correlation with any particular experience, then the mental model is not a model at all.
So, what is meaningful for the logical positivist? When the logical positivist says that a proposition is meaningful, she means only that the proposition is a valid model of mental or physical experience.
This is a far more practical scheme for avoiding category errors than any attempt to place individual words in categories. Words have different meanings in different contexts (language games), so it is important to establish meaningfulness at the model or proposition level.
Parody 3: Logical Positivism cannot accommodate concepts like love or justice.
The meaning of a proposition (a mental model) is contained in its predictions of experience. The meaning of "unicorns exist in Africa" is in its predictions about what experiences will constitute its verification or falsification. The meaning of the Golbach Conjecture is contained in its predictions about prime numbers. Similarly, the meaning of "I love you", while somewhat imprecise, still makes predictions in behaviors and emotional experience.
From here, it is easy to see that the claim that logical positivism is blind to justice or dignity couldn't be further from the truth. I have a mental model of justice and dignity that specify what experiences justify such labels (for me and for most people I know). Logical positivism would only deny the meaning of justice if it could show that there could be no experience that validates the mental model of justice.
Parody 4: Logical Positivism rules out many things accepted in daily life.
Logical positivism excludes only a handful of purported mental models. It only rules out those thoughts which by definition have no experiential test. For example, whether or not we have "free will" has no experiential test whatsoever. Therefore, logical positivism says that it is not a model at all. It's just a thought (and a rather confusing one at that).
Sometimes, mental models are deliberately defined as being untestable through experience. "God is good" is one such model. It is generally claimed that no experience can falsify the proposition. But of what could such a thought possibly be a model? Nothing at all and everything at once. It's like statement "God is everything you experience," which is at best a relabeling of "everything you experience."
My view of logical positivism might be considered unorthodox. I don't aim to create some "unity of science" program, or rule out courses of study that have well-defined experiential tests. I am just a proponent of the Principle of Verifiability in its broadest sense.