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Why is positivism seen as belonging to leftist philosophers? I would have thought that the principle of following the law as it is and not as it ought to be is more right wing than left wing?
In his article The Radicalism of Legal Positivism Leiter states that positivism is a radical theory of law "unfriendly to the status quo and anyone, judge or citizen, who thinks obedience to the law is paramount".
(By left I mean socialist... I think.)
I think this is a VERY interest question that gets to the heart of what logical positivism, and empiricism in general, are really about.
I remember Peter Hacker in his book 'Wittgenstein's Place in 20th Century Philosophy' explaining the Marxist leanings of some (but not all) of the leading positivists. Logical positivism was a epistemic reductive movement with a tendency to elevate the status of science culturally and strongly reject metaphysics/religion. In this respect logical positivism broadly belongs to empiricism. Ever since Hume, empiricism has had a strong connection with atheism, the rejection of religion, and the promotion of science in its place. Logical positivists tended to continue in this tradition. To some positivists, Marxism probably seemed more compatible with their empiricist dogmas than the free market based political systems that most Western democracies had implemented in the early 20th century. There was certainly a strong cultural match between the progressivism towards science inherent in logical positivism and the cultural progressivism of Marxist idealology. The positivist manifesto seems to be influenced by the earlier Communist Manifesto, for example.
I think it is reasonable to say that to this day there persists a general cultural connection between scientific materialism (the successor to positivist scientism), atheism, and Marxist/socialist ideologies. But this is my own humble opinion which needs further argument.
I am not convinced that positivism is routinely asociated to a leftist ideology. Postmodernism is usually adopted by the cultivated left, and it is well known for its attacks towards logical positivism.
The term "legal positivism" in the Leiter article that you mention does include the word "positivism", but its semantics do not necessarily match those of logical positivism. Sometimes Leiter even uses "positivism" alone, omitting "legal", but he obviously refers to legal positivism. SEP contains a description of legal positivism and how it relates to logical positivism, and states that:
Legal positivism is here sometimes associated with the homonymic but independent doctrines of logical positivism or sociological positivism.
So I wouldn't think that positivism, as in logical positivism, is linked necessarily to a leftist ideology.
This isn't really an answer but an extended comment.
I've only come across positivism in epistemology - and there the question of politics isn't explicit. Certainly I can see why positivism is more rightist - as per your argument: Following the letter of the law and not its spirit.
Certainly Marx is paradigmitically on the left, but he famously said that he turned Hegel upside down: That is economics and the law determine spirit. I suspect it was Auguste Comtes formulation of Positivism influenced him.
I don't think that positivism is a position of mostly leftist philosophers. According to this article, the positivism dispute was between the critical rationalists and the Frankfurt school. I don't want to say that the critical rationalists are politically right, but I can say for sure that the Frankfurt school is left:
The term Positivismusstreit itself is controversial, since it was the Frankfurt School proponents who accused the critical rationalists of being positivists—while the latter considered themselves as opponents of positivism. On the political level, it was a dispute between the "leftist" Frankfurt School proponents supporting revolution, and the allegedly "bourgeois" critical rationalists supporting reform as the method to be preferred to change society.
