Positive economics, that is, value-free theory, is contrasted with normative economics which is value-laden.
What is the etymology of positive economics?
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Positive doesn't refer to the common sense of optimistic, but to Positivism, a philosophical framework that advocates using empirical data to understand a concept. Positivism subsequently comes from the verb posit, which is to put forth an idea as a matter of fact for the purposes of an argument.
So, it's called positive economics because its based on empirical data as opposed to arguments about morality, and thus is, as you said, value-free.
Jumping in more than a decade later, there is one more aspect to the weird use of 'positive' in economics. Fundamentally, it seems that several key writers in the late 1800s simply did not know that the obviously better word 'descriptive' existed, though it is already attested in English more than 100 years prior. Here's John Neville Keynes–father of the other one–in his Scope and Method of Political Economy (1891):
As the terms are here used, a positive science may be defined as a body of systematized knowledge concerning what is; a normative or regulative science as a body of systematized knowledge relating to criteria of what ought to be...
Which is a very standard rendition of the is/ought – descriptive/prescriptive distinction in philosophy.
In the footnotes for that section, Keynes explicitly calls out that is a weird word choice, but claims to be unable to find a word that works:
The use of the term positive to mark this kind of enquiry is not altogether satisfactory; for the same term is used by Cairnes and others in contrast to hypothetical, which is not the antithesis here intended. It is difficult, however, to find any word that is quite free from ambiguity. Theoretical is in some respects a good term and may sometimes be conveniently used. In certain connexions, however, it is to be avoided, inasmuch as it may be understood to imply an antithesis with actual, as when theory and fact are contrasted; it may also suggest that the enquiries referred to have little or no bearing on practical questions, which is of course far from being the case. Professor Sidgwick in his Methods of Ethics employs the term speculative; but this term, even more than the term theoretical, suggests something very much in the air, something remote from the common events of every-day life. It seems best, therefore, not to use it in the present connexion.
If you dig into it, Henry Sidgwick uses the term 'positive' in Methods of Ethics (1874) in even more confusing ways, because he uses it in a bunch of different senses over the course of the book, including the normal positive/negative contrast.
So 'positive' wasn't being chosen as a way of affirming a linkage to positivism so much as falling out of the indirect influence of positivists calling everything positive for a few decades.
Anyways, the clearer word choice is descriptive, and economics people should stop using 'positive' in an unclear and wildly non-standard way just because some dead guys had a less than ideal command of the English language. You can keep 'normative', if you like, though.