This is not so much a coherent theory as a general reaction and move away from
positivism. Postpositivism emerged amongst a group of thinkers in the
philosophy of science, such as Kuhn and Feyerabend, and in analytic philosophy, or the philosophy of language, such as with Quine, Putnam and Rorty. More generally, the term is also applied to alternative approaches such as
hermeneutics. A heterogenous group, all, to differing degrees, criticise the empiricist basis of
positivism. In particular,
positivism of the Vienna School, and to a lesser extent, the 'positivism' of Karl Popper, held several key tenets as part of its orienting methodology and epistemology. Among these, the post-positivists most severly questioned 1) the cumulative growth of scientific knowledge, or the 'cumulative convergence on truth' which justifies belief in a scientific realism (Kuhn and Feyerabend); and 2) a correspondence theory of such knowledge, in that such aggrandizing truths of science
really do pertain to phenomena
as they are in the world (Lakatos, Goodman, Putnam, Rorty, ~Quine) - ie. a justification of knowledge because it grants direct access to the real.
Postprocessual archaeology can certainly, though only partly, be associated with postpositivist philosophy because of its constitution as a reaction against the positivist bias of much processual archaeology. The postpositivist strain in postprocessual archaeology is a reinstatement of the social foundations and responsibilities of archaeological inquiry, a refusal to separate archaeological ‘science’ from discourse, and a suspicion of the value of unrestrained application of quantitative techniques.
References
Feyerabend, P. 1977: Against Method, London.
Kuhn, T.S. 1969: The Structure of Scientific Revolutions, Chicago.
Putnam, H. 1979: Mind, Language, and Reality: philosophical papers, vol.2, Cambridge.
Quine, V.W. 1953: From a Logical Point of View, Cambridge, MA.
