Front Page Titles (by Subject) Relativism - Literature of Liberty, April/June 1978, vol. 1, No. 2
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Relativism - Leonard P. Liggio, Literature of Liberty, April/June 1978, vol. 1, No. 2 
Literature of Liberty: A Review of Contemporary Liberal Thought was published first by the Cato Institute (1978-1979) and later by the Institute for Humane Studies (1980-1982) under the editorial direction of Leonard P. Liggio.
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“Is Cultural Relativism Self-Refuting?” British Journal of Sociology 27 (March 1977): 75–88.
Relativism, in general, claims that all truth is relative, that is, it completely depends on and varies with time, place, age, person, or environment. One truth could hold for John while, at the same time, its opposite holds for Ken. Man thus becomes the subjective measure of all things. A priori cultural relativism is one variety of relativism and asserts that all evaluations and statements about human behavior must be culturally internal and relative. Cultural relativism, so described, requires denying the very possibility of explanation.
The statement, “All explanation must be understood as internal to or relative to a particular culture,” is not necessarily self-refuting. It need not be meant as a universally valid statement (true for all cultures), but rather as one having validity only within the isolated culture in which it is stated. To render cultural relativism self-contradictory, a statement “X is Y” would have to be accompanied by the further claim: “‘X is Y’ is true.“
Thus, a modest, nondogmatic form of cultural relativism is not self-refuting, but it doesn't really explain too much or advance our understanding. We need another approach. From analyzing a number of concepts of rationality we can demonstrate that any explanation requires a “universal principle of rationality.” To make behavior intelligible two crucial presuppositions are essential: a procedural norm for determining what is to count as intelligible, and a firm belief that sharing procedural norms is a precondition of both meaningful statements and the explanation of behavior.
Herein we see the fatal flaw of cultural relativism. It attempts to make the social world intelligible by using explanations which depend on cultural consensus or personal perceptions. However, this presupposes that there is a criterion for judging what is to count as a “cultural consensus” about the meaning of any act or the validity of any particular perception.
More crucially, in attempting to determine “cultural consensus” or personal perceptions, the investigator is forced to look back to “some previously defined concept of social reality.” Here's the rub! The relativist, by the very logic of his own argument, is precluded from using any external judgment to determine what constitutes a “cultural consensus” or a valid perception.
An unsolvable dilemma confronts the cultural relativist. He “does not even allow for the possibility that one can negotiate meaning with other actors, for what basis is there for negotiation of common conceptions if the very notion is epistemologically suspect?”