Limitations of operational definitions:
The scale of measurement depends upon the operational definition.
And if truth is relative, then there is no singleshared definite aim for any given assertion (see MacFarlane2014: ch. 12 for a discussion). The relativists however, couldrespond that truth is relative to a group (conceptual scheme,framework) and they take speakers to be aiming a truth relative tothe scheme that they and their interlocutors are presumed toshare. The difficulty with this approach is that it seems to makecommunication across frameworks impossible.
4.5 Construct operational definitions of the concepts in the model.
Plato’s argument, as it stands, appears to be damaging onlyif we assume that Protagoras, at least implicitly, is committed to theuniversal or objective truth of relativism. On this view, Plato begsthe question on behalf of an absolutist conception of truth (Burnyeat1976a: 44). Protagoras, the relativists counter, could indeed acceptthat his own doctrine is false for those who acceptabsolutism but continue believing that his doctrine is truefor him. He could also try to persuade others to become the sortof thinker for whom relativism is true without being entangled inself-contradiction. Such an effort at persuasions, however, couldinvolve Protagoras in a performative contradiction as the relativistcannot assume that her arguments are good for persuadingothers. Ordinarily, the very act of defending a philosophical positioncommits us to the dialectical move of attempting to convince ourinterlocutors of the superior value of what we are arguingfor. The relativist cannot make such a commitment and therefore hisattempts to persuade others to accept his position may bepragmatically self-refuting. The relativist can avoid the standardcharge of self-refutation by accepting that relativism cannot beproven true in any non-relative sense—viz., thatrelativism itself as a philosophical position is at best true onlyrelative to a cultural or historical context and therefore could befalse in other frameworks or cultures. But such an admission willundermine the relativist’s attempt to convince others of herposition, for the very act of argumentation, as it is commonlyunderstood, is an attempt to convince those who disagree with us ofthe falsehood of their position. In other words, if Protagoras reallybelieves in relativism why would he bother to argue for it?