I have in mind the regular use of "real" figures in economics (i.e. those that are "inflation-adjusted," as well as those based on "purchasing power parity" etc.). These concepts are in principle dissolvable -- when citing some "real" figures, economists could address the questions of what exact index was used to adjust the value, what would be the implications of choosing a different index, how much the figures vary under different more or less reasonable definitions of indexes, what political and bureaucratic incentives have influenced the design of the official government indexes, etc., etc. Trouble is, in practice they almost never do, and except for some narrow and specialized work that studies indexes as such, the de facto standard of discourse in economics is to treat the "real" values as having a Platonic reality. (Even people who specifically study price indexes typically speak about "overestimating" or "underestimating" their value, as if there existed some Platonic "true" value out there.)

As an example of nonsense along these lines, you can take almost any paper that discusses how much some "real" variables have changed over a period of several decades (sometimes they'll even talk about centuries). Of course, if you read that something cost a dollar in 1950, you'll want to know how that compares with the 1950 prices of, say, a loaf of bread, an hour of unskilled labor, etc., to get the feel for how much a dollar was worth back then. However, asking what the "real" value of a 1950 dollar is in 2011 dollars, as a unique and well-defined number, is simply meaningless, considering that you can't trade dollars across time, and the world has changed so much, both technologically and socially, that what counts as "living" in the typical "cost of living" in each era is incommensurable. (The same of course goes for comparing very different places in the same era, and even for similar places, what you count as the "typical" cost of living is largely arbitrary, especially considering the increasing prominence of status goods and conspicuous consumption in the modern economy.)

Yet such numbers are regularly cited with three, four, or even more significant digits, without any consideration of how their value depends on arbitrary conventions and how this dependence influences the argument at hand. (And even if such problems are acknowledged, they are usually presented as imprecise knowledge of the Platonic "true" value, not as the fundamental arbitrariness of the whole concept.)