“As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one.”
The stated goal of this “law” is to try to prevent commentators from making this sort of comparison.
First, it must be absolutely noted that the self-anointed status of this saying as a “law” is hubris of the highest order — it is no such thing, at most only a hypothesis or theory. This is really just lowest-level sociological guesswork. But beyond that, the essential characteristic of this viewpoint is that it is nothing but an assertion of political liberalism. No more, no less.
Liberalism tends to disavow political difference, and instead asserts that political disagreements about injustices are merely the product of misunderstanding. In other words, it is ideology at its purest, which is to say that is denies that it is ideology at all. The liberal position is presupposed to be the correct and neutral position — all others are confused applications of other ideologies that distort the “true facts”. This takes us to the position Carl Schmitt described in Politische Theologie. Vier Kapitel zur Lehre von der Souveränität (1922), “The essence of liberalism is negotiation, a cautious half measure, in the hope that the definitive dispute, the decisive bloody battle, can be transformed into a parliamentary debate and permit the decision to be suspended forever in an everlasting discussion.”
The usage of “Godwin’s law”, also called “playing the Hitler card,” as applied to Internet commentary runs from two basic assumptions: (1) that fascistic sentiments are not common in expression on the Internet; and (2) it is at present universally acknowledged that Hitler and Nazism are evil, perhaps some of the supreme evils.
Leo Strauss made a much more humorous comment about reductio ad Hitlerum, a play on the term reductio ad absurdum. Wikipedia has a useful section of a web page (as of December 2015) discussing the limits of the supposed fallacy of comparisons to Hitler and Nazism. Attempts to delineate this spectrum of political views include Theodor Adorno‘s F-Scale and the Right-Wing Authoritarianism (RWA) scale. These scales really speak to point (1), are authoritarian positions common (on the Internet)?
Point (2) runs from the idea that these arguments are about comparisons that associate someone with the worst elements of history, and therefore are attempts to assign guilt by association, or that these rebuttals are simply used at a frequency that much exceeds the actual presence of fascistic sentiments. This is where things get a little trickier. Things like the F-Scale or RWA scale might help here, but this really becomes the domain of reasoned argument. Invoking “Godwin’s Law” or accusing someone of “playing the Hitler card” is meant to silence debate, labeling the argument/comparison as unworthy of response. The problem is that often this is the very thing that the person accused of “playing the Hitler card” has supposedly done! This often begs the question, and implies a pre-judgment as to which ideologies are acceptable — something of a disavowed yet central tenet of liberalism. But more importantly, going back to Schmitt’s famous comment — and glossing past the issue of Schmitt being a Nazi sympathizer — the liberal-normative aspect of “Godwin’s Law” seeks to eliminate arguments/tactics that terminate debates, to keep the “decisive bloody battle” at bay “and permit the decision to be suspended forever in an everlasting discussion.”