What kind of fallacy attributes cause to chance when the cause is unknown?

Question

What kind of fallacy is it if one attributes a cause to chance when a cause is unknown? e.g., Scientists don't know why X, therefore X must be due to chance.

Take for example the masses of leptons. There's no known law of physics that governs their masses (yes, there's the Koide formula, but that's purely empirical). Some take this as evidence that the relative masses of leptons in our universe are due to chance, and that there are other universes where the roll of the dice had a different outcome, and the masses there are different. This seems premature -- we may someday find a such a law.

Answer 1

The title question is somewhat too vague. Depending on context it may not be a fallacy at all, or it may be a false dilemma, because causality and chance are arguably not the only two possibilities. Some events may be only partially random, such as outcomes of quantum experiments, and in a way where the random and the caused can not be separated in principle. Some consider free will to be both non-causal and non-random, see Is free will a third option aside from chance and necessity? The supposition that everything has a cause/reason to exist is known as the Principle of Sufficient Reason. Although popular in traditional metaphysics it can at best be defended as a methodological maxim rather than a "principle", so affirming it as the latter would in itself be unsound. Used as a maxim it only suggests that we should always try to look for reasons that explain what happens and why. It should be noted that the traditional identification of reasons with causes is also questionable, see What counters are there to Spinoza's argument that acts of free will create infinite regress?

The example with lepton masses in the Standard Model is not as much about a cause, as about a reason, a reason for having these values, as opposed to some others. One hope is that a "theory of everything" will provide such a reason, i.e. derive all these values from a much smaller number of parameters. An alternative (non)explanation is the existence of the multiverse, which would allow some choice of values without any particular reason for it. Sometimes this is combined with the thesis of "fine tuning" of physical constants to give an "anthropic principle" explanation: we find ourselves in a universe with these values because sentient life would not be possible otherwise.

The "anthropic principle" is only explanatory if there is a multiplicity of "universes" and we find ourselves in one of them, otherwise the question shifts to why we should have been so lucky as to get the favorable values. At this point there is no way to know which answer is right, if any. So to pass a judgement would be to foreclose research prematurely, and to take absence of evidence for evidence of absence, a case of ad ignorantiam, appeal to ignorance, see What fallacy dismisses a conclusion because supporters give invalid arguments for it?

Answer 2

As with many philosophy quandaries, you'll need to clearly define the term "chance" (or "randomness") in order to resolve this. I don't see any other way to ultimately define "chance" except for subjectively, i.e. I/we don't see a pattern or haven't identified a cause. (If someone has a candidate definition, please offer it.)

Under such a subjective definition of "chance":

Some take this as evidence that the relative masses of leptons in our universe are due to chance

would be an empty statement, or equivalent to your final point. It would merely say, "We don't know the reason for the relative masses of leptons in our universe." Thus it wouldn't be a fallacy, just a roundabout way of saying, "We don't know."

Now if someone nevertheless claimed that this was a positive statement that solves the matter, your next move is to ask them to define "chance," because clearly it differs from the definition I gave above.