If propositional calculus (simpler than it sounds is a good way of describing causality in the territory, I very much doubt there is a fourth option. If I'm doing logic right:
1.¬A is A's cause(1)∨A is A's cause (1)(By NOT-3)
2.A has a cause→ ¬A is A's cause(1)∨A is A's cause(1)(By THEN-1)
3.A has a cause→ ¬A is A's cause(1)∨A is A's cause(1)→A has a cause ∧¬A is A's cause(1)∨A is A's cause(1)(By AND-3)
4.A has a cause→A has a cause ∧¬A is A's cause(1)∨ A is A's cause(1)(Modus Ponens on 3)
6.¬A has a cause∨A has a cause ∧ A is A's cause(1)∨¬A is A's cause(1)(Modus ponens on 5)
Which, translated back into English, means that something either has a cause apart from itself, is it's own cause*,or has no cause. If you apply "has a cause apart from itself" recursively, you end up with an infinite chain of causes. Otherwise, you have to go with "is it's own cause(1)", which means the causal chain loops back on itself or "has no cause" which means the causal chain ends.
Nothing thus far, to my knowledge, has been found to defy the axioms of PC, and thus, if PC were wrong, it would seem not only unsatisfying but downright crazy. I believe that I could make at least a thousand claims which I believe as strongly as "If the Universe defied the principles of logic, it would seem crazy to me." and be wrong at most once, so I assign at least a 99.9% probability to the claim that "Why is everything" has no satisfying answer if "It spontaneously sprang into being", "Causality is cyclical." and "an infinite chain of causes" are unsatisfying.
(1)Directly or indirectly
If I recall correctly, they actually do. It falls under their incest taboo. So "bad" in any culture could probably be defined by a list of generalised principals which don't necessarily share any characteristics other than being labelled as "bad".
That works a bit better, at least for the art example. A better example of where you'd best "define" a set by memorising all of it's members might be the morality of a particular culture. For instance, some African tribes consider it evil to marry someone whose sibling has the same first name as oneself. Not only is it hard to put into words, in English or Ju|'hoan, a definition of "bad" (or |kàù) which would encompass this, but one couldn't look at a bunch of other things that these tribes consider bad and infer that one shouldn't marry someone who has a sibling who share's one's first name. Better to just know that that's one of the things that is said to |kàù in that culture.
What about words that "can't be defined"? (e.g. "art")
If you can't think of any unifying features of a category, but you still want to use it, you could go about listing members: "Art" Includes (for all known English-speaking humans):
If the effect of knowing what "art" is (although that one's common-usage definition can be articulated in terms of features) is understanding what English-speakers mean when they say it, then a list-based definition is as effective, though not as efficient, as a feature based one. (You can make up for not knowing what criterion someone uses with a bit of Bayesian updating: The probability that Alice will call a Jackson Pollock piece "art" is greater if she called Léger's "Railway Crossing" "art" than if she did not)
It seems as though Pascal's mugging may be vulnerable to the same "professor god" problem as Pascal's wager. With probabilities that low, the difference between P(3^^^^3 people being tortured|you give the mugger $5) and P(3^^^^3 people being tortured| you spend $5 on a sandwich) may not even be calculable. It's also possible that the guy is trying to deprive the sandwich maker of the money he would otherwise spend on the Simulated People Protection Fund. If you're going to say that P(X is true|someone says X is true)>P(X is true|~someone says X is true) in all cases, then that should apply to Pascal's wager as well; P(Any given untestable god is real|there are several churches devoted to it)>P(Any given untestable god is real|it was only ever proposed hypothetically, tongue-in-cheek) and thus P(Pascal's God)>P(professor god). In this respect, I'm not sure how the two problems are different.
Many thanks!
Or one where the differences are small, or trivial. I don't think this is "miraculous" or "implausible". Before the invention of agriculture, about seven to twelve thousand years ago, I'm not sure what pressures there could have been on Europeans to develop higher intelligence than Africans, so in contrast to physical differences, many of which have well-established links to specific climates, intellectual genetic differences would probably be attributable to genetic drift and >~10,000 years of natural selection. To be clear, my position isn't that I have good evidence for this, merely that I don't know and I don't assign this scenario as low a prior probability as you seem to.
Really? I've seen twin studies that purport a genetic explanation for IQ differences between individuals, but never between racial groups. If you've saved a link to a study of the latter type, I'd be really interested to read it.
Not a priori, but there has been at least one study performed on black children adopted by white families, this one, which comes to the conclusion that environment plays a key role. In all honesty, I haven't even read the study, because I can't find the full text online, but if more studies like it are performed and come to similar conclusions, then that could be taken as evidence of a largely environmental explanation.
You're considering just the word "boss". Consider the phrase "real boss". Regardless of the meanings of the constituent words, the phrase itself can often be replaced with "the one with the real power", or "the one who actually makes the decisions." For example, "The king may have nominal power, but he's really only a figurehead, his vizier is the real boss."
Now, we still find something lacking in that the mice don't actually make decisions, the people observing the mice do. However, if the people observing the mice care about doing good research, then decisions about what course of action to take in the future must take into account what happens with the mice. What happens with the mice provides evidence which forces the researchers to update their models, possibly changing the optimal course of action, or fail. The literal meaning "The mice provide evidence, forcing us to update our models, making us, in order to do our job correctly, change our decisions." may be expressed metaphorically as "The mice make decisions on how to do our job correctly" or "The mice are the real boss."
From the context of the article, in which he uses this as an argument for not coming up with certain specific goals before beginning research, this is likely what the author meant.