Taking the universe as a QM event most definitely implies there are uncountably many universes. The OP very clearly asked for non-standard instances of the question, and a generalization of the question most certainly applies thereto.

I certainly hope others do not continue to down-vote what they don't grasp, because LW will only be the worse off for it. (Not implying you down-voted, but if you weren't, then the one who did obviously hasn't the wherewithal to state an outright objection.)

Edit: if you don't "follow", at least state in what exactly you don't follow so that I can actually provide something to your explicit satisfaction.

When did I say that color was a near-universal attribute?

Here's what indicated as much:

There really are attributes for colors that are near-universal, for humans.

An "attribute for color" is not much different from showing that a name is an attribute for a color. Again, you were making the same mistake by thinking that a name for a color is an absolute. Definitely not the case, which you recognize:

You are right though--for that claim to make sense colors also have to be assumed to be near-universal.

To continue –

However, notice how color blindness and tetrachromacy are considered exceptions to the norm. These exceptions are largely the reason I specified near-universal for humans rather than simply universal for humans.

– I further pointed out that humans do not live in a mono-culture with a universal language that predetermines the arrangement of linguistic space in connection to perceived colors. That is the norm, such that the claim of near-universality does not apply. (And were such a mono-culture present, all it would take is a small deviation to accumulate to undermine it. Think of the Tower of Babel.)

The objection I posited covers all cases, even the exceptions. It's really the mind-projection fallacy, such that one human regards their "normal" experience as the "normal" experience of "normal" humans, more or less.

This is also reminiscent of Descartes' cogito:

X cannot occur without Y. X occurs. Therefore, Y exists.

(X=thought; Y=a thinking thing)

...I don't see how you can talk about "defeat" if you're not talking about justified believing

"Defeat" would solely consist in the recognition of admitting to ~T instead of T. Not a matter of belief per se.

You agree with what I said in the first bullet or not?

No, I don't.

The problem I see here is: it seems like you are assuming that the proof of ~T shows clearly the problem (i.e. the invalid reasoning step) with the proof of T I previously reasoned. If it doesn't, all the information I have is that both T and ~T are derived apparently validly from the axioms F, P1, P2, and P3.

T cannot be derived from [P1, P2, and P3], but ~T can on account of F serving as a corrective that invalidates T. The only assumptions I've made are 1) Ms. Math is not an ivory tower authoritarian and 2) that she wouldn't be so illogical as to assert a circular argument where F would merely be a premiss, instead of being equivalent to the proper (valid) conclusion ~T.

Anyway, I suppose there's no more to be said about this, but you can ask for further clarification if you want.

Funny. I thought of pointing that out as well, but I thought it probably wasn't worth mentioning.

As I've imagined it being said before: "I'm either a genius or I'm not. That's a 50% chance of my being a genius. Just pray luck isn't on my side!" :)

Colors-as-near-universal-attributes is really a false claim. Consider examples of the varieties of color blindness, tetrachromacy, and cultures in which certain colors go by names that other cultures distinguish as being different. Your last paragraph seems to indicate that you still hold to the Mind Projection Fallacy which you had assumed to have overcome by realizing your favorite isn't everyone's favorite. Well, even their "blue" might be your "green". Generally, this goes unnoticed because we tend to acculturate and inhabit more or less similar linguistic spaces.

C1 is a presumption, namely, a belief in the truth of T, which is apparently a theorem of P1, P2, and P3. As a belief, it's validity is not what is at issue here, because we are concerned with the truth of T.

F comes in, but is improperly treated as a premiss to conclude ~T, when it is equivalent to ~T. Again, we should not be concerned with belief, because we are dealing with statements that are either true or false. Either but not both (T or ~T) can be true (which is the definition of a logical tautology).

Hence C2 is another presumption with which we should not concern ourselves. Belief has no influence on the outcome of T or ~T.

For the first bullet: no, it is not possible, in any case, to conclude C2, for not to agree that one made a mistake (i.e., reasoned invalidly to T) is to deny the truth of ~T which was shown by Ms. Math to be true (a valid deduction).

Second bullet: in the case of a theorem, to show the falsity of a conclusion (of a theorem) is to show that it is invalid. To say there is a mistake is a straightforward corollary of the nature of deductive inference that an invalid motion was committed.

Third bullet: I assume that the problem is stated in general terms, for had Ms. Math shown that T is false in explicit terms (contained in F), then the proper form of ~T would be: F -> ~T. Note that it is wrong to frame it the following way: F, P1, P2, and P3 -> ~T. It is wrong because F states ~T. There is no "decision" to be made here! Bayesian reasoning in this instance (if not many others) is a misapplication and obfuscation of the original problem from a poor grasp of the nature of deduction.

(N.B.: However, if the nature of the problem were to consist in merely being told by some authority a contradiction to what one supposes to be true, then there is no logically necessity for us to suddenly switch camps and begin to believe in the contradiction over one's prior conviction. Appeal to Authority is a logical fallacy, and if one supposes Bayesian reasoning is a help there, then there is much for that person to learn of the nature of deduction proper.)

Let me give you an example of what I really mean:

Note statements P, Q, and Z:

(P) Something equals something and something else equals that same something such that both equal each other. (Q) This something equals that. This other something also equals that. (Z) The aforementioned somethings equal each other.

It is clear that Z follows from P and Q, no? In effect, you're forced to accept it, correct? Is there any "belief" involved in this setting? Decidedly not. However, let's suppose we meet up with someone who disagrees and states: "I accept the truths of P and Q but not Z."

Then we'll add the following to help this poor fellow:

(R) If P and Q are true, then Z must be true.

They may respond: "I accept P, Q, and R as true, but not Z."

And so on ad infinitum. What went wrong here? They failed to reason deductively. We might very well be in the same situation with T, where

(P and Q) are equivalent to (P1, P2, and P3) (namely, all of these premisses are true), such that whatever Z is, it must be equivalent to the theorem (which would in this case be ~T, if Ms. Math is doing her job and not merely deigning to inform the peons at the foot of her ivory tower).

P1, P2, and P3 are axiomatic statements. And their particular relationship indicates (the theorem) S, at least to the one who drew the conclusion. If a Ms. Math comes to show the invalidity of T (by F), such that ~T is valid (such that S = ~T), then that immediately shows that the claim of T (~S) was false. There is no need for belief here; ~T (or S) is true, and our fellow can continue in the vain belief that he wasn't defeated, but that would be absolutely illogical; therefore, our fellow must accept the truth of ~T and admit defeat, or else he'll have departed from the sphere of logic completely. Note that if Ms. Math merely says "T is false" (F) such that F is really ~T, then the form [F, P1, P2, and P3] implies ~T is really a circular argument, for the conclusion is already assumed within the premisses. But, as I said, I was being charitable with the puzzles and not assuming that that was being communicated.

Read my latest comments. If you need further clarity, ask me specific questions and I will attempt to accommodate them.

But to give some additional note on the quote you provide, look to reductio ad absurdum as a case where it would be incorrect to aver to the truth of what is really contradictory in nature. If it still isn't clear, ask yourself this: "does it make sense to say something is true when it is actually false?" Anyone who answers this in the affirmative is either being silly or needs to have their head checked (for some fascinating stuff, indeed).