Cantor did mathematics. This is about metaphysics. It really has more to do with the concept of "existence" than of "infinity." [Even David Hilbert, who endorsed Cantor, denied the sense of a physically existing infinite.]

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Have you updated your writings on infinity to take Canter into account.

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Do we live in a universe where "moral value" can be restated as a physics problem, if we find the right equations? Or is there something inherently subjective & fuzzy about what makes some conscious experience or state of affairs 'better' than another?

Either possibility would be pretty astonishing. A related question would be: does strong emergence exist, or not?

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Even if so, two things having a common factor doesn't make one a version of the other. And the Conjunction Fallacy isn't a result of "specific vivid images", but rather of weighing descriptions such as "bank teller" vs. "feminist bank teller" by how representative they are, rather than how mathematically likely they are to apply ... people think "the latter sounds like her", but that's not the question being asked. There are various ways to defeat the Conjunction Fallacy by clarifying what question *is* being asked.

But you're certainly right that astonishment is about emotional weight, rather than Bayesian analysis. Consider, for example, scientists finding proof that there are alien civilizations ... that would be astonishing, but not unlikely.

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Emotional weight of specific vivid images skews probability judgement in the conjunction fallacy.

Emotional weight of imagining "astonishing outcomes" skews probability judgement in Robin's post.

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Most of those questions seem astonishing because they carry a ton of hidden assumptions. If you don't acknowledge them, it's easy to give non-astonishing default answers to those questions. Don't get me wrong, these answers aren't necessarily the most likely options. But they're possible, and they're not astonishing.

Is world peace possible? Of course: just eliminate all life.

Effective world governance? Easy in a totalitarian surveillance state.

Will we contact real advanced aliens? No. The universe is too big, light speed is a hard limit and the technological civilization will be gone in a couple of centuries because we rely too much on an temporary abundance of resources.

Will we develop immortality? No. Everything dies eventually, according to the laws of thermodynamics. If you say, postponing death by a century would be sufficient: we already tripled our life expectancy with a combination of technology and culture and apparently that doesn't count as immortality. The amazement of Immortality is conditional on not everyone having it.

Will growth rates keep accelerating, or slow down forever? Neither: all phases of growth will be followed by equal phases of contraction. We can stack phases of growth to prevent contraction, but not indefinitely. The highest possible long-term growth exponent is zero.

Will we learn to effectively share info so that we don’t knowingly disagree, or will we continue forever to irrationally disagree? We'll forever disagree.

Will it eventually be possible to make time machines, or will that be forever impossible? Time machines are actually possible today, with just one small issue: they can only work forwards. That may seem exciting, expect that you literally waste time (and a ton of energy) when using one.

Will we eventually write software that is as smart as humans across the board / Will we become able to upload/emulate human brains on computers? No, we'll kill each other over food, energy or water before that.

Who will win the lottery? Me. I'm the only participant in my own daily drawings, so I'm guaranteed to win.

Do human brains have some special capacity for consciousness? No, all mammals (and possibly insects too) do too. And it's a survival process like making spores (fungi) or producing scents (flowers), not a "special capacity". If we compare complexity, photosynthesis is much more advanced than consciousness since it chlorophyll employs quantum tunneling, neurons do not

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There are no conjunctions in your examples (as opposed to "feminist bank teller", which *is* a conjunction).

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I wouldn't be astonished at either of those. In the first case I would chalk it up to bad judgment and in the second case to a clerical error. What would astonish me would be to learn that he had actually earned either of them. Astonishment isn't so much about low probability as it is about a recognition that one had fundamentally mistaken beliefs.

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"does the universe go back forever in time, or was there a first time?"

Neither. Astonishing, isn't it?

Were it not for the 2nd law of thermodynamics , the universe going back in time forever would not be in the least astonishing, and was in fact the prevailing scientific view until the discovery of the 3 degree background radiation demolished the Steady State theory. "a first time" is simply incoherent ... but a beginning to time itself is not, if one recognizes "time" as a formally defined component of a physical theory (a theory that we know to be incomplete). As Stephen Hawking has speculated and observation agrees with, "space-time is finite in extent, but doesn't have any boundary or edge".

"when we’ve looked inside things, we’ve always found more detail so far."

Um, no, we haven't. Not all economists are so ignorant of basic physics, I hope.

"Is there really a level of detail where we never ever find anything inside that?"

Certainly, which is not astonishing to anyone with the above mentioned basic education.

"The existence of astonishing questions makes it dangerous to rely on the following form of argument: It would be astonishing if X were not true, therefore probably X. Seems like a safe solid argument, but it isn’t. "

You seem to be new at this sort of thing:https://en.wikipedia.org/wi...

And: "Seems like a safe solid argument, but it isn’t."

It doesn't seem that way to me, and not because of "astonishing questions", but rather because astonishment is largely about ignorance and dogma. Many people would be astonished to learn numerous well-established facts.

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Yes, fixed; thanks.

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Questions such as this seem to have often been resolved by revising or discarding unjustified assumptions. Not everyone can put their finger on such assumptions a la an Einstein; but I wonder whether a more systematic, axiomatic approach could help resolve answers to some such questions with a little less inspiration (but more perspiration).

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An astonishing claim is one that, if true, has some sort of surprising hard-to-accept implication. You stare at that implication, and wow, who would have believed that?

Certainly if "astonishing" corresponds to "low probability," showing an astonishing implication is a good argument against a claim.

Where either apparent alternative has highly implausible implications, it constitutes reason to think the alternatives aren't truly exhaustive, that you've failed to imagine all of them. For instance, it's implausible that the universe goes on forever spatially, but it's also implausible that it's bounded. Non-Euclidean geometry and general relativity theory imagined curved space, resolving the antimony.

Perhaps the paradoxes of infinite time have a similar solution. (See "Can Infinite Quantities Exist," section 4, The nonexistence of actually realized infinite sets and the principle of the identity of indistinguishable sets together imply the Gold model of the cosmos. - http://juridicalcoherence.b... )

Astonishment as you define it can have (probably does have) senses beside "improbable" (of which I take "implausible" to be the subjective side). [One important distinction is astonishment ex ante versus astonishment ex post.] Without distinguishing those senses, in rejecting proofs from "astonishment" you throw out the baby with the bath water.

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These all focus on the infinite and the unknown or unknowable. About the only way we could know is by mathematical proof and even then it would be uncertain whether it applied to the real world forever. The other way would be answering it through our own actions which would be more productive than speculating on ill defined questions.

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"The existence of astonishing claims make it dangerous..."

Do you mean "The existence of astonishing QUESTIONS make it dangerous..." here?

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I'll be mildly surprised, but not astonished, if someday you win a Nobel prize in economics. On the other hand, I'll be astonished if you win a Nobel prize in literature! And no, I don't mean that as a snide criticism of your writing... :)

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So is this a version of Conjunction Fallacy? (about the "feminist bank teller"). In this case, are you suggesting that humans confuse distant but massive scale outcomes with low probability outcomes?

"low probability": lottery, Nobel prize."massive scale": universe and time, future ancestors, consciousness.

Another version was the shipwrecked "Essex" whalers in the Pacific that chose a much more distant route to Chile instead of the closer Marquesas Islands because of the vivid stories of Marquesas cannibals. (a mistake in retrospect)

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