Michael Egnor talks with podcaster Lucas Skrobot about how we can know we are not zombies

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July 5, 2020

Mind, Neuroscience

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Mind
Neuroscience}

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Also: Egnor , a neurosurgeon, told Skrobot: “My wife jokes with me that meeting me is always the worst part of a person’s life.”

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If they had the same cardinality then set subtraction should verify and validate that. But it contradicts it.ET_{July 16, 2020
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Mike1962, I'm not sure what you mean. We know {1, 2, 3, ...} and {2, 4, 6, ...} are both countably infinite, therefore they have the same cardinality. Correct?daveS_{July 16, 2020
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daveS, No such thing as an infinite search space. You're leaning on mere symbols.mike1962_{July 16, 2020
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But if we already know the two sets are countably infinite, we know they can be put in one-to-one correspondence with each other, so they have the same cardinality (as post #433 shows).daveS_{July 16, 2020
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My mistake. I misread 542 as being finite sets. All you are doing is repeating the very thing I am disputing. Given that we canNOT count the elements contained in a set of infinite elements and given that infinity is a journey, relativity rules. One set of countably infinite elements relative to some other set of countably infinite elements.ET_{July 16, 2020
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ET, None of the sets I have described are finite. The ellipses indicate that. In case you're referring to the triangular number example, it's defined using the function f(n) = n(n + 1)/2 for all positive integers n.daveS_{July 16, 2020
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Well, daves, with your continued examples involving finite sets I just wanted to make it clear what we were facing. And it was an opening to the point. *sigh*ET_{July 16, 2020
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ET, No one is talking about literally counting elements of an infinite set, so I don't know why you keep saying this:
Mapping (one-to-one correspondence) just proves the two sets are countable. That doesn’t mean they can be counted.
*shrugs*daveS_{July 16, 2020
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Clearly you do not understand the word "match".ET_{July 16, 2020
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ET: They do NOT match. Again, you prove to have difficulty with the language. I can match up their eleents one-to-one and show they have the same cardinality, aleph-0. And now you are saying that mathematicians are dolts. Nice own goal. You're showing that you are the dolt. The liar/denier. You just don't get it.JVL_{July 16, 2020
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Mapping (one-to-one correspondence) just proves the two sets are countable. That doesn’t mean they can be counted. It means they follow a logical, ascending order with a clear starting point. Given that we canNOT count the elements contained in a set of infinite elements and given that infinity is a journey, relativity rules. One set of countably infinite elements relative to some other set of countably infinite elements.ET_{July 16, 2020
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daves, if you wanted to be accurate your sets would have been{1,2,3,4,5,6,7,8,9,10} and {2,4,6,8,10}. Try your one-to-one on reality.ET_{July 16, 2020
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ET,
Earth to daves- Finite sets. You can actually count the number of elements in the set. Try that with infinity, or grow up, really.
Huh? The point is these pairs of sets can be put in one-to-one correspondence, which be definition means they have the same cardinality. Come on---you admit they are all countable, and I explained yesterday why all countably infinite sets have equal cardinality. Give it up.daveS_{July 16, 2020
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JVL:
They are countably infinite and match up one-to-one.
They do NOT match. Again, you prove to have difficulty with the language. And now you are saying that mathematicians are dolts. Nice own goal.ET_{July 16, 2020
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How about these two sets: A = {1, 2, 3, 4, 5, 6 . . . . } P = {-x, x^2/2, -x^3/6, x^4/16, -x^5/120, x^6/720 . . . . }JVL_{July 16, 2020
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How about these two sets: A = {1, 2, 3, 4, 5, 6 . . . .} L = {0, 0.6931, 1.0986, 1.3863, 1.6094, 1.7918 .. . } values of L accurate to 4 decimal places. Can't use set subtraction. IF you figure out the pattern what does that tell you about the 'relative cardinality'?JVL_{July 16, 2020
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ET: What prevents someone from determining the pattern and hence the bijective function of your childish example? Try that with sets A and F then. Or set A and the primes.JVL_{July 16, 2020
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ET: Again- your mapping just proves the two sets are countable. That doesn’t mean they can be counted. It means they follow a logical, ascending order with a clear starting point. They are countably infinite and match up one-to-one. That can only happen if they have the same number of elements. They must have the same cardinality. Given that we canNOT count the elements contained in a set of infinite elements and given that infinity is a journey, relativity rules. One set of countably infinite elements relative to some other set of countably infinite elements. Nope, not true. As for your sets A, B and C, we went over that years ago. You are willfully ignorant. Set addition works, too. You use the proper mathematical tool for the job. Really, JVL? Is that your big play against me? Something that we went over years ago? Really? hahahahahahahah I didn't even say set C in the last few examples! hahahahahahahah Wow, you're really not even trying to pay attention. Too funny. Look, it's clear you are just avoiding dealing with these examples of sets that are all the same size. Your own method can't handle them but you won't admit it. Everyone can see it. And no one is taking you seriously anymore. If they ever did.JVL_{July 16, 2020
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What prevents someone from determining the pattern and hence the bijective function of your childish example? Or is this just you, the wanker, wanting to get personal, again?ET_{July 16, 2020
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Oh, I forgot about a really easy example! set A = {1, 2, 3, 4, 5, 6 . . . .} set F = {1, 2, 6, 24, 120, 720 . . . } You can 'subtract' one set from the other but you can't tell me what the 'relative cardinality of set F is. Can you?JVL_{July 16, 2020
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JVL:
How about: set A = {1, 2, 3, 4, 5 . . . } set I2 = {1, 1/4, 1/9, 1/16, 1/25 . . . } Another easy to show one-to-one correspondence but set subtraction . . . . dead in the water.
JVL's head is the hammer and everything else is a nail.ET_{July 16, 2020
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Again- your mapping just proves the two sets are countable. That doesn't mean they can be counted. It means they follow a logical, ascending order with a clear starting point. Given that we canNOT count the elements contained in a set of infinite elements and given that infinity is a journey, relativity rules. One set of countably infinite elements relative to some other set of countably infinite elements. As for your sets A, B and C, we went over that years ago. You are willfully ignorant. Set addition works, too. You use the proper mathematical tool for the job. Really, JVL? Is that your big play against me? Something that we went over years ago? Really? Priceless...ET_{July 16, 2020
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How about: set A = {1, 2, 3, 4, 5 . . . } set I2 = {1, 1/4, 1/9, 1/16, 1/25 . . . } Another easy to show one-to-one correspondence but set subtraction . . . . dead in the water.JVL_{July 16, 2020
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Oh hey, I just thought of another great example: set A = {1, 2, 3, 4, 5, 6 . . . . } set S = {-1, 4, -9, 16, -25, 36 . . . .} Again, it's painfully easy to find a one-to-one mapping between the sets so theyi have the same cardinality. Which is aleph-0. I can keep coming up with examples that 'set substraction' can't handle if you like.JVL_{July 16, 2020
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I'm just going to state my example again: set A = {1, 2, 3, 4, 5 . . . . } set B = {2, 4, 6, 8, 10 . . . . } set B2 = {-2, -4, -6, -8, -10 . . . . } Clearly sets B and B2 have the same cardinality, the only difference is that the elements of set B2 have a negative sign. So, let's consider the following matching/mapping/linking/whatever: 1 in set A is mapped to -2 in set B2 2 in set A is mapped to -4 in set B2 3 in set A is mapped to -6 in set B2 4 in set A is mapped to -8 in set B2 etc Every element in set A is mapped to/matched with one and only one element in set B2. Every element in set B2 is mapped to/matched with one and only one element in set A. The elements of both sets are in a one-to-one correspondence. No element of either set is left out or unmatched. The only way that could possibly be true is if both sets have the same number of elements. Which means they have the same cordinality. Set A is countably infinite which means it has a cardinality of aleph-0, therefore so does set B2. ET's set subtraction won't work because the sets have no elements in common. But it's clear that you can line the elements up one-to-one. But ET won't deal with this example. If he did he'd have to admit he's been wrong for years and years. And he can't do that. He'll continue to lie and deny. Just watch.JVL_{July 16, 2020
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ET: Why don’t you grow up and learn to think? YOU are NO ONE to issue challenges to me. I don’t even read your trope all the way through. You are nauseating. Ooo, big man ET don't have to take no guff from nobody. If you won't address my example then I'll take it to mean you can't. If you can't deal with my example then you were wrong. A 1 matches a 2- go pound sand. Whatever that means. You're still wrong.JVL_{July 16, 2020
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Why don't you grow up and learn to think? YOU are NO ONE to issue challenges to me. I don't even read your trope all the way through. You are nauseating. A 1 matches a 2- go pound sand.ET_{July 16, 2020
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ET: LoL! JVL proves he doesn’t even grasp the language. I will admit that I am wrong when someone demonstrates A – B = {}. Until then you guys just don’t understand infinity. That’s just a fact. Lie and deny. Why don't you deal with my example of sets A and B2 given above. Or are you too afraid to?JVL_{July 16, 2020
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LoL! JVL proves he doesn't even grasp the language. I will admit that I am wrong when someone demonstrates A - B = {}. Until then you guys just don't understand infinity. That's just a fact. Earth to daves- Finite sets. You can actually count the number of elements in the set. Try that with infinity, or grow up, really.ET_{July 16, 2020
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ET clearly thinks that he can win this argument by a very narrow use of the word match as in: two identical things. Well fine, substitute the word link or couple or connect in my examples. They still work. They still show that sets A and B or sets A and B2 have the same cardinality. ET is just desparately flailing about trying to avoid admitting he's wrong.JVL_{July 16, 2020
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