A more interesting line of arguing would be to ask Reductive Materialists how they are lumping all of these material things together to form the idea of a bit. Clearly there is some property of sameness between the different objects, but bit is really this property which they are trying to capture. It's very circular.
@RoboJasonMan I've asked reductive materialists that, and their answer was that it was perfectly possible to express what all of the bits had in common using physicalistic language. After all, its perfectly possible to express, say, what all electrons have in common using physicalistic language, why should we expect not to be able to express what all bits have in common using physicalistic language? This video is my answer to that question.
I don't get your point. All you've shown is that there are uncountably many possible ways to represent a bit materially. There's no contradiction there. Maybe you believe that this contradicts some finiteness assumption of the universe? Obviously, we can't realize all of them at once. However conceptually, we can think of uncountably many ways to physically represent a bit. So what?
@RoboJasonMan What this proof shows is not that there are an uncountably infinite number of ways to represent a bit materially. What this proof shows is that there is literally no such thing as "all the ways" to represent a bit materially. For the same reason that there is no such thing as the universal set--the very concept is self-contradictory.
A set of all true/false bits is just that, ALL true/false bits and you can't just add a new one that you 'thought' of. If you allow for infinity you can prove anything. Unfortunately for your argument, infinity does not exist in this universe and this is easy to prove.
@randyhelzerman I seriously can't remember why I told you to read Wittgenstein and post another video, lol. Anyway, are you assuming that there's a finite list of yes/no bits? If you are, your assumption is wrong. I don't think physicists say there's a finite list of yes/no bits. Furthermore, when Jaegwon Kim tells you to reduce the concept of a yes/no bit to all possible material implementations AND all their combinations (that's implied).
@randyhelzerman What makes you think you created a new thing when you put together a beer can and a yes/no switch? Those two things already existed in the world and no new thing magically appeared in the world when you created the Frankenstein yes/no bit made with a beer can and a yes/no switch. You're not adding anything to the world as it is.
Well you can have "physics uber alles" and get away from eliminative materialism, just so long as your underlying philosophy of science is not materialist. This makes sense as the holographic principle suggests that the world is actually made of information rather than matter.
Just because we can't define or categorize or even approximate all of these laws, doesn't mean they aren't reducible to the material. The only claim the reductive materialist is committed to is that all phenomena are reducible *in principle* to the material. This is a metaphysical claim which is independent of our epistemology (which your argument seems to target).
@AWASHA Hi Awasha, it all depends upon what you mean by "reduce to physics". In this video, I give a very precise definition of what I mean by reduction, and given that reduction, I show that the notion of bit cannot be reduced to physics. If you want to convince me that I'm wrong, you'll have to show me that another definition of "reduction" is better, or find a flaw in the proof.
What does the correspondence of sentences with facts have to do with reductive materialism? The reductive materialist is not committed to the claim that humans know all laws which govern nature nor the claim that humans can even potentially ascertain all laws which govern nature (and I think quantum physics indicates that we can't, in principle, ascertain all laws which govern nature). But the laws which govern nature exist and are what they are totally independent of cognizant observers.
You seem to also only be considering bits in terms of some sort of external existence--let me put it this way, unicorns don't exist but mental representations of unicorns exist. Horses exist and mental representations of horses exist. The mental representations can, in theory, be reduced to physics, and perhaps in our lifetime technology will be invented that can take snapshots of mental imagery. Well anyway, Boolean logic, mathematics, and many other things are unicorns in a sense.
@eppursimuove22 Hmmm......it seems like you actually agree with me that humans and aliens could both, for example, imagine a unicorn--but nevertheless be using two completely different chemical/physical mechanisms to do so. But this implies that whatever it is to imagine a unicorn, it _can't_ just be to have the same kind of chemical/physical reactions which human brains have. Because if it were the aliens (or computers) wouldn't be able to.
"Reduction is saying that is the ONLY way it could be explained. It would be denying, for example, that you could ever build a robot brain out of silicon which could imagine having a date with Marlynn Monroe. " Bullshit. AI researchers are by and large reductionists, at least in principle ie basketball can be reduced to physics but it is impractical for a merely human basketball player to think in those terms.
@eppursimuove22 Think about it this way: water has been REDUCED to h2o,meaning that everywhere there's water there is also h2o. If AI researchers really believed that imagination reduced to human brain chemistry, then they would believe that everywhere there was imagination, there had to be a human brain, just like they believe that everywhere there is water there is h2o. But AI researchers don't believe this; they CAN"T be reductionistic,they just are confused enough to think they are.
Your alien argument is a straw man. If alien chemistry isn't identical to human chemistry then alien imagination isn't identical to human imagination. That's doesn't make it not "really" imagination. Among humans, imaginative abilities are far from identical as is brain chemistry, yet John & Charles both have imagination. John can vividly imagine complex geometric figures and recall memories w/ lifelike accuracy & Charles can only imagine a dim haze. This can be reduced to physical differences
@TheDrunkenCabDriver Suppose there were aliens from another planet, where life had a very different chemestry, and their nervous systems were very different. But these aliens could nevertheless learn English, and describe vividly to you what they image a date with Maralynn Monroe would be like. Would you say they weren't "really" imagining, because to "really" imagine, you have to have the same chemistry and neurological functions that humans have?
@TheDrunkenCabDriver So reduction isn't merely saying that some mental function (say, imagining a date with Maralynn Monroe) can't be implemented by chemical and neurological functions. Reduction is saying that is the ONLY way it could be explained. It would be denying, for example, that you could ever build a robot brain out of silicon which could imagine having a date with Marlynn Monroe.
@Deliratio Suppose I have a set of bits { b1, b2....}. I can define a new bit, b_new, which is true iff b1 AND be AND .... is true. Its false otherwise. Make sense?
@Deliratio There's no assumptions on the number of bit implementations. Since you are studying math to death, I can state the argument in a more clear and consise form: Say B is the set of all possible bit implementations. Now form the set B*, which is the power set of B. Cantor proved that B* has a higher cardinality than B. Now, form a new bit B_new, which is just the AND of all bits in B*. B_new can be one of the previously existing bits. Q.E.D.
@Deliratio wow, you watched every video I put out? Amazing. No, this wasn't private; probably what happened is one of my other videos put you to sleep right before you watched this one :-) Thanks for watching, you made my day.
You make the mistakie that reality is most likely finite. If it was not, you would get logical contradictions. Hence, there are only a finite number of realizations of the bit. Hence, your diagonal argument fails.
hi jbweimar, it works for infinite universes as well. You just need to be able to construct bits which are infinitely large :-) Suppose by way of contradiction that B is the set of all bits. B could be finite or infinite. Let B* be the power set of B, and define a new bit, B_alpha, which is true iff all of the bits in B* are true, and false otherwise. B_alfpha is not an element of B, but it is a bit, thus showing the contradiction.
@randyhelzerman: Even if your arguments works, I fail to see how it destroys reductive materialism. What is exactly your argument? And do you have the reference to Jaegwon Kim's paper where he claims this?
Reductive materialism is the claim that for any real scientific concept b (say the concept of a bit) we can define that concept in physical termsl. Formally, if b(x) is true of all x's which are bits, reductive materialism states that we can find a physical predicate p(x) such that for all x, b(x) is true iff p(x). This proof shows that cannot be done in general, because there is no such p(x) for bits. See Kims book "physicalism or something near enough".
In other words, WHAT makes it different? The answer you give to this question determines whether your argument is analogous to Cantor's Diagonalization technique.
Obviously the word "obj" is different from "objobjobj"; is THIS what you mean by "different"?
What makes the new bit (composed of a beer can and a coin) different from either the beer can or the coin? Is that what you are asking? That's kind of like asking why your fingernail is different from your left earlobe, no?
The anti-diagonal IS DIFFERENT, but it is NECESSARILY DIFFERENT. And it is necessarily different for a reason that is not fully explained by a concept of CONCATENATION or COMPOSITION.
These concepts play a role in Cantor's argument, sure, but they do not fully explain or capture WHY the anti-diagonal is DIFFERENT. Though we should all agree that it IS different.
Saying "the anti-diagonal is different like fingernails are different from earlobes" is just hand-wavy, as I said, bullsh*t.
Hi nerdfiles, I'm not making any arguments (and therefore I'm not waving my hands) I'm just asking questions because I don't think I understand your point. I don't see why I can't make a new bit which is composed of two pre existing bits. You seem to be quite convinced of this fact, but I don't understand why.
I'll just make my point here. Presumably your "binary objects" map to Cantor's real numbers. So you'd have a "infinite set of binary possibilities" placed at each row. That's fine, but this term "concatenation" is being used in a hand-wavy manner. The anti-diagonal is constructed from the diagonal of the reals; it is not a concatenation *of them*. It may be a concatenation of their parts, sure, but you left that out while leaving out the deliberate trick that must be used on the diagonal.
Hi nerdfiles, no, the binary objects don't map to the real numbers (although cantor did invent the diagonal method to prove that there were more real numbers than there were integers). The thing is you can once again apply the diagonal method to the real numbers, and come up with an even bigger infinity--there's no limit to the number of ever-larger sets. (cont)
(cont, to nerdfiles) as far as the concatenation being hand wavy.....well, the new bit is the logical AND of all the previous bits. That's about as precise and exactly specified as you can get. I don't see how its hand-wavy.
Spare the summary of the interpretations one can draw from Cantor's "Proof." Obviously you can "once again" apply the d.method to reals. That's Cantor's Argument. So I don't get why you're stating it as if you've made a discovery or a novel point. Your "binary possibilities" either represent a real number or they don't. For instance, we could represent pi in terms of binary symbols (0, 1), etc. This obviously isn't going on in your argument.
And yes, I realize it's the logical concatenation. Are you assuming that I don't have idea as to the meaning of the terms you use? Lose the tacit ad hominem and condescension. The point I'm making is that the *anti-diagonal* is not generated from a *mere* concatenation of first-order arbitrary numbers. The anti-diagonal is generated from the diagonal which is itself, *perhaps one may say this*, a concatenation of the numbers that fall along the diagonal of the presumed list of the reals. (cont)
But the *anti-diagonal* is [not] just a concatenation. You have to apply a deliberate rule-governed manipulative principle to the sequence of the diagonal to generate the anti-diagonal. And it is the anti-diagonal which cannot appear on the list, on pain of contradiction. In what way is "resultant of concatenation of binary possibilities," even generally, map to the anti-diagonal. The anti-diagonal is not a merely concatenation. It is a concatenation PLUS the manipulation of the diagonal.
hi nerdfile, the "deliberate rule-0governed manipulative principle" I'm using is just logical and. What could be more precise, deliberate, or rule governed than that?
... Do you not understand that I'm saying that is not enough? I've admitted that logical AND plays a role. It generates the diagonal. It gives you:
1101...
But the construction of the anti-diagonal presupposes that one has done the logical AND, for one would need the diagonal to generate the anti-diagonal. Fine. But the anti-diagonal is not just a result of concatenation. You have to manipulate the numbers in the sequence directly. The rule applies to how one manipulates the numbers.
No, I don't understand your objection at all. I don't understand why you say that the logical and gives you 1101... ? The logical and of any number of bits just gives you 1 bit, not a sequence of bits. I don't understand why you say I have to manipulate the numbers directly? And I don't understand which numbers you are talking about; these are bits not numbers. The rule is just take the logical and of all the bits. The result of that is always another bit which isn't on the list.
What? (true && true && false) is logically equivalent to (false && false); that is, they're both logically equivalent to (false). It's pretty obvious that (false) and (true) appear on the list a countably infinite number of times. In list
(true, (true && true), true, false)
true appears three times. If we add another (true) member to the list, we have a bit whose value does appear within the list, it's the ordinal placement which makes it unique. Thus, we have to be talking about [numbers]...
As a criterion for uniqueness of these members. Thus, we have to say that their ordinal position gives us the grounds for saying that they are [new] to the list. "not being on the list" is possible in virtue of the number of members the result has, for it is obvious that in:
(true && true && true && true) = truetruetruetrue
the latter and the former are logically equivalent. Moreover, they're logically, or categorically, indistinguishable. What makes them [different] is that the latter (cont)
(cont) has [looks] different. But this has nothing to do with logical AND.
It's obvious that in:
(true && true && true && true) == true
the latter is no different, in significant and relevant respects, from the the first or the third "true." And obviously it's on the "list": that which falls inside the parentheses.
But you keep talking about infinites. Look, you can only mean some number that corresponds to:
1001010010101...
Your "boolean images" are not themselves "infinities."
nerdfiles, you are confusing the value of the bits with the bits. there are only 2 values (true, false) which a bit can take, but there can be any number of bits.
That's four bits. Obviously IT LOOKS different from (true), but that is IRRELEVANT to LOGICAL AND.
Logical AND gives you a VALUE.
This is logical AND: &&
So in (true && true) in any programming language, you get (true) as value. That is what logical AND MEANS.
If you mean concatenation of symbol strings, then OBVIOUSLY "truetrue" LOOKS different from "true". One has 8 characters, the other 4. But that is IRRELEVANT
So, suppose an enumeration of the reals. At any time, t, you will be able to derive a DIAGONAL.
13823
13743
03933
13923
02323...
The diagonal is 13923, and the number at the fourth row is 13923.
The diagonal IS A CONCATENATION, but it LOOKS the same as row four. However, Cantor's Argument applies to to enumerably FINITE and INFINITE collections. The above is FINITE and obviously the diagonal is the same. And it is a CONCATENATION. So the question becomes: What do you mean by concatenation?
hmmm.....I really don't get your point. Lets try just one step: I have a beer can used as a bit, and I have a coin used as a bit. So far so good? Now, I make a new bit out of them, which is composed of the coffee can and the bit. The value of this new bit is the logical and of the values of the beer can and the coin. Now, my new bit is indeed new (its different from its component bits) and a bit, because it has a well-defined truth value (the logical and of its component bits). make sense?
2. Do you know what the "anti-diagonal number" is?
3. And do you know how they are different? How they are related?
The diagonal number would appear on the list; thus, it is in principle not "new"; the anti-diagonal could not appear on the list. It would be "new."
The anti-diagonal is not a MERE PRODUCT OF COMPOSITION. What is so hard to understand about this? The anti-diagonal is not merely obj+obj+obj=objobjobj. Address this point, PLEASE.
Now suppose that each number expansion on each row corresponds to or represents a real number. So, each row will be infinitely long.
The diagonal is 1101... It would be a concatenation of the numbers found along the diagonal, sure. But now, I can generate *an* anti-diagonal by switching each of the numbers along the sequence. So, the anti-diagonal is... 0010 ...
That is, the concept of "switching" or "manipulation" is missing from your argument. Thus, your argument is not analogous with Cantor's. It's missing a crucial concept, that of deliberate manipulation of the diagonal.
If you represent Kim correctly in your video, then it seemas to me he's arguing that we can get rid of talk of bits with talk of some or all of their physical realizations. But that's not the same as saying we can get rid of talk of bits with talk of SETS of some or all of their physical realizations. If sets are needed in Kim's maneouver, then fair enough, he's susceptible to a diagonal argument. Otherwise not, however, and I wonder myself whether Kim DOES need sets...
Hmmm.....but given that you can make a new physical implementation of a bit from pre-existing physical implementations of bits, wouldn't we have to talk about sets of bits as well?
Perhaps. The problems for Kim only come in as I see it when he tries to appeal to a set of *all possible* physical realizations (Sets of 'all Xs' are typically susceptible to diagonal arguments) of a bit. I wonder whether he needs to appeal to that particular variety of [impossible] set.
Hi excatomorfismo, it depends upon what sense of "possible" we're talking about, but it seems to me that all possible worlds can't form a set, or at least you could argue that way from cantor's theorem. There would seem to be at least as many possible worlds as there are sets, and there's no set of all sets. I don't see how intensional vs. extensional characterizations figure in here; seems like you could run the same argument for extensoinal characterizations of bits as well...no?
I still don't understand your argument. All you've shown was that you cannot write down a COUNTABLE set of all bit implementations. This does not mean that the set of all bit implementations doesn't exist, just as there is no countable set of real numbers between 0 and 1 but the numbers still exist as an uncountable set, right?
Honestly I don't even understand why, if the set didn't exist, this would imply materialism is wrong.
I think I agree with your conclusion just not your argument.
Hi 126altf4, if you form the power set of a countable set, you get an uncountable set, right? Well, what if you form the power set of an uncountable set? you get an even higher infinity! :-) This is what cantor showed, you can keep doing diagonalization without limit. And I'm not trying to show that materialism is wrong, I'm trying to show that reductive materialism is wrong, i.e. you cannot reduce bithood to any set of material objects, because no such set can exist. (cont)
(cont, to 126altf4) it was a late night last night and I"m a bit strung out, so let me know if that didn't make any sense and I'll reply again when I'm more coherent :-)
But why do I have to stop at a finite number of diagonalizations? Can't I just 'represent them all' just as we represent an infinite number of integers?
Also, can you expain why I can't just take any bit implementation and call it good? Like say: bits can be represented by eigenstates (of a magnetic field) of non-entangled spin 1/2 particles along a particular axis, or whatever. Why isn't that good enough?
Hi 126altf4, there is no stopping, that's just the point! Every time you think you have 'represented them all' you can just reapply the diagonal argument onemore time and find that you haven't really represented them all after all. That's what Cantor proved. Hofstader's book "Godel, Escher, Bach" has the best description of this, if you'd like a good read. (cont)
(cont, to 126altf4) Your second question (if I understand it correctly) is why couldn't we just pick one of the physical representations of a bit (say, spin of an electron) and annoint it as being what a bit is. Well, the reason is that the spin of an electron can be used as a bit, but it can't be the definition of a bit, because other things are bits too (like magnetic patterns on your hard drive, those are bits). (cont)
(cont, to 126altf4) Also, beer cans can be bits, switches can be bits, charges in the memory of your ipod are bits.....all these things are not electron spin, but are bits. We would need some physical concept which encompases ALL kinds of bits, but what I've tried to show in this video is that there is no such thing as "ALL kinds of bits" because whenever you think you've thought of all kinds of bits, you can use the diagonal argument to think of one more.
U({n},n,1,infinity) = N - The union of all positive integers is the natural numbers
If I list a finite number of natural numbers you could say that you could find a number that is a natural number that I did not include in my set and you would be right.
But the set still exits. Why can't I just union all the set together?
All bits = U(P({your initial collection},n),n,0,infinity)
P(S,n) means take the power set of S, n times.
Also why couldn't I have instructions that tell me if X is a bit?
Hi 126aslf4, suppose we do this. Suppose that S is the set of all possible bits. The thing is that I can take that set and create a new bit which was not already in S. I do it by first creating the power set of S, call that pow(S). pow(S) is (by cantor's theorem) always going to be a larger set than S is, and is therefore going to be a different set than S is. Now, with pow(S) I can create a new bit (which is true if all of the bits in pow(S) are true, false otherwise). (cont)
(cont, to 126altf4) Call this new bit B. B cannot be a member of S, because it was formed from the powerset of S. Therefore, S could not have been the set of all sets. I suppose you want to know now why I couldn't just form the set S1 which is the union of {B} and S? Well, sure, I could, but then I could do the whole thing over again, taking the power set of S1, and using it to form B1. yadda yadda.
All bits = U(P({your initial collection},n),n,0,infinity),
just as I form the set:
U({n},n,1,infinity) which is the natural numbers?
And,
2) If there happens to be only a finite number of things in the universe how you reasonably unendingly compound them since the new set must be made from other physical objects as in your video? In which case the set is actually finite.
1. Say I did that. I form the power set of the natural numbers, and I make a new bit from that powerset. Bingo, I've got a bit which wasn't in the original set. So the original set must not have been the set of all bits. Repeat as necessary :-)
2. It doesn't matter how many things there actually are in the universe, because we are talking about the concept of bithood. (cont)
(cont, to 126altf4) for example, suppose the universe only had enough aluminum to make 100 beer cans :-) would that mean that 101 isn't really a number, because we couldn't make that many beer cans? Of course not. And it wouldn't mean that a bit made out of 101 beer cans wouldn't be a bit either.
Sorry for the dialogue below, but it's the easiest way I can explain why I'm confused.
(Setting the stage) Let's say that I give you a finite (and greater than size 1) list of natural numbers and then make the claim that I have found all of them.
You then say, "Ah hah! You have not listed all numbers as you claimed, for I Lord Randy can simply can simply create the sum of all the elements you have listed to find a natural number you failed to include. (cont'd)
For obviously this new number is greater than any number you listed, and thereby not included in the original set, and still a natural number. Thus no set of natural numbers can exist because every list is incomplete because I can always find an element you forgot to include by this trick." (evil laugh)
Then I say, "But look if I simply union all of them together then your trick will not work, for if you sum the numbers together as paradoxical as it may seem that number actually is in the set.
Similarly I can union all the power sets together, also let us assume for the sake of argument that there are only 100 beer cans in the universe to make the sets finite."
"But I can still take the power set of it to find representations of bits that you left out."
"But I have taken the power set of an infinity of sets already so that set is already included right?"
Sometimes when you are doing physics you ARE doing computer science contrary to your claim, an electron spin is represented a qubit a photon polarization is represented by a qubit. So it does seem like that part of the language can be represented by physics...
Does that explain why I don't completely get your reasoning?
Hi 126altf4, yeah, that's not parallel, because forming the power set is not like summing together all the natural numbers. The power set of a set S ALWAYS has more elements in it than the original set did. It doesn't matter if you start with a set of natural number, real number, or anything else. The power set ALWAYS ALWAYS has more elements that the original set. Even if you start with an infinitely bit set, if you take the power set, you get a bigger infinity.
(cont to 126altf). There's no such thing as the biggest infinity, there's no such thing as a set which contains all sets. Cantor's theorem was one of the major mind-melter theorems of all time, please do read up on it. (cont)
On to your next question, whether there can be a machine which will tell me whether X is a bit or not? The answer is "no". If you know turing's the halting theorem, you might be able to prove that yourself, give it a try! If you need some hints, I can give them. But in another sense, the theorem presented in this video is another way of proving that there can be no machine which can tell whether any X is a bit or not.
As to whether you can be doing computer science when you are doing physics, well you can do both at the same time, but you have to use BOTH the vocabulary of computer science and the vocabulary of physics at the same time. If you limit yourself to ONLY using the vocabulary of physics, you cannot do computer science.
Okay, I'll go get that book. In the mean time I agree to the statement "there exists no set of all bit implementations". It does make a lot of sense. :)
Do you think that any particular computer that can actually be built can be described in the language of physics? Since you think humans can understand bithood shouldn't it follow from there that you think this means that a.i.'s can never do some things that humans can?
Hi 126altf4, sorry it took me so long to get back to you. Let me answer your questions...lets see here. A true sentence which cannot be translated into the language of physics? Sure, "the result of or-ing two bits, one which is true and one which is false, is true". you probably don't like that one though :-) What is it about humans which allows them to understand the concept of bithood? They have the ability to learn new languages. (cont)
(cont, to 126altf4) You have to learn the language of boolean logic before you can understand what a bit is. Humans have this ability. I think that eventually a.i. will progress to the point where machines can do anything humans can. But I don't think that either humans or A.I. can always identify when something is being used as a bit. For example, consider an encoded message sent between two spies. They hope that it is impossible for humans to tell where the bits are (cont)
(cont, to 126altf4) I do think you can describe any computer in the language of physics. But you can't describe it as being a computer. Say its a computer made out of vacuum tubes, you can say "here are some tungten atoms, here are some oxygen atoms, . . . " a very detailed description. But if you gave that description of the computer to somebody else, they would not be able to identify where the input was, where the output was, etc.
I think your argument is very similar to Block's. Block simply uses consciousness/brain while you used boolean logic/physical objects.
You said that since there are infinite number of instanciation of showing true or false. I am not sure why this would be an argument against Kim's notion of reduction. Don't you and Kim both believe that there really is only physical substance?
Hi ContraWagner, the thing is that (if I understand him correctly) Kim seems to think that we could form a bridge law between the mental and the physical--a bridge law being a law of the form (∀x)( m(x) ↔ ϕ1(x) ∨ ϕ1(x) ∨ ... ∨ ϕ(x) ). (cont)
where m() is a mental predicate and ϕi are physical predicates. I believe this video shows that it is impossible to create such a bridge law. And Yes, I do think that Block's point is very similar, but I don't think he has a PROOF that multiple realizability implies the impossibility of bridge laws; rather, he just points out that it raises some doubts about it. (cont)
(cont, to ContraWagner) And I think that Kim, Block, and I all think that physical "stuff" is the only "stuff" there is, but I do believe that physical facts arn't the only facts there are, in the following sense: suppose we had a complete and exhaustive description of every physical fact ϕ1, ϕ2, . . . that is or was or ever will be true (cont)
(cont, to ContraWagner) The absense of bridge laws means that from those ϕi, we could not determine which regions of spacetime were in pain, or which were seeing red, or even which regions of spacetime were people or not. In order to do these things, we must also have descriptions of regions of spacetime couched in mental terms, in other words, mental vocabulary is non eliminatable. Make any sense?
Yes, I understand your point. Given that multiple realizability poses serious problem for reductive physicalism, there seems like no possible reduction is ever possible. And this position seems even more absurd that absurdities caused by multiple realizability.
Instead of talking mental and physical, let us consider what we would indubitably consider to be a successful reduction in science. m() be an increasing H+ ions in acqueous solutions, and ϕi be physical state of acid. And multiple realizability problem would be valid here as well. And it seems like there is no reduction in science at all..
Hm...maybe I'm missing something, but I don't see your proposed rebuttal as being valid?
Your rebuttal involved redundant bits which means they can be simply reduced to the individual bits they're composed of (which bring us back to the members of the original set of all possible material representations of bits).
In other words, you haven't used a Cantor diagonal to construct a truly unique bit. Ie, Two redundant bits /= 1 unique bit.
To sum up what I mean, a redundant set of identical bits could simply be considered a subset of the set of all bits. Even if you take all the bits in the set of all possible bits and make them redundant, as you did in your video, you don't have a unique set....you simply have a redundant set that's equal to the original set.
Think about it this way: suppose I have two metal switches. Then I melt them down, and create one new, bigger switch from the atoms. The new switch would be a new bit, distinct from the original two switches, no? Same would hold if I created a redundant switch out of two switches.
The analogy here seems not very convicing, the new metal switch indeed has a unique internal composition from the two old ones, however, the new redundant "bit" has an internal structure that is describable by using the two old "bit"s.
Hi spiritpunker, sure, the new bit is describable by using the descriptions of the two old bits (plus a description of how they are wired up). But that just proves that the new bit is, well, a new bit, distinct from the two old bits, right?
I think that link died, so I'll post here instead.
1) In order to specify what is "yes - no", you need to give an account of what it takes to _come to_ represent something in attention. If you do not, and merely assume that one specifies x as an output of some function, then that is going to be problematic when it comes to the metaphysics i.e. ontological commitment. Why so? Well, if representating something in consciousness is not a function,then we're dealing here with
the power set of the natural numbers has a one-to-one correspondence with the reals, I guess what I was wondering was: what is the interpretaion of the power set of the reals?
Also randy what did you score on the test in the sidebar of the video this is a response to?
Hi 126altf4, yeah, the power set of the reals has a one-to-one correspondence with many other sets, all of which have yet more elements in them than there are real numbers. ha, I totally forgot the score, but just for you, I took it over again. I scored 95% "cultural creative" 75% "postmodernist"
Hi 126altf4, sure. There are some sets which have, say, 5 objects in them. the cardinality of those sets are 5. There are some sets which have as many items in them as there are natural numbers. The cardinality of those sets are Aleph null. There are some sets which contain as many items as there are real numbers. The cardinality of those sets are Aleph 1. There are sets which contain even MORE elements than real numbers!!! For each size set, there is a number which expresses (cont)
"We use the set of real numbers, but real numbers arn't all the numbers there are. Just like we apply diagonalization on rational numbers to yield reals, we can apply diagonalization on reals to yield numbers of even higher cardinality. And we do say that there is no such thing as the set of all numbers of all cardinalities."
OK, so using the diagonal argument on reals(don't know how you would set that up), you can prove there are numbers not elements of the reals?
Yeah. For every set, there is a number which says "how many" elements there are in that set. More formally, there is a number which expresses the cardinality of the set. To show that there is a set which has more elements in it than there are real numbers, you can use the diagonal method like this. Consider all of the real numbers. Now, make a set of the real numbers---call this set R. (cont)
(cont, to 126altf4). Now, for the diagonal step--construct a new set, S, like this: S is the set of all of the subsets of R. This is also called the "powerset" of R. The theorem which cantor proved is that the powerset of R will have "more elements" (more formally, a higher cardinality) than R has. But of course, we could let T be the power set of S, and get an even higher cardinality, or let U be the power set of T, etc, without limit.
Good discussion b.t.w. Randy! As you can probably tell, I'm very sympathetic to the whole Chalmer's/Jackson project, but its quite controversial. I think the assumption that physicalists can help themselves to the languages of logic and math is much less controversial.
sure, i totally agree. but you don't have to accept the canberra plan to allow certain stuff into physicalism a priori, like the notion of a bit (which, although i don't know exactly how to classify your characterization, is certainly encompassed by math, logic and the relevant meta-theory). Whether or not this is truly "physical reduction" is just terminology as far as i'm concerned. Whatever it is, if we can use it as a supervenience basis for the mental, normative, etc. then (cont)
hey jerewho, my battery on my laptop is about to die, so it might be a few hours before I can respond to your further points :-) again, good discussion.
But that is an extreme. Others (Block/Stalneker 1999, e.g.) think that reduction DOES require rewrites into the language of physics. But but they can still help themselves to mathematics/logic/meta-logic and some modal notions without endorsing Jackson/Chalmers style "modal rationalism."
Also, Jackson's df of supervenience is: "Physicalism is true at a possible world W if and only if any world which is a minimal physical duplicate of W is a duplicate of W simpliciter."
Yeah, Jackson and Chalmers help themselves to a real a priori buffet. The trick is that they do their conceptual analysis without translations from the reduced language to the language of microphysics. They do this by employing possible worlds. As long as they (idealized) can evaluate the extension of a concept at any possible world, then that's enough (they argue). I find their 2001 paper very convincing and explicit.
Hi jerewho, but this video proves that you can't evaluate the concept of "bit" at any possible world, if all you know are the physical facts about the world. This is true EVEN IF physicalism holds for this world. If all you have is a physical description of the world, in order to identify all the bits and only the bits, you need a predicate Phi(x) such that forall x, Phi(x) is true iff x is a bit. But you can't have this. (cont)
2 points. One, I still don't buy your df of a bit. I wasn't arguing that you have to define the concept of a question (although I do doubt that questions are a primitive in a theory of Boolean algebra). Lets assume them are. The problem is that you haven't told me WHAT questions you're talking about. All questions? Any question? A specific question? Telling me that the variable Q ranges over questions doesn't tell me which question it denotes or, if it is bound, by what quantifier?
Hi jerewho, ok, lets go with your definition of a bit as something which signifies a truth value. You can run the same diagonal argument over again. In fact, the diagonal argument is meant to be a general technique for showing that two vocabularies are not reducible to each other.
Hi jerewho, that doesn't work, for several reasons (1) there are things which have a state space of two elements which are not bits (2) "metaphysically possible" is not part of the vocabulary of physics. (that's as close to an a priori truth as they come: "metaphysics' means "beyond physics")
I don't want to argue about the definition of "bits" anymore. Regardless of the adequacy of my definition (which I do doubt) what matters is the adequacy of yours. I am still not clear what the semantic value of your "yes/no question" variable is. At ant rate, this is irrelevant, since I've argued below that physicalists take concepts like "bit" for granted, because the kind of things they care about reducing are not bits and the like, but rather goodness and tables and pains. (cont)
Hi jerewho, perhaps I missed it, but I didn't see an argument that the language of physics includes bits, just a statement thereof. My argument that physics does NOT use this language is that all the laws of physics which I've ever seen are differential equations over real and complex vector spaces, which can be defined without reference to bits at all. (cont)
(cont, to jerewho) w.r.t. my definition of bits as an answer to a yes/no question, I still don't see what the difficulty is. A yes/no question is just a sentence which has a certain grammatical form. We could flesh out the definitions of a language as being a certain subset of strings over an alphabet, etc, but you get the picture. Just like the concepts of "point" and "line" are defined by the axioms of geometry, "question" and "answer" would be defined by whatever axioms we are to give.
well, it seems crazy to me to think of linguistic objects such as questions and answers as necessart primitives for a theory bits, which seem to me (pretheoretically) as a purely informational concept. (cont)
Hi jerewho, what kind of information are you thinking about? Shannon information or Kolmogorov information is very much defined with respect to language. Shannon entropy for example is defined in terms of the code words you are expecting to recieve. There can be no information without language.
My point is this: Let Axy be a two place predicate interpreted as "x is a y/n question and y is its answer." So, is your definition of a bit:
1) b is a bit iff (there exists an x)(Axb) or
2) b is a bit iff (for all y/n questions x)(Axb) or
3) b is a bit iff for question q, Aqb (in which case I'd need to know what q is as a function of b)?
Also I think it's reasonable to interpret information theory as assuming that language semantically corresponds to states of affairs. But enough info theory
Hi Jerewho, none of the above. I'd start with something like this: let A be an alphabet. Let A* be the set of all finite strings on that alphabet. Let a language L be a subset of A*. Let D be the subset of L such that the elements of D are either true or false--these are the declarative sentences. If d is a declarative sentence, let d? be its corresponding question. The correct answer to a question "d?" is "yes" if d is true, and "no" if d is false.
(cont, to jerewho) notice that NONE of those concepts (alphabet, string, true, false, question, answer, yes, no) can be reduced to physics, but those concepts are none the worse for that. If you ask me, for example, what "true" is, I'd just point to those axioms and say true is defined by those axioms. Same way that "point" and "line" are defined by the axioms of euclidean geometry.
ok, but on this theory the only "answers" are the "yes" and the "no" bits of language L. but the answers were supposed to be bits: heterogeneous arrangements of matter!
Hi jerewho, so? e.g. I can talk about the point which is the center of gravity of the sun, and still say that "point" is defined by the axioms of geometry.
right! points are geometric objects, fine, but what matters is that the concept of a point is part of the language of physics. so, an physics duplicate of a world is a geometric duplicate of it as well. at least that's the idea.
Hi jerewho, ok, I see what you mean. Well there is nothing wrong with saying that, say, a particular spatio-temporal region is BOTH a beercan AND an answer to a yes-no question. That doesn't contradict any of the postulates of yes-no-question-answer-hood nor does it contradict any of the postulate of beer-can-hood.
On a less substantive not, metaphysics doesn't mean anything at all (it's not like other "meta" constructions). It comes from the fact that Aristotle's writings on the topic were filed after his "physics" in the library of Alexandria, so they came to be called "meta-physics." I think the physics is riddles with metaphysical commitments, w.r.t. ontology, causation, counterfactual dependance, etc.
LOL jerewho, that's true, but "metaphysically possible" uses the word metaphysical in the sense of being beyond physics. E.g. we might ask whether it is metaphysically possible for the world to have had a different kind of physics than it does now.
Not at all. To illustrate: say a painting is impressionistic iff it has the color structure I. There are artistically possible paintings that do not have color structure I. That does not mean that color concepts do not figure in impressionism. (cont)
Hi jerewho, I don't understand your point here. Seems like that would just reinforce the point I want to make: just like the language of impressionism isn't the language of painting, the language of physics is not the language of the metaphicallly possible.
ok, but a can isn't INTRINSICALLY an answer to anything. it is all relative to someone who interprets it as such. but your definition leaves that all relational aspect out. here's my request: i would like a definition of a bit of the form:
a state of affairs x is a bit iff ...
where the ... does not contain the words "question" or "answer" unless they are explicitly defined (you define an answer above as a piece of LANGUAGE, but then bits cannot be answers because they are bits of matter!)
Hi Jerewho, well, kinda the whole point of the video is that it really isn't possible to fill in the blank "a state of affairs x is a bit iff...." in any other language than one which also contains the terms "question", "ansswer, "yes", "no" etc. The whole point is to claim that this language is irreducible to any other language. And unless you are a dualist of a rather extreme kind, I don't see how you could say that language isn't material.
(cont, to jerewho) I mean, would you request me to fill in the blank "X is a line iff ...." in a language which doesn't contain the word "Point"? BTW, saying that something isn't "intrinsically" something else is a curious thing to say to somebody who doesn't believe in the a priori :-)
haha, alright. but you don't need to use the language of physics, english would be fine. i just don't feel that the notion of a bit that figures in your argument is precise enough for me to understand/believe the argument. i really just want clarification that doesn't reduce the concept of a bit to something else i don't understand!
Hi jerewho, what's not to understand? I gave you a 100% formal definition of language, question, declarative sentence, etc above. It was as rigorous as the definition of Euclidean geometry. And sure, we could use English or any other language which was a superset of the language I defined. You know what a question is. You know what an answer is. You know what a bit is. You know what physics is. What don't you know?
A more interesting line of arguing would be to ask Reductive Materialists how they are lumping all of these material things together to form the idea of a bit. Clearly there is some property of sameness between the different objects, but bit is really this property which they are trying to capture. It's very circular.
RoboJasonMan 9 months ago
@RoboJasonMan I've asked reductive materialists that, and their answer was that it was perfectly possible to express what all of the bits had in common using physicalistic language. After all, its perfectly possible to express, say, what all electrons have in common using physicalistic language, why should we expect not to be able to express what all bits have in common using physicalistic language? This video is my answer to that question.
randyhelzerman 9 months ago
I don't get your point. All you've shown is that there are uncountably many possible ways to represent a bit materially. There's no contradiction there. Maybe you believe that this contradicts some finiteness assumption of the universe? Obviously, we can't realize all of them at once. However conceptually, we can think of uncountably many ways to physically represent a bit. So what?
RoboJasonMan 9 months ago
@RoboJasonMan What this proof shows is not that there are an uncountably infinite number of ways to represent a bit materially. What this proof shows is that there is literally no such thing as "all the ways" to represent a bit materially. For the same reason that there is no such thing as the universal set--the very concept is self-contradictory.
randyhelzerman 9 months ago
A set of all true/false bits is just that, ALL true/false bits and you can't just add a new one that you 'thought' of. If you allow for infinity you can prove anything. Unfortunately for your argument, infinity does not exist in this universe and this is easy to prove.
harmonicdog 9 months ago
Go read Wittgenstein and then post a different video.
Frutoses 10 months ago
@Frutoses *chuckle* I've both read Wittgenstein and posted videos which are different from this ;=0 what's your point?
randyhelzerman 9 months ago
@randyhelzerman I seriously can't remember why I told you to read Wittgenstein and post another video, lol. Anyway, are you assuming that there's a finite list of yes/no bits? If you are, your assumption is wrong. I don't think physicists say there's a finite list of yes/no bits. Furthermore, when Jaegwon Kim tells you to reduce the concept of a yes/no bit to all possible material implementations AND all their combinations (that's implied).
Frutoses 9 months ago
@randyhelzerman What makes you think you created a new thing when you put together a beer can and a yes/no switch? Those two things already existed in the world and no new thing magically appeared in the world when you created the Frankenstein yes/no bit made with a beer can and a yes/no switch. You're not adding anything to the world as it is.
Frutoses 9 months ago
(cont.) If the world is indeed information then physics would suggest that the fundamental stuff is in fact "bits" rather than particles!
JohananRaatz 1 year ago
Well you can have "physics uber alles" and get away from eliminative materialism, just so long as your underlying philosophy of science is not materialist. This makes sense as the holographic principle suggests that the world is actually made of information rather than matter.
JohananRaatz 1 year ago
Just because we can't define or categorize or even approximate all of these laws, doesn't mean they aren't reducible to the material. The only claim the reductive materialist is committed to is that all phenomena are reducible *in principle* to the material. This is a metaphysical claim which is independent of our epistemology (which your argument seems to target).
AWASHA 1 year ago
@AWASHA Hi Awasha, it all depends upon what you mean by "reduce to physics". In this video, I give a very precise definition of what I mean by reduction, and given that reduction, I show that the notion of bit cannot be reduced to physics. If you want to convince me that I'm wrong, you'll have to show me that another definition of "reduction" is better, or find a flaw in the proof.
randyhelzerman 1 year ago
What does the correspondence of sentences with facts have to do with reductive materialism? The reductive materialist is not committed to the claim that humans know all laws which govern nature nor the claim that humans can even potentially ascertain all laws which govern nature (and I think quantum physics indicates that we can't, in principle, ascertain all laws which govern nature). But the laws which govern nature exist and are what they are totally independent of cognizant observers.
AWASHA 1 year ago
You seem to also only be considering bits in terms of some sort of external existence--let me put it this way, unicorns don't exist but mental representations of unicorns exist. Horses exist and mental representations of horses exist. The mental representations can, in theory, be reduced to physics, and perhaps in our lifetime technology will be invented that can take snapshots of mental imagery. Well anyway, Boolean logic, mathematics, and many other things are unicorns in a sense.
eppursimuove22 1 year ago
@eppursimuove22 Hmmm......it seems like you actually agree with me that humans and aliens could both, for example, imagine a unicorn--but nevertheless be using two completely different chemical/physical mechanisms to do so. But this implies that whatever it is to imagine a unicorn, it _can't_ just be to have the same kind of chemical/physical reactions which human brains have. Because if it were the aliens (or computers) wouldn't be able to.
randyhelzerman 1 year ago
"Reduction is saying that is the ONLY way it could be explained. It would be denying, for example, that you could ever build a robot brain out of silicon which could imagine having a date with Marlynn Monroe. " Bullshit. AI researchers are by and large reductionists, at least in principle ie basketball can be reduced to physics but it is impractical for a merely human basketball player to think in those terms.
eppursimuove22 1 year ago
@eppursimuove22 Think about it this way: water has been REDUCED to h2o,meaning that everywhere there's water there is also h2o. If AI researchers really believed that imagination reduced to human brain chemistry, then they would believe that everywhere there was imagination, there had to be a human brain, just like they believe that everywhere there is water there is h2o. But AI researchers don't believe this; they CAN"T be reductionistic,they just are confused enough to think they are.
randyhelzerman 1 year ago
Your alien argument is a straw man. If alien chemistry isn't identical to human chemistry then alien imagination isn't identical to human imagination. That's doesn't make it not "really" imagination. Among humans, imaginative abilities are far from identical as is brain chemistry, yet John & Charles both have imagination. John can vividly imagine complex geometric figures and recall memories w/ lifelike accuracy & Charles can only imagine a dim haze. This can be reduced to physical differences
eppursimuove22 1 year ago
@TheDrunkenCabDriver Suppose there were aliens from another planet, where life had a very different chemestry, and their nervous systems were very different. But these aliens could nevertheless learn English, and describe vividly to you what they image a date with Maralynn Monroe would be like. Would you say they weren't "really" imagining, because to "really" imagine, you have to have the same chemistry and neurological functions that humans have?
randyhelzerman 1 year ago
@TheDrunkenCabDriver So reduction isn't merely saying that some mental function (say, imagining a date with Maralynn Monroe) can't be implemented by chemical and neurological functions. Reduction is saying that is the ONLY way it could be explained. It would be denying, for example, that you could ever build a robot brain out of silicon which could imagine having a date with Marlynn Monroe.
randyhelzerman 1 year ago
what about quarks?
fannnnntasticly 1 year ago
@Deliratio Suppose I have a set of bits { b1, b2....}. I can define a new bit, b_new, which is true iff b1 AND be AND .... is true. Its false otherwise. Make sense?
randyhelzerman 1 year ago
@Deliratio There's no assumptions on the number of bit implementations. Since you are studying math to death, I can state the argument in a more clear and consise form: Say B is the set of all possible bit implementations. Now form the set B*, which is the power set of B. Cantor proved that B* has a higher cardinality than B. Now, form a new bit B_new, which is just the AND of all bits in B*. B_new can be one of the previously existing bits. Q.E.D.
randyhelzerman 1 year ago
@Deliratio wow, you watched every video I put out? Amazing. No, this wasn't private; probably what happened is one of my other videos put you to sleep right before you watched this one :-) Thanks for watching, you made my day.
randyhelzerman 1 year ago
LOL the marriage analogy
badbunny 2 years ago
:-)
randyhelzerman 2 years ago
You make the mistakie that reality is most likely finite. If it was not, you would get logical contradictions. Hence, there are only a finite number of realizations of the bit. Hence, your diagonal argument fails.
jbweimar 2 years ago
hi jbweimar, it works for infinite universes as well. You just need to be able to construct bits which are infinitely large :-) Suppose by way of contradiction that B is the set of all bits. B could be finite or infinite. Let B* be the power set of B, and define a new bit, B_alpha, which is true iff all of the bits in B* are true, and false otherwise. B_alfpha is not an element of B, but it is a bit, thus showing the contradiction.
randyhelzerman 2 years ago
@randyhelzerman: Even if your arguments works, I fail to see how it destroys reductive materialism. What is exactly your argument? And do you have the reference to Jaegwon Kim's paper where he claims this?
jbweimar 2 years ago
Reductive materialism is the claim that for any real scientific concept b (say the concept of a bit) we can define that concept in physical termsl. Formally, if b(x) is true of all x's which are bits, reductive materialism states that we can find a physical predicate p(x) such that for all x, b(x) is true iff p(x). This proof shows that cannot be done in general, because there is no such p(x) for bits. See Kims book "physicalism or something near enough".
randyhelzerman 2 years ago
I think you and nerdfiles both make some good points. I'll have to do some reading on this, but good video nonetheless.
KieIicious 2 years ago
Awesome, Randy! Keep it up! It's nice to see philosophers on youtube who know what they're talking about .
GodlessPhilosopher 2 years ago
In other words, WHAT makes it different? The answer you give to this question determines whether your argument is analogous to Cantor's Diagonalization technique.
Obviously the word "obj" is different from "objobjobj"; is THIS what you mean by "different"?
nerdfiles 2 years ago
What makes the new bit (composed of a beer can and a coin) different from either the beer can or the coin? Is that what you are asking? That's kind of like asking why your fingernail is different from your left earlobe, no?
randyhelzerman 2 years ago
This is a waste of time. I'm telling you that
(a) "is different" has a sense in Cantorian terms,
(b) "is different" in your sense is not analogous with the sense of "is different" in (a)
(c) Therefore, your argument is not analogous.
You do understand why I'm making these points, right? I'm talking about the analogical status of your argument.
The anti-diagonal is NOT, while the diagonal is, a mere composition of parts to make a whole.
Address that point. For the last time, seriously.
nerdfiles 2 years ago
The anti-diagonal IS DIFFERENT, but it is NECESSARILY DIFFERENT. And it is necessarily different for a reason that is not fully explained by a concept of CONCATENATION or COMPOSITION.
These concepts play a role in Cantor's argument, sure, but they do not fully explain or capture WHY the anti-diagonal is DIFFERENT. Though we should all agree that it IS different.
Saying "the anti-diagonal is different like fingernails are different from earlobes" is just hand-wavy, as I said, bullsh*t.
nerdfiles 2 years ago
And I'm done responding. It's now plain to me, indeed, that you have no idea what conceptual framework grounds Cantor's Diagonalization technique.
Cheers.
nerdfiles 2 years ago
Hi nerdfiles, I'm not making any arguments (and therefore I'm not waving my hands) I'm just asking questions because I don't think I understand your point. I don't see why I can't make a new bit which is composed of two pre existing bits. You seem to be quite convinced of this fact, but I don't understand why.
randyhelzerman 2 years ago
I'll just make my point here. Presumably your "binary objects" map to Cantor's real numbers. So you'd have a "infinite set of binary possibilities" placed at each row. That's fine, but this term "concatenation" is being used in a hand-wavy manner. The anti-diagonal is constructed from the diagonal of the reals; it is not a concatenation *of them*. It may be a concatenation of their parts, sure, but you left that out while leaving out the deliberate trick that must be used on the diagonal.
nerdfiles 2 years ago
Hi nerdfiles, no, the binary objects don't map to the real numbers (although cantor did invent the diagonal method to prove that there were more real numbers than there were integers). The thing is you can once again apply the diagonal method to the real numbers, and come up with an even bigger infinity--there's no limit to the number of ever-larger sets. (cont)
randyhelzerman 2 years ago
(cont, to nerdfiles) as far as the concatenation being hand wavy.....well, the new bit is the logical AND of all the previous bits. That's about as precise and exactly specified as you can get. I don't see how its hand-wavy.
randyhelzerman 2 years ago
Spare the summary of the interpretations one can draw from Cantor's "Proof." Obviously you can "once again" apply the d.method to reals. That's Cantor's Argument. So I don't get why you're stating it as if you've made a discovery or a novel point. Your "binary possibilities" either represent a real number or they don't. For instance, we could represent pi in terms of binary symbols (0, 1), etc. This obviously isn't going on in your argument.
nerdfiles 2 years ago
And yes, I realize it's the logical concatenation. Are you assuming that I don't have idea as to the meaning of the terms you use? Lose the tacit ad hominem and condescension. The point I'm making is that the *anti-diagonal* is not generated from a *mere* concatenation of first-order arbitrary numbers. The anti-diagonal is generated from the diagonal which is itself, *perhaps one may say this*, a concatenation of the numbers that fall along the diagonal of the presumed list of the reals. (cont)
nerdfiles 2 years ago
But the *anti-diagonal* is [not] just a concatenation. You have to apply a deliberate rule-governed manipulative principle to the sequence of the diagonal to generate the anti-diagonal. And it is the anti-diagonal which cannot appear on the list, on pain of contradiction. In what way is "resultant of concatenation of binary possibilities," even generally, map to the anti-diagonal. The anti-diagonal is not a merely concatenation. It is a concatenation PLUS the manipulation of the diagonal.
nerdfiles 2 years ago
hi nerdfile, the "deliberate rule-0governed manipulative principle" I'm using is just logical and. What could be more precise, deliberate, or rule governed than that?
randyhelzerman 2 years ago
... Do you not understand that I'm saying that is not enough? I've admitted that logical AND plays a role. It generates the diagonal. It gives you:
1101...
But the construction of the anti-diagonal presupposes that one has done the logical AND, for one would need the diagonal to generate the anti-diagonal. Fine. But the anti-diagonal is not just a result of concatenation. You have to manipulate the numbers in the sequence directly. The rule applies to how one manipulates the numbers.
nerdfiles 2 years ago
Point being:
1101...
to
0010 ...
has absolutely nothing to do with concatenation. Yeah, you are using [just] logical AND; and it ain't enough.
nerdfiles 2 years ago
No, I don't understand your objection at all. I don't understand why you say that the logical and gives you 1101... ? The logical and of any number of bits just gives you 1 bit, not a sequence of bits. I don't understand why you say I have to manipulate the numbers directly? And I don't understand which numbers you are talking about; these are bits not numbers. The rule is just take the logical and of all the bits. The result of that is always another bit which isn't on the list.
randyhelzerman 2 years ago
What? (true && true && false) is logically equivalent to (false && false); that is, they're both logically equivalent to (false). It's pretty obvious that (false) and (true) appear on the list a countably infinite number of times. In list
(true, (true && true), true, false)
true appears three times. If we add another (true) member to the list, we have a bit whose value does appear within the list, it's the ordinal placement which makes it unique. Thus, we have to be talking about [numbers]...
nerdfiles 2 years ago
As a criterion for uniqueness of these members. Thus, we have to say that their ordinal position gives us the grounds for saying that they are [new] to the list. "not being on the list" is possible in virtue of the number of members the result has, for it is obvious that in:
(true && true && true && true) = truetruetruetrue
the latter and the former are logically equivalent. Moreover, they're logically, or categorically, indistinguishable. What makes them [different] is that the latter (cont)
nerdfiles 2 years ago
(cont) has [looks] different. But this has nothing to do with logical AND.
It's obvious that in:
(true && true && true && true) == true
the latter is no different, in significant and relevant respects, from the the first or the third "true." And obviously it's on the "list": that which falls inside the parentheses.
But you keep talking about infinites. Look, you can only mean some number that corresponds to:
1001010010101...
Your "boolean images" are not themselves "infinities."
nerdfiles 2 years ago
Comment removed
nerdfiles 2 years ago
nerdfiles, you are confusing the value of the bits with the bits. there are only 2 values (true, false) which a bit can take, but there can be any number of bits.
randyhelzerman 2 years ago
Are you serious? I've already made that point.
Look at:
truetruetruetrue
That's four bits. Obviously IT LOOKS different from (true), but that is IRRELEVANT to LOGICAL AND.
Logical AND gives you a VALUE.
This is logical AND: &&
So in (true && true) in any programming language, you get (true) as value. That is what logical AND MEANS.
If you mean concatenation of symbol strings, then OBVIOUSLY "truetrue" LOOKS different from "true". One has 8 characters, the other 4. But that is IRRELEVANT
nerdfiles 2 years ago
So, suppose an enumeration of the reals. At any time, t, you will be able to derive a DIAGONAL.
13823
13743
03933
13923
02323...
The diagonal is 13923, and the number at the fourth row is 13923.
The diagonal IS A CONCATENATION, but it LOOKS the same as row four. However, Cantor's Argument applies to to enumerably FINITE and INFINITE collections. The above is FINITE and obviously the diagonal is the same. And it is a CONCATENATION. So the question becomes: What do you mean by concatenation?
nerdfiles 2 years ago
Because obviously the concatenation only plays ONE PART in Cantor's Proof. There's MORE TO IT than just concatenation.
The ANTI-DIAGONAL is a result of two methods: Concatenation and the Deliberation Manipulation of the Diagonal's Members.
At best your argument captures Concatenation, but it says nothing about the latter.
nerdfiles 2 years ago
hmmm.....I really don't get your point. Lets try just one step: I have a beer can used as a bit, and I have a coin used as a bit. So far so good? Now, I make a new bit out of them, which is composed of the coffee can and the bit. The value of this new bit is the logical and of the values of the beer can and the coin. Now, my new bit is indeed new (its different from its component bits) and a bit, because it has a well-defined truth value (the logical and of its component bits). make sense?
randyhelzerman 2 years ago
...
1. Do you know what the "diagonal number" is?
2. Do you know what the "anti-diagonal number" is?
3. And do you know how they are different? How they are related?
The diagonal number would appear on the list; thus, it is in principle not "new"; the anti-diagonal could not appear on the list. It would be "new."
The anti-diagonal is not a MERE PRODUCT OF COMPOSITION. What is so hard to understand about this? The anti-diagonal is not merely obj+obj+obj=objobjobj. Address this point, PLEASE.
nerdfiles 2 years ago
In any case, suppose:
101010010
010100101
010101001
100101010
...
Now suppose that each number expansion on each row corresponds to or represents a real number. So, each row will be infinitely long.
The diagonal is 1101... It would be a concatenation of the numbers found along the diagonal, sure. But now, I can generate *an* anti-diagonal by switching each of the numbers along the sequence. So, the anti-diagonal is... 0010 ...
Now this concept of "switching" is missing. Why?
nerdfiles 2 years ago
That is, the concept of "switching" or "manipulation" is missing from your argument. Thus, your argument is not analogous with Cantor's. It's missing a crucial concept, that of deliberate manipulation of the diagonal.
nerdfiles 2 years ago
A nice video! Very clear.
redetrigan 2 years ago
thank you.
randyhelzerman 2 years ago
If you represent Kim correctly in your video, then it seemas to me he's arguing that we can get rid of talk of bits with talk of some or all of their physical realizations. But that's not the same as saying we can get rid of talk of bits with talk of SETS of some or all of their physical realizations. If sets are needed in Kim's maneouver, then fair enough, he's susceptible to a diagonal argument. Otherwise not, however, and I wonder myself whether Kim DOES need sets...
jonobrow 2 years ago
Hmmm.....but given that you can make a new physical implementation of a bit from pre-existing physical implementations of bits, wouldn't we have to talk about sets of bits as well?
randyhelzerman 2 years ago
Perhaps. The problems for Kim only come in as I see it when he tries to appeal to a set of *all possible* physical realizations (Sets of 'all Xs' are typically susceptible to diagonal arguments) of a bit. I wonder whether he needs to appeal to that particular variety of [impossible] set.
jonobrow 2 years ago
Hi excatomorfismo, it depends upon what sense of "possible" we're talking about, but it seems to me that all possible worlds can't form a set, or at least you could argue that way from cantor's theorem. There would seem to be at least as many possible worlds as there are sets, and there's no set of all sets. I don't see how intensional vs. extensional characterizations figure in here; seems like you could run the same argument for extensoinal characterizations of bits as well...no?
randyhelzerman 2 years ago
I still don't understand your argument. All you've shown was that you cannot write down a COUNTABLE set of all bit implementations. This does not mean that the set of all bit implementations doesn't exist, just as there is no countable set of real numbers between 0 and 1 but the numbers still exist as an uncountable set, right?
Honestly I don't even understand why, if the set didn't exist, this would imply materialism is wrong.
I think I agree with your conclusion just not your argument.
126altf4 2 years ago
Hi 126altf4, if you form the power set of a countable set, you get an uncountable set, right? Well, what if you form the power set of an uncountable set? you get an even higher infinity! :-) This is what cantor showed, you can keep doing diagonalization without limit. And I'm not trying to show that materialism is wrong, I'm trying to show that reductive materialism is wrong, i.e. you cannot reduce bithood to any set of material objects, because no such set can exist. (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) it was a late night last night and I"m a bit strung out, so let me know if that didn't make any sense and I'll reply again when I'm more coherent :-)
randyhelzerman 2 years ago
But why do I have to stop at a finite number of diagonalizations? Can't I just 'represent them all' just as we represent an infinite number of integers?
Also, can you expain why I can't just take any bit implementation and call it good? Like say: bits can be represented by eigenstates (of a magnetic field) of non-entangled spin 1/2 particles along a particular axis, or whatever. Why isn't that good enough?
126altf4 2 years ago
Hi 126altf4, there is no stopping, that's just the point! Every time you think you have 'represented them all' you can just reapply the diagonal argument onemore time and find that you haven't really represented them all after all. That's what Cantor proved. Hofstader's book "Godel, Escher, Bach" has the best description of this, if you'd like a good read. (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) Your second question (if I understand it correctly) is why couldn't we just pick one of the physical representations of a bit (say, spin of an electron) and annoint it as being what a bit is. Well, the reason is that the spin of an electron can be used as a bit, but it can't be the definition of a bit, because other things are bits too (like magnetic patterns on your hard drive, those are bits). (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) Also, beer cans can be bits, switches can be bits, charges in the memory of your ipod are bits.....all these things are not electron spin, but are bits. We would need some physical concept which encompases ALL kinds of bits, but what I've tried to show in this video is that there is no such thing as "ALL kinds of bits" because whenever you think you've thought of all kinds of bits, you can use the diagonal argument to think of one more.
randyhelzerman 2 years ago
Comment removed
126altf4 2 years ago
This has been flagged as spam show
U({n},n,1,infinity) = N - The union of all positive integers is the natural numbers
If I list a finite number of natural numbers you could say that you could find a number that is a natural number that I did not include in my set and you would be right.
But the set still exits. Why can't I just union all the set together?
All bits = U(P({your initial collection},n),n,0,infinity)
P(S,n) means take the power set of S, n times.
Also why couldn't I have instructions that tell me if X is a bit?
126altf4 2 years ago
Also why should we think your initial collection is infinitely large, there may be only a finite number of things that can represent bits.
The above removed comment was merely a repeat, the comment was posted twice so I removed one.
126altf4 2 years ago
Hi 126aslf4, suppose we do this. Suppose that S is the set of all possible bits. The thing is that I can take that set and create a new bit which was not already in S. I do it by first creating the power set of S, call that pow(S). pow(S) is (by cantor's theorem) always going to be a larger set than S is, and is therefore going to be a different set than S is. Now, with pow(S) I can create a new bit (which is true if all of the bits in pow(S) are true, false otherwise). (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) Call this new bit B. B cannot be a member of S, because it was formed from the powerset of S. Therefore, S could not have been the set of all sets. I suppose you want to know now why I couldn't just form the set S1 which is the union of {B} and S? Well, sure, I could, but then I could do the whole thing over again, taking the power set of S1, and using it to form B1. yadda yadda.
randyhelzerman 2 years ago
Right, so:
1) Is there a reason why I can't form the set:
All bits = U(P({your initial collection},n),n,0,infinity),
just as I form the set:
U({n},n,1,infinity) which is the natural numbers?
And,
2) If there happens to be only a finite number of things in the universe how you reasonably unendingly compound them since the new set must be made from other physical objects as in your video? In which case the set is actually finite.
126altf4 2 years ago
1. Say I did that. I form the power set of the natural numbers, and I make a new bit from that powerset. Bingo, I've got a bit which wasn't in the original set. So the original set must not have been the set of all bits. Repeat as necessary :-)
2. It doesn't matter how many things there actually are in the universe, because we are talking about the concept of bithood. (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) for example, suppose the universe only had enough aluminum to make 100 beer cans :-) would that mean that 101 isn't really a number, because we couldn't make that many beer cans? Of course not. And it wouldn't mean that a bit made out of 101 beer cans wouldn't be a bit either.
randyhelzerman 2 years ago
Sorry for the dialogue below, but it's the easiest way I can explain why I'm confused.
(Setting the stage) Let's say that I give you a finite (and greater than size 1) list of natural numbers and then make the claim that I have found all of them.
You then say, "Ah hah! You have not listed all numbers as you claimed, for I Lord Randy can simply can simply create the sum of all the elements you have listed to find a natural number you failed to include. (cont'd)
126altf4 2 years ago
For obviously this new number is greater than any number you listed, and thereby not included in the original set, and still a natural number. Thus no set of natural numbers can exist because every list is incomplete because I can always find an element you forgot to include by this trick." (evil laugh)
Then I say, "But look if I simply union all of them together then your trick will not work, for if you sum the numbers together as paradoxical as it may seem that number actually is in the set.
126altf4 2 years ago
Similarly I can union all the power sets together, also let us assume for the sake of argument that there are only 100 beer cans in the universe to make the sets finite."
"But I can still take the power set of it to find representations of bits that you left out."
"But I have taken the power set of an infinity of sets already so that set is already included right?"
126altf4 2 years ago
Also, instead of specifying all the bits can't I specify some machine that will tell me if X is or is not a bit? Or do I misunderstand?
Can you give me a statement that cannot be translated into the language of physics that involves bithood?
126altf4 2 years ago
Sometimes when you are doing physics you ARE doing computer science contrary to your claim, an electron spin is represented a qubit a photon polarization is represented by a qubit. So it does seem like that part of the language can be represented by physics...
Does that explain why I don't completely get your reasoning?
i hope you didn't mind this long reply
126altf4 2 years ago
Hi 126altf4, yeah, that's not parallel, because forming the power set is not like summing together all the natural numbers. The power set of a set S ALWAYS has more elements in it than the original set did. It doesn't matter if you start with a set of natural number, real number, or anything else. The power set ALWAYS ALWAYS has more elements that the original set. Even if you start with an infinitely bit set, if you take the power set, you get a bigger infinity.
randyhelzerman 2 years ago
(cont to 126altf). There's no such thing as the biggest infinity, there's no such thing as a set which contains all sets. Cantor's theorem was one of the major mind-melter theorems of all time, please do read up on it. (cont)
randyhelzerman 2 years ago
On to your next question, whether there can be a machine which will tell me whether X is a bit or not? The answer is "no". If you know turing's the halting theorem, you might be able to prove that yourself, give it a try! If you need some hints, I can give them. But in another sense, the theorem presented in this video is another way of proving that there can be no machine which can tell whether any X is a bit or not.
randyhelzerman 2 years ago
As to whether you can be doing computer science when you are doing physics, well you can do both at the same time, but you have to use BOTH the vocabulary of computer science and the vocabulary of physics at the same time. If you limit yourself to ONLY using the vocabulary of physics, you cannot do computer science.
randyhelzerman 2 years ago
Okay, I'll go get that book. In the mean time I agree to the statement "there exists no set of all bit implementations". It does make a lot of sense. :)
Do you think that any particular computer that can actually be built can be described in the language of physics? Since you think humans can understand bithood shouldn't it follow from there that you think this means that a.i.'s can never do some things that humans can?
Do you believe that to be true?
126altf4 2 years ago
I don't even know why I asked that, you've clearly stated in other video's that humans can't be treated as input output machines.
What is it about a human that allows them to understand the concept of bithood?
126altf4 2 years ago
Can you give a true sentence that cannot be translated into the language of physics?
126altf4 2 years ago
Hi 126altf4, sorry it took me so long to get back to you. Let me answer your questions...lets see here. A true sentence which cannot be translated into the language of physics? Sure, "the result of or-ing two bits, one which is true and one which is false, is true". you probably don't like that one though :-) What is it about humans which allows them to understand the concept of bithood? They have the ability to learn new languages. (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) You have to learn the language of boolean logic before you can understand what a bit is. Humans have this ability. I think that eventually a.i. will progress to the point where machines can do anything humans can. But I don't think that either humans or A.I. can always identify when something is being used as a bit. For example, consider an encoded message sent between two spies. They hope that it is impossible for humans to tell where the bits are (cont)
randyhelzerman 2 years ago
(cont, to 126altf4) I do think you can describe any computer in the language of physics. But you can't describe it as being a computer. Say its a computer made out of vacuum tubes, you can say "here are some tungten atoms, here are some oxygen atoms, . . . " a very detailed description. But if you gave that description of the computer to somebody else, they would not be able to identify where the input was, where the output was, etc.
randyhelzerman 2 years ago
how do you define, in short, reductive functionalism?
Is it: functional mental states can be reduced to functional physical states; thus, physical states give rise to mental states? is that correct?
trufkin1000 3 years ago
and another thing, plantinga is all you guys got lol -
robotaholic 3 years ago
?? um, yeah, I agree that Plantinga's argument is circular, but this video isn't about that at all...
randyhelzerman 3 years ago
you really think ontological circular reasoning like plantinga's argument can really be used to decide if there is a god or not? that is rediculous-
robotaholic 3 years ago
I think your argument is very similar to Block's. Block simply uses consciousness/brain while you used boolean logic/physical objects.
You said that since there are infinite number of instanciation of showing true or false. I am not sure why this would be an argument against Kim's notion of reduction. Don't you and Kim both believe that there really is only physical substance?
ContraWagner 3 years ago
Hi ContraWagner, the thing is that (if I understand him correctly) Kim seems to think that we could form a bridge law between the mental and the physical--a bridge law being a law of the form (∀x)( m(x) ↔ ϕ1(x) ∨ ϕ1(x) ∨ ... ∨ ϕ(x) ). (cont)
randyhelzerman 3 years ago
where m() is a mental predicate and ϕi are physical predicates. I believe this video shows that it is impossible to create such a bridge law. And Yes, I do think that Block's point is very similar, but I don't think he has a PROOF that multiple realizability implies the impossibility of bridge laws; rather, he just points out that it raises some doubts about it. (cont)
randyhelzerman 3 years ago
(cont, to ContraWagner) And I think that Kim, Block, and I all think that physical "stuff" is the only "stuff" there is, but I do believe that physical facts arn't the only facts there are, in the following sense: suppose we had a complete and exhaustive description of every physical fact ϕ1, ϕ2, . . . that is or was or ever will be true (cont)
randyhelzerman 3 years ago
(cont, to ContraWagner) The absense of bridge laws means that from those ϕi, we could not determine which regions of spacetime were in pain, or which were seeing red, or even which regions of spacetime were people or not. In order to do these things, we must also have descriptions of regions of spacetime couched in mental terms, in other words, mental vocabulary is non eliminatable. Make any sense?
randyhelzerman 3 years ago
Yes, I understand your point. Given that multiple realizability poses serious problem for reductive physicalism, there seems like no possible reduction is ever possible. And this position seems even more absurd that absurdities caused by multiple realizability.
ContraWagner 3 years ago
Instead of talking mental and physical, let us consider what we would indubitably consider to be a successful reduction in science. m() be an increasing H+ ions in acqueous solutions, and ϕi be physical state of acid. And multiple realizability problem would be valid here as well. And it seems like there is no reduction in science at all..
ContraWagner 3 years ago
Hm...maybe I'm missing something, but I don't see your proposed rebuttal as being valid?
Your rebuttal involved redundant bits which means they can be simply reduced to the individual bits they're composed of (which bring us back to the members of the original set of all possible material representations of bits).
In other words, you haven't used a Cantor diagonal to construct a truly unique bit. Ie, Two redundant bits /= 1 unique bit.
ivanisavich 3 years ago
To sum up what I mean, a redundant set of identical bits could simply be considered a subset of the set of all bits. Even if you take all the bits in the set of all possible bits and make them redundant, as you did in your video, you don't have a unique set....you simply have a redundant set that's equal to the original set.
[1,1,1,1] = [1,(1,1),1] ....
[1, 1, 1, 1] = [(1,1,1,1)]...no?
ivanisavich 3 years ago
Think about it this way: suppose I have two metal switches. Then I melt them down, and create one new, bigger switch from the atoms. The new switch would be a new bit, distinct from the original two switches, no? Same would hold if I created a redundant switch out of two switches.
randyhelzerman 3 years ago
The analogy here seems not very convicing, the new metal switch indeed has a unique internal composition from the two old ones, however, the new redundant "bit" has an internal structure that is describable by using the two old "bit"s.
spiritpunker 3 years ago
Hi spiritpunker, sure, the new bit is describable by using the descriptions of the two old bits (plus a description of how they are wired up). But that just proves that the new bit is, well, a new bit, distinct from the two old bits, right?
randyhelzerman 3 years ago
Was that at all convincing, ivanisavich?
randyhelzerman 3 years ago
I think that link died, so I'll post here instead.
1) In order to specify what is "yes - no", you need to give an account of what it takes to _come to_ represent something in attention. If you do not, and merely assume that one specifies x as an output of some function, then that is going to be problematic when it comes to the metaphysics i.e. ontological commitment. Why so? Well, if representating something in consciousness is not a function,then we're dealing here with
sssswwwsssss 3 years ago
test:
the instaniation of real physical phenomena
sssswwwsssss 3 years ago
I give up. I'll PM you.
sssswwwsssss 3 years ago
Why does this work, and not the comments I've typed out twice!!!!
sssswwwsssss 3 years ago
Poor s.....
randyhelzerman 3 years ago
sorry to change topics on you guys.
the power set of the natural numbers has a one-to-one correspondence with the reals, I guess what I was wondering was: what is the interpretaion of the power set of the reals?
Also randy what did you score on the test in the sidebar of the video this is a response to?
126altf4 3 years ago
Hi 126altf4, yeah, the power set of the reals has a one-to-one correspondence with many other sets, all of which have yet more elements in them than there are real numbers. ha, I totally forgot the score, but just for you, I took it over again. I scored 95% "cultural creative" 75% "postmodernist"
randyhelzerman 3 years ago
hey randy can you clarify your earlier statement about higher order cardinals and if possible give a reference, thanks.
126altf4 3 years ago
Hi 126altf4, sure. There are some sets which have, say, 5 objects in them. the cardinality of those sets are 5. There are some sets which have as many items in them as there are natural numbers. The cardinality of those sets are Aleph null. There are some sets which contain as many items as there are real numbers. The cardinality of those sets are Aleph 1. There are sets which contain even MORE elements than real numbers!!! For each size set, there is a number which expresses (cont)
randyhelzerman 3 years ago
the cardinality thereof. A lame-ass reference is the wiki article: "Aleph number".
randyhelzerman 3 years ago
"We use the set of real numbers, but real numbers arn't all the numbers there are. Just like we apply diagonalization on rational numbers to yield reals, we can apply diagonalization on reals to yield numbers of even higher cardinality. And we do say that there is no such thing as the set of all numbers of all cardinalities."
OK, so using the diagonal argument on reals(don't know how you would set that up), you can prove there are numbers not elements of the reals?
126altf4 3 years ago
Yeah. For every set, there is a number which says "how many" elements there are in that set. More formally, there is a number which expresses the cardinality of the set. To show that there is a set which has more elements in it than there are real numbers, you can use the diagonal method like this. Consider all of the real numbers. Now, make a set of the real numbers---call this set R. (cont)
randyhelzerman 3 years ago
(cont, to 126altf4). Now, for the diagonal step--construct a new set, S, like this: S is the set of all of the subsets of R. This is also called the "powerset" of R. The theorem which cantor proved is that the powerset of R will have "more elements" (more formally, a higher cardinality) than R has. But of course, we could let T be the power set of S, and get an even higher cardinality, or let U be the power set of T, etc, without limit.
randyhelzerman 3 years ago
Good discussion b.t.w. Randy! As you can probably tell, I'm very sympathetic to the whole Chalmer's/Jackson project, but its quite controversial. I think the assumption that physicalists can help themselves to the languages of logic and math is much less controversial.
Best
jerewho 3 years ago
Hi jerewho, thanks, yes, I'm enjoying the discussion quite a bit as well. As you can tell, I have some doubts about the whole Canberra Plan :)
randyhelzerman 3 years ago
sure, i totally agree. but you don't have to accept the canberra plan to allow certain stuff into physicalism a priori, like the notion of a bit (which, although i don't know exactly how to classify your characterization, is certainly encompassed by math, logic and the relevant meta-theory). Whether or not this is truly "physical reduction" is just terminology as far as i'm concerned. Whatever it is, if we can use it as a supervenience basis for the mental, normative, etc. then (cont)
jerewho 3 years ago
it does exactly what physicalists want,reducing the "controversial" to the "better grounded" concepts.
jerewho 3 years ago
hey jerewho, my battery on my laptop is about to die, so it might be a few hours before I can respond to your further points :-) again, good discussion.
randyhelzerman 3 years ago
But that is an extreme. Others (Block/Stalneker 1999, e.g.) think that reduction DOES require rewrites into the language of physics. But but they can still help themselves to mathematics/logic/meta-logic and some modal notions without endorsing Jackson/Chalmers style "modal rationalism."
Also, Jackson's df of supervenience is: "Physicalism is true at a possible world W if and only if any world which is a minimal physical duplicate of W is a duplicate of W simpliciter."
jerewho 3 years ago
Yeah, Jackson and Chalmers help themselves to a real a priori buffet. The trick is that they do their conceptual analysis without translations from the reduced language to the language of microphysics. They do this by employing possible worlds. As long as they (idealized) can evaluate the extension of a concept at any possible world, then that's enough (they argue). I find their 2001 paper very convincing and explicit.
jerewho 3 years ago
Hi jerewho, but this video proves that you can't evaluate the concept of "bit" at any possible world, if all you know are the physical facts about the world. This is true EVEN IF physicalism holds for this world. If all you have is a physical description of the world, in order to identify all the bits and only the bits, you need a predicate Phi(x) such that forall x, Phi(x) is true iff x is a bit. But you can't have this. (cont)
randyhelzerman 3 years ago
(cont, to Jerewho) Sure, Jackson and chamers explicitly state their thesis. But by no means to they prove their thesis.
randyhelzerman 3 years ago
2 points. One, I still don't buy your df of a bit. I wasn't arguing that you have to define the concept of a question (although I do doubt that questions are a primitive in a theory of Boolean algebra). Lets assume them are. The problem is that you haven't told me WHAT questions you're talking about. All questions? Any question? A specific question? Telling me that the variable Q ranges over questions doesn't tell me which question it denotes or, if it is bound, by what quantifier?
jerewho 3 years ago
Hi jerewho, ok, lets go with your definition of a bit as something which signifies a truth value. You can run the same diagonal argument over again. In fact, the diagonal argument is meant to be a general technique for showing that two vocabularies are not reducible to each other.
randyhelzerman 3 years ago
That's just not right. Here's the definition again:
A is a bit iff it is (metaphysically) possible that there is a B such that 1) B has a 2d state space; 2) P(B=0|A=x)=0 or 1; 3) 1>P(0|A exists)>0.
All you need to evaluate this is basic modal apparatus.
jerewho 3 years ago
Hi jerewho, that doesn't work, for several reasons (1) there are things which have a state space of two elements which are not bits (2) "metaphysically possible" is not part of the vocabulary of physics. (that's as close to an a priori truth as they come: "metaphysics' means "beyond physics")
randyhelzerman 3 years ago
I don't want to argue about the definition of "bits" anymore. Regardless of the adequacy of my definition (which I do doubt) what matters is the adequacy of yours. I am still not clear what the semantic value of your "yes/no question" variable is. At ant rate, this is irrelevant, since I've argued below that physicalists take concepts like "bit" for granted, because the kind of things they care about reducing are not bits and the like, but rather goodness and tables and pains. (cont)
jerewho 3 years ago
Hi jerewho, perhaps I missed it, but I didn't see an argument that the language of physics includes bits, just a statement thereof. My argument that physics does NOT use this language is that all the laws of physics which I've ever seen are differential equations over real and complex vector spaces, which can be defined without reference to bits at all. (cont)
randyhelzerman 3 years ago
(cont, to jerewho) w.r.t. my definition of bits as an answer to a yes/no question, I still don't see what the difficulty is. A yes/no question is just a sentence which has a certain grammatical form. We could flesh out the definitions of a language as being a certain subset of strings over an alphabet, etc, but you get the picture. Just like the concepts of "point" and "line" are defined by the axioms of geometry, "question" and "answer" would be defined by whatever axioms we are to give.
randyhelzerman 3 years ago
well, it seems crazy to me to think of linguistic objects such as questions and answers as necessart primitives for a theory bits, which seem to me (pretheoretically) as a purely informational concept. (cont)
jerewho 3 years ago
Hi jerewho, what kind of information are you thinking about? Shannon information or Kolmogorov information is very much defined with respect to language. Shannon entropy for example is defined in terms of the code words you are expecting to recieve. There can be no information without language.
randyhelzerman 3 years ago
My point is this: Let Axy be a two place predicate interpreted as "x is a y/n question and y is its answer." So, is your definition of a bit:
1) b is a bit iff (there exists an x)(Axb) or
2) b is a bit iff (for all y/n questions x)(Axb) or
3) b is a bit iff for question q, Aqb (in which case I'd need to know what q is as a function of b)?
Also I think it's reasonable to interpret information theory as assuming that language semantically corresponds to states of affairs. But enough info theory
jerewho 3 years ago
Hi Jerewho, none of the above. I'd start with something like this: let A be an alphabet. Let A* be the set of all finite strings on that alphabet. Let a language L be a subset of A*. Let D be the subset of L such that the elements of D are either true or false--these are the declarative sentences. If d is a declarative sentence, let d? be its corresponding question. The correct answer to a question "d?" is "yes" if d is true, and "no" if d is false.
randyhelzerman 3 years ago
(cont, to jerewho) notice that NONE of those concepts (alphabet, string, true, false, question, answer, yes, no) can be reduced to physics, but those concepts are none the worse for that. If you ask me, for example, what "true" is, I'd just point to those axioms and say true is defined by those axioms. Same way that "point" and "line" are defined by the axioms of euclidean geometry.
randyhelzerman 3 years ago
ok, but on this theory the only "answers" are the "yes" and the "no" bits of language L. but the answers were supposed to be bits: heterogeneous arrangements of matter!
jerewho 3 years ago
Hi jerewho, so? e.g. I can talk about the point which is the center of gravity of the sun, and still say that "point" is defined by the axioms of geometry.
randyhelzerman 3 years ago
right! points are geometric objects, fine, but what matters is that the concept of a point is part of the language of physics. so, an physics duplicate of a world is a geometric duplicate of it as well. at least that's the idea.
jerewho 3 years ago
Hi jerewho, ok, I see what you mean. Well there is nothing wrong with saying that, say, a particular spatio-temporal region is BOTH a beercan AND an answer to a yes-no question. That doesn't contradict any of the postulates of yes-no-question-answer-hood nor does it contradict any of the postulate of beer-can-hood.
randyhelzerman 3 years ago
On a less substantive not, metaphysics doesn't mean anything at all (it's not like other "meta" constructions). It comes from the fact that Aristotle's writings on the topic were filed after his "physics" in the library of Alexandria, so they came to be called "meta-physics." I think the physics is riddles with metaphysical commitments, w.r.t. ontology, causation, counterfactual dependance, etc.
jerewho 3 years ago
LOL jerewho, that's true, but "metaphysically possible" uses the word metaphysical in the sense of being beyond physics. E.g. we might ask whether it is metaphysically possible for the world to have had a different kind of physics than it does now.
randyhelzerman 3 years ago
absolutely
jerewho 3 years ago
hi jerewho, so wouldn't the corellary then be that metaphysical modalities cannot be part of the language of physics then?
randyhelzerman 3 years ago
Not at all. To illustrate: say a painting is impressionistic iff it has the color structure I. There are artistically possible paintings that do not have color structure I. That does not mean that color concepts do not figure in impressionism. (cont)
jerewho 3 years ago
Hi jerewho, I don't understand your point here. Seems like that would just reinforce the point I want to make: just like the language of impressionism isn't the language of painting, the language of physics is not the language of the metaphicallly possible.
randyhelzerman 3 years ago
ok, but a can isn't INTRINSICALLY an answer to anything. it is all relative to someone who interprets it as such. but your definition leaves that all relational aspect out. here's my request: i would like a definition of a bit of the form:
a state of affairs x is a bit iff ...
where the ... does not contain the words "question" or "answer" unless they are explicitly defined (you define an answer above as a piece of LANGUAGE, but then bits cannot be answers because they are bits of matter!)
jerewho 3 years ago
Hi Jerewho, well, kinda the whole point of the video is that it really isn't possible to fill in the blank "a state of affairs x is a bit iff...." in any other language than one which also contains the terms "question", "ansswer, "yes", "no" etc. The whole point is to claim that this language is irreducible to any other language. And unless you are a dualist of a rather extreme kind, I don't see how you could say that language isn't material.
randyhelzerman 3 years ago
(cont, to jerewho) I mean, would you request me to fill in the blank "X is a line iff ...." in a language which doesn't contain the word "Point"? BTW, saying that something isn't "intrinsically" something else is a curious thing to say to somebody who doesn't believe in the a priori :-)
randyhelzerman 3 years ago
haha, alright. but you don't need to use the language of physics, english would be fine. i just don't feel that the notion of a bit that figures in your argument is precise enough for me to understand/believe the argument. i really just want clarification that doesn't reduce the concept of a bit to something else i don't understand!
jerewho 3 years ago
Hi jerewho, what's not to understand? I gave you a 100% formal definition of language, question, declarative sentence, etc above. It was as rigorous as the definition of Euclidean geometry. And sure, we could use English or any other language which was a superset of the language I defined. You know what a question is. You know what an answer is. You know what a bit is. You know what physics is. What don't you know?
randyhelzerman 3 years ago