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Post by Eva Yojimbo on Mar 23, 2017 0:08:02 GMT
I disagree with the notion of math being a priori. Without access to the empirical we have nothing to model via math. The only reason we accept the mathematical axioms we do is because they agree without empirical experience. If they didn't, we wouldn't have them. That said, I essentially agree that such a thing wouldn't really count as evidence in the a posteriori sense either. Still, I often think that Occam is often the only real "evidence" that needs considering on some matters where a posteriori evidence can't distinguish between hypotheses (as in the case of quantum mechanics). Surely you don't need to have something to model with mathematics in order to do mathematics. Modelling empirical phenomena is one application of mathematics. It's not the only application. Some mathematical systems might not have any application whatsoever. A mathematician might develop a mathematical system just for fun, without any particular application in mind. In what sense, exactly, does the justification for a claim like "17 is a prime number" depend on experience? You don't distinguish the primes from non-primes by e.g. splitting the light of the natural numbers with a spectrometer or peering at the natural numbers through a microscope. Maybe our acceptance of an arithmetic system derived from the Peano axioms is based on our experience. Perhaps the thought is that our best models of the world appeal to such an arithmetic. But there are other arithmetics, such as modular arithmetics and inconsistent arithmetics, and these can also be used to model aspects of our experiences (most obviously, modular arithmetics can be used to model clocks). In any case, we can weaken the claim to "in the standard Peano arithmetic, 17 is a prime number". That's all that's needed for the purposes of mathematics. In what sense does the justification for this claim depend on experience? I suppose we need experience in order to acquire the relevant concepts. I learn about arithmetic, 17, primes, etc, in school. But obviously this is much broader than is usually meant by " a posteriori justification". Of course it's possible to develop mathematical systems that don't have any empirical application, but I think are rather atypical examples of what people think of as math. Empirical modeling surely accounts for the vast majority of all learned maths: I mean, if you go into any other field where math is required you can bet that the math is going to be relevant to the empirical aspects of that field (physics, eg). So, yes, math CAN be a priori in that we can create systems that don't have any empirical basis. If you want to say that "non-empirical math is still math" then I'd say "fine, fair enough," but when I made that statement I was thinking more about the majority of practical math that is most commonly used. Now, from within those systems we can invent definitions for how it functions, and these can also be true a priori: prime numbers are a perfect example of that. They exist because of the rules of the system and because we invented a term to describe an aspect of that system. Yet the only reason the system itself exists is because we have an empirical justification and need for it.
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Post by 🌵 on Mar 23, 2017 0:23:57 GMT
Surely you don't need to have something to model with mathematics in order to do mathematics. Modelling empirical phenomena is one application of mathematics. It's not the only application. Some mathematical systems might not have any application whatsoever. A mathematician might develop a mathematical system just for fun, without any particular application in mind. In what sense, exactly, does the justification for a claim like "17 is a prime number" depend on experience? You don't distinguish the primes from non-primes by e.g. splitting the light of the natural numbers with a spectrometer or peering at the natural numbers through a microscope. Maybe our acceptance of an arithmetic system derived from the Peano axioms is based on our experience. Perhaps the thought is that our best models of the world appeal to such an arithmetic. But there are other arithmetics, such as modular arithmetics and inconsistent arithmetics, and these can also be used to model aspects of our experiences (most obviously, modular arithmetics can be used to model clocks). In any case, we can weaken the claim to "in the standard Peano arithmetic, 17 is a prime number". That's all that's needed for the purposes of mathematics. In what sense does the justification for this claim depend on experience? I suppose we need experience in order to acquire the relevant concepts. I learn about arithmetic, 17, primes, etc, in school. But obviously this is much broader than is usually meant by " a posteriori justification". Of course it's possible to develop mathematical systems that don't have any empirical application, but I think are rather atypical examples of what people think of as math. Empirical modeling surely accounts for the vast majority of all learned maths: I mean, if you go into any other field where math is required you can bet that the math is going to be relevant to the empirical aspects of that field (physics, eg). So, yes, math CAN be a priori in that we can create systems that don't have any empirical basis. If you want to say that "non-empirical math is still math" then I'd say "fine, fair enough," but when I made that statement I was thinking more about the majority of practical math that is most commonly used. Now, from within those systems we can invent definitions for how it functions, and these can also be true a priori: prime numbers are a perfect example of that. They exist because of the rules of the system and because we invented a term to describe an aspect of that system. Yet the only reason the system itself exists is because we have an empirical justification and need for it. The point is that there is a distinction between the mathematics itself and the application of the mathematics to empirical phenomena. Very few people these days would say that the latter is a priori. When people give mathematics as an example of an a priori discipline, what they have in mind is the former. Admittedly I'm not an expert on what goes on in mathematics departments, but I would expect that many mathematicians, in their work qua mathematicians, aren't especially concerned about how mathematics is used in empirical modelling. They are focused simply on developing and exploring the formal systems. Indeed, if they're doing empirical modelling, they must be doing something else in addition to mathematics (physics, biology, economics, or whatever). Anyway, to return to the disagreement that started this discussion: showing that one theory is mathematically simpler than another is, surely, more analogous to e.g. deriving that 17 is a prime number than to observing a bacterium under a microscope. The justification for the claim that one theory is simpler than another seems to be a priori. How could it not be? The simplicity of a theory is a property of the theory itself; it has nothing to do with the world. (As noted though, we might argue on a posteriori grounds that simpler theories tend to be correct. So in this sense simplicity can count as empirical evidence.)
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Post by Aj_June on Mar 23, 2017 10:09:39 GMT
Well...you are good for a poor man's IshIsha. But her French sounded much more elegant. Probably you can fill her place somewhat.
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Post by Terrapin Station on Mar 23, 2017 13:12:04 GMT
One problem is that you have to assume that we're in a simulation to start the argument, because if you don't assume that, then you only can conclude that such simulations are possible in the future, but we haven't created them yet. So it's pretty question-begging. I don't think you have to assume we are, merely that such simulations are possible. They don't even have to be possible in OUR future, they just have to be metaphysically possible. They may not be. I take much the same approach with philosophical zombies. In my view p-zombies aren't possible in any sense.
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Post by Eva Yojimbo on Apr 7, 2017 18:15:49 GMT
I don't think you have to assume we are, merely that such simulations are possible. They don't even have to be possible in OUR future, they just have to be metaphysically possible. They may not be. I take much the same approach with philosophical zombies. In my view p-zombies aren't possible in any sense. They're only logically possible, meaning that there isn't anything inherently contradictory about them.
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Post by Terrapin Station on Apr 7, 2017 18:20:49 GMT
In my view p-zombies aren't possible in any sense. They're only logically possible, meaning that there isn't anything inherently contradictory about them. I don't agree that they're logically possible in any robust way, though, which is why I said "in any sense." If we have the slightest understanding of what brains are and how they work, then we can't posit creatures with functioning brains just like human brains yet that are not conscious, because we'd be positing a logical contradiction to that understanding. p-zombies are only logically possible if we feign complete ignorance.
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Post by Eva Yojimbo on Apr 7, 2017 18:43:26 GMT
Of course it's possible to develop mathematical systems that don't have any empirical application, but I think are rather atypical examples of what people think of as math. Empirical modeling surely accounts for the vast majority of all learned maths: I mean, if you go into any other field where math is required you can bet that the math is going to be relevant to the empirical aspects of that field (physics, eg). So, yes, math CAN be a priori in that we can create systems that don't have any empirical basis. If you want to say that "non-empirical math is still math" then I'd say "fine, fair enough," but when I made that statement I was thinking more about the majority of practical math that is most commonly used. Now, from within those systems we can invent definitions for how it functions, and these can also be true a priori: prime numbers are a perfect example of that. They exist because of the rules of the system and because we invented a term to describe an aspect of that system. Yet the only reason the system itself exists is because we have an empirical justification and need for it. The point is that there is a distinction between the mathematics itself and the application of the mathematics to empirical phenomena. Very few people these days would say that the latter is a priori. When people give mathematics as an example of an a priori discipline, what they have in mind is the former. Admittedly I'm not an expert on what goes on in mathematics departments, but I would expect that many mathematicians, in their work qua mathematicians, aren't especially concerned about how mathematics is used in empirical modelling. They are focused simply on developing and exploring the formal systems. Indeed, if they're doing empirical modelling, they must be doing something else in addition to mathematics (physics, biology, economics, or whatever). Anyway, to return to the disagreement that started this discussion: showing that one theory is mathematically simpler than another is, surely, more analogous to e.g. deriving that 17 is a prime number than to observing a bacterium under a microscope. The justification for the claim that one theory is simpler than another seems to be a priori. How could it not be? The simplicity of a theory is a property of the theory itself; it has nothing to do with the world. (As noted though, we might argue on a posteriori grounds that simpler theories tend to be correct. So in this sense simplicity can count as empirical evidence.) I essentially agree with your first paragraph, but I do think it's important to understand that math initially developed out of the need (and usefulness) of modeling empirical reality, and that the vast majority of math that's done is of that variety. I'm sure mathematicians aren't solely--perhaps even primarily--concerned with such things; but that's like noting that musicologists concern themselves with forms, styles, and theories that have no connection to the vast majority of music that is made and that people actually listen to. When people think of "music" most don't think of aleatory stuff, nor do most think of non-empirical mathematical systems when thinking of math. RE Simplicity: I think this comes down to whether or not you believe things are ontologically simpler/more complex than other things and whether or not you believe we have the capacity to model them mathematically. If you answer "yes" to both questions then there's no reason why the theories that can be used to explain phenomena wouldn't be subject to the same rules--that's the entire point of Solomonoff Induction: model phenomena in binary, use a Universal Turing Machine to find all possible theories that can "explain it"--ie, output the same data--, and, because those theories will also be in binary, compare their level of complexity/simplicity. The latter is easy to do when it's in the same language that is itself mathematical. Yes, the simplicity is a "property" of the theory, but the theory very much "has something to do with the world:" namely, it's whatever in the world we think explains whatever we're trying to explain. This should make sense on an intuitive level: if I observe a glass of spilled milk, then whatever theory I could concoct to explain it--the cat, the kid, messy robbers--are necessarily parts of the world. In a more "macro" context like this, the simplicity will vary on various situational circumstances (the "cat" explanation becomes much more complicated if I don't own a cat), but it's working on the same general principle. In all cases, the more you have to assume in order for a theory to be right, and the less probable those assumptions are, the less likely the theory is to be true compared to theories that require fewer and more probable assumptions.
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Post by Eva Yojimbo on Apr 7, 2017 18:51:46 GMT
They're only logically possible, meaning that there isn't anything inherently contradictory about them. I don't agree that they're logically possible in any robust way, though, which is why I said "in any sense." If we have the slightest understanding of what brains are and how they work, then we can't posit creatures with functioning brains just like human brains yet that are not conscious, because we'd be positing a logical contradiction to that understanding. p-zombies are only logically possible if we feign complete ignorance. What you're describing is metaphysical impossibility, not logical impossibility. To use a classic example, saying "water is not H20" is logically possible, but metaphysically impossible.
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Post by Deleted on Apr 7, 2017 18:53:47 GMT
Use an autocorrect program.
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Post by Deleted on Apr 7, 2017 19:00:35 GMT
I don't agree that they're logically possible in any robust way, though, which is why I said "in any sense." If we have the slightest understanding of what brains are and how they work, then we can't posit creatures with functioning brains just like human brains yet that are not conscious, because we'd be positing a logical contradiction to that understanding. p-zombies are only logically possible if we feign complete ignorance. What you're describing is metaphysical impossibility, not logical impossibility. To use a classic example, saying "water is not H20" is logically possible, but metaphysically impossible. If water is used as a rigid designator for a specific relationship that exists within every possible world. Then it isn't logically possible to be anything else but that relationship (unless of course you add additional properties to it after it being defined, but then it's not just the relationship). I use relationship there because it's possible we may be mistaken about the explanation of water. Edit:To go a little further, it is true that anything imagined (made up) can do anything to anything even contradict the previous declarations/agreements that come before. But I believe the zombie argument arises from a presumption that the relationship between two things is understood and defined and still has additional identity after the fact. Example, Sam Harris refers to humans as bio-chemical puppets/ writes a book about free will and still identifies as a mysterian.
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Post by Terrapin Station on Apr 7, 2017 19:35:39 GMT
I don't agree that they're logically possible in any robust way, though, which is why I said "in any sense." If we have the slightest understanding of what brains are and how they work, then we can't posit creatures with functioning brains just like human brains yet that are not conscious, because we'd be positing a logical contradiction to that understanding. p-zombies are only logically possible if we feign complete ignorance. What you're describing is metaphysical impossibility, not logical impossibility. To use a classic example, saying "water is not H20" is logically possible, but metaphysically impossible. And immediately you go into patronizing ass mode, as if you know more about this than I do. No, it's a logical impossibility. You can't do logical possibilities/impossibilities without semantics--you have to have some idea of what water and H2O even refer to (and didn't we get into a similar discussion re semantics on some other issue? Or was that someone else . . . anyway), and again, the only way that it's a logical possibiilty is if we play dumb with respect to any understanding whatsoever.
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Post by Cinemachinery on Apr 7, 2017 20:45:11 GMT
I'm starting to get the sense that a church fell on Stanton's family when he was a kid or something.
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Post by Eva Yojimbo on Apr 7, 2017 20:53:52 GMT
What you're describing is metaphysical impossibility, not logical impossibility. To use a classic example, saying "water is not H20" is logically possible, but metaphysically impossible. And immediately you go into patronizing ass mode, as if you know more about this than I do. No, it's a logical impossibility. You can't do logical possibilities/impossibilities without semantics--you have to have some idea of what water and H2O even refer to (and didn't we get into a similar discussion re semantics on some other issue? Or was that someone else . . . anyway), and again, the only way that it's a logical possibiilty is if we play dumb with respect to any understanding whatsoever. Well that was completely unnecessary. I'm just saying that, as far as I understand it, the distinction you're making and the way you're describing it is metaphysical rather than logical. To take the water example, we have "an idea" of what water refers to by experiencing water. We could know about hydrogen and oxygen atoms and could conceive of "h20" without knowing it was what water was made of. So saying "'H20 is not water' is logically possible" just means that it's conceivable without any inherent contradiction. We only know it's metaphysically impossible by discovering what water was made of. Just like we could conceive of experiencing water as it is without it being made of H20, we can conceive of P-zombies that act like humans but don't experience consciousness. Frankly, I don't think the "logical possibility" has much significance anyway. It should be obvious there's plenty we can imagine without any inherent contradictions partly due to the limits of our knowledge about what reality is and is made of; the challenge is figuring out what it is/made of, not in just imagining what it could be.
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Post by Eva Yojimbo on Apr 7, 2017 21:12:12 GMT
What you're describing is metaphysical impossibility, not logical impossibility. To use a classic example, saying "water is not H20" is logically possible, but metaphysically impossible. If water is used as a rigid designator for a specific relationship that exists within every possible world. Then it isn't logically possible to be anything else but that relationship (unless of course you add additional properties to it after it being defined, but then it's not just the relationship). I use relationship there because it's possible we may be mistaken about the explanation of water. Edit:To go a little further, it is true that anything imagined (made up) can do anything to anything even contradict the previous declarations/agreements that come before. But I believe the zombie argument arises from a presumption that the relationship between two things is understood and defined and still has additional identity after the fact. Example, Sam Harris refers to humans as bio-chemical puppets/ writes a book about free will and still identifies as a mysterian. The "specific relationship that exists in every possible world" could simply be our experience with water, which, AFAICT, doesn't logically require it being its precise atomic composition: could not another atomic composition give an exact kind of experiential relationship so that we call it "water?" You lose me a bit with the second paragraph: specifically, the zombie argument arises from a presumption that the relationship between WHAT two things is understood and defined?
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Post by fatpaul on Apr 8, 2017 7:03:46 GMT
P-zombies begs the question: what is consciousness? If a possible answer is given then it begs another question: why posit p-zombies if a possible answer for consciousness? Moreover: x = liquid/humans; A = H 2O/brain states; B = water/mental states (I say brain states and mental states to mean the physical and the consciousness, respectively). Ax&-Bx -- this is contradictory if, and only if, Ax is functionally equivalent to Bx. If you say that H 2O molecules and water are functionally the same then H 2O being not water is impossible, else, if not functionally the same, then possible. If you say that brain states and mental states are functionally the same then p-zombies are impossible, else, if not functionally the same, then possible. Also, Ax&-Bx is equivalent to -[Ax→Bx] -- A does not imply B. If you say that H 2O is not water is possible, then you say that H 2O not implying water is possible. If you say that brain states and not mental states is possible, then you say that brain states not implying mental states is possible. You're basically saying it's possible that A is not dependent on B, A is an independent entity. Traditionally, to say that p-zombies are possible is anti-materialism and/or anti-functionalism, and to say them impossible is pro-materialism and/or pro-functionalism.
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Post by The Herald Erjen on Apr 8, 2017 7:13:42 GMT
I'm starting to get the sense that a church fell on Stanton's family when he was a kid or something. Yes, he's a real embarrassment to the logical, critically-thinking, peer-reviewed globalist "cause," isn't he, Cine?
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Post by The Herald Erjen on Apr 8, 2017 7:54:08 GMT
Well...you are good for a poor man's IshIsha. But her French sounded much more elegant. Probably you can fill her place somewhat. The main problem for me is visual. Whenever I think of IshIsha I will remember a beautiful Da Vinci painting, and not something that looks like a Doonesbury character.
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Post by Aj_June on Apr 8, 2017 7:56:48 GMT
Well...you are good for a poor man's IshIsha. But her French sounded much more elegant. Probably you can fill her place somewhat. The main problem for me is visual. Whenever I think of IshIsha I will remember a beautiful Da Vinci painting, and not something looks like a Doonesbury character. Yeah, IshIsha is sorely missed here. I remember you and I were among very few people who tried to understand her and talk to her. I hope she finds about us but I had already invited her but she said it's over for her.
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Post by The Herald Erjen on Apr 8, 2017 8:02:35 GMT
The main problem for me is visual. Whenever I think of IshIsha I will remember a beautiful Da Vinci painting, and not something looks like a Doonesbury character. Yeah, IshIsha is sorely missed here. I remember you and I were among very few people who tried to understand her and talk to her. I hope she finds about us but I had already invited her but she said it's over for her. Thanks for trying. In the last days before IMDb closed its boards I sent her a pm (in French) and asked if she was moving to one of the new boards. She didn't go for it.
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Post by Cinemachinery on Apr 8, 2017 9:09:19 GMT
I'm starting to get the sense that a church fell on Stanton's family when he was a kid or something. Yes, he's a real embarrassment to the logical, critically-thinking, peer-reviewed globalist "cause," isn't he, Cine? Ah, fantasy Cinemachinery is also a "globalist"! The legend grows.
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