Re: Origin of mathematics
On Wed, Apr 22, 2015 at 9:20 PM, Bruce Kellett bhkell...@optusnet.com.au wrote: LizR wrote: On 23 April 2015 at 13:24, meekerdb meeke...@verizon.net So is chess real? No, chess is an agreed-upon set of conventions invented by the human mind. It didn't exist before people, and it has rules which can be changed without it kicking back (Castling, the pawn's two-square starting move - and hence en passant - were introduced to speed up the game). So how do you respond to this paragraph from Pigliucci: The obvious example that is most close to mathematics (and logic?) itself is provided by board games: “When a game like chess is invented a whole bundle of facts become demonstrable, some of which indeed are theorems that become provable through straightforward mathematical reasoning. As we do not believe in timeless Platonic realities, we do not want to say that chess always existed — in our view of the world, chess came into existence at the moment the rules were codified. This means we have to say that all the facts about it became not only demonstrable, but true, at that moment as well … Once evoked, the facts about chess are objective, in that if any one person can demonstrate one, anyone can. And they are independent of time or particular context: they will be the same facts no matter who considers them or when they are considered” (p. 423). And how does chess, once defined, differ from mathematics? How do other universes we can't see differ from mathematics, or objects in mathematics? In both cases, between them: size is incomparable, time is incomparable, distance is incomparable, communication is impossible, change is impossible and yet we can prove things about them, simulate them, discover things about them, think about them, etc. To any self-aware-substructure (SAS) in that alternate universe we discover and think about/simulate, our universe would seem just as abstract. In fact, we might simulate a that SAS living in his world in his universe, and find him to be simulating you on our planet in our universe. Would that SAS be correct in concluding our universe is only abstract? We could analyze what his brain does and know his thoughts, he might even do the same to you and your brain, and find that you've wrongly concluded that the SAS's universe is only abstract and not real. How rude you are! Perhaps he changes his mind and credits you with some degree of concreteness. Jason -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
You think in terms of computing reality. That is not my point. I mean computing the salient aspects of reality approximately by living beings. with the purpose of avoid entropic decay. For example, a flower must compute when the amount of light is right for opening the petals, the insect that pollinate the flower, must compute when to start the journey fliying to detect the flower. A lion that attack laterally must compute speed and direction in the line to calculate in which direction run after the antelope. A bacteria must compute which quantity of marker indicates that the density of the colony is enough to synchronize the production of antigen etc. 2015-04-25 23:22 GMT+02:00 Bruno Marchal marc...@ulb.ac.be: On 25 Apr 2015, at 15:50, Alberto G. Corona wrote: Mathematics may be the simplest rules that produce complexity that can be computed. ... and not computed. Always remember that the computable is only a tiny part of the arithmetical reality, which is 99,999..998 % non computable. Reality may be the most complex game possible with the simplest rules possible, so that some elements can exist and live while responding to what happens around them. To live is to compute. If the rules of the game were a bit more complicated than necessary, the world would not exist, because nobody would live and thus observe it. The problem is that we cannot distinguish the non computable from the computable empirically. A machine much more complex than ourselves can fail us into believing in non-computable, in a computable way, but comp offers indirect clues, like finding trace of the non-computable below our substitution level. QM confirms this, somehow. Life occurs at the frontier between the computable and the non computable. Bruno 2015-04-25 3:48 GMT+02:00 Russell Standish li...@hpcoders.com.au: On Fri, Apr 24, 2015 at 05:23:38PM -0700, meekerdb wrote: On 4/24/2015 2:57 PM, John Mikes wrote: Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). I deny random, it would eliminate all our technology, science, physics, etc. etc. Random doesn't mean anything goes, it means not-deterministic. It means exactly the same system may produce different outcomes. And if you try to add two meters to two meters your result may well be 4.123 or 3.999876. So far this has not destroyed technology, science, or physics. Engineers deal with it in every system. Brent 2+2=5 for large values of 2. Exactly. Thanks Brent. -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- Alberto. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- Alberto. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
Hi John, On 24 Apr 2015, at 23:57, John Mikes wrote: Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). Without changing the game? I lend you 2 dollars, and then once again, now you owe me 175,384 dollars. Nice! I deny random, it would eliminate all our technology, science, physics, etc. etc. Why would randomness eliminate technology? We can, and do, exploit randomness. Also, some things can be random and other things being not random. You need both to see the difference and get the concept. My non-IndoEuropean mother tongue has no 'random, we use the translation of the German exbeliebig (~ from what we like??) - well I don't LIKE it, so I have no random? Russell wrote more than a decade ago: 'yes', it seems there should be a 'relative random' - but nothing further from him. Nor anybody else. The math provides a tool for measuring a form of randomness inherent from the number's perspective in arithmetic. A machine cannot distinguish randomness from a non random production of a machine much more complex than herself, so randomness is always based on theoretical, and non random deeper beliefs/assumptions. Randomly yours (no random qgnosticism, however) I appreciate your agnosticism has no random reason. You asked also: what is a number? In science, we don't know. But we can agree on some basic first principles and deduce from there. Number can be defined axiomatically by axioms like: 0 ≠ (x + 1) ((x + 1) = (y + 1)) - x = y x = 0 v Ey(x = y + 1) x + 0 = x x + (y + 1) = (x + y) + 1 x * 0 = 0 x * (y + 1) = (x * y) + x You, and all universal machines, are free to propose another theory, but up to now, everyone agrees with the axioms above for the natural numbers (0, 1, 2, ...), and in that theory, you can already prove the existence of universal numbers, and of universal numbers developing beliefs. But that theory is not Löbian. It might be conscious in some trivial sense, but it has no self-consciousness, for which you need to add the infinitely many axioms of induction: If P is true for zero, and if P is such that (if p is true for x then P is true for x + 1) then you can derive that P is true for all x. This makes the entity as much conscious than you and me, but with so less prejudices than us, the humans, that you see the theological first principle that such machine can't avoid when looking inward. More on this in a reply to Brent. Bruno John Mikes On Thu, Apr 23, 2015 at 8:02 PM, LizR lizj...@gmail.com wrote: On 23 Apr 2015, at 08:37, meekerdb wrote: 2+2=1 in mod 3 arithmetic. If you change the game you change what can be proven. You can't keep the old version and assume its proofs apply to the new game. But you haven't changed the game. 2+2=4, still, in normal arithmetic, and unless you can change THAT you are still in the same game. (All you've done is to discover that there's more to the game than you originally thought.) I'm a little disappointed. Although I'm of the opinion that maths isn't made up (based on its unreasonable effectiveness in the physical sciences) I still expected a slightly more sophisticated level of argument. If that's the type of argument that supposedly shows maths is made up, it doesn't look like physicists need fear that the mathematical rug they've been relying on for the last 300 years will be pulled out from beneath them anytime soon. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 25 Apr 2015, at 15:50, Alberto G. Corona wrote: Mathematics may be the simplest rules that produce complexity that can be computed. ... and not computed. Always remember that the computable is only a tiny part of the arithmetical reality, which is 99,999..998 % non computable. Reality may be the most complex game possible with the simplest rules possible, so that some elements can exist and live while responding to what happens around them. To live is to compute. If the rules of the game were a bit more complicated than necessary, the world would not exist, because nobody would live and thus observe it. The problem is that we cannot distinguish the non computable from the computable empirically. A machine much more complex than ourselves can fail us into believing in non-computable, in a computable way, but comp offers indirect clues, like finding trace of the non-computable below our substitution level. QM confirms this, somehow. Life occurs at the frontier between the computable and the non computable. Bruno 2015-04-25 3:48 GMT+02:00 Russell Standish li...@hpcoders.com.au: On Fri, Apr 24, 2015 at 05:23:38PM -0700, meekerdb wrote: On 4/24/2015 2:57 PM, John Mikes wrote: Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). I deny random, it would eliminate all our technology, science, physics, etc. etc. Random doesn't mean anything goes, it means not-deterministic. It means exactly the same system may produce different outcomes. And if you try to add two meters to two meters your result may well be 4.123 or 3.999876. So far this has not destroyed technology, science, or physics. Engineers deal with it in every system. Brent 2+2=5 for large values of 2. Exactly. Thanks Brent. -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- Alberto. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
Mathematics may be the simplest rules that produce complexity that can be computed. Reality may be the most complex game possible with the simplest rules possible, so that some elements can exist and live while responding to what happens around them. To live is to compute. If the rules of the game were a bit more complicated than necessary, the world would not exist, because nobody would live and thus observe it. 2015-04-25 3:48 GMT+02:00 Russell Standish li...@hpcoders.com.au: On Fri, Apr 24, 2015 at 05:23:38PM -0700, meekerdb wrote: On 4/24/2015 2:57 PM, John Mikes wrote: Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). I deny random, it would eliminate all our technology, science, physics, etc. etc. Random doesn't mean anything goes, it means not-deterministic. It means exactly the same system may produce different outcomes. And if you try to add two meters to two meters your result may well be 4.123 or 3.999876. So far this has not destroyed technology, science, or physics. Engineers deal with it in every system. Brent 2+2=5 for large values of 2. Exactly. Thanks Brent. -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- Alberto. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 4/24/2015 2:57 PM, John Mikes wrote: Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). I deny random, it would eliminate all our technology, science, physics, etc. etc. Random doesn't mean anything goes, it means not-deterministic. It means exactly the same system may produce different outcomes. And if you try to add two meters to two meters your result may well be 4.123 or 3.999876. So far this has not destroyed technology, science, or physics. Engineers deal with it in every system. Brent 2+2=5 for large values of 2. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On Fri, Apr 24, 2015 at 05:23:38PM -0700, meekerdb wrote: On 4/24/2015 2:57 PM, John Mikes wrote: Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). I deny random, it would eliminate all our technology, science, physics, etc. etc. Random doesn't mean anything goes, it means not-deterministic. It means exactly the same system may produce different outcomes. And if you try to add two meters to two meters your result may well be 4.123 or 3.999876. So far this has not destroyed technology, science, or physics. Engineers deal with it in every system. Brent 2+2=5 for large values of 2. Exactly. Thanks Brent. -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
Liz and Friends of Nearer Geography: I wrote so many times and nobody reflected so far. WHY is 2 + 2 = 4 if there is a VALID concept like RANDOM? Why not 2 + 2 = -175,834? or even '1'? (Without changing the game). I deny random, it would eliminate all our technology, science, physics, etc. etc. My non-IndoEuropean mother tongue has no 'random, we use the translation of the German exbeliebig (~ from what we like??) - well I don't LIKE it, so I have no random? Russell wrote more than a decade ago: 'yes', it seems there should be a 'relative random' - but nothing further from him. Nor anybody else. Randomly yours (no random qgnosticism, however) John Mikes On Thu, Apr 23, 2015 at 8:02 PM, LizR lizj...@gmail.com wrote: On 23 Apr 2015, at 08:37, meekerdb wrote: 2+2=1 in mod 3 arithmetic. If you change the game you change what can be proven. You can't keep the old version and assume its proofs apply to the new game. But you haven't changed the game. 2+2=4, still, in normal arithmetic, and unless you can change THAT you are still in the same game. (All you've done is to discover that there's more to the game than you originally thought.) I'm a little disappointed. Although I'm of the opinion that maths isn't made up (based on its unreasonable effectiveness in the physical sciences) I still expected a slightly more sophisticated level of argument. If that's the type of argument that supposedly shows maths is made up, it doesn't look like physicists need fear that the mathematical rug they've been relying on for the last 300 years will be pulled out from beneath them anytime soon. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 23 Apr 2015, at 03:46, LizR wrote: On 23 April 2015 at 13:24, meekerdb meeke...@verizon.net wrote: On 4/22/2015 6:06 PM, LizR wrote: I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is not covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. So is chess real? No, chess is an agreed-upon set of conventions invented by the human mind. Oh I agree with what you say above, but here you fell in a trap here. Chess is a finite game, so it exists, at least in the theory of the finite games, which is itself embedded in arithmetic. not only chess exists like prime number, but it can be decomposed cannonically into Nim-like simpler game, and they obeys laws which can kick back, especially if you play with someone knowing those laws! It didn't exist before people, Well, it existed before, but it was not yet discovered by humans in some history. In UD*, even the chess players exist out of time. They are, roughly speaking, the number i such that the phi_i plays chess. That includes deep blues and Gasparov. Chess exists in arithmetic, as long with the (roughly) 10^120 games of chess, and even those non stopping (and thus recurring) where the local standard laws of stopping the play does not apply. They exist in abstract form, but also in relatively concrete form, like in the i such that phi_i emulates the Milky-Way at a very low subst. level. That emulation can go through the emulation of a chess board de luxe, in a rare wood with a special perfume. and it has rules which can be changed without it kicking back (Castling, the pawn's two-square starting move - and hence en passant - were introduced to speed up the game). Well, we can have a problem with the identity of chess, but that's the same with humans, animals and plants, and that makes them not not existing (in some modal sense) in arithmetic, once we assume computationalism, of course. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 23 Apr 2015, at 08:37, meekerdb wrote: On 4/22/2015 10:41 PM, LizR wrote: On 23 April 2015 at 16:31, meekerdb meeke...@verizon.net wrote: On 4/22/2015 9:25 PM, LizR wrote: On 23 April 2015 at 16:16, meekerdb meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446) The question they need to answer is why these things don't change. Humans can change other things they make up - as already mentioned, the rules of chess are one example. They can change things. Robinson arithmetic is a change of Peano's. But we give it a different name instead of saying we've changed arithmetic. It's just as if we'd kept the old version of chess around and given a different name to the new version. It's a nominal distinction whether it's changed or it's a new thing. As far as I know, we keep the old version. Surely the new one is an addition? Or are you saying these changes could be made any which way, that there is no kicking back? That 2+2 can equal 5, as O'Brien claimed? That seems kind of unlikely, to be honest. 2+2=1 in mod 3 arithmetic. If you change the game you change what can be proven. You can't keep the old version and assume its proofs apply to the new game. OK, but 2+2 is not equal to 1 in arithmetic. It is equal to 1 in modular arithmetic, which is a way to assert that the rest of the division by 3 of 2 + 2 is equal to 1 in arithmetic. Modular arithmetic makes sense because we know already that 2+2= 4 in arithmetic. The very existence of the many modular arithmetic is a consequence of arithmetical laws. It confirms 2=2=4, without throwing any doubt on it. Bruno Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 4/22/2015 10:41 PM, LizR wrote: On 23 April 2015 at 16:31, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: On 4/22/2015 9:25 PM, LizR wrote: On 23 April 2015 at 16:16, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446) The question they need to answer is /why/ these things don't change. Humans can change other things they make up - as already mentioned, the rules of chess are one example. They can change things. Robinson arithmetic is a change of Peano's. But we give it a different name instead of saying we've changed arithmetic. It's just as if we'd kept the old version of chess around and given a different name to the new version. It's a nominal distinction whether it's changed or it's a new thing. As far as I know, we keep the old version. Surely the new one is an addition? Or are you saying these changes could be made any which way, that there is no kicking back? That 2+2 can equal 5, as O'Brien claimed? That seems kind of unlikely, to be honest. 2+2=1 in mod 3 arithmetic. If you change the game you change what can be proven. You can't keep the old version and assume its proofs apply to the new game. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 23 Apr 2015, at 08:37, meekerdb wrote: 2+2=1 in mod 3 arithmetic. If you change the game you change what can be proven. You can't keep the old version and assume its proofs apply to the new game. But you haven't changed the game. 2+2=4, still, in normal arithmetic, and unless you can change THAT you are still in the same game. (All you've done is to discover that there's more to the game than you originally thought.) I'm a little disappointed. Although I'm of the opinion that maths isn't made up (based on its unreasonable effectiveness in the physical sciences) I still expected a slightly more sophisticated level of argument. If that's the type of argument that supposedly shows maths is made up, it doesn't look like physicists need fear that the mathematical rug they've been relying on for the last 300 years will be pulled out from beneath them anytime soon. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 4/22/2015 6:06 PM, LizR wrote: I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is /not/ covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. So is chess real? Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 23 April 2015 at 13:24, meekerdb meeke...@verizon.net wrote: On 4/22/2015 6:06 PM, LizR wrote: I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is *not* covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. So is chess real? No, chess is an agreed-upon set of conventions invented by the human mind. It didn't exist before people, and it has rules which can be changed without it kicking back (Castling, the pawn's two-square starting move - and hence en passant - were introduced to speed up the game). -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On Thursday, April 23, 2015 at 3:24:22 AM UTC+2, Brent wrote: On 4/22/2015 6:06 PM, LizR wrote: I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is *not* covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. So is chess real? If we want to be that fuzzy, assuming something can have rigid, verifiable objective properties but not before humans can think of it, then the answer is yes, chess exists, but it's a different game from 3 days ago when Anand beat Wesley So with algorithm that started with Knight to B8 on the 10th move of a Spanish. As stated in the article, there's always the risk of confusing some set of rules with the implications of that set of rules. But this itself kicks back too with the claimed discovery of rigid/prior existence or not categories as well. Consequently, this classification was not true a moment before the authors thought of it, becoming true, when the authors did their magic. This would be consistent by giving single universe/time/human primacy, but also has the ring to it, of people trying to sell us the world revolves around the human and time but not before we thought of it. How convenient, one may smile plausibly. Quote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446). That's a statement of faith/dogma with pretensions of un-transcendental truth, which is as unclear and esoteric as how they appear to start their reasoning. We can't have it both ways unless we really, really will it... then it shall be evoked humans! Ok, I guess they're running out of time and I should by the book of un-transcendental truth to see the light that isn't lit before they thought of it? Uhm, no sale here at the moment, although it seems a nice try, even if perhaps a bit naive on theological subtleties, fictions and truth. PGC -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 4/22/2015 7:38 PM, PGC wrote: On Thursday, April 23, 2015 at 3:24:22 AM UTC+2, Brent wrote: On 4/22/2015 6:06 PM, LizR wrote: I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is /not/ covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. So is chess real? If we want to be that fuzzy, assuming something can have rigid, verifiable objective properties but not before humans can think of it, then the answer is yes, chess exists, but it's a different game from 3 days ago when Anand beat Wesley So with algorithm that started with Knight to B8 on the 10th move of a Spanish. As stated in the article, there's always the risk of confusing some set of rules with the implications of that set of rules. But this itself kicks back too with the claimed discovery of rigid/prior existence or not categories as well. Consequently, this classification was not true a moment before the authors thought of it, becoming true, when the authors did their magic. This would be consistent by giving single universe/time/human primacy, but also has the ring to it, of people trying to sell us the world revolves around the human and time but not before we thought of it. How convenient, one may smile plausibly. Quote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446). That's a statement of faith/dogma with pretensions of un-transcendental truth, which is as unclear and esoteric as how they appear to start their reasoning. Why isn't is just their hypothetical explanation of how to look at the world - like Bruno's comp hypothesis? You seem to be holding them to some standard of axiomatic reasoning when their thesis is to explain the origin of axiomatic reasoning. Brent We can't have it both ways unless we really, really will it... then it shall be evoked humans! Ok, I guess they're running out of time and I should by the book of un-transcendental truth to see the light that isn't lit before they thought of it? Uhm, no sale here at the moment, although it seems a nice try, even if perhaps a bit naive on theological subtleties, fictions and truth. PGC -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 23 April 2015 at 16:16, meekerdb meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446) The question they need to answer is *why* these things don't change. Humans can change other things they make up - as already mentioned, the rules of chess are one example. I haven't read the whole thing, so perhaps they do have an explanation for why made up things can't be changed? If so, I'd be interested to know what it is (not having time, sadly, to read every paper published on this list). -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
meekerdb wrote: Is mathematics neither invented nor discovered, but evoked? https://scientiasalon.wordpress.com/2015/04/21/smolin-on-mathematics/ The review by Pigliucci is fascinating. It almost makes me want to buy Smolin's book -- he seems to be saying much of what I have always thought about the nature and origin of mathematics. Bruce -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is *not* covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
LizR wrote: On 23 April 2015 at 13:24, meekerdb meeke...@verizon.net So is chess real? No, chess is an agreed-upon set of conventions invented by the human mind. It didn't exist before people, and it has rules which can be changed without it kicking back (Castling, the pawn's two-square starting move - and hence en passant - were introduced to speed up the game). So how do you respond to this paragraph from Pigliucci: The obvious example that is most close to mathematics (and logic?) itself is provided by board games: “When a game like chess is invented a whole bundle of facts become demonstrable, some of which indeed are theorems that become provable through straightforward mathematical reasoning. As we do not believe in timeless Platonic realities, we do not want to say that chess always existed — in our view of the world, chess came into existence at the moment the rules were codified. This means we have to say that all the facts about it became not only demonstrable, but true, at that moment as well … Once evoked, the facts about chess are objective, in that if any one person can demonstrate one, anyone can. And they are independent of time or particular context: they will be the same facts no matter who considers them or when they are considered” (p. 423). And how does chess, once defined, differ from mathematics? Bruce -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 4/22/2015 6:46 PM, LizR wrote: On 23 April 2015 at 13:24, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: On 4/22/2015 6:06 PM, LizR wrote: I can't see how his categorisation works. Existence is generally considered to be a property of kicking back - of something existing independently of us, and not conforming to whatever we'd like it to be. For example. a planet is generally considered to exist - we can observer it (or land things on it) and discover unexpected results - Mars is /not/ covered in H.G.Wells' Martian civilisation or Ray Bradbury's crystal cities, no matter how much we might want it to be. God (in the conventional sense of supreme being who created the universe) is sometimes considered not to exist because it's a concept that gets modified to account for new scientific discoveries - few Christians nowadays consider that God created the Earth 6000 years ago, or directly caused it to be entirely flooded, for example. Roberto Unger and Lee Smolin are trying to claim that something can exist (kick back - or as they put it, have rigid properties) yet not have existed prior to being thought of by human minds. It seems hard to reconcile these properties. Something thought up that describes something that exists could reasonably be called an accurate scientific theory; something thought up that describes something that doesn't exist could reasonably be called fictional (or a failed scientific theory). I can see no reason why a fiction should have rigid properties. Conversely, if the subject of some theory kicks back, it's reasonable to consider it a (possibly) accurate theory describing something that should be considered (at least provisionally) real. So is chess real? No, chess is an agreed-upon set of conventions invented by the human mind. It didn't exist before people, and it has rules which can be changed without it kicking back (Castling, the pawn's two-square starting move - and hence en passant - were introduced to speed up the game). But isn't the fact that we call it chess with a change also a convention. If we'd called the game with castling etc, Chass then chass would be a new rigid invention...like arithmetic. I can imagine some Homo Neanderthalis saying,Look over there. There's Thog, Glug, and Drod. His companion says,That's sorta the same as me, you, and Crak. Let's call it 'three'. And so they invented arithmetic. Arithmetic depends on seeing similarities to group individuals and abstract away all the count. Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
RE: Origin of mathematics
Really interesting! Good to find someone that concurs with a one-at-a-time universe. I think this will emerge as being right, in the end. Thanks. Colin -Original Message- From: meekerdb meeke...@verizon.net Sent: 23/04/2015 5:36 AM To: EveryThing everything-list@googlegroups.com Subject: Origin of mathematics Is mathematics neither invented nor discovered, but evoked? https://scientiasalon.wordpress.com/2015/04/21/smolin-on-mathematics/ Brent -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 4/22/2015 9:25 PM, LizR wrote: On 23 April 2015 at 16:16, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446) The question they need to answer is /why/ these things don't change. Humans can change other things they make up - as already mentioned, the rules of chess are one example. They can change things. Robinson arithmetic is a change of Peano's. But we give it a different name instead of saying we've changed arithmetic. It's just as if we'd kept the old version of chess around and given a different name to the new version. It's a nominal distinction whether it's changed or it's a new thing. Brent I haven't read the whole thing, so perhaps they do have an explanation for why made up things can't be changed? If so, I'd be interested to know what it is (not having time, sadly, to read every paper published on this list). -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
LizR wrote: On 23 April 2015 at 16:16, meekerdb meeke...@verizon.net mailto:meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446) The question they need to answer is /why/ these things don't change. Humans can change other things they make up - as already mentioned, the rules of chess are one example. I haven't read the whole thing, so perhaps they do have an explanation for why made up things can't be changed? If so, I'd be interested to know what it is (not having time, sadly, to read every paper published on this list). This is part of the excerpt I posted before: Once evoked, the facts about chess are objective, in that if any one person can demonstrate one, anyone can. And they are independent of time or particular context: they will be the same facts no matter who considers them or when they are considered. I think this answers your question. If you change the rules of chess, you create a new and different game -- you do not change things that were true of the old game. Bruce -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On Thu, Apr 23, 2015 at 6:16 AM, meekerdb meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Quote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446). That's a statement of faith/dogma with pretensions of un-transcendental truth, which is as unclear and esoteric as how they appear to start their reasoning. Why isn't is just their hypothetical explanation of how to look at the world - like Bruno's comp hypothesis? Everybody can choose their own theology. How/to what degree this bears on truth is much more subtle. They seem to confuse this because they first state false dichotomy between Platonism and some humanism/nominalism implies their system. Then they reason and conclude, see above, that some humanist magic will is responsible for discoveries. So they do side with a flavor of nominalism and, in strong fashion, state abstract truth of their faith. This strongly, they leave realm of hypothesis + reasoning and do what seems to be closer to advertising, with self-reinforcing messages. Looks circular without much consequence, although I haven't read it and rely on the interpretation and quotes. How that's different from Bruno's hypothesis? He doesn't state in any paper or post (to my knowledge) that comp is true. You seem to be holding them to some standard of axiomatic reasoning when their thesis is to explain the origin of axiomatic reasoning. With fuzzy elements, humans, prior existence etc. which is not wrong, but this doesn't seem to clarify anything, nor do they advance with anything novel from their proposal of the stated flawed dichotomy. PGC -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
Re: Origin of mathematics
On 23 April 2015 at 16:31, meekerdb meeke...@verizon.net wrote: On 4/22/2015 9:25 PM, LizR wrote: On 23 April 2015 at 16:16, meekerdb meeke...@verizon.net wrote: On 4/22/2015 7:38 PM, PGC wrote: Both the records and the mathematical objects are human constructions which are brought into existence by exercises of human will; neither has any transcendental existence. Both are static, not in the sense of existing outside of time, but in the weak sense that, once they come to exist, they don’t change” (pp. 445-446) The question they need to answer is *why* these things don't change. Humans can change other things they make up - as already mentioned, the rules of chess are one example. They can change things. Robinson arithmetic is a change of Peano's. But we give it a different name instead of saying we've changed arithmetic. It's just as if we'd kept the old version of chess around and given a different name to the new version. It's a nominal distinction whether it's changed or it's a new thing. As far as I know, we keep the old version. Surely the new one is an addition? Or are you saying these changes could be made any which way, that there is no kicking back? That 2+2 can equal 5, as O'Brien claimed? That seems kind of unlikely, to be honest. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
