Re: Where do numbers and geometry come from ?
On 06 Sep 2012, at 16:28, Brian Tenneson wrote: All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? I would say invented, as many different notion of sets can exist. You can take sets for the ontology, but it makes everything more complex, and possibly confusing. With comp the cardinal ontology is undecidable, and I think it is simpler to limit to the finite things. If you want set, with comp a good choice would be the hereditarily finite sets, but it is equivalent (for the computability and provability) with PA. A set seems to me to be a typical construction of the mind. Like physics, analysis, etc. But comp is consistent with set theory, a priori, so no real problems here. Bruno On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. If numbers are platonic, I wonder what the presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Stephen P. King Receiver: everything-list Time: 2012-09-06, 07:53:18 Subject: Re: Could we have invented the prime numbers ? Dear Roger, Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou If the prime numbers were there from the beginning, before man, then I think they were mind-created (platonic) not brain-created (human creations). Are the prime numbers an invention by man or one of man's discoveries ? I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced 6 apart, plus or minus one) Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 etc. for n5, they can be placed +-1 on a grid with a spacing of 6 That spacing seems to me at least to be a priori, out of man's control. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Stathis Papaioannou Receiver: everything-list Time: 2012-09-06, 01:24:31 Subject: Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at
Re: Re: Where do numbers and geometry come from ?
Hi Bruno Marchal What is always either true or false cannot have been invented, only discovered. Necessary or rational truths are such. Contingent truths are not. Rational or necessary truths are therefore a prioi and can only be discovered. Contingent truths or facts are therefore a posteriori and can only be invented. I suppose that knowing which type is at hand is the crucial problem. Roger Clough, rclo...@verizon.net 9/7/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Bruno Marchal Receiver: everything-list Time: 2012-09-07, 03:21:21 Subject: Re: Where do numbers and geometry come from ? On 06 Sep 2012, at 16:28, Brian Tenneson wrote: All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? I would say invented, as many different notion of sets can exist. You can take sets for the ontology, but it makes everything more complex, and possibly confusing. With comp the cardinal ontology is undecidable, and I think it is simpler to limit to the finite things. If you want set, with comp a good choice would be the hereditarily finite sets, but it is equivalent (for the computability and provability) with PA. A set seems to me to be a typical construction of the mind. Like physics, analysis, etc. But comp is consistent with set theory, a priori, so no real problems here. Bruno On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. If numbers are platonic, I wonder what the presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Stephen P. King Receiver: everything-list Time: 2012-09-06, 07:53:18 Subject: Re: Could we have invented the prime numbers ? Dear Roger, Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou If the prime numbers were there from the beginning, before man, then I think they were mind-created (platonic) not brain-created (human creations). Are the prime numbers an invention by man or one of man's discoveries ? I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced 6 apart, plus or minus one) Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 etc. for n5, they can be placed +-1 on a grid with a spacing of 6 That spacing seems to me at least to be a priori, out of man's control. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Stathis Papaioannou Receiver: everything-list Time: 2012-09-06, 01:24:31 Subject: Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received
Re: Where do numbers and geometry come from ?
On 9/7/2012 7:21 AM, Roger Clough wrote: Hi Stephen P. King I believe that what is necessarily true (rationally true) had to be always true and thus a priori. Dear Roger, But this is just a matter of definition. It remains to be explained how the necessity is achived and how it is so in the many possible worlds. Man may think he created numbers or whatever, but whatever was there before man (to allow physics etc. to happen) something else had to create.Man simply discovered numbers. Certainly we can agree that we have a common concept of numbers but they are not concrete entities that we can locate in our space and time and do not have any other properties such as mass, charge, spin, duration. Therefore we have to not use the same terminology and common sense with numbers as we do with ordinary objects of the world. One of my motivations as a student of philosophy, is to explore multiple ways to bring the common sense in alignment with the requirements of abstractions, like numbers and to look forward from this alignment to see what might be indicated or predicted. Roger Clough, rclo...@verizon.net mailto:rclo...@verizon.net 9/7/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King mailto:stephe...@charter.net *Receiver:* everything-list mailto:everything-list@googlegroups.com *Time:* 2012-09-06, 11:35:56 *Subject:* Re: Where do numbers and geometry come from ? Dear Roger, Why is it that people persist in even suggesting that numbers are created by man? Why the anthropocentric bias? Pink Ponies might have actually crated them, or Polka-dotted Unicorns! The idea is just silly! The point is that properties do not occur at the whim of any one thing, never have and never will. -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Where do numbers and geometry come from ?
Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. If numbers are platonic, I wonder what the presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Stephen P. King Receiver: everything-list Time: 2012-09-06, 07:53:18 Subject: Re: Could we have invented the prime numbers ? Dear Roger, Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou If the prime numbers were there from the beginning, before man, then I think they were mind-created (platonic) not brain-created (human creations). Are the prime numbers an invention by man or one of man's discoveries ? I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced 6 apart, plus or minus one) Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 etc. for n5, they can be placed +-1 on a grid with a spacing of 6 That spacing seems to me at least to be a priori, out of man's control. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - From: Stathis Papaioannou Receiver: everything-list Time: 2012-09-06, 01:24:31 Subject: Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Where do numbers and geometry come from ?
All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. If numbers are platonic, I wonder what the presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King stephe...@charter.net *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou If the prime numbers were there from the beginning, before man, then I think they were mind-created (platonic) not brain-created (human creations). Are the prime numbers an invention by man or one of man's discoveries ? I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced 6 apart, plus or minus one) Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 etc. for n5, they can be placed +-1 on a grid with a spacing of 6 That spacing seems to me at least to be a priori, out of man's control. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou stath...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Where do numbers and geometry come from ?
On 9/6/2012 11:09 AM, Brian Tenneson wrote: Correct me if I'm wrong but my understanding is that sets and membership cannot be defined in terms of a more primary mathematical concept. Functions can be defined in terms of this primitive called sets. Numbers are sets; natural numbers are defined directly in terms of sets (via the Von Neumann approach) and every more complicated number set can be defined in terms of the previous type of number set all the way up to real numbers, complex numbers, and nonstandard number sets. The only type of number I am not sure how they can be seen as sets is that of surreal numbers described by Conway I believe. I don't know much about surreal numbers. Yes, this approach necessitates the existence of sets and membership. Hi Brian, Surreals and hyperreals and non-standard numbers and so on, the list is long! My point is that there really is no such thing as an absolutely irreducible entity. There probably are other ways to define numbers but all properties that we want numbers to have can come from how they are defined in terms of sets. In other words, the set theoretical description of various number sets is sufficient. Depending on what intends to try to explain, but sure. Kronecker said God made the integers; all else is the work of man. I would amend that to say God made sets (and membership); all else is the work of man. Balderdash! We can use the God concept as a way to capture the sum of what exists and its evolution and so forth, but it is just another word that may not refer to anything that really exists. On Thu, Sep 6, 2012 at 7:45 AM, Stephen P. King stephe...@charter.net mailto:stephe...@charter.net wrote: Dear Brian, can be defined ... implies the necessary existence of something or process or whatever that does the act of defining the set. Truth values do not do this, btw. Sets are collections defined in terms of functions, but numbers in-themselves are not those functions.. Unless you are considering some other ideas of what sets are... If we are going to think of set as having ontological primacy we have to have a notion of a set that does not need a membership function. On 9/6/2012 10:28 AM, Brian Tenneson wrote: All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net mailto:rclo...@verizon.net wrote: Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. If numbers are platonic, I wonder what the presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. Roger Clough, rclo...@verizon.net mailto:rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King mailto:stephe...@charter.net *Receiver:* everything-list mailto:everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com mailto:everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com mailto:everything-list%2bunsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message
Re: Re: Where do numbers and geometry come from ?
Sure you can have sets without numbers. The popular set theory's development known as ZFC is not based on numbers. http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory Numbers are defined in terms of sets. What that means is that all numbers are sets but not all sets are numbers. I do agree that numbers are not created by man but neither are sets. On Thu, Sep 6, 2012 at 8:19 AM, Roger Clough rclo...@verizon.net wrote: Hi Brian Tenneson I'm just to establish the fact that numbers are a priori and so not created by man. Given that, it doesn't matter if sets are a priori or not. Presumably (I am not a mathematician) you cannot have sets without numbers, so the numbers rule. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King � � Yes, of course, but I wanted a more obvious, dramatic爀xample. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change爄tself 爄s a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. � If numbers are platonic,營 wonder what the� presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. � � � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King stephe...@charter.net *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, 牋� Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou � If the prime numbers were there from the beginning, before man, then� I think they were mind-created (platonic) not brain-created (human creations). � Are the prime numbers an invention by man or one of man's discoveries ?� � I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced� 6 apart, plus or minus one) � Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 6747%2053%2059%2061%206771 etc. � � for n5, they can be placed +-1 on a grid with a spacing of 6 � That spacing seems to me at least to be a priori, out of man's control. � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou stath...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You received this message because you
Re: Where do numbers and geometry come from ?
Dear Roger, Why is it that people persist in even suggesting that numbers are created by man? Why the anthropocentric bias? Pink Ponies might have actually crated them, or Polka-dotted Unicorns! The idea is just silly! The point is that properties do not occur at the whim of any one thing, never have and never will. On 9/6/2012 11:19 AM, Roger Clough wrote: Hi Brian Tenneson I'm just to establish the fact that numbers are a priori and so not created by man. Given that, it doesn't matter if sets are a priori or not. Presumably (I am not a mathematician) you cannot have sets without numbers, so the numbers rule. Roger Clough, rclo...@verizon.net mailto:rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Brian Tenneson mailto:tenn...@gmail.com *Receiver:* everything-list mailto:everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net mailto:rclo...@verizon.net wrote: Hi Stephen P. King � � Yes, of course, but I wanted a more obvious, dramatic爀xample. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change爄tself 爄s a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. � If numbers are platonic,營 wonder what the� presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. � � � Roger Clough, rclo...@verizon.net mailto:rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King mailto:stephe...@charter.net *Receiver:* everything-list mailto:everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, 牋� Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou � If the prime numbers were there from the beginning, before man, then� I think they were mind-created (platonic) not brain-created (human creations). � Are the prime numbers an invention by man or one of man's discoveries ?� � I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced� 6 apart, plus or minus one) � Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 tel:47%2053%2059%2061%2067 71 etc. � � for n5, they can be placed +-1 on a grid with a spacing of 6 � That spacing seems to me at least to be a priori, out of man's control. � Roger Clough, rclo...@verizon.net mailto:rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou mailto:stath...@gmail.com *Receiver:* everything-list mailto:everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com mailto:%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed
Re: Where do numbers and geometry come from ?
I couldn't agree more. On Thu, Sep 6, 2012 at 8:35 AM, Stephen P. King stephe...@charter.netwrote: Dear Roger, Why is it that people persist in even suggesting that numbers are created by man? Why the anthropocentric bias? Pink Ponies might have actually crated them, or Polka-dotted Unicorns! The idea is just silly! The point is that properties do not occur at the whim of any one thing, never have and never will. On 9/6/2012 11:19 AM, Roger Clough wrote: Hi Brian Tenneson I'm just to establish the fact that numbers are a priori and so not created by man. Given that, it doesn't matter if sets are a priori or not. Presumably (I am not a mathematician) you cannot have sets without numbers, so the numbers rule. Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King � � Yes, of course, but I wanted a more obvious, dramatic爀xample. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change爄tself 爄s a property of geometry. Numbers and geometry thus belong to the platonic world, which is forbidden or at least not consistent with the philosophy of materialism, IMHO. � If numbers are platonic,營 wonder what the� presumably materialist Steven Hawkings has to say about their origin in his recent book on numbers. � � � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stephen P. King stephe...@charter.net *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 07:53:18 *Subject:* Re: Could we have invented the prime numbers ? Dear Roger, 牋� Could the mere possibility of being a number (without the specificity of which one) be considered to be there from the beginning? On 9/6/2012 7:47 AM, Roger Clough wrote: Hi Stathis Papaioannou � If the prime numbers were there from the beginning, before man, then� I think they were mind-created (platonic) not brain-created (human creations). � Are the prime numbers an invention by man or one of man's discoveries ?� � I believe that the prime numbers are not a human invention, they were there from the beginning. Humans can discover them by brute calculation, but there is a pattern to them (except for 1, 3 and 5, spaced� 6 apart, plus or minus one) � Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 6747%2053%2059%2061%206771 etc. � � for n5, they can be placed +-1 on a grid with a spacing of 6 � That spacing seems to me at least to be a priori, out of man's control. � Roger Clough, rclo...@verizon.net 9/6/2012 Leibniz would say, If there's no God, we'd have to invent him so that everything could function. - Receiving the following content - *From:* Stathis Papaioannou stath...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 01:24:31 *Subject:* Re: Sane2004 Step One On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg whatsons...@gmail.com%20whatsons...@gmail.com wrote: But you couldn't realise you felt different if the part of your brain responsible for realising were receiving exactly the same inputs from the rest of the brain. So you could feel different, or feel nothing, but maintain the delusional belief that nothing had changed. That's begging the question. You are assuming that the brain is a machine which produces consciousness. I think that the brain is the three dimensional shadow of many levels of experience and it produces nothing but neurochemistry and alterations in our ability to access an individual set of human experiences. The brain does not produce consciousness, it defines the form of many conscious relations. But you believe that the neurochemicals do things contrary to what chemists would predict, for example an ion channel opening or closing without any cause such as a change in transmembrane potential or ligand concentration. We've talked about this before and it just isn't consistent with any scientific evidence. You interpret the existence spontaneous neural activity as meaning that something magical like this happens, but it doesn't mean that at all. -- Stathis Papaioannou -- Onward! Stephen http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html -- You
