### Re: Question about PA and 1p

On 17 Jan 2012, at 20:06, Stephen P. King wrote: On 1/17/2012 5:08 AM, Bruno Marchal wrote: SNIP - I disagree that set theory might be more primitive than arithmetic. Why? First because arithmetic has been proved more primitive than set theory, and less primitive than logic. With

### Re: Question about PA and 1p

On 16 Jan 2012, at 20:42, David Nyman wrote: On 16 January 2012 18:08, Bruno Marchal marc...@ulb.ac.be wrote: I do not need an extra God or observer of arithmetical truth, to interpret some number relation as computations, because the numbers, relatively to each other, already do that

### Re: Question about PA and 1p

On 17 January 2012 14:51, Bruno Marchal marc...@ulb.ac.be wrote: I think we are very close. And very close to Schroedinger intuition indeed. I think we are. However, I'm still uncomfortable about the single glance. I can see how one can talk about points of view in a 3p sense by, in effect,

### Re: Question about PA and 1p

On 1/17/2012 5:08 AM, Bruno Marchal wrote: SNIP - I disagree that set theory might be more primitive than arithmetic. Why? First because arithmetic has been proved more primitive than set theory, and less primitive than logic. With logic we cannot define numbers. with set, we can define

### Re: Question about PA and 1p

On 17 January 2012 20:02, Bruno Marchal marc...@ulb.ac.be wrote: The consciousness is the same, but with different input bits. It *is* the relative indeterminacy, intrinsic to all computational state rich enough to code a relatively universal number. The question why here and now is a

### Re: Question about PA and 1p

On 14 Jan 2012, at 18:51, David Nyman wrote: On 14 January 2012 16:50, Stephen P. King stephe...@charter.net wrote: The problem is that mathematics cannot represent matter other than by invariance with respect to time, etc. absent an interpreter. Sure, but do you mean to say that the

### Re: Question about PA and 1p

On 16 January 2012 10:04, Bruno Marchal marc...@ulb.ac.be wrote: Actually you can define computation, even universal machine, by using only addition and multiplication. So universal machine exists in elementary arithmetic in the same sense as in the existence of prime number. That may be, but

### Re: Question about PA and 1p

On 16 Jan 2012, at 15:32, David Nyman wrote: On 16 January 2012 10:04, Bruno Marchal marc...@ulb.ac.be wrote: Actually you can define computation, even universal machine, by using only addition and multiplication. So universal machine exists in elementary arithmetic in the same sense as

### Re: Question about PA and 1p

On 16 January 2012 18:08, Bruno Marchal marc...@ulb.ac.be wrote: I do not need an extra God or observer of arithmetical truth, to interpret some number relation as computations, because the numbers, relatively to each other, already do that task. From their view, to believe that we need some

### Re: Question about PA and 1p

Hi Bruno, You seem to not understand the role that the physical plays at all! This reminds me of an inversion of how most people cannot understand the way that math is abstract and have to work very hard to understand notions like in principle a coffee cup is the same as a doughnut. On

### Re: Question about PA and 1p

On 14 January 2012 16:50, Stephen P. King stephe...@charter.net wrote: The problem is that mathematics cannot represent matter other than by invariance with respect to time, etc. absent an interpreter. Sure, but do you mean to say that the interpreter must be physical? I don't see why. And

### Re: Question about PA and 1p

On 1/14/2012 10:41 AM, Stephen P. King wrote: I suppose that that is the case, but how do mathematical entities implement themselves other than via physical processes? We seem to be thinking that this is a solvable Chicken and Egg problem and I argue that we cannot use the argument of

### Re: Question about PA and 1p

On 1/14/2012 4:05 PM, meekerdb wrote: On 1/14/2012 10:41 AM, Stephen P. King wrote: I suppose that that is the case, but how do mathematical entities implement themselves other than via physical processes? We seem to be thinking that this is a solvable Chicken and Egg problem and I argue

### Re: Question about PA and 1p

On 1/14/2012 6:21 PM, Stephen P. King wrote: On 1/14/2012 4:05 PM, meekerdb wrote: On 1/14/2012 10:41 AM, Stephen P. King wrote: I suppose that that is the case, but how do mathematical entities implement themselves other than via physical processes? We seem to be thinking that this is a

### Re: Question about PA and 1p

On 1/15/2012 1:07 AM, meekerdb wrote: On 1/14/2012 6:21 PM, Stephen P. King wrote: On 1/14/2012 4:05 PM, meekerdb wrote: On 1/14/2012 10:41 AM, Stephen P. King wrote: I suppose that that is the case, but how do mathematical entities implement themselves other than via physical processes?

### Re: Question about PA and 1p

On 1/14/2012 10:32 PM, Stephen P. King wrote: On 1/15/2012 1:07 AM, meekerdb wrote: On 1/14/2012 6:21 PM, Stephen P. King wrote: On 1/14/2012 4:05 PM, meekerdb wrote: On 1/14/2012 10:41 AM, Stephen P. King wrote: I suppose that that is the case, but how do mathematical entities implement

### Re: Question about PA and 1p

Hi Stephen, On 13 Jan 2012, at 00:58, Stephen P. King wrote: Hi Bruno, On 1/12/2012 1:01 PM, Bruno Marchal wrote: On 11 Jan 2012, at 19:35, acw wrote: On 1/11/2012 19:22, Stephen P. King wrote: Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person

### Re: Question about PA and 1p

On 13 January 2012 17:24, Stephen P. King stephe...@charter.net wrote: I submit to you that you cannot just ignore the universals vs. nominal problem and posit by fiat that just because one can proof the truth of some statement that that statement's existence determines its properties. Our

### Re: Question about PA and 1p

On 1/11/2012 19:22, Stephen P. King wrote: Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person plural from having a coherent meaning, since it seems to makes PA unique and singular? In other words, how can multiple copies of PA generate a plurality of

### Re: Question about PA and 1p

Hi David, I do appreciate your remarks and thank you for writing them up and posting them. Let me interleave some comments in reply. On 1/13/2012 1:43 PM, David Nyman wrote: On 13 January 2012 17:24, Stephen P. Kingstephe...@charter.net wrote: I submit to you that you cannot just

### Re: Question about PA and 1p

Hi Stephen Thanks for responding to my post in such detail. I'll need some time to digest your points, although I'm not at all sure I have the necessary background to grasp all of what you are saying. However, I would just like to remark at this point that my characterisation of the sought-for

### Re: Question about PA and 1p

On 1/13/2012 7:29 PM, David Nyman wrote: Hi Stephen Thanks for responding to my post in such detail. I'll need some time to digest your points, although I'm not at all sure I have the necessary background to grasp all of what you are saying. However, I would just like to remark at this point

### Re: Question about PA and 1p

On 11 Jan 2012, at 19:35, acw wrote: On 1/11/2012 19:22, Stephen P. King wrote: Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person plural from having a coherent meaning, since it seems to makes PA unique and singular? In other words, how can

### Re: Question about PA and 1p

Hi Bruno, On 1/12/2012 1:01 PM, Bruno Marchal wrote: On 11 Jan 2012, at 19:35, acw wrote: On 1/11/2012 19:22, Stephen P. King wrote: Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person plural from having a coherent meaning, since it seems to makes PA

### Re: Question about PA and 1p

Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person plural from having a coherent meaning, since it seems to makes PA unique and singular? In other words, how can multiple copies of PA generate a plurality of first person since they would be an

### Re: Question about PA and 1p

On 1/11/2012 19:22, Stephen P. King wrote: Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person plural from having a coherent meaning, since it seems to makes PA unique and singular? In other words, how can multiple copies of PA generate a plurality of

### Re: Question about PA and 1p

Hi Acw, On 1/11/2012 1:35 PM, acw wrote: On 1/11/2012 19:22, Stephen P. King wrote: Hi, I have a question. Does not the Tennenbaum Theorem prevent the concept of first person plural from having a coherent meaning, since it seems to makes PA unique and singular? In other words, how can