On 1/20/2014 6:28 PM, Jason Resch wrote:
On Mon, Jan 20, 2014 at 6:59 PM, meekerdb <[email protected] <mailto:[email protected]>> wrote:On 1/20/2014 4:41 PM, Jason Resch wrote:On Mon, Jan 20, 2014 at 11:32 AM, meekerdb <[email protected] <mailto:[email protected]>> wrote: On 1/20/2014 12:25 AM, Bruno Marchal wrote: And to answer this properly, you have to define "physical existence of Brent" without using arithmetic. Brent:=the being who typed this sentence. (Or next time you're in California, come by and I'll give an ostensive definition - and a cup of coffee.) Thanks very much for the coffee cup, I appreciate. But frankly this will not work. If I need to define number by invoking a being typing a sentence in a post dated the 19 janvier 2014, oops: I am using some numbers here. You didn't ask to define a number, you asked to define "physical existence of Brent". And 19 January 2014 can easily be defined as when Brent typed the above message. I think you (understandably as a logician) are so immersed in the axiomatic method that you lose of sight of its connection to the physical world. Definitions become nothing but relations between symbols if you never ground them in pointing. Don't ask someone who want to compute 2+2=4 to come in California and drink four cups of coffee, if all computers have to do that I am afraid the net will become extremely slow ... I find much more plausible that I can explain numbers behavior, and Brent's brain and ideas, from elementary arithmetical axioms, than explain arithmetic from Brent and other humans ideas. Come on ... I'm quite sure you can explain Brent's brain and ideas without using any number bigger than 10^100. Just the sentence: "I'm quite sure you can explain Brent's brain and ideas without using any number bigger than 10^100." Takes a number larger than 10^100 to represent.No, the sentence only uses the description "any number bigger than 10^100". It's logically equivalent to, "Every explanation of Brent's brain and ideas uses only number less than 10^100".Okay, then you should have clarified "no single number bigger than 10^100". It is possible to represent your ideas as a series of much smaller numbers, however their combined product will almost certainly be bigger than 10^100, even for very short sentences. (10^100 is less than 42 bytes of information.)
But you don't need the product to explain my brain. And in any case there is still an unbound on the biggest number you will need. You will never need "..." or "and so forth".
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