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, [email protected] 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 <[email protected]> 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, [email protected] 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 n>5, 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, [email protected] 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 <[email protected]> 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 [email protected]. To unsubscribe from this group, send email to [email protected]. 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 [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
