According to my argument below, all rational truths must be a priori and all contingent truths (facts) have to be a posteriori.
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: Roger Clough Receiver: everything-list Time: 2012-09-07, 06:51:10 Subject: A leibnizian argument that necessary truths would seem to be a priori Hi Brian Tenneson Whether or not sets were there (true) a priori is a subject of debate. You might want to see http://en.wikipedia.org/wiki/Philosophy_of_mathematics My own (uninformed) view is based on Leibnizian thinking. He lists two kinds oif logic, necessary or rational logic, which is always either true or false, and contingent logic, which can be true in some cases and no0t uin other ones. To this way of thinking, all neccessary (rational) truths since tyhey must always be either true or false, if true were always true and therefore necessary truths must be a priori. 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: Brian Tenneson Receiver: everything-list Time: 2012-09-06, 11:31:35 Subject: 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 Receiver: everything-list 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?xample. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change?tself ?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,? 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 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, 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. 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