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 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


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