Hi Brent and Bruno,
Thank you for pointing this out! I did mean infinite subsets, or
else the isomorphism would obviously not obtain, but in what Brent wrote is
the escape from the reason why infinities are not observable; we can only
observe those finite parts because we can distinguish those from each other
and from the whole of which they are subsets. In a sense you are making the
point that I was trying to make. Hopefully I will finish the sketch of my
bisimulation idea by this weekend.
Thanks! J
Stephen
From: everything-list@googlegroups.com
[mailto:everything-l...@googlegroups.com] On Behalf Of Bruno Marchal
Sent: Saturday, September 25, 2010 3:33 PM
To: everything-list@googlegroups.com
Subject: Re: What's wrong with this?
Stephen P. King wrote:
Umm, I had no idea that this would be so difficult to understand! I am
claiming that if there does not exist a means to determine a difference then
no difference can be said to exist. This is just a restatement of the
principle of identity of indiscernibles. If the totality of all that exists
is such that it does not exclude any possibility then it is infinite and as
such would have that property of infinities, namely that any proper subset
of that infinity is isomorphic with the infinity itself. This is equivalent
to saying that an infinity is such that is cannot distinguish itself as a
whole from any "part" of itself. To distinguish objects from each other
there must be some form of deviation and/or weakening from this isomorphism
relationship.
On 25 Sep 2010, at 18:06, Brent Meeker wrote:
This is wrong. Proper subsets of infinite sets may well be finite, {1,2} is
a proper subset of the integers.
On 9/25/2010 12:38 AM, Bruno Marchal wrote:
Perhaps Stephen meant infinite subset, in which case it is correct for N or
any enumerable set (N is isomorphe (in bijection) with all its infinite
proper and improper subsets). But still incorrect in general. N is an
infinite proper subset of R. All infinite set injects properly in bigger
sets; by Cantor theorem.
People are usually more intrigued by improper subset. That {1, 2} is
included in {1, 2, 3} is normal, but that {1, 2, 3} is included in {1, 2, 3}
astonished the beginners. Of course A is included in B means just that x in
A implies x in B.
I guess everyone know the "argument" that cannabis is a gateway drug. I goes
like that: 90 % of the heroine user have begun with Cannabis. Of course it
is non valid. 100% of the heroin users have begun with water. This does not
imply that water is a gateway product to heroin. To evaluate if cannabis
leads to heroin, you have to count the proportion of heroin user in the
cannabis smoker population; not to count the number of cannabis smoker among
the heroin user. This error is a confusion between A included in B and B
included in A, or between (x in A -> x in B) with (x in B -> x in A)..
That error is widespread and is due to local associative reasoning (itself
due to Darwinian selection). Logical validity distinguish the relevant
association, making some emotional association irrelevant, despite natural
predisposition.
You can be sure that innocent people have been condemned to the death
penalty due to that error.
Paul Valery said that in life the only choice you have is the choice between
logic and war. He said: ask for proof, and if you don't get them understand
that some people are doing a war against you. Proof, said Valery, is
elementary politeness.
I think logic is a tool for preventing manipulation indeed. But alas logic
is not well taught nor even applied in the human affair. It is a false
secret that nobody has found any evidence that cannabis is toxic or
addictive so they insist: it is gateway drug, and parents can blame cannabis
for leading their children to heroin, but it is a mistake, an error, a
confusion between p -> q and q -> p. I am paid for giving bad notes to
students, but in the health politics it is done all the time, since more
than a century. By doing such error you can manipulate people for fearing or
hating anything, and do the war to anyone, just use emotional association.
Actually when you do the correct statistics, despite illegality there is no
evidence at all that cannabis lead to other drug, on the contrary it seems
to prevent it slightly (and would be more so if legalized probably).
The whole prohibition stuff is a complete hoax. Prohibition of a drug
literally creates a huge non taxed black market. Prohibitionism does not
protect the children, it makes them the main target of that unregulated
market. It creates the drug problem. It leads also to misinformation. If all
the drug were legalized and taxed with respect to their damage cost, people
would quickly understand what are the real dangerous drug, and I bet many
would be astonished. Democracy did not prevent brain washing. Cannabis and
salvia divinorum are about infinitely less dangerous than aspirin or
caffeine. The hardest drug today are alcohol and tobacco, mainly.
I'm optimist. The prohibition of drug policy will crash down like Berlin
wall. Too much lies accumulate.
OK, apology for my rambling. It is not completely unrelated to löbianity
though, if you consider "good" as being a löbian virtue. No one can decide
for you what is good or bad for you, in the world of ideally
self-referential correct machines. It is natural respect by modesty of the
ever known first person. Löbianity would imply a form of libertarianity 'for
the others', like it implies already a form of universal dissidence for one
self (as I explained once in a post to John). Machine's theology might be
very *practically* deeply antireductionist. Consciousness is the possibility
of waking up.
Bruno
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 everything-l...@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
