Re: Relation between sets and their elements
- From: "Peter Webb" <webbfamily-diespamdie@xxxxxxxxxxxxxxx>
- Date: Mon, 25 Apr 2005 23:34:29 +1000
"Paul Holbach" <paulholbachSPAMBAN@xxxxxxxxxx> wrote in message
news:1114412068.348941.79470@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>> Peter Webb wrote:
>> > "Paul Holbach" <paulholbachSPAMBAN@xxxxxxxxxx> wrote:
>
>> > Was there a contingently empty set called
>> > "the set of dinosaurs"
>> > *before* the first dinosaur appeared on earth, and
>> > is there still a
>> > contingently empty set called "the set of dinosaurs"
>> > now that there
>> > aren't any anymore?
>
>> Your set of dinosaurs is poorly defined.
>>
>> If you tighten up your definition of the set of dinsoaurs, then issue
>
>> disappears. Your set of dinosaurs may be "all dinosaurs
>> alive 100 million
>> years ago", "all types of dinosaurs alive 100 million
>> years ago", "all
>> dinosaurs that ever lived", or "all dinosaurs alive today"
>> (the empty set).
>> If you define exactly what the set is, the problem goes away.
>
> Okay, the set of all dinosaurs alive today is the empty set.
> But what about the set of all dinosaurs alive 100 million years ago.
> Does it still exist today or did it cease to exist when the dinosaurs
> had died out?
Of course the set of all dinosaurs that were alive 100 million years ago
exists, just as the set of all 19th Century British Prime Ministers or the
set of characters in the Wizard of Oz or the set of intelligent life forms
in the Andromeda galaxy all exist.
> Put naively, what happens to sets who happen to lose all their members?
>
Sets cannot lose their members - or rather, if they lose their members, it
is a different set. Set theory doesn't contain a concept of time or of
before and after. Sets are fixed things.
>> If you want the set to have different membership
>> depending upon the date,
>> then its not a "set" in the mathematical logic sense.
>> There is no concept of time in set theory. If something
>> happens (like comets
>> hitting the earth) that changes set membership, it creates a new set.
>
> I see.
> To take your "comet example", the earth is an element of the set of all
> planets in our solar system in 2005.
> And in case the earth is destroyed by a comet impact this year, the set
> of all planets in our solar system before the impact ceases to exist
> and a new set pops into existence: the set of all planets in our solar
> system after the impact. - Is that what you mean?
>
Well, I was more alluding to the popular belief that the dinosaurs were
wiped out by a comet hitting the earth.
No new set "pops into" existence. If we should be hit by a comet and the
earth destroyed, there is a set of planets before the impact, and a set of
planets after the impact - two different sets. We don't yet know the set of
planets after the impact, but that doesn't mean the set doesn't yet exist -
we don't know the members of the set of intelligent lifeforms in the
Andromeda galaxy, or the set of odd perfect numbers either but that doesn't
mean these sets don't exist (they do).
.
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