The Set of Everything?

[peter]

(This is the set of:- (This is the set of eveything that has, does, or will exist) + (This is the set of everything that does not, has never or will never exist) + (This is the set of everything that is not, has never been nor will ever be encompassed in the other two sets).)

Have I included everything in the above set, or have I missed anything out? (also, as an aside, was the third added set an empty set).

Finally, if I define God as this Everything have I proven that God exists.

I was musing along these lines the other day and wondered what you guys might think. I doubt I'll have any more to say on it but I would be interested to know if my attempt to include 'everything' in one set works (logically) or not.

[Vain]

You need a fourth set

This is the set of everything that is , has ever been or will never be encompassed in the other three sets

[Fist and Faith]

Then a fifth set. Of everything that isn't, has never been, and never will be encompassed in the other four sets.



You're probably safe with "Everything".

If God does not exist, then the idea of God is in the set. If God exists, then God and the idea of God are both in the set. The idea that the definition of God is Everything is in the set.

[peter]

Is this going to hit up upon that Bertrand Russell thing about 'the catalogue of catalogues that include their own name' and 'the catalogue of catalogues that don't include their own name'.

Seriously is there not a sentance, or a few short sentances that will include 'everything' in the sense that I have tried (though badly it seems ) to describe. I mean one that would stand up to the scrutiny of logic without getting into an ad infinitum ad absurdium situation.

[Hashi Lebwohl]

Let A = the set of all things that we human beings can imagine, whether or not the thing we imagine is real or only an idea.

Let B = the set of all things that we human beings cannot imagine--the things we have never thought of before.

Let C = A union B, and this should be the set you want. However, you might also want the power set of C (the set of all subsets of C).

[Fist and Faith]

I still think Everything covers Everything.

[aliantha]

What's all this math junk doing in a philosophy forum, anyhow?

[Hashi Lebwohl]

What's all this math junk doing in a philosophy forum, anyhow?

Mathematics started off as a subset of philosophy, at least in the classical set of studies. The two have long been linked.

[Fist and Faith]

Is this going to hit up upon that Bertrand Russell thing about 'the catalogue of catalogues that include their own name' and 'the catalogue of catalogues that don't include their own name'.

I've never read Russell. But he's referred to in (among a million other places, eh?) Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid. Hofstadter talks about two different kinds of sets.
-Self-swallowing sets are members of themselves. The set of all sets is a member of itself. The set of Everything is a member of itself.
-Run-of-the-mill sets, which are more numerous, are not members of themselves. The set of all walruses is not a member of itself. Only walruses are member of the set.

The question is: Is the set of all run-of-the-mill sets run-of-the-mill? It doesn't work either way. Let's say it is run-of-the-mill. It is therefore a member of itself. Which means it is self-swallowing, and, therefore, not run-of-the-mill. Not being run-of-the-mill, it is not a member of itself. And if it's not a member of itself, then it is run-of-the-mill. Which means it is a member of itself. Which means it is self-swallowing...

[Vain]

Is a thought, a feeling, or a belief something?

[peter]

Vraith - yes, thats the Russell paradox(?) I was thinking of - I believe he was the first to frame it. The version I heard refers to a man given the job of cataloguing all the books in a huge library. All goes fine untill he has to catalogue the catalogues the library holds into two master catalogues on the basis of whether they contain their own name or not. Now when it comes to his own master catalogue of catalogues that dont contain their own name, because it doesn't contain it's own name he puts it in the catalogue - but......!

Love it Hashi - does this really do it! Presumably the stuff we don't imagine is scattered about in the other sets on the basis of whether we could imagine it or not. In set B, are the things we have never thought of the same as the things we cannot think of because there seems a possible difference there. I don't quite get the power set of C thing - Isn't C the set of all the subsets of C (and aren't they all contained in A and B above). It's also interesting that you have framed your response in terms of Man's imagination rather than in terms of existence or non-existence. Is this the only way it can be done or was it a choice on your part.

I would say yes - most definitely Vain. It was after all the only thing in the end that Descartes was able to utilise to establish his own existence beyond any doubt. He could doubt everything else but even if he doubted he was thinking - he was still thinking (a shot in the arm for Idealism over Materealism I should say, that when the chips were down it was only idealist stuff that saved the day for existence!)

[Hashi Lebwohl]

Love it Hashi - does this really do it! Presumably the stuff we don't imagine is scattered about in the other sets on the basis of whether we could imagine it or not. In set B, are the things we have never thought of the same as the things we cannot think of because there seems a possible difference there. I don't quite get the power set of C thing - Isn't C the set of all the subsets of C (and aren't they all contained in A and B above). It's also interesting that you have framed your response in terms of Man's imagination rather than in terms of existence or non-existence. Is this the only way it can be done or was it a choice on your part.

I chose "that which we can imagine" and "that which we cannot imagine" because there are things we can image that exist--the computer you are using--and things that we can imagine that do not exist--the untied shoestrings and the dirty glasses belonging to the "real" Hashi.

I cannot describe "that which we cannot imagine" because, obviously, I cannot imagine what those things might be. Some of them will exist--the solution to the three-body problem in physics--and some of them will not--the actor who will be cast as Lord Mhoram in the movie version of Lord Foul's Bane.

[peter]

Thanks (once again) for your tolerance and patience Hashi. Can I just be clear. You are happy (it goes above my head and I'm not going to pretend any different) the your set C (comprisied of the union of sets A and B as you define them) contains everything that can be thought, not thought, exist and not exist within its compass. ie there is nothing cosmic, quantum, spiritual, n-dimensional, anything or anythought anywhere - that aint in it. You name it - it's in it. You don't name it - it's in it. You can't name it - it's in it!

If that is indeed the case - and I am more than happy to take your word, because I'll never be able to suss it out - then my friend I think it's a damn fine thing and I take my hat of to you! (I just wonder if it's ever been done before - it probably seems a pretty purile thing to do, but I'm just damn impresed that it can be achieved.

[Hashi Lebwohl]

If that is indeed the case - and I am more than happy to take your word, because I'll never be able to suss it out - then my friend I think it's a damn fine thing and I take my hat of to you! (I just wonder if it's ever been done before - it probably seems a pretty purile thing to do, but I'm just damn impresed that it can be achieved.

Yes, I am quite satisfied with the definition of set C. Even things that don't exist and never will exist are in the set.

[peter]

Thanks Hashi,

[peter]

Thoughts on the set that contains everything.

The 'set that contains everything' must (by it's definition) contain itself. It must also contain the set containing itself and the furthur set containing the set that contains itself ad infinitum (or absurdium if you prefer ). It is thus an infinite regression to a singularity of sorts (I think).

Since the set contains things like 'Love' and 'Beauty' that are not amenable to mathematical expression, it is unlikely or even impossible that the set could ever be expressed mathematically. Does it then follow that the scientist who on a recnt BBC 'Horizon' program said that in his opinion the ultimate nature of reality was mathematical, was wrong. I think this must be so because of the existence (or not) of things that cannot be reduced to numbers within the Universe(s).

[Avatar]

*shrug* The set is imaginary anyway. Everything means every thing. Everything doesn't need to be contained in a set. Everything is the set. By definition it includes all those things that can and can't exist or be imagined etc. etc.

--A

[Hashi Lebwohl]

*shrug* The set is imaginary anyway.

What he said. The way I define the set of everything means that it would include itself--it is its own power set but that doesn't cause any problems.

The nature of reality is not mathematical; however, our understanding of the nature of reality is. No matter how advanced our mathematics becomes in the future, we will still never be able to completely understand reality.

[Avatar]

Because there is convincing evidence that reality does not make sense.

--A

[Hashi Lebwohl]

Because there is convincing evidence that reality does not make sense.

--A

Exhibit A: the platypus.