EthanKahn

Just now, FreeWill said:

You kind of already imagined and even expessed the impossible (absolute infinity)

Why could not he imagine something contradictory?

You can never fully imagine Absolute Infinity because no matter how much of it you imagine, there will always be more. That's true of infinity, by definition. Absolute Infinity never ends and will always posit more. I never claimed to imagine all of Absolute Infinity. That's contradictory. You can never reach the end of an endless thing. Therefore, you can never encompass it, even in the mind.

You can't imagine anything contradictory because it asks you to imagine something without imagining that thing.

1 hour ago, zapatos said:

It wasn't a question about containing something that has no boundary, it was a question about your assertion that it is impossible to imagine such a thing. I can imagine lots of impossible things. What is the basis for your assertion that  this particular bit of imagination is impossible?

You can't imagine a container of an uncontainable thing. If you imagine something being contained, then you haven't imagined something uncontained, by definition. It's impossible to imagine anything that contradicts itself, because it's asking you to imagine something without imagining it. 

10 hours ago, zapatos said:

I assume you have some scientific basis for this assertion?

It's self-evident logic. Absolute Infinity goes on forever. You can't contain something that has no boundary.

1 hour ago, MigL said:

What do you mean ?
There is an infinity of decimal places between 0 and 1.

But, getting back to the cookies...
They are NOT impossible.
This website hands them out every time I log on.
( although they leave a bad taste in my mouth )

That's why I said Absolute Infinity

On September 20, 2013 at 6:03 AM, ydoaPs said:

The title is a common view among crackpots. They often think that the ability to imagine something means that the universe might actually be that way or could have been that way were things differently. To use philosophy words, they often think that conceivability means epistemic or metaphysical possibility. But, the question is, is that true?

 

To find that out, we need to find something that is conceivable but is impossible. For the first sense of possibility, (how things might actually be), that is incredibly easy. All we have to do is find something that is conceivable but not the case. Have you ever been wrong about something? If you have, you've shown that conceivability does not mean epistemic possibility.

 

The second one is a bit harder, since there's disagreement on the exact requirements of what makes something metaphysically possible, but we do know that for something to be metaphysically possible, it must also be logically possible. That is, were things different, an accurate description of the universe still wouldn't entail a contradiction.

 

So, we can knock this out by finding something which is conceivable, yet logically impossible. Can we imagine things which are contradictions? You might be tempted to say "No one can imagine a square circle!". But I'd like to talk about one which almost everyone intuitively conceives.

 

People intuitively like to group things. It's how we make sense of the world. We have apples, chairs, etc. All you have to do is put things together and you have a group. In mathematics, we call these kind of groupings 'sets'. The things in these groups are called "members". Any group of members of a set is called a "subset". This does mean that all sets are subsets of themselves, but that's not of interest to us here. What we're interested in is the idea that you can group whatever you want into a set. You can make sets of sets. You can take your set of cats and your set of dogs and put them together into a new set!

 

So, let's take a look at a specific set: the set of all sets which are not members of themselves. The set of all cats is not a member of the set of all cats-it's a set of cats, not of sets! So, it goes in! Likewise, any set consisting of no sets will go in this set of all sets which are not members of themselves.

 

So, we pose a question: Is this set of all sets which are not members of themselves (from here on out, we'll call it 'R') a member of itself? If R is a member of R, then it fails to meet the requirements to be in R, so it isn't a member of R. That's a contradiction, so that's no good. That means R must not be a member of itself. But what happens if R is a member of itself? If R is a member of itself, it meets the requirement to be in R. Since R is the set of ALL sets meeting this requirements, it goes in. Again we have R both being a member of itself and not being a member of itself. So, either way, we get a contradiction. This means something is logically impossible. But we got this result simply from the definitions of sets and members and from the very conceivable idea that you can group whatever you want together.

 

This is a situation in which something is conceivable, but logically impossible. This means it is not the case that whatever you can imagine is possible. Crackpots, take note: the fact that you can imagine something in no way implies that it is possible. It doesn't matter how clear your perpetual motion device/unified theory/God/electric universe is, imagining it doesn't cut the mustard. This is one of the reasons you NEED the math.

Yes, the set of all sets is a logical contradiction because no set can contain itself, but would have to, if it is to truly be the set of all sets. In other words, there is no such thing as the set of all sets. It's logically contradictory and logically impossible, as you've shown. However, I'm utterly unconvinced of your claim that you can imagine the set of all sets. Such a set would have to include an Absolute Infinitely large set within it.

Yet, Absolute Infinity can never be contained (even in the imagination). There's no possible way that you have the ability to imagine a container of a truly infinite set. Therefore, there's no possible way to imagine the set of all sets.