# If I can imagine it, it is possible!

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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.

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Your argument seems to be a case of what's termed "reductio ad absurdum"

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Your argument seems to be a case of what's termed "reductio ad absurdum"

The main thrust of the argument is known as Russell's paradox, which shows a contradiction in naive set theory. It was one of the motivations for axiomatic set theory, but lets not digress.

The point is I can naively imagine that such a set exists. But when I really think about it and use some basic logic applied to the mathematics I reach a contradiction. But without thinking about the mathematics properly I may have never realised the contradiction. I may even have used this set to establish other results, which of course would be pants!

No mathematics, or at best a poor interpretation of the mathematics, coupled with little knowledge of physics is a recipe for failure. I can imagine what I can imagine, but there is no reason why the world has to agree with my mental pictures.

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Your argument seems to be a case of what's termed "reductio ad absurdum"

There's a difference between Reductio Ad Absurdum and Indirect Proof. The former shows an absurd result while the latter shows an impossible result. Russel's Paradox (there's a reason I named the set 'R' ) is a case of the later and it acts as a counterexample to the general principle. This principle actually has a name. Despite having been used as early as Descartes, it has come to be called 'Hume's Law'.

The main thrust of the argument is known as Russell's paradox, which shows a contradiction in naive set theory. It was one of the motivations for axiomatic set theory, but lets not digress.

The point is I can naively imagine that such a set exists. But when I really think about it and use some basic logic applied to the mathematics I reach a contradiction. But without thinking about the mathematics properly I may have never realised the contradiction. I may even have used this set to establish other results, which of course would be pants!

No mathematics, or at best a poor interpretation of the mathematics, coupled with little knowledge of physics is a recipe for failure. I can imagine what I can imagine, but there is no reason why the world has to agree with my mental pictures.

Indeed. This sort of thinking is one of the foundations of crackpottery. They sincerely think that since they can imagine their perpetual motion device working that it simply must work. Just think of how many times you've heard people proclaim that they don't need math because they "understand" reality with their idea.

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Indeed. This sort of thinking is one of the foundations of crackpottery. They sincerely think that since they can imagine their perpetual motion device working that it simply must work. Just think of how many times you've heard people proclaim that they don't need math because they "understand" reality with their idea.

They also miss the fact that concepts in physics are inherently mathematical as they are tied to theory. Some seem more natural than others, but when it really comes to it we are phrasing things within a model and comparing this with nature.

Discussions about energy not being real, or time or whatever can more or less be applied to any concept in physics. The objections become very metaphysical quickly and rarely clarify the understanding of what physics is and what physics can really do.

Edited by ajb

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This entire Thread needs to go in the Trash Bin.

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This entire Thread needs to go in the Trash Bin.

Why?

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They also miss the fact that concepts in physics are inherently mathematical as they are tied to theory

Regretfully I have to disagree.

This discussion has occured several times recently and each time a mathematical proponent have backed away from offering a mathematical solution or route to a mathematical solution to a part of physics that requires a physical process to take place in order to determine the result.

I repeat that challenge here.

I will tell you as exactly as you like how much coarse aggregate, fine aggregate and cement (or you can tell me it doesn't matter) and I ask for a mathematically exact quantity of water to add to make concrete of desired consistency and strength.

There are methods which will get you near, but the final exact quantity has to be trimmed to suit as part of the process.

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Regretfully I have to disagree.

This discussion has occured several times recently and each time a mathematical proponent have backed away from offering a mathematical solution or route to a mathematical solution to a part of physics that requires a physical process to take place in order to determine the result.

I repeat that challenge here.

I will tell you as exactly as you like how much coarse aggregate, fine aggregate and cement (or you can tell me it doesn't matter) and I ask for a mathematically exact quantity of water to add to make concrete of desired consistency and strength.

There are methods which will get you near, but the final exact quantity has to be trimmed to suit as part of the process.

That's actually something which could in principle have an exact formula, but would be far too unwieldy for practical use. There are just too many variables. You would have to have terms for humidity of the air, how moist the mixture already was, how dense the mixture is, etc. That there are formulas that give approximate answers defeats your point.

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I am highly disappointed, tricked, mislead, I was sure I could be a centaur... If I just believed hard enough...

Edited by Moontanman

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You can't imagine a square circle, that's illogical. The only things you can imagine are life alike things, since that is where your pool of knowledge comes from. If you can imagine it, it is possible, because the universe(s) is without limit. It is infinite, if you can build a mental picture of something, it is likely it is already in the universe, since the universe is much greater than you and probably had a similar thought. You may even create it, the universe(s) are so massive that they have infinite dimensions- each move you make is but a ripple in space-time, creating possibilities for future events. Your imagination, with the correct powers, could create life. It is in that much harmony with the universe; if you try to imagine a square circle you cannot but if you try to imagine a dragon you can; that's because it is more life alike. That was a illogical example.

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How do you deal with the content of the OP? How is something blatantly inconsistent any less 'illogical' than a square circle? A contradiction is a contradiction.

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0.11111111111111111... goes on to infinity. That doesn't mean that every numeral from 0-9 is found somewhere within it.

And it certainly doesn't mean that just because I can imagine one of the numerical places in the sequence being occupied by a miniature drawing of an elephant that there must be an elephant somewhere in that number just because it has infinitely many places.

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"If I can imagine it, it is possible!"

Can you imagine a rational square root of two?

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"If I can imagine it, it is possible!"

Can you imagine a rational square root of two?

Did you only read the title?

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Hi YodaP;

I really enjoyed your post right up to the last paragraph, then I wondered.

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.

G

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Hi YodaP;

I really enjoyed your post right up to the last paragraph, then I wondered.

G

I wasn't specifically talking about any one person, but if the shoe fits, wear it.

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YodaP;

I wasn't specifically talking about any one person, but if the shoe fits, wear it.

Not even close.

I was first attracted to your title because I just spent 15 pages in the thread, Supernatural, explaining that imagination is a poor tool to use in philosophy. But I don't think anyone was really listening. I do think that my explanation that rationalization can not be used to find an unknown was understood, but I don't think that people realized that rationalization is just logic applied to imagination. People take an unknown, imagine what they think it is, then create logical steps to whatever they have imagined--and they call this rational. The problem here being that the rational part of the mind is the only part that knows how to lie.

It seems to me that imagination is a coping ability. We take what we don't know or don't understand and use our imaginations to make it more palatable. But that does not make it more real. Philosophy studies what is real, not what is palatable.

I do agree with you that math is a definite way to find and establish truth, and suspect that this is because math evolves from innate understanding. The innate understanding of more and less is at the root of math, but this is not the only innate understanding--not the only available truth.

I study consciousness and life, so I do a lot of work on awareness and emotion, which are also innate understandings. If you can supply me with a formula that explains awareness and/or emotion it would be wonderful. Until you do, I will have to simply rely on the old tools of observation, experience, logic and reason.

G

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Well, if you can imagine it, it always is indeed possible. This is always true, not only with certifiable crackpots like myself (DSM V as with 50 to 80 % of the population of the world and neigh 100 % for all agreed upon geniuses). It is true until disproven on an agreed upon norm. It is called an hypotheses. Per definition an hypothesis is held to be true until falsified.

Your hypothesis that an hypothesis always requires mathematics is thus herewith falsified.

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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.

Woh, something doesnt add up here; To use russels paradox to prove that you can conceive of something that is logically impossible means that mathematics cant be used as an ultimate proof. All paradoxes show this, if mathematics cant be used to prove it one way or the other, the system doesnt work. Then in the very next statement declare you NEED to use this broken system of math as proof.

If you can find another example that isnt a paradox i'd be content. Otherwise your saying "This proves the system is broken, you are required to use the broken system as your proof".

I remember seeing the set of all sets on portal, a little easter egg i suppose.

Edited by DevilSolution

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Well, if you can imagine it, it always is indeed possible.

Not only is that false, but has conclusively been shown to be false. Your hypothesis has been falsified.

Woh, something doesnt add up here; To use russels paradox to prove that you can conceive of something that is logically impossible means that mathematics cant be used as an ultimate proof. All paradoxes show this, if mathematics cant be used to prove it one way or the other, the system doesnt work. Then in the very next statement declare you NEED to use this broken system of math as proof.

hint: we don't use naive set theory anymore

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Not only is that false, but has conclusively been shown to be false. Your hypothesis has been falsified.

I haven't given bad rep points much if any. You got one for this one from me. (IMO bad form not to owe up to using this button BTW. So, of course I do such. Question of honour.)

Now pose proper argument concerning my argument you left out in your partial quote. You are obliged to by the rules of the site BTW.

You pinned this topic so you're stuck mate. Simply owe up to your mistake.

Do you need me to provide you an exclusive list of possible ways to logically refute my position?

Edited by kristalris

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Not only is that false, but has conclusively been shown to be false. Your hypothesis has been falsified.

hint: we don't use naive set theory anymore

Can it still be used as proof then?? I would argue not.

If you require the use of math for proof but use a flawed piece of math as the proof, then im left quite confused.

Is there no other way to conclusively show that you can imagine something that is illogical??

I think you could create a very strong argument against "if you can imagine it, it exists", but it should not include the use of paradox, im also not sure whether it would be conclusive.

Edited by DevilSolution

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I haven't given bad rep points much if any. You got one for this one from me. (IMO bad form not to owe up to using this button BTW. So, of course I do such. Question of honour.)

Now pose proper argument concerning my argument you left out in your partial quote. You are obliged to by the rules of the site BTW.

You pinned this topic so you're stuck mate. Simply owe up to your mistake.

Do you need me to provide you an exclusive list of possible ways to logically refute my position?

You made no argument. You made assertions. Your assertions are falsified by the counter-example in the OP. It is simply not the case that anything you imagine is possible.

Can it still be used as proof then?? I would argue not.

Yes. It is an example of something which is incredibly intuitive and imaginable, but impossible. That means it falsifies the claim "Anything I can imagine is possible".

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You made no argument. You made assertions. Your assertions are falsified by the counter-example in the OP. It is simply not the case that anything you imagine is possible.

Yes. It is an example of something which is incredibly intuitive and imaginable, but impossible. That means it falsifies the claim "Anything I can imagine is possible".

Made no argument? Hilarious: you don't even grasp Monty Python that take the mickey out of your way of reasoning.

http://en.wiktionary.org/wiki/possible possible means per definition especially in a scientific context a statistical possibility. If you imagine it it thus is the hypothesized a priori or prior odds. Only logically if you have absolute proof (I indeed assert that you don't state that or want to state that) can prevent you from making the fallacy of hindsight bias. You may thus logically and thus scientifically take - absolutely - anything you imagine to be true. As an hypothesis that is. This stands even if science as such already had the falsification on the highest level of proof possible before you imagined anything. Or if you imagine something that you already know to be untrue. In that case you are of bad faith, because a fraud. I already explained this sufficiently for any high school kid should be able to understand. Now I've even bothered to elaborate. These aren't thus simple assertions but a complete logically fine argument. You really don't get further than: "no it isn't / yes it is" Hilarious.

Anyway Krauss et all imagine that something can come from nothing. I.e. believe in magic because it is a contradiction. The imagine that this is possible because the mathematics shows that it is, given certain assumptions such as that c = max is the only way to interpret all the known data. Now what if this indeed proves true? (even though being far less probable than a trillion to the trillionth) Or if it proves impossible? Which on a reasonable norm has already been done, even Krauss acknowledges this stating improbable but true.

Edited by kristalris