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Ani_Ibi
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:newidea:
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tdgesq
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Not the logically impossible. It is possible to imagine things that are not in existence. Such as flying fire breathing purple dragons. It is also possible to imagine the concept of impossibility.
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quasimodo
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sure it is. Imagine yourself flying (under your own un-aided power) through good old Sol and not being hurt.
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promethius95945
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correct… or simply imagine dropping a bowling ball (non-magnetized) in a null magnetic field and having it fall up…
incidently, it is not possible to properly understand/imagine the INFINITE
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tdgesq
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Not sure if you are responding to me or not, but it is not logically impossible for a person to fly through the sun unscathed under the correct conditions. It is a practical impossibility in that it is monumentally improbable. Answer me this, can you imagine being burned by the sun and not being burned by the sun in the same way while flying through it?
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tdgesq
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True, but it is possible to understand the concept of infinity.
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Ani_Ibi
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Let’s define imagination. Is it different from knowledge? Is it a kind of knowledge? Thoughts?
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john_doran
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not only is it possible to imagine a logically impossible state of affairs, it is possible to believe in a logically impossible proposition.
what can’t be done is to imagine or believe in something you know is logically impossible.
the historical example is frege: as the second volume of frege’s Grundgesetze der Arithmetik (The Basic Laws of Arithmetic) was being printed, russell famously wrote frege revealing a self-contradiction in the principles frege was using to formalize his logic (namely, Rule V); he pointed out that frege’s set theory entailed that there could be a set of all sets that do not contain themselves, but that such a set could only be a member of itself if it was not a member of itself.
until russell made this observation to frege (burali-forti and cantor himself made an earlier and similar observation about naive set-theory concerning sets of ordinals), frege believed his theory to be true; following the revelation of the paradox, however, it became clear that the theory, as stated by frege, was in fact logically impossible, despite his belief in its truth.
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TimOliv
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With God, all things are possible. So then, what is impossible?
Perhaps impossibility does not exist.
Perhaps impossibility does not exist.
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Ani_Ibi
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Thanks for this example, john. I sense a distinction is at hand between ‘believe/imagine’ and ‘know.’
And perhaps even a three-way distinction between ‘believe,’ ‘imagine,’ and ‘know.’
Before the paradox was pointed out to frege, what did that impossible set look like in his mind? Because sure and all he had an image of the impossible set in his mind.
Was it simply that the impossible set sat there as an imposter in the realm of the possible – as a kind of wolf in sheep’s clothing? And frege didn’t realize (anagnoresis) the impossibility?
I want to understand this.
What is the mechanism by which an impossibility can fool us into thinking it is possible? What then is the mechanism of anagnoresis? Where does anagnoresis come from – first principles, experience, both?
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Pius_X
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But then wouldn’t that mean impossibility is an impossibility?
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promethius95945
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no, actually. And I’m talking from the perspective of a bachelor of science, physics, here. People have an abstract concept of what they THINK infinite is, but they all lack the core understanding of the true nature of infinite. even terms like omniscient, omnipotent, and omnibenevolent have only vague understanding in the human mind.
The difference is this: we have experience with finite physical laws, so it is easy for us to imagine the antithesis of physics. We have no experience with anything which exists solely in this universe and is infinite… therefore, while we can talk about infinite as a concept, we can never REALLy understand it.
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kell0618
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It must be possible to imagine the impossible; I imagined the end of these philosophical posts!
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john_doran
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well, that’s the thing - he hadn’t considered the “set of all sets that are not self-membered”.
that having been said, i’m not sure that sets “look” like anything.
Ani Ibi:
he simply didn’t perceive the problematic entailment. although it would also have been possible for him to consider the paradoxical set without perceiving the paradox. i guess it depends on how astute one is at any given time.
Ani Ibi:
i’m not sure that there’s much mystery to it…logical impossibilities are a feature of formal sciences like math, logic, and other branches of philosophy. all of these topics are difficult and often vexed, which can make the successful unravelling of all the logical strands in a given theory, painstaking. basically, sometimes people just miss stuff.
realization, when it comes, can come as the result of clear-headed reasoning, or it can “just come”. i don’t understand the latter, though i (and i’m sure everyone else) have experienced it.
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Ani_Ibi
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Yes and no. Our imagining of the infinite may be inadequate but inadequacy of imagination is not the same as total failure of imagination.
Moreover inadequacy or failure of imagination is time-bound. The limits of our imagination are set by how far ahead we can see from our vantage point on the shoulders of thinkers who have gone before us.
The question then turns from one of epistemology to pragmatics.
How much time is necessary for us to imagine the infinite? (Hey, prove its as straightforward as some want to think it is!)
What does our limited imagination do as compared to what perfect imagination does?
Is the difference negligible or significant?
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freesoulhope
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Yes, but such things are meshed together fragments of an already existing reality, that has be twisted by our minds eye; a dreamy place where such things can be made possible.
The qeustion is, can you imagine a colour that does not exist?
Imagine finding a new colour; could you imagine what it would look like?
:nope: Impossible!!!
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Ani_Ibi
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There is the idea that we cannot know something without having language for it. Chomsky says that we have an underlying language and that facilitates our knowing of most things.
The Everett article I posted on another thread on the Piraha tribe turns all that on its head. The Piraha tribe may not in fact have an underlying language, but make up sentences as their experience of the immediate present dictates. The Piraha cannot think in abstractions. They have no words for colours or numbers.
What is ‘the impossible’? Is it merely not self-evident? Is it merely counter-intuitive? Is it merely unimaginable in the context of time and culture? Is it merely a term for what we cannot or will not imagine?
Certainly one line of approach is to consider the possibility of imagining the impossible. Another line of approach is to imagine the effect of imagining the possible. Many buddhist koans are of the latter bent; for instance, what is the sound of one hand clapping?
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tdgesq
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Not only is an appeal to authority an unconvincing argument, it is also an informal fallacy. And if you are going to appeal to an authority, how about next time pick a theoretical physicist like Anthony Rizzi who writes books about these things.
I never argued that we do have a perfect understanding of infinity. I don’t know where you’re getting this. My only point was that we can and do have a concept of infinity even though we can’t imagine infinity.
If infinity constitutes something that is the antithesis of physics, then why do theoretical physicists use it not infrequently in mathematical equations? For crying out loud, mathematicians use the concept of infinity all the time. Think about asymptotes. I don’t know what you mean by “really” understand it, but if you mean that we don’t know everything there is to know about infinity, then I’m not arguing with you.
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Ani_Ibi
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We didn’t know about x-rays before more or less a century ago. (OK, when?) X-rays are part of the electromagnetic spectrum of which visible light forms a part. I know in my mind’s eye I can visualize x-rays, although I can’t see them.Imagine finding a new colour; could you imagine what it would look like?
Much of the universe at the sub-atomic level has to be visualized because we can’t see it. We would not be able to manipulate it if we could not visualize what is going on and this goes way beyond calculus. My lab prof used to burst a vessel running up and down the lab yelling “where’s your diagram!”
Yeah, and here comes my Euros in the big ships story. The First Nations couldn’t see the Euros coming because they came in big ships. They clued in when the Euros disembarked into small boats because their experience was of men in small fishing boats. After a period of scurvy-ridden white men landing on the beaches, the First Nations suddenly “saw” big ships.
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freesoulhope
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Yes, but you can imagine looking through somebody. You can’t imagine what a new colour would look like. And if you try, you will only end up with either a bloody nose or a very bad head ache!:banghead:. The physical laws of reality can only allow you to actualise within your mind, what reality is made of. Sorry thats an error, since we can imagine something invisble, however, we need the visible world to imagine it and can imagine it because there is something that already exists.
It was possible to imagine atoms because atoms in some form or another exist, even if it only exists as an distorted version of something that is real and atualised in the real world.
I can imagine flying, even though i cannot, simply because there are things that do fly, and reality at some level allows it to be at least a potential possiblity, even if its highly improbable. A unicorn does not exist, but we can imagine one by recreating what already exists in the material world. We cut up things up in are minds that exist in the real world, and reshape them into things that we like.
I may be wrong, but theres my 2 pence for what its worth.
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