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Discussing with a philosopher about impossible things existing or being allowed within a particular logic system, he told me:

"This is a funny thing about logically impossible things. You can prove that they exist in any non-consistent or paraconsistent logic system. You might even be able to give a (nonsensical) description that satisfies some specific definition of said thing. But that still doesn't give you anything that makes sense. There, you are asking not only to prove that a very particular impossible thing exists, but you are asking for a detailed description of it to exist as well. I know of no method for doing that" (talking mainly about a solution that makes sense to Russell's set paradox)

So ia it there any method/logic system or anything else where impossible/illogical/inconsistent things would be allowed? For example, If a solution to Russell's set paradox cannot exist and it is impossible to exist, is there any method/logic system or anything else where this solution could exist?

bautzeman
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  • Talking with that philosopher I told you about about whether dialetheism was the right "method" to do what he was saying, he said "dialetheism is not unique in any way. It doesn't let you construct the impossible in a way that was not previously available to you, though it may change your mind about what is impossible, and it may change how you handle it." so I was wondering if someone knew an alternative "method" @Conifold – bautzeman Aug 29 '18 at 21:50
  • There can not be any "objective" yes or no answer to the title question. Unfortunately, people can not mind read what would satisfy your philosopher, so you should decide for yourself if the "methods" described, dialetheism, epistemic logic, dialectic, etc., do it. And logic does not let you construct anything in a way not previously available to you, it can only reorganize what is already available. – Conifold Aug 29 '18 at 22:06
  • Assigning a noun to any concept provides the basic tools you need to analyse the problem. Faster than light travel. Ok. Let's discuss it. In the programming language Java there is the concept of marker interfaces. I define the name grape and assign it to an object. But I can assign the name grape to a set of grape objects too. Mind bending stuff. It:s a kind of simplistic polymorphism. – Richard Aug 29 '18 at 22:48
  • @Conifold "And logic does not let you construct anything in a way not previously available to you, it can only reorganize what is already available." but for example, in "standard" logic,impossible things like a solution to Russell's set paradox does no exist, but you said that in dialetheism for example it could exist. So something that was not available in one logic system is valid in another one – bautzeman Aug 29 '18 at 23:22
  • Or in paraconsistent logic @Conifold – bautzeman Aug 29 '18 at 23:39
  • They "exist" in both of course, we couldn't talk about them otherwise. Just in one they are considered "illegitimate" and in the other accepted. Logic does not make things vanish by declaring them inconsistent, nor does it make them appear by declaring them consistent. Magnetic monopoles are consistent with modern physics, for example, but we still don't know if they exist. Round squares do not exist physically, but they "exist" inasmuch as we are talking about them, whatever logic we adopt. All logic does is assign labels to what is already there and shuffle them. – Conifold Aug 29 '18 at 23:59
  • So if even the impossible does "exist" in all logic system/"method", does everything exist in every logic system/"method"? @Conifold – bautzeman Aug 30 '18 at 00:13
  • This is a point where your questions become pointless. Choose yes or no to your liking, it changes nothing. – Conifold Aug 30 '18 at 00:16
  • But isn't this kind of an objective thing? I mean, if even impossible things can "exist" in all logic systems (maybe they are illegitimate in one system and in other they are accepted, but they "exist" in all of them, isn't it?) wouldn't that mean that everything (even impossible things) do exist in all logic systems? @Conifold – bautzeman Aug 30 '18 at 23:53
  • "Exist" is not a term in this context, it is a piece of informal banter about logic. So no, it is not an objective thing, it depends on one's conversational preferences. – Conifold Aug 30 '18 at 23:56
  • @Conifold Hmm...I'm not sure if I understand this. I mean, if 1+1=2 is valid/exists in mathematics, everyone would agree on that. Why wouldn't this happen also with logic? – bautzeman Aug 31 '18 at 21:09
  • Yet people still disagree if 1 or 2 "exist" or are just fictions. – Conifold Sep 01 '18 at 03:06
  • So, when you say that not all people agrees in that everything exists (even impossible things) in all logic systems, are you saying that they do not agree that they exist physically (in reality)? @Conifold – bautzeman Sep 01 '18 at 03:09
  • To many people "physically" and "in reality" are two different things as well, particularly where 1 and 2 are concerned. – Conifold Sep 01 '18 at 03:15
  • @Conifold well, the thing I'm trying to say is, if logic systems are imaginary/abstract things, and we can make logic systems where impossible things can be true/allowed/exist, then, they exist, at least, as imaginary things, isn't it? – bautzeman Sep 01 '18 at 12:56
  • As I said before, this question is pointless because it depends on conversational preferences concerning the word "exist". – Conifold Sep 02 '18 at 19:57

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There, you are asking not only to prove that a very particular impossible thing exists, but you are asking for a detailed description of it to exist as well. I know of no method for doing that" (talking mainly about a solution that makes sense to Russell's set paradox)

Relax. Russell's Paradox was resolved over a century ago using what is now just ordinary logic and set theory. The problem was with the earliest axioms of set theory, those introduced by Cantor and Frege around 1900. They didn't work. The problem was resolved by introducing other axioms of set theory (ZFC being the most popular to date) from which it could be proven that the problematic set did not exist.

Dan Christensen
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  • Don't you think that common sense alone was enough to work out that the problematic set could not exist? I never grasped why this wasn't obvious to Russell right from the start. –  Aug 30 '18 at 09:29
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    The non-existence of the Russell set could be proven using the rules of ordinary logic. The problem was that its existence could be formally proven using Cantor and Frege's axioms of set theory. For any formula F, they assumed that there existed a set S = {x | F(x) }. Seems reasonable even today, but it blows up for F(x) = x not in x.. Their axioms didn't work. They needed new axioms of set theory that avoided this problem. – Dan Christensen Aug 30 '18 at 14:58
  • Thanks Dan. This is a useful comment. I wonder why they didn't simply accept that this set doesn't exist. I've never quite grasped this. It may not matter in maths which approach we take but it sure does in metaphysics. –  Aug 30 '18 at 16:04
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    @PeterJ The problem was the above proposed axiom of set theory. It led to an inconsistency with basic logic. Some (the intuitionists) blamed the system of logic and banned proofs by contradiction. That, too, got rid of Russell's Paradox because it relied on this method to prove the non-existence of the Russell set. That was throwing the baby out with the bathwater IMHO. – Dan Christensen Aug 30 '18 at 16:32
  • Thanks again. I'd agree with the your last sentence. This 'paradox' would be the central problem of metaphysics for me and you've explained why so few can solve it and why so many prefer to throw out the baby and allow contradictions. Fascinating issue but off-topic here. –  Aug 30 '18 at 17:09