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What proof is valid that a thing cannot exist? The only one I can think of is: 1) Exhaustively compare all things that exist, to your objective 2) Terminate

What proof is valid that a thing cannot exist? The only one I can think of is: 1) Exhaustively compare all things that exist, to your objective 2) Terminate when identity is detected This brings up all kinds of problems, such as the fundamental: "what is a 'thing'?". Can you actually enumerate all of them? How do you validate identity?

Retra 11y ago
The more relevant question you should be asking is "what is a proof?" A proof, essentially, is that which compels an unbiased rational mind into agreement. Thus we have to ask what compels a rational mind. (And what is a rational mind?) The answer, roughly, is "information." And if your claim requires information behavior that hasn't been observed, one cannot accept the claim. So all you have to do is identify a structure internal to the claim that contradicts what is known about information processing rules. Which induces a kind of language dependence, but this is not a problem because you cannot make language-independent claims in the first place. And more importantly, language cannot be meaningful unless it obeys some laws, so naturally any claim that violates them cannot be true. (E.g., Conservation of Probability prevents the existence of true claims of supernatural phenomena or self-contradiction.) In this manner, truth is a 'stack' of verifiable justifications. Something is true if: * you are justified in believing it, and * you are justified in asserting your justification, and * you are justified in asserting the previous assertion, and * Et cetera., ad infinitum, or for as far as the flow of entropy in your environment allows. You don't have to enumerate things. You just have to properly understand the claim. You have to accurately process the information encoded in its expression. To ask for a full enumeration is to ask for infinite information -- something that doesn't exist -- and thus cannot be what proof is about, or else the word 'proof' would be meaningless.
- jsprogrammer 11y ago
  I do think 'proof' is mostly meaningless in this circumstance (non-existence). You've touched on the issue of language, which I think is key to the confusion people have in this discussion. My current thinking is that the proposition of "X does not exist" has no answer/proof because the statement is meaningless. To consider that proposition, at some level you must assume that X does not exist, so the most obvious question is: What is X? If it doesn't exist, how can we even refer to it, or know its properties? If we can actually define X, then it must exist (in the most technical sense of a 'proof': X is an element of the current system you are working in). It's a contradiction, likely caused by malformed propositions.
  - Retra 11y ago
    >My current thinking is that the proposition of "X does not exist" has no answer/proof because the statement is meaningless. I would agree with that, given that I would take existence to be a tautological primitive if left to my own devices. But normally, I interpret it as "X does not exist independently of mental constructs and their derivative effects," which is a workable claim that can be false. And that's how most people mean it when making those kinds of claims. So there are two meanings to existence: existence 'proper', and existence as a name for the extra-mental nature of a thing.
    - jsprogrammer 11y ago
      If, I'm reading you right, I think you are saying there is a distinction between: a) The thing itself b) A name for the thing itself The question is then, can there be a real b) if there is no corresponding "a)", the thing that is being named. It would seem the obvious answer is, no. However, I'm sure you could try to construct some twisted logic in an attempt to allow it. Such a logic would probably have flaws (incompleteness theorems likely have something to do with it) and are likely near useless. I would agree that there are multiple definitions of existence that can be considered fruitfully. However, as a matter of formal logic, attempting to disprove/prove the non-existence of a 'thing' [0] is a trap. [0] I use quotes here, because I'm not sure anyone here has yet defined what exactly a 'thing' is. :)
      - Dylan16807 11y ago
        >The question is then, can there be a real b) if there is no corresponding "a)", the thing that is being named. If you can describe a thing that exists, in sufficient detail to check the description, then you can describe a thing that doesn't exist too. For the answer to be 'no', you have to reject the entire idea of descriptions. You have to reject the entire idea of categories, leaving only sets with predefined member lists. I think that line of thought is a waste. If you reject language as too imprecise to use on reality, you end up concluding that proofs cannot exist, so you must not actually be talking about proofs. Plus, it's easy to name something that doesn't exist. There is no piece of paper on Earth that has printed on it the string T5hYEQdla6ZLTjxQnA3D. This is something that could exist. You could even make one yourself! But as I make this comment, it does not exist.
shkkmo 11y ago
There are generally two approaches to proving non-existence. 1) An inductive proof that everything that does exist is not that thing. 2) A proof by contradiction where you start by assuming the thing does exist and then derive a contradiction. #1 only works if you accept induction is valid for the set of items you are working on. #2 actually only proves that one of your assumptions is not valid, not which one. Presumably all your other assumptions are without reproach

Retra 11y ago

The more relevant question you should be asking is "what is a proof?" A proof, essentially, is that which compels an unbiased rational mind into agreement. Thus we have to ask what compels a rational mind. (And what is a rational mind?) The answer, roughly, is "information." And if your claim requires information behavior that hasn't been observed, one cannot accept the claim. So all you have to do is identify a structure internal to the claim that contradicts what is known about information processing rules. Which induces a kind of language dependence, but this is not a problem because you cannot make language-independent claims in the first place. And more importantly, language cannot be meaningful unless it obeys some laws, so naturally any claim that violates them cannot be true. (E.g., Conservation of Probability prevents the existence of true claims of supernatural phenomena or self-contradiction.) In this manner, truth is a 'stack' of verifiable justifications. Something is true if: * you are justified in believing it, and * you are justified in asserting your justification, and * you are justified in asserting the previous assertion, and * Et cetera., ad infinitum, or for as far as the flow of entropy in your environment allows. You don't have to enumerate things. You just have to properly understand the claim. You have to accurately process the information encoded in its expression. To ask for a full enumeration is to ask for infinite information -- something that doesn't exist -- and thus cannot be what proof is about, or else the word 'proof' would be meaningless.

jsprogrammer 11y ago
I do think 'proof' is mostly meaningless in this circumstance (non-existence). You've touched on the issue of language, which I think is key to the confusion people have in this discussion. My current thinking is that the proposition of "X does not exist" has no answer/proof because the statement is meaningless. To consider that proposition, at some level you must assume that X does not exist, so the most obvious question is: What is X? If it doesn't exist, how can we even refer to it, or know its properties? If we can actually define X, then it must exist (in the most technical sense of a 'proof': X is an element of the current system you are working in). It's a contradiction, likely caused by malformed propositions.
- Retra 11y ago
  >My current thinking is that the proposition of "X does not exist" has no answer/proof because the statement is meaningless. I would agree with that, given that I would take existence to be a tautological primitive if left to my own devices. But normally, I interpret it as "X does not exist independently of mental constructs and their derivative effects," which is a workable claim that can be false. And that's how most people mean it when making those kinds of claims. So there are two meanings to existence: existence 'proper', and existence as a name for the extra-mental nature of a thing.
  - jsprogrammer 11y ago
    If, I'm reading you right, I think you are saying there is a distinction between: a) The thing itself b) A name for the thing itself The question is then, can there be a real b) if there is no corresponding "a)", the thing that is being named. It would seem the obvious answer is, no. However, I'm sure you could try to construct some twisted logic in an attempt to allow it. Such a logic would probably have flaws (incompleteness theorems likely have something to do with it) and are likely near useless. I would agree that there are multiple definitions of existence that can be considered fruitfully. However, as a matter of formal logic, attempting to disprove/prove the non-existence of a 'thing' [0] is a trap. [0] I use quotes here, because I'm not sure anyone here has yet defined what exactly a 'thing' is. :)
    - Dylan16807 11y ago
      >The question is then, can there be a real b) if there is no corresponding "a)", the thing that is being named. If you can describe a thing that exists, in sufficient detail to check the description, then you can describe a thing that doesn't exist too. For the answer to be 'no', you have to reject the entire idea of descriptions. You have to reject the entire idea of categories, leaving only sets with predefined member lists. I think that line of thought is a waste. If you reject language as too imprecise to use on reality, you end up concluding that proofs cannot exist, so you must not actually be talking about proofs. Plus, it's easy to name something that doesn't exist. There is no piece of paper on Earth that has printed on it the string T5hYEQdla6ZLTjxQnA3D. This is something that could exist. You could even make one yourself! But as I make this comment, it does not exist.

shkkmo 11y ago

There are generally two approaches to proving non-existence. 1) An inductive proof that everything that does exist is not that thing. 2) A proof by contradiction where you start by assuming the thing does exist and then derive a contradiction. #1 only works if you accept induction is valid for the set of items you are working on. #2 actually only proves that one of your assumptions is not valid, not which one. Presumably all your other assumptions are without reproach