blike Posted March 16, 2003 Share Posted March 16, 2003 I'm trying to find examples of statements that are neither true or false. The criteria for the statement is that it must state something about the nature of an idea or physical object, and it cannot be something subjective (i.e. feeling, emotion, etc). Can you guys think of any? Link to comment Share on other sites More sharing options...
Deslaar Posted March 16, 2003 Share Posted March 16, 2003 This sentence is false. Link to comment Share on other sites More sharing options...
Sayonara Posted March 16, 2003 Share Posted March 16, 2003 Originally posted by blike I'm trying to find examples of statements that are neither true or false. Zarkov may have been a certifiable lunatic. Link to comment Share on other sites More sharing options...
blike Posted March 16, 2003 Author Share Posted March 16, 2003 heres another example: the sentence below is false the sentence above is true Link to comment Share on other sites More sharing options...
JaKiri Posted March 16, 2003 Share Posted March 16, 2003 Anything involving absolute positioning or velocity, due to Heisenberg. Link to comment Share on other sites More sharing options...
Glider Posted March 16, 2003 Share Posted March 16, 2003 Beige is the new black? Link to comment Share on other sites More sharing options...
Skye Posted March 16, 2003 Share Posted March 16, 2003 Now how can beige be the new black? It doesn't go with yellow:-p Link to comment Share on other sites More sharing options...
MajinVegeta Posted March 17, 2003 Share Posted March 17, 2003 Originally posted by Deslaar This sentence is false. ooh! This reminds me of the liar paradox! anyway, there aren't any statements that are niether true or false because something has to be on or the other. Also, I believe that (as I intend on not saying never) it is relative? Link to comment Share on other sites More sharing options...
blike Posted March 17, 2003 Author Share Posted March 17, 2003 anyway, there aren't any statements that are niether true or false because something has to be on or the other. Thats what I always thought, but I was looking into some stuff about fuzzy logic. "the sentence below is false the sentence above is true" heres another "All John's are liars". [i am John] None of these sentences can be true or false. They have values between true and false. Also, I believe that (as I intend on not saying never) it is relative? thats why i wanted to exclude subjective statements Link to comment Share on other sites More sharing options...
MajinVegeta Posted March 17, 2003 Share Posted March 17, 2003 now that you put it that way, your conclusion lies in my favirote paradox: the liar paradox! have ever heard of it? Link to comment Share on other sites More sharing options...
Radical Edward Posted March 17, 2003 Share Posted March 17, 2003 Originally posted by blike None of these sentences can be true or false. They have values between true and false. what do you mean by "between true and false" since it is a binary choice when we consider short statements like these. If one wants to talk about 'partial truth' then one is immediately accepting falsehood in the statement, and is talking in general terms... for example with the John statement... it may well be that all johns other than that particular John are liars. All I can see, is true, false or not either/paradoxical. everything I say is wrong. Link to comment Share on other sites More sharing options...
blike Posted March 17, 2003 Author Share Posted March 17, 2003 In classical logic,a statement has a truth value of either 1 for true or 0 for false. The statement "the sun is shining" has a truth value of 0 if it is cloudy. In general, statement P has a truth value p equal to 1 or 0. In fuzzy logic, a statement can have a truth value of between 1 and 0. If a cloud obscures a quarter of the sun, then statement P has a value of 0.25. In fuzzy logic, like the classical theory, the truth value of a statement will change when applying the operators NOT, AND, OR, IMPLIES and IF AND ONLY IF. NOT-P has a truth value of 1-p. EXAMPLE: If the sun is shining with a truth value of 0.25, then the sun is NOT shining with a truth value of 0.75. P AND Q has a truth value equal to the lesser of p and q where q is the truth value of statement Q. EXAMPLE: The sun is shining with a truth value of 0.25, AND Jane is getting tan with a truth value of 0.10. The value of the example is 0.10. P OR Q has a truth value equal to 1 the greater of p and q. EXAMPLE: The sun is shining with a truth value of 0.25, OR Jane is getting tan with a truth value of 0.10. The value of the example is 0.25. P IMPLIES Q has a truth value equal to the lesser of 1 and 1 - p + q. EXAMPLE: If the sun is shining with a truth value of 0.25, then Jane is getting tan with a truth value of 0.10. The value of the example is 0.85. P IF AND ONLY IF Q has a truth value equal to 1 - |p - q|, that is, one minus the absolute value of p minus q. EXAMPLE: The sun is shining with a truth value of 0.25 IF AND ONLY IF Jane is getting tan with a truth value of 0.10. The value of the example is 0.85. From scientific american. Feb., 1993 Link to comment Share on other sites More sharing options...
Radical Edward Posted March 17, 2003 Share Posted March 17, 2003 that's because the original statement is in itself slightly vague, and open to interpretation. One could argue that the sun is shining even if it is night time. The fact that the earth is in the way is irrelevant A statement like "Everything I say is a lie" however does not fit in with this fuzzy logic, since it is purely self contradictory. Link to comment Share on other sites More sharing options...
blike Posted March 17, 2003 Author Share Posted March 17, 2003 Here's another excerpt. The article is in story form, which makes it kind of confusing sometimes. Lukasiewicz grasped my arm. "Oh, but it does. It helps to resolve paradoxes. For instance, you claim to be a complete liar. Let's think about your statement 'I am lying.' Or, more simply,this statement is false.' In classical logic, it is a paradox, yes? If it is true, then it is false; if it is false, then it is true. To put it another way, you have a statement P with truth value p, which is 0 or 1, and P says the truth value of this sentence is 1 - p." Sorry, I didn't quite get that." "Ah. If P is true, then its negation, not-P, is false, and its truth value is 0. And conversely. Now, 1 - 0 = 1 and 1 - 1 = 0, so if the truth value of P is p, then the truth value of not-P is 1 - p." Oh. I see." Right. Now the problem is that 'this statement' is P, so P is telling us that the truth value of P is 1 - p. That's where the paradox comes from. If p = 0, then P tells us that p = 1 - 0 = 1. And if p = 1, then P tells us that p = 1 - 1 = 0. Neither choice is consistent." I gave him a condescending smile. "Luke, all you've done is reformulate in complicated algebraic language what was obvious all along." He smirked. " Maybe. But in fuzzy logic, there is a consistent solution to the equation p = 1 - p, namely, p = 0.5. So your claim to be a permanent liar is a half-truth, and everything works out fine. Your own statement leads inevitably to fuzzy logic." Link to comment Share on other sites More sharing options...
Radical Edward Posted March 17, 2003 Share Posted March 17, 2003 okay, I can see how it might apply to that, since the example is of something external to the statement, however you also have to make assumptions about the position of the thing being talked about. but how does the 'this statement is false' example fit in? even in a fuzzy way, it can't be partially correct. Furthermore, that statement is different to mine, which taking the strict meaning of the words, is still contradictory, regardless of what mathematical formalism you use. Link to comment Share on other sites More sharing options...
Glider Posted March 18, 2003 Share Posted March 18, 2003 This seems to me to be just like a (simplified) correlation coefficient where the value (between 0 and 1) is an indication of the strength of the relationship between reality and a statement describing it. Link to comment Share on other sites More sharing options...
Radical Edward Posted March 18, 2003 Share Posted March 18, 2003 but if the statement is entirely self contained and denies it`s own reality, then what can you say? Link to comment Share on other sites More sharing options...
Glider Posted March 18, 2003 Share Posted March 18, 2003 Then I suppose you could say that it fails to fulfil the criteria that: ...it must state something about the nature of an idea or physical object, and it cannot be something subjective... Link to comment Share on other sites More sharing options...
blike Posted March 18, 2003 Author Share Posted March 18, 2003 Originally posted by Glider Then I suppose you could say that it fails to fulfil the criteria that: But it describes the nature of itself, or does it? Link to comment Share on other sites More sharing options...
Glider Posted March 18, 2003 Share Posted March 18, 2003 A bit like a signpost stating "this is a signpost"? Link to comment Share on other sites More sharing options...
blike Posted March 18, 2003 Author Share Posted March 18, 2003 Even so, I still think it fits the criteria i put forth. Link to comment Share on other sites More sharing options...
Glider Posted March 19, 2003 Share Posted March 19, 2003 Hmmm....tricky. If a concept exists only to describe itself, how can it be said to state anything concerning the nature of an idea or object objective to itself? As a result, how can it be said that it is not entirely subjective? I think I just popped an anurism :uhh: Link to comment Share on other sites More sharing options...
DocBill Posted March 20, 2003 Share Posted March 20, 2003 I emailed my friend at Princeron's math department. He said to look no further than Topology to find many problems that are true..sort of, but not false, kinda. So....I guess it is a good place to begin. Bill PS: as they say on Cronos: "Imcha" Link to comment Share on other sites More sharing options...
Radical Edward Posted March 20, 2003 Share Posted March 20, 2003 say I say "this statement is false" and you apply that logic to it, and declare that it is a partial truth, then you are saying that the statement "this statement is false" is entirely equivalent to the statement "this statement is partially false" which, it obviously isn't because you have added something to the statement. I know this is a special example, and for anything else such as "Everything I say is a lie" it doesn't really apply, as that statement can realistically be a partial truth, because it applies to a term that is in itself fuzzy and not always certain. Link to comment Share on other sites More sharing options...
Radical Edward Posted March 20, 2003 Share Posted March 20, 2003 Topology... so it rears it's ugly head... no chance of inviting your friend to comment on that thread (and maybe this one) is there? Link to comment Share on other sites More sharing options...
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