Sorry, I don't understand that. I assume you're aware that most mathematicians and most philosophers, for the last 2,500 years, have seen it as a paradox. EB
Could another interpretation be, "I am a liar?" Anything I say is a lie, including the statement, "I am a liar," which makes it the truth.
Well, sure, isn't that what we call a contradiction? And herein lies the problem... This sentence is false; Assume the sentence true; Therefore it is, false; Therefore it is true; Therefore it is, false;Therefore it is true; ... So, the problem here seems to be that logic doesn't produce one result, but two contradictory ones. EB
... soo... mathematics has stayed the same for the last 2500 years ? they haven't learnt anything new ?
It's grammatical masterbation. It makes sense only grammatically but does not convey a meaningful idea that can either be true or false. The 'falseness' that the sentence claims does not apply to a meaningful idea embodied in the words of the sentence, but only to the sentence itself. There is no meaning or information there to be true or false. It's like a saying "this sentence makes sense". From a grammatical point, it does. But there is no real idea there, no meaningful information is contained
The sentence is talking about something real, itself. It convey a meaningful idea: "This sentence is true" conveys a meaningful idea if meant to apply to any other sentence, therefore it conveys a meaningful idea also if understood as applying to itself. You want to infer that the sentence is meaningless from the fact, incontrovertible fact, that you cannot decide whether it's true or false. Yet, it is meaningful. We all understand what it means. The only problem there is with it is that we cannot decide whether it's true or false. EB
To have meaning, a statement must convey information. Because this sentence is totally self-referential, there is no information there. I think it's more obvious if you reverse it to say " This sentence is true". At first glance it seems to say something, it has a subject and predicate and is grammatically correct. But look deeper, no information is imparted to the reader. It's a meaningless concept.
But that's true of the whole of logic, Sir. And people have known this fact since at least the Stoics, more than 2,000 years ago. Some people have objected to that, including Descartes, and following Descartes, people like Humes and Locke. But, most people have seemed comfortable with it, including most philosophers, most mathematicians, most computer scientists, and indeed most people, unless you want to argue that logic is useless as Descartes tried to do, making a fool of himself. Still, you'd be in league apparently with Aristotle. Notice how all his syllogisms had true premises, or at least premises we can all believe are true: All men are mortal... But, his perspective was seen by his followers as limited and they decided logic was to be understood as independent from the actual truth of the premises considered. In the abstract, so to speak... And the whole of mathematics have followed suit, only much later. EB
Thanks for the philosophy and history lesson. I'm not arguing against logic. I'm arguing that the sentence is not logical. A logical sentence need to impart information that can be judged for its logic or truth. This sentence provides 0 information. It's a non- statement
The sentence is not an argument so of course it has no logic. The sentence "Men are mortal" is not logical either. It is just true or false. The sentence "If Socrates is a man and all men are mortal, then Socrates is mortal" is logically valid so I supposed it is a logical sentence. So, sure, "This sentence is false" is not logical and we don't expect it to be. Instead, we expect it to true or false and that's where the problem is because it seems we can't decide which it is, which is one particular species of paradox. It's a statement. We just don't know whether it is true or not and because of that it doesn't provide any information. But it is nonetheless meaningful. Hence, its paradoxical nature. EB
What about the statement "this sentence is true. " Is that meaningful? It provides no information. Any statement that provides no information has no meaning. You don't learn anything from it, it can't be tested for truth. It's just a grammatically correct collection of words like the original 'false' form of the sentence.
That's why it's called a paradox. I'm not sure why you seem to think it's not enough and that the thing should be dismiss as meaningless. Again, we all understand what it means, so it would be strange to then label it as meaningless. And it's a paradox precisely because it means something to us. A meaningless sentence doesn't even register as a paradox to begin with. If it was meaningless, people wouldn't even ask themselves if the sentence is true to begin with and it wouldn't be seen as a paradox. EB
philosophy mathematics 2 subjects that rely on each other as a determinant form of expression ? 0 + -1 = -1 ? philosophy relys on the interpretation as a form of perception mathematics relys on the contents assumed value to be a numeric constant to its perception of terms ... ?
