Have you ever heard of a paradoxical sentence like, "This sentence isn't true"?
I think it's a mechanics-of-language failure.
See, when we try to express an idea using language, it's often not possible to capture the pure essence of the idea.
There's concepts that don't have words for them and there's words that exist that describe a number of different things ("happiness"). Then, on top of that, there's structures and grammar and traditions and "implied meanings." When someone makes a sarcastic reference to "Mission Accomplished" you'd need to know a considerable amount of recent American politics and history to entirely get their meaning.
In the end, language exists to try to communicate meaning. It takes the thought or concept and puts it into verbal form. But because language does so many different things at the same time, loopholes and broken constructions emerge.
"This sentence isn't true" is around the borders of language, attempting to use a loophole to do something weird. It's a statement that identifies itself as the object, simultaneously looking to change the object by making the statement.
It's like dividing by zero. It doesn't work. How do you divide an apple into zero parts? You basically can't do it.
The same is true with our language. "This sentence isn't true" is playing around with faulty mechanics.
Well, for one, P != P is essentially how clock cycles are regulated in computers chips. A gate is constructed such that being set to on (true) cuts its own power, setting it to off (false), which completes its circuit again. This behavior is necessary for modern computers to function.
That's one way to see it. You can also see the beauty of having these seemingly paradoxes in the language, which enables one to express in a more wider and varied palette of colors. If you think for example about poetry, I think one of the things I appreciate is that a subtle choice of words can convey a profound meaning or meanings, and sometimes all of the different meanings make sense and enrich what the poet is saying. I like paradoxes, it fits the human being.
As someone else above said, I suggest you read up on Godel's incompleteness theorems. You shouldn't dismiss self-contradictions as mere illogical errors that shouldn't be made just because they lead to paradoxical situations that make one's (yours?) brain hurt; in Godel's work, such self-contradictions are valid mathematical constructs that are useful in answering important mathematical questions.
Maybe the loophole or why it exists is exactly what the speaker wants to notice and think about. Language need not define something or convey meaning all the time. Lots of art deals with this kind of thinking (René Magritte's "Ceci n'est pas une pipe", for instance, although in a more visual point of view).
You may find Gödel's work interesting. Put *extremely* informally, a logical language (as used in mathematics) that is strong enough to allow counting is either inconsistent (A and not-A can both be proven) or incomplete (for some A, neither A nor not-A can be proven within the system).
This strongly suggests that such language failures are inevitable.
I had a course about language philosophy which certainly gave me some insight in this. Earlier language philosophers (or more logicians) like Gottlob Frege and Bertrand Russell tried to replace our ordinary-day language with logic symbols that improve our language. It restricts language incredibly, but that's sometimes necessary and I think their approaches can certainly help with analysing scientific and philosophical statements.
There are several approaches to this. I know that Alfred Tarski dealt with this explicitly in "The Semantic Conception of Truth and the Foundations of Semantics". From the top of my head I think his solution is to restrict language so that it can say anything, except something about itself (let's call this language T). You can then make a meta-language (T'), for which the same rules apply, but it can also say something about language T. And so you can construct meta-languages (T'', T''') until you are bored.
And, maybe even more interesting, these kind of logic answers were certainly useful for artificial intelligence, since they are logic ways to get rid of ambiguity in language (including computer languages).
Request: I got a fascinating email about thinking. I'm sharing my thoughts, but I'd appreciate yours too. It's kind of a difficult question - how do you think? But it's fascinating, so I'd like you to weigh in after reading this post.
Fascinating email from Huy Nguyen -
My name is Huy, 21 years old from Vietnam currently studying in Singapore. I've been reading your blog and I must say you're 1 hell of an inspiring guy! Recently I have been pondering on the topic of mindfulness/self-consciousness and I thought why not drop you an email to say hi and seek for some help :)
My current problem is my thought speed is restricted to how much I can spell the thoughts out (in words and sentence) in my minds. And that'd be really slow. Sometimes, I'm able to speed-thinking (if that's the right word). I don't actually need to spell out the words in my mind, just link to some picture/scene and somehow I'm able to articulate and understand the situation in my mind. But this is a very rare case and I'm not fully able to control it. Have you ever encountered this problem? Do your mind think in English as well, or some special-made brain language?
Learning a new language can be on of the most difficult yet rewarding things one can do with their time. If done correctly, one will fail numerous times, be able to express themselves in unique ways and have easier access to a new culture. Currently Language-learning has been quite the rage, with services such as Rosetta Stone and Rocket languages selling like hotcakes and blogs such as fluentin3months having massive success. New services, such as duolingo and italki are changing the landscape of language learning business and making language learning ridiculously cheaper, and more accessible to everyone. I’ve undertaken learning 3 different languages, with varying success in each, but with each subsequent one being much easier to learn. I’ve tried to see how fast the human mind can learn a new language, especially ones that are radically different from ones native tongue. Currently I’ve learned a good amount of Japanese, Chinese and German, with my Japanese and German being significantly better than Chinese, but still not good enough to be able to have effortless conversations, which means I must keep pressing on.
I’ve found learning languages to be a very dynamic process. Each language has its own way of expressing itself, Some are very clear, cut and use short, direct words, as I have found to be the case with Chinese. Others are more vague, longwinded, or emphasize particular things, such as Japanese having a verb ending that signals the completion of something. Regardless, learning a new language will definitely bestow you with a new way of looking at the world. Here I want to share 4 things to keep in mind that have radically helped me when learning languages.
1. Spend sometime understanding the aspects of the language you are about to learn. Specifically try to focus on sentence structure and how meaning is added to the sentence. For example, German is very similar to English, it is subject-verb-object (sometimes its gets mumbled up, but for the most part it is), is preposition heavy and is written in the same scripture, which makes it significantly easier to learn than say Japanese or Chinese. But German is also high agglunative, which means it building meaning by joining words together. German also has an emphasis on cases and gender that is not present in English.
This might seem obvious, but it is very rarely done. Before you embark on the journey of learning a language and learning detailed grammar rules for a specific cases focus on things such as how nouns relate in the sentence, where conjugation happens, and how important is it. A good exercise is usually to get sentences with varying structure and translate them into your target language, something tim ferris suggests in the 4-hour-chef. Exercises like this allow you to find the pattern that will most likely hold true in 80%+ of all sentences. This is makes for a very solid foundation that would otherwise take weeks if one were just frantically reviewing, and learning step by step, instead focus on what the majority of sentences look like, dissect the key elements, and apply them.
2. Find and use a handful of excellent resources at a time; get involved in online communities. The most important thing to keep in mind when one is beginning to learn a language is to find high-quality resources. Find online communities for your target language by googling something like “learn german forum” and see what people are saying, which books their recommending etc. Another good way to find solid resources is to go on Amazon see which books in your target language have good reviews/sales. When I started learning my first foreign language, Japanese, I bought 4-5 books on Japanese, enrolled in two podcasts, had various decks in my flash card program, ranging from beginner to advanced, and used 4 different websites. This was a HORRIBLE idea. Not only was grammar, and vocabulary introduced at different times in each book, but managing progress was very hard, with notes in one book, flash cards, on my computer, and trying to juggle which activity I should do next.