But "true/false" isn't actually binary, is it? A great trait (and, simultaneously, a great failure) of languages in general is that of the characteristic cultural exclusivities each language (or dialect) serves. Any language derives & determines connotation and denotation, word by word, in its lexicon, and even the same word in the same language can have different meanings in different regions (British & American English, for example).
So what's truth by one language's (and culture's) standard of truth isn't necessarily truth in another's; are either of them accurately reflecting anything objectively? If not, is their truth wrong, if it fits their cultural paradigm of truth? And how many contingencies affect those assigned values?
Hello! The word "language" in this article refers to "formal language". This is the type of language used in Math to build propositions and demonstrations.
It is not the same that the "natural language" we use to communicate with each other. In natural languages we have those kinds of ambiguity and cultural influences you described.
Formal languages are all about the syntax. They are only a bunch of rules that tell us whether a "word" is part of the language or not. That is all what matters.
Programming languages are formal languages. We have a set of rules (a compiler) that tell us whether our code is valid or not. Note that we are not asking if the program does what we need to do. It is just about whether the program is syntactically correct.
With such a language we can say some expression is true if it is part of the language or false if it is not. No ambiguity here. There is no Python code that is both correct and incorrect at the same time (considering a fixed language version :P).
Logicians and Mathematicians wondered if all human knowledge (or at least all the math) could be described with a single formal language.
This is what this article is about and I'll stop here because I don't want to spoil the series 🙃
Hello! Thank you for taking the time and trouble to provide such excellent clarification. I appreciate not being left out of the sense of the post’s content and miss the meaning through my ignorance. I really enjoy learning and understanding.
I find all of this even more interesting in that context, even though I’m not approaching the ideas from the same place. I recognize the formal language” you describe as effectively similar to my experience of the concept of a dialect, replacing the “ alphabet” symbology with a different set of with other functions... still deeply interesting, even coming to the subject knowing nothing about it!
My pleasure! This is one of the theoretical topics I love the most. It is very interesting what we can do with these formalisms.
The good news is that you are in a good place to get started because Alejandro knows a lot about it (he was my Compilers teacher) and, more importantly, he knows how to explain it better than anyone!
To add a little bit to JJs already great explanation, I think that beyond formal systems, it is impossible to find truths that are absolute, exact, and objective. You can have absolute and objective but approximate truths, like in Physics, or you can have absolute and subjective truths, like in religion, or you can have relative but objective truths, like in economics... I wrote a rather long piece of the different philosophical frameworks for truth a while back, and it's a topic I still have much to think and learn about.
Loved it!
I was thinking of starting to write about how Geometry and Logic ended up with a radical revolution in Math and the birth of Computer Science.
It is fascinating how those two different fields helped us to discover the same problem.
Wanna collab?
Sure! I don't have a clear idea yet, but yes.
Let's do a standalone piece on the zairja! I've learned (and written) a ton about the Antikythera mechanism, but the zairja needs some love.
Definitely!
Your place or mine for this one?
I have a few things in my plate at the moment so if you want to, go ahead and draft something ;)
But "true/false" isn't actually binary, is it? A great trait (and, simultaneously, a great failure) of languages in general is that of the characteristic cultural exclusivities each language (or dialect) serves. Any language derives & determines connotation and denotation, word by word, in its lexicon, and even the same word in the same language can have different meanings in different regions (British & American English, for example).
So what's truth by one language's (and culture's) standard of truth isn't necessarily truth in another's; are either of them accurately reflecting anything objectively? If not, is their truth wrong, if it fits their cultural paradigm of truth? And how many contingencies affect those assigned values?
I do love the idea of a universal language. I believe we actually possess something close to it in our ability to visualize, though that's not the standard sense we're used to using to communicate, it's becoming more popular (image-based help manuals & so on), and already translating to real life through AI, no words necessary: https://www.linkedin.com/posts/customclarity_ai-tech-technology-activity-7127718768717266947-Lg-0?utm_source=share&utm_medium=member_desktop
Hello! The word "language" in this article refers to "formal language". This is the type of language used in Math to build propositions and demonstrations.
It is not the same that the "natural language" we use to communicate with each other. In natural languages we have those kinds of ambiguity and cultural influences you described.
Formal languages are all about the syntax. They are only a bunch of rules that tell us whether a "word" is part of the language or not. That is all what matters.
Programming languages are formal languages. We have a set of rules (a compiler) that tell us whether our code is valid or not. Note that we are not asking if the program does what we need to do. It is just about whether the program is syntactically correct.
With such a language we can say some expression is true if it is part of the language or false if it is not. No ambiguity here. There is no Python code that is both correct and incorrect at the same time (considering a fixed language version :P).
Logicians and Mathematicians wondered if all human knowledge (or at least all the math) could be described with a single formal language.
This is what this article is about and I'll stop here because I don't want to spoil the series 🙃
Hello! Thank you for taking the time and trouble to provide such excellent clarification. I appreciate not being left out of the sense of the post’s content and miss the meaning through my ignorance. I really enjoy learning and understanding.
I find all of this even more interesting in that context, even though I’m not approaching the ideas from the same place. I recognize the formal language” you describe as effectively similar to my experience of the concept of a dialect, replacing the “ alphabet” symbology with a different set of with other functions... still deeply interesting, even coming to the subject knowing nothing about it!
Thank you again.
My pleasure! This is one of the theoretical topics I love the most. It is very interesting what we can do with these formalisms.
The good news is that you are in a good place to get started because Alejandro knows a lot about it (he was my Compilers teacher) and, more importantly, he knows how to explain it better than anyone!
I’m very glad I have found him and this place! And you. :)
❤️❤️❤️
To add a little bit to JJs already great explanation, I think that beyond formal systems, it is impossible to find truths that are absolute, exact, and objective. You can have absolute and objective but approximate truths, like in Physics, or you can have absolute and subjective truths, like in religion, or you can have relative but objective truths, like in economics... I wrote a rather long piece of the different philosophical frameworks for truth a while back, and it's a topic I still have much to think and learn about.