Here's why you should find the challenge the paradoxes pose to classical logic philosophically interesting--even if you're the kind of person whose eyes glaze over when you encounter logical symbols.
What interests me about semantic paradoxes and vague predicates is that they are examples of how ordinary language is not and cannot be like a formal language. It is produced by people interacting with each other and with nature, and does not obey these formal laws. You can try to make these logical laws work but only at the price of stipulating meanings that don’t get at everything humans using these words in the wild actually communicate. And we also have to start banning certain sentences that make perfect sense in ordinary discourse. In other words, you can only make ordinary language formal by creating a sub-language in which the participants agree that they are talking in special ways - although they inevitably borrow from ordinary language implicitly, generating new formal problems.
I notice your argument for doing that is ultimately a pragmatic one: if we are more precise in our use of concepts, we will come to understand the domain better. The “dialectical” response is “Sure that could work for some purposes, but the price of that system is going to be some implicit presupposition you can’t even formulate within the system”. The big leaps are when that suppressed implicit presupposition become a barrier to solving the pragmatic problems the formalized system of concepts is designed to address, are then brought to awareness and new, more general, implicit presuppositions are substituted.
At that point you have to stop *applying* your rules for discourse and have to reform them. That involves making the presupposition explicit. It also need not point to a single determinate answer, as your discussion of various ways of resolving the Liar’s Paradoxes shows.
While Marx himself never had much to say about these issues, I think if you see ordinary language as a social force of production - and more specialized formal languages as also forces of production- it leads to some insight. Both the ordinary language and specialized formal languages have to be reproduced and are constrained by the metabolism between humans and nature, the pragmatic tasks both are expected to solve are shapes by the class structure and so on. A democratic observation is that ordinary language is already produced socialistically without state or market (although shaped somewhat by both) and specialized, formal ways of talking depend on ordinary language.
IT IS NOT A Bivalence but a TRINITY; TRUTH FALSE and forgotten by us today but most important FAITH. trinities are everywhere; mind, body, soul. Father Son You. God Jesus Believers. Left Right Center. You Me US ❤️❤️❤️
Here Ben do you know this cool Liar Paradox-titled song by Nick Lowe, All Men Are Liars and That's the Truth? : 'Do you remember Rick Astley? He had a big fat hit it was ghastly': https://youtu.be/m6hzkBihaew
What interests me about semantic paradoxes and vague predicates is that they are examples of how ordinary language is not and cannot be like a formal language. It is produced by people interacting with each other and with nature, and does not obey these formal laws. You can try to make these logical laws work but only at the price of stipulating meanings that don’t get at everything humans using these words in the wild actually communicate. And we also have to start banning certain sentences that make perfect sense in ordinary discourse. In other words, you can only make ordinary language formal by creating a sub-language in which the participants agree that they are talking in special ways - although they inevitably borrow from ordinary language implicitly, generating new formal problems.
I notice your argument for doing that is ultimately a pragmatic one: if we are more precise in our use of concepts, we will come to understand the domain better. The “dialectical” response is “Sure that could work for some purposes, but the price of that system is going to be some implicit presupposition you can’t even formulate within the system”. The big leaps are when that suppressed implicit presupposition become a barrier to solving the pragmatic problems the formalized system of concepts is designed to address, are then brought to awareness and new, more general, implicit presuppositions are substituted.
At that point you have to stop *applying* your rules for discourse and have to reform them. That involves making the presupposition explicit. It also need not point to a single determinate answer, as your discussion of various ways of resolving the Liar’s Paradoxes shows.
While Marx himself never had much to say about these issues, I think if you see ordinary language as a social force of production - and more specialized formal languages as also forces of production- it leads to some insight. Both the ordinary language and specialized formal languages have to be reproduced and are constrained by the metabolism between humans and nature, the pragmatic tasks both are expected to solve are shapes by the class structure and so on. A democratic observation is that ordinary language is already produced socialistically without state or market (although shaped somewhat by both) and specialized, formal ways of talking depend on ordinary language.
IT IS NOT A Bivalence but a TRINITY; TRUTH FALSE and forgotten by us today but most important FAITH. trinities are everywhere; mind, body, soul. Father Son You. God Jesus Believers. Left Right Center. You Me US ❤️❤️❤️
Here Ben do you know this cool Liar Paradox-titled song by Nick Lowe, All Men Are Liars and That's the Truth? : 'Do you remember Rick Astley? He had a big fat hit it was ghastly': https://youtu.be/m6hzkBihaew