Why are paradoxes/contradictions (so) important? — Agent Smith
Classical logic has to use Occam's broom — Agent Smith
Why are paradoxes/contradictions (so) important?
Their significance to all (real) thinkers is that renders trivial the logical systems in which they arise. — Agent Smith
Not sure this is relevant but I generally accept that humans are clever animals who use language to help manage their environment. As a consequence, meanings and worldviews are riddled with inconstancies and subversions, some of them more striking than others. When I encounter a paradox it tends to remind me of the poetic, imprecise nature of language and the manufactured character of human understanding. — Tom Storm
My main concern is the existence/nonexistence of (true) paradoxes. If they exist then, classical logic is trivial unless it excludes some rule of natural deduction that prevents ex falso quodlibet. The rule that most logicians choose to exclude from natural deduction in order to prevent explosion is disjunction introduction/addition. Should we do that? It seems the right course of action assuming there are (true/real) paradoxes. — Agent Smith
It strikes me that many (most? all?) so-called paradoxes are really just playing with language. — T Clark
Escher's paradoxical ever up or down going stairs is about the angle of vision (that resolved the seeming contradiction). The twin paradox is about everyday experience and gravity, resolved by general relativity. "Contra-diction" is not always about diction. — EugeneW
Perhaps I am not a (real) thinker, but all the excitement about paradoxes goes over my head. I just can't see how they have any practical meaning. — T Clark
Negative self reference.
Just ask yourself, how many paradoxes involve this. Starting from Russell's paradox. — ssu
It's not that complicated. — Agent Smith
I didn't say that the idea of paradoxes goes over my head, I said the excitement about them does. I just don't see why it's a big deal. They're not that hard to recognize. It's not like they can sneak up on you — T Clark
Oh! Sorry, my bad. You didn't read my post thoroughly. I explain why paradoxes are a big deal. — Agent Smith
Mr. Snooty. Agent Snooty — T Clark
Read my last post, the post before you lost your mind. — Agent Smith
I went back and reread your posts. I don't think there is any misunderstanding between us about the issue on the table. We just disagree on the implications. I have four answers to the question "What difference does it make that language paradoxes seem to undermine the value of logic?" Those answers are, in no particular order, none, zero, zilch, and nada. — T Clark
Paradoxes break (classical) logic — Agent Smith
Usually the mathematical paradoxes/logical paradoxes are structured this way.I've seen at least two negative self-referential paradoxes: the liar sentence and Curry's paradox.
Your point? — Agent Smith
You noticed the point! — ssu
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