Daniel: Why don’t you believe in the principle of noncontradiction?
Graham: As I explained in my blog post, the Liar Paradox proves that some things are both true and false.
Daniel: But the Liar Paradox is cyclical. Cyclical propositions are meaningless.
Graham: Actually, the proposition “all cyclical propositions are meaningless” *is* a cyclical proposition.
Daniel: Which would seem to imply that it’s meaningless.
Graham: And how can you solve a paradox with a meaningless proposition?
Daniel: Hmmm, I hadn’t thought of that. But doesn’t mainstream logic assume that ZFC solves the Liar Paradox?
Graham: ZFC is a formality. If you take it as a proposition logico philosophicus, it’s cyclical, and therefore declares itself meaningless.
Daniel: But can’t you separate the rules for constructing propositions from the system of propositions themselves?
Graham: Some people think you can. You’re welcome to try if you have the time. But you need to explain who rules the rules.
Daniel: True...I’m starting to see how the “outlawing cycles” approach may be a dead end. And your paraconsistent logic does seem like a simple solution. But maybe there’s a simpler one.
Graham: What do you have in mind?
Daniel: Maybe we should just forget about logic altogether. Who needs logic?
Graham: Whoa, Daniel. Slow down there. You’re throwing out the family with the bathwater.
Daniel: We had mathematical proofs before Frege. Have proofs really gotten better? As Logicomix points out, symbolic logic proved to be extremely useful in telling computers what to do, but is it really useful in resolving The Problems of Philosophy?
Graham: Logic can certainly help expose philosophical fallacies.
Daniel: You mean, like the ontological argument?
Graham: Touche, touche. But come on. Without logic, how can you start with premises and arrive at a conclusion? How can you make inferences?
Daniel: The same way you do anything. With intuition.
Graham: What do you mean?
Daniel: When you start with some premise and you infer a conclusion, your confidence in the conclusion is proportional to your confidence in the premise and your confidence in the inference. In other words, you’re convinced to the extent that the argument is convincing.
Graham: Sure. So logic gives you rules of inference, that you can use to infer things.
Daniel: But maybe logic is a mistake. Maybe there are no rules. Maybe each inference is its own axiom. Its own act of gnosis.
Graham: You and your gnosis again. You know, Daniel, you’re starting to creep me out. How can I even have a Platonic dialogue with you? You talk like an analytic philosopher, but deep down you’re just another mystic.
Daniel: I think Winston Churchill said it best. “He who is not an analytic philosopher at 20 has never been young; he who is not a mystic at 30 has never matured.”
Graham: As I explained in my blog post, the Liar Paradox proves that some things are both true and false.
Daniel: But the Liar Paradox is cyclical. Cyclical propositions are meaningless.
Graham: Actually, the proposition “all cyclical propositions are meaningless” *is* a cyclical proposition.
Daniel: Which would seem to imply that it’s meaningless.
Graham: And how can you solve a paradox with a meaningless proposition?
Daniel: Hmmm, I hadn’t thought of that. But doesn’t mainstream logic assume that ZFC solves the Liar Paradox?
Graham: ZFC is a formality. If you take it as a proposition logico philosophicus, it’s cyclical, and therefore declares itself meaningless.
Daniel: But can’t you separate the rules for constructing propositions from the system of propositions themselves?
Graham: Some people think you can. You’re welcome to try if you have the time. But you need to explain who rules the rules.
Daniel: True...I’m starting to see how the “outlawing cycles” approach may be a dead end. And your paraconsistent logic does seem like a simple solution. But maybe there’s a simpler one.
Graham: What do you have in mind?
Daniel: Maybe we should just forget about logic altogether. Who needs logic?
Graham: Whoa, Daniel. Slow down there. You’re throwing out the family with the bathwater.
Daniel: We had mathematical proofs before Frege. Have proofs really gotten better? As Logicomix points out, symbolic logic proved to be extremely useful in telling computers what to do, but is it really useful in resolving The Problems of Philosophy?
Graham: Logic can certainly help expose philosophical fallacies.
Daniel: You mean, like the ontological argument?
Graham: Touche, touche. But come on. Without logic, how can you start with premises and arrive at a conclusion? How can you make inferences?
Daniel: The same way you do anything. With intuition.
Graham: What do you mean?
Daniel: When you start with some premise and you infer a conclusion, your confidence in the conclusion is proportional to your confidence in the premise and your confidence in the inference. In other words, you’re convinced to the extent that the argument is convincing.
Graham: Sure. So logic gives you rules of inference, that you can use to infer things.
Daniel: But maybe logic is a mistake. Maybe there are no rules. Maybe each inference is its own axiom. Its own act of gnosis.
Graham: You and your gnosis again. You know, Daniel, you’re starting to creep me out. How can I even have a Platonic dialogue with you? You talk like an analytic philosopher, but deep down you’re just another mystic.
Daniel: I think Winston Churchill said it best. “He who is not an analytic philosopher at 20 has never been young; he who is not a mystic at 30 has never matured.”
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