I agree with your (and Priest's) assessment that Aristotle's logic is pararaconsistent in nature. It seems to me that Aristotle (together with almost anyone who has never taken at least an introductory course in classical logic, for that matter) has what we would nowadays call a "relevant" conception of logical consequence. Most likely, so do Hegel and Marx. That said, I have the impression that this is as far as it goes, in regards to how similarly their conceptions of logic deal with contradictions. It is clear from the outset that Aristotle would reject dialetheism, or anything akin to it. I have no stance on whether Hegel and Marx are to be taken as dialetheists, but in any case I suspect that their conception of logic (whatever it may ultimately be) would fit in the "something akin to dialetheism" category.
In sum, Aristotle's logic is certainly paraconsistent in the technical sense, but as far as I can see it is not paraconsistent in any interesting sense (i.e. in a sense that makes some good of all the logical room left by the rejection of ex contradictione quodlibet).
In any event, thanks for this very insightful article!
If you would allow any exception to the law of non-contradiction you invalidate non-contradiction as a law of logic (one counter-example invalidates any law), and once you reject it as a law then all your words, symbols, theorems cease to have any meaning, since they could be intended to both mean and not-mean what they are usually understood to mean, including any assertions about selective compliance with the laws. This is an implicit acceptance of explosion (disjunctive introduction is logically implied, not merely asserted). Moreover, every other law of logic is conditional on the law of non-contradiction, so to reject non-contradiction is to also reject identity and excluded middle. The result in non-sense, as is the statement “it is now raining here and it is now not raining here”; it does not mean anything, but is just a series of assertions that cannot be integrated into a meaningful idea or situation.
Well, yeah, the law of noncontradiction is false, but it doesn't follow that "all my words, symbols, and theorems cease to have any meaning." That's just an absurd conclusion that only follows if you accept the (dubious) principle of explosion.
I mean, why should I believe that if I allow for some exceptions to the LNC, every single utterance could be intended to both mean and not mean what they are understood to mean? That's just silly.
Even in the case "it is now raining here and it is now not raining here," you claim it is meaningless, but you don't actually find it meaningless. You say it is meaningless, yet you recognize that it is a contradiction, which implicitly demonstrates that you DO understand the meaning enough to recognize that it is meaningless. Now, you might not be able to imagine a scenario where it's both true and not true that it's raining here and now, but you still understand the meaning enough to know that you can't imagine a situation where it's possible.
I can give different arguments against the law of identity and the law of excluded middle some other time.
While the rain example might not actually hold for reality, I can give a whole list of examples of things that can be clearly and distinctly shown to be inherently contradictory, starting with self-reference paradoxes in logic (the liar paradox, Russell's paradox), problems related to the instant of motion and the instant of time, limits and boundaries generally, possibility/the ought/inclinations generally.
I just explained to you just that: if you reject the law, then nothing you say can be assumed to comply with the law. Consequently, your words have no meaning.
Yeah, I don't think that follows, because if contradictory statements didn't have meaning, you couldn't recognize that they were contradictory in the first place. Clearly, you can recognize when statements are contradictory, so adherence to the law of non-contradiction is not a criterion of meaningfulness.
And yeah, if we reject the law (which we should), then things can be assumed to be either true, false, or both true and false. Yet in this scenario, the true things and the false things (but not the true and false things) would appear to still conform to the (false) law, so no, none of what you are saying follows and seems to just be some dogmas you uncritically accept.
You equivocate between the meaning of a logical relation between individually meaningful parts and the absence of meaning that results in putting those parts together as a whole. For example, you cannot imagine a cat that is all black and not all black at the same time, but you can write a sentence asserting the synthesis of these incompatible characteristics: the sentence is meaningful, but there can be no such cat.
I agree with your (and Priest's) assessment that Aristotle's logic is pararaconsistent in nature. It seems to me that Aristotle (together with almost anyone who has never taken at least an introductory course in classical logic, for that matter) has what we would nowadays call a "relevant" conception of logical consequence. Most likely, so do Hegel and Marx. That said, I have the impression that this is as far as it goes, in regards to how similarly their conceptions of logic deal with contradictions. It is clear from the outset that Aristotle would reject dialetheism, or anything akin to it. I have no stance on whether Hegel and Marx are to be taken as dialetheists, but in any case I suspect that their conception of logic (whatever it may ultimately be) would fit in the "something akin to dialetheism" category.
In sum, Aristotle's logic is certainly paraconsistent in the technical sense, but as far as I can see it is not paraconsistent in any interesting sense (i.e. in a sense that makes some good of all the logical room left by the rejection of ex contradictione quodlibet).
In any event, thanks for this very insightful article!
If you would allow any exception to the law of non-contradiction you invalidate non-contradiction as a law of logic (one counter-example invalidates any law), and once you reject it as a law then all your words, symbols, theorems cease to have any meaning, since they could be intended to both mean and not-mean what they are usually understood to mean, including any assertions about selective compliance with the laws. This is an implicit acceptance of explosion (disjunctive introduction is logically implied, not merely asserted). Moreover, every other law of logic is conditional on the law of non-contradiction, so to reject non-contradiction is to also reject identity and excluded middle. The result in non-sense, as is the statement “it is now raining here and it is now not raining here”; it does not mean anything, but is just a series of assertions that cannot be integrated into a meaningful idea or situation.
BTW, Hegel made some basic logical errors that invalidate his arguments about ‘logic’: https://michaelkowalik.substack.com/p/hegel-on-identity-by-double-negation
Well, yeah, the law of noncontradiction is false, but it doesn't follow that "all my words, symbols, and theorems cease to have any meaning." That's just an absurd conclusion that only follows if you accept the (dubious) principle of explosion.
I mean, why should I believe that if I allow for some exceptions to the LNC, every single utterance could be intended to both mean and not mean what they are understood to mean? That's just silly.
Even in the case "it is now raining here and it is now not raining here," you claim it is meaningless, but you don't actually find it meaningless. You say it is meaningless, yet you recognize that it is a contradiction, which implicitly demonstrates that you DO understand the meaning enough to recognize that it is meaningless. Now, you might not be able to imagine a scenario where it's both true and not true that it's raining here and now, but you still understand the meaning enough to know that you can't imagine a situation where it's possible.
I can give different arguments against the law of identity and the law of excluded middle some other time.
While the rain example might not actually hold for reality, I can give a whole list of examples of things that can be clearly and distinctly shown to be inherently contradictory, starting with self-reference paradoxes in logic (the liar paradox, Russell's paradox), problems related to the instant of motion and the instant of time, limits and boundaries generally, possibility/the ought/inclinations generally.
*enough to recognize that it is a contradiction
I just explained to you just that: if you reject the law, then nothing you say can be assumed to comply with the law. Consequently, your words have no meaning.
Yeah, I don't think that follows, because if contradictory statements didn't have meaning, you couldn't recognize that they were contradictory in the first place. Clearly, you can recognize when statements are contradictory, so adherence to the law of non-contradiction is not a criterion of meaningfulness.
And yeah, if we reject the law (which we should), then things can be assumed to be either true, false, or both true and false. Yet in this scenario, the true things and the false things (but not the true and false things) would appear to still conform to the (false) law, so no, none of what you are saying follows and seems to just be some dogmas you uncritically accept.
You equivocate between the meaning of a logical relation between individually meaningful parts and the absence of meaning that results in putting those parts together as a whole. For example, you cannot imagine a cat that is all black and not all black at the same time, but you can write a sentence asserting the synthesis of these incompatible characteristics: the sentence is meaningful, but there can be no such cat.
Like I said, you’re reducing meaning to imagination
That’s what examples are literally meant to do.