Logic Is Axiomatic, Not Provisional or Merely Useful
"We cannot think [therefore, or say] anything unlogical...." --Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Prolific atheist celebrity Matt Dillahunty -- who has done many videos on logic, reason, and certainty -- thinks the problem with the laws of logic is that it they not axiomatic -- self-evidently true -- and cannot be validated because you have to use them in the very attempt to refute them. I guess he thinks that involves circular reasoning or question-begging. Most generally, he thinks logic (along with reason) is no demonstrable.
Here's how he puts it in a YouTube video:
What he's saying, then, is that Aristotle's negative validation of logic -- his demonstration that any argument against the Law of Identity must smuggle the law back in or the argument makes no sense -- has a problem because it claims that a contradiction lies at the end of it. Note he says, "you’re in a position where you have to say, 'But if [the laws of logic] are not true then there’s no problem with the contradiction'" [for the logician, apparently].
But the logician never says there's no problem with the contradiction -- namely, that if the laws of logic are misconceived, then the conclusion of any argument, including the one against logic, can be both false and true. The contradiction is the problem, but it's a problem for the anti-logician, who is supposedly trying to show that logic is false, not the logician! Rather the logician says:
As they say, Quod Erat Demonstrandum.
This slices Dillahunty's position to the bone. Obviously, reason, logic, and language are joined at the hip. Every proposition begins with the unspoken words, "The following is true." If instead every proposition must begin with the words, "The following can be both true and false," language and discourse are emptied of all worth. So is the human mind. Even Dillahunty's case for negative atheism is tossed in the bin. Unless logic is understood as axiomatic, what's the point of asking for evidence of anything?
To be fair, Dillahunty does not want to throw out logic. On the contrary, he invokes it routinely. But on what grounds does he do so if he rejects its axiomatic status? On the grounds that it has proved useful. (Tomorrow? Who can say with certainty?) They work. Thus, he says, they are reasonably accepted by rational people.
But this can't be right. Reason does not judge the laws of logic. Instead, reason is founded on logic, namely, that A is A. Part of what it means to be reasonable is to be attentive to the requirements of logic. Dillahunty's put the cart before the horse.
Yes, we are "stuck," as it were, with logic. But that's a feature, not a bug. As Wittgenstein taught: "Logic fills the world: the limits of the world are also its limits.... What we cannot think, that we cannot think: we cannot therefore say what we cannot think." He went on to add that we cannot even imagine reaching a line with something else on the far side. What would be on the other side? An illogical world? All such talk is literally nonsense.
One final thought: Dillahunty goes to great pains to rebut those who think that "reason is in fact absolute." I'm not sure whom he has in mind, Descartes maybe, but for him, God made certainty possible, so that has no relevance for atheists. What would it mean for reason to be absolute? If it would mean that reason can make us infallible and omniscient, then he's right: reason is not absolute. But that is a ridiculous standard. Nor is it what any naturalist has expected from reason.
Dillahunty, in fact, has turned the truth upside down. Fallibility is not what limits reason. Quite the reverse, reason limits fallibility. We need reason and logic precisely because we are not omniscient. God would not need reason. He'd know everything instantly and without effort. He'd just know. We can't do that. So we need a guide in our quest for knowledge. Reason and logic are guides. You can't reasonably complain that reason doesn't deliver omniscience ("absolute certainty" -- a red herring) because it never promised to do that. On the contrary, it's a faculty and a set of tools exactly appropriate to fallible beings. Again, infallible beings would have no use for reason.
Try this analogy: reason is like a hammer. If a carpenter hits his thumb instead of the nail, it's not a shortcoming of the hammer. Similarly, if a reasoning person makes a mistake, it's not a shortcoming of reason. It demonstrates the uncontroversial truth that people are fallible, which is why they need reason.
Dillahunty may agree with a lot of what I say here. Yet he also says, "The problem is you can’t demonstrate ... that nothing that can violate reason. And I would agree that seems to be the case. The problem is you can’t demonstrate it.” Just before that he says, “At some point, when you’re trying to figure out just how confident you are [about a knowledge claim], you have to get to the point of all of this being contingent on reason being reasonable." Yikes!
This is more nonsense. Is he saying the reasonableness of reason is a contingent fact subject to being discredited someday? (Would he say that about arithmetic?) What does that mean? What would constitute evidence of reason's unreasonableness? How would the alleged evidence be examined if we're not allowed to use reason for that purpose without being accused of circularity?
And what does it mean for something to "violate reason"? Is he thinking of miracles? What Dillahunty consistently fails to understand is the contextual nature of knowledge and concepts. The concept demonstration (like proof and evidence) PRESUPPOSES reason and its efficacy, not vice versa. If reason were inefficacious, asking for a demonstration of anything would be a waste of time.
In other words, reason and logic are self-validating.
Prolific atheist celebrity Matt Dillahunty -- who has done many videos on logic, reason, and certainty -- thinks the problem with the laws of logic is that it they not axiomatic -- self-evidently true -- and cannot be validated because you have to use them in the very attempt to refute them. I guess he thinks that involves circular reasoning or question-begging. Most generally, he thinks logic (along with reason) is no demonstrable.
Here's how he puts it in a YouTube video:
There are people who believe that reason is in fact absolute. I used to be one of them. Even as an atheist I would argue that the only absolutes are identity, non-contradiction, and excluded middle. And now I recognize that while this is a reasonable position to hold, that all of the evidence shows that these things are inviolate and absolute, we have no way of demonstrating that because you would have to assume that they’re true to try to show that they're false, which sets up a contradiction. Now you’re in a position where you have to say, "But if they’re not true then there’s no problem with the contradiction." So why would you use a proof by contradiction to get there when as soon as you show that the laws of logic or laws of thought aren’t absolute, you now have no justification for saying that the contradiction is or isn’t a problem. [Emphasis added.]
What he's saying, then, is that Aristotle's negative validation of logic -- his demonstration that any argument against the Law of Identity must smuggle the law back in or the argument makes no sense -- has a problem because it claims that a contradiction lies at the end of it. Note he says, "you’re in a position where you have to say, 'But if [the laws of logic] are not true then there’s no problem with the contradiction'" [for the logician, apparently].
But the logician never says there's no problem with the contradiction -- namely, that if the laws of logic are misconceived, then the conclusion of any argument, including the one against logic, can be both false and true. The contradiction is the problem, but it's a problem for the anti-logician, who is supposedly trying to show that logic is false, not the logician! Rather the logician says:
To qualify as an argument (about anything) a set of statements must close with a therefore, that is, with a proposition that is said to be warranted by what preceded it and that is necessarily represented as being the case or not being being the case -- in other words, true rather than false or false rather than true -- but not both. If an alleged argument does not have that feature, it is not an argument; it's something else -- a rant perhaps.
Thus it follows that if you make an argument intended to refute the Law of Identity, Contradiction, or Excluded Middle, it would require that the supposed conclusion -- namely, that the law is not true -- could be both true and false at the same time and in the same respect. You can't set out to argue that the law is not true and at the same time maintain that propositions can be both true and not true. In other words, the "argument" only looks like an argument. It's really a pseudo-argument because it does not -- and cannot -- assert that something is true rather than false or false rather than true. Logicians thus have nothing to respond to.
As they say, Quod Erat Demonstrandum.
This slices Dillahunty's position to the bone. Obviously, reason, logic, and language are joined at the hip. Every proposition begins with the unspoken words, "The following is true." If instead every proposition must begin with the words, "The following can be both true and false," language and discourse are emptied of all worth. So is the human mind. Even Dillahunty's case for negative atheism is tossed in the bin. Unless logic is understood as axiomatic, what's the point of asking for evidence of anything?
To be fair, Dillahunty does not want to throw out logic. On the contrary, he invokes it routinely. But on what grounds does he do so if he rejects its axiomatic status? On the grounds that it has proved useful. (Tomorrow? Who can say with certainty?) They work. Thus, he says, they are reasonably accepted by rational people.
But this can't be right. Reason does not judge the laws of logic. Instead, reason is founded on logic, namely, that A is A. Part of what it means to be reasonable is to be attentive to the requirements of logic. Dillahunty's put the cart before the horse.
Yes, we are "stuck," as it were, with logic. But that's a feature, not a bug. As Wittgenstein taught: "Logic fills the world: the limits of the world are also its limits.... What we cannot think, that we cannot think: we cannot therefore say what we cannot think." He went on to add that we cannot even imagine reaching a line with something else on the far side. What would be on the other side? An illogical world? All such talk is literally nonsense.
One final thought: Dillahunty goes to great pains to rebut those who think that "reason is in fact absolute." I'm not sure whom he has in mind, Descartes maybe, but for him, God made certainty possible, so that has no relevance for atheists. What would it mean for reason to be absolute? If it would mean that reason can make us infallible and omniscient, then he's right: reason is not absolute. But that is a ridiculous standard. Nor is it what any naturalist has expected from reason.
Dillahunty, in fact, has turned the truth upside down. Fallibility is not what limits reason. Quite the reverse, reason limits fallibility. We need reason and logic precisely because we are not omniscient. God would not need reason. He'd know everything instantly and without effort. He'd just know. We can't do that. So we need a guide in our quest for knowledge. Reason and logic are guides. You can't reasonably complain that reason doesn't deliver omniscience ("absolute certainty" -- a red herring) because it never promised to do that. On the contrary, it's a faculty and a set of tools exactly appropriate to fallible beings. Again, infallible beings would have no use for reason.
Try this analogy: reason is like a hammer. If a carpenter hits his thumb instead of the nail, it's not a shortcoming of the hammer. Similarly, if a reasoning person makes a mistake, it's not a shortcoming of reason. It demonstrates the uncontroversial truth that people are fallible, which is why they need reason.
Dillahunty may agree with a lot of what I say here. Yet he also says, "The problem is you can’t demonstrate ... that nothing that can violate reason. And I would agree that seems to be the case. The problem is you can’t demonstrate it.” Just before that he says, “At some point, when you’re trying to figure out just how confident you are [about a knowledge claim], you have to get to the point of all of this being contingent on reason being reasonable." Yikes!
This is more nonsense. Is he saying the reasonableness of reason is a contingent fact subject to being discredited someday? (Would he say that about arithmetic?) What does that mean? What would constitute evidence of reason's unreasonableness? How would the alleged evidence be examined if we're not allowed to use reason for that purpose without being accused of circularity?
And what does it mean for something to "violate reason"? Is he thinking of miracles? What Dillahunty consistently fails to understand is the contextual nature of knowledge and concepts. The concept demonstration (like proof and evidence) PRESUPPOSES reason and its efficacy, not vice versa. If reason were inefficacious, asking for a demonstration of anything would be a waste of time.
In other words, reason and logic are self-validating.
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