Are the laws of logic invented or are they independent of human reason? If they are independent, how can they exist immaterially? What does it mean for such laws to exist in a nonphysical way?

The human brain is a physical object, and many people think that logical relationships are the way they are only because our brains happen to work in a particular manner. But there’s a problem with this theory: Our brains work properly in the first place only because they recognize logical relationships—if they didn’t, we would reason incorrectly and would harvest at the wrong times, or drive in the wrong direction, or fail in our efforts to operate a computer. In that case, however, our brains’ mechanisms can’t define what counts as logic. Instead, logic helps to define what counts as a functioning brain. Since we survive only by making logically correct inferences, a correct sense of logical relationships is already part of what constitutes a viable brain, and thus it is the demands of logic, over the course of human evolution, that have shaped the physical structure of the brain, not the other way around.

Another common theory is that logical relations are the way they are only in virtue of the rules of language—whatever language we happen to speak. If our language had different rules (it is supposed), then different things would be logical. The trouble this time is that no rules are intelligible in the first place unless they already have logical implications, and so it is the existence of these logical implications that makes the rules of language possible from the start. Rules are useless unless they already have a logical connection to the consequences that they entail, and as a result, our ability to distinguish the logical from the illogical is part of what allows us to have a language at all, not vice versa.

Still another common idea is that what we think of as logical is really just a consequence of the particular culture in which we are raised, and thus, in a different culture, different things would be logical. Cultures can indeed differ in a great many respects, but if two cultures shared nothing in common, not even in the way they logically inferred one proposition from another, then what would it mean for one culture to understand another? And what would disciplines such as anthropology or sociology be about?

To understand another culture even partially is presumably to understand how a different tradition or experience would lead one to draw different conclusions about the world. But what does it mean to understand someone else’s conclusions—if not to understand how different conclusions would follow logically from different assumptions? Yet in that case, one must still assume some sort of logic in common.

All these considerations were actually anticipated centuries ago by medieval philosophers who, working in the tradition of Aristotle, insisted that logic was the common tool of all the sciences. Their meaning? That all attempts at analysis, explanation, method, procedure, science, and rulemaking must take some notion of logic for granted. Some sense of logic is always presupposed. On the other hand, if we seek a further basis for this presupposition, our efforts end in stalemate. Given various logical principles, we can show that other principles follow necessarily, but as to why there should be any logical principles at all, this question seems to be unanswerable.

It is hard to see, moreover, how any other discipline could ever help us to escape from this difficulty—the difficulty of explaining why logical relationships exist. Logic can’t follow from other disciplines such as neurology, linguistics, physics, anthropology, or sociology, because logic defines what it means to “follow” in the first place. Nor is it easy to see how logic could ever be a consequence of anything else. Why? Because logic already defines what counts as a consequence. In essence, logic is a horizon beyond which none of our earnest and self-reflecting arguments can help us see.

Let me add a further word of caution: Many people working in academic philosophy today will regard at least some of what I have written here as controversial, and so you’ll want to take all of it with a grain of salt. Nevertheless, if you want to find this outlook defended at further length, Heidi White and I discuss these matters in chapter 1 of our recent book If A, Then B: How the World Discovered Logic.

Good question, and as fundamental a question as anyone could ask. I think that the laws of logic must be not only independent of human minds but independent of any minds, including God's mind if such exists. At any rate, I don't think anyone can see how it could be otherwise.

To say that the laws of logic depend on human or divine minds is to imply that the following conditional statement is nontrivially true:

If (1) human or divine minds had been different enough, then (2) all of the laws of logic would be different from what they are.

(By "nontrivially true," I mean that the statement is true not merely on the ground that (1), its antecedent, is logically impossible. If (1) is logically impossible, then the conditional statement is trivially true, even if (2), its consequent, is also logically impossible.)

We can't make sense of the italicized statement without presupposing that (2) is false. If the italicized statement means anything, then it doesn't mean this: If (1) human or divine minds had been different enough, then (~ 2) not all of the laws of logic would be different from what they are. But, of course, my assertion just now about the statement's meaning itself depends on holding fixed at least some of the laws of logic, i.e., it depends on presupposing (~ 2) even on the assumption that (1) is true. Therefore, we understand the italicized statement only if we presuppose that it can't be nontrivially true.

As for the nonphysical existence of the laws of logic, you might look at what I wrote in reply to Question 24874.

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