Debates over what a term “is” are always amusing. They’re arguments over definitions. Definitions are stipulated. There’s nothing more to what a term “is” than what people agree to have it mean. I can say that the colloquial name for the species felis catus is “parlock,” and so long as you agree with me, we can have a perfectly meaningful conversation about parlock whiskers. Now imagine someone comes along and says to us, “what are you guys talking about? Parlocks don’t have whiskers, they have 88 black and white keys and are used to make music.” We wouldn’t get into a debate with this person; we would simply let them know that we use the word differently. If the person were to respond, “no, it’s not a matter of use. Parlocks are a type of musical instrument,” we’d quickly come to the conclusion that this person doesn’t understand how language works.
With this point in mind, a question: what do you think logic is?
I’m willing to bet your answer is something like “the fundamental laws governing the universe,” “the laws of existence,” or “the laws of rationality.”
None of those is right. You might want to argue with me. But if you do, you’ll be arguing that a word doesn’t mean what people have historically taken it to mean. You can use the sound and letter-combo “logic” in whatever way you like. But the word has a definition, a history, and a way that it is used by philosophers and logicians.
“Logic” is the study of rules of entailment. It inquires into rules about what follows from what. That’s it.
Perhaps you still want to push back. You just know that logic is really the laws of how the world works. You probably feel this way because you think that logic, even as I’m defining it – the laws of entailment – is an expression of the fundamental laws of how the world works. That’s a fine metaphysical theory about the source and significance of logic. It is not, however, what logic by definition is. Definition and explanation are not equivalent.
“If I know that either A or B must be true, and that B is not true, do I therefore know that A is true?” This is a logical question. “Is the answer to that question a fundamental fact about the nature of the universe?” That’s a metaphysical question.
Now that the definition is cleared up, it’s natural to ask: how do we know that there’s such a thing as entailment, anyway? How do we know that ideas follow from each other in the way assumed by the definition of logic?
The answer can’t be that logically it must be so – that would be presupposing the very thing we’re questioning. Say your best friend were to come you, holding a frog in her hand, and claim, “this frog both is and is not also a dog in the same sense and at the same time.” You might reply that that’s impossible, and you might cite the logical law of noncontradiction: a statement and its negation cannot both be true in the same sense and at the same time. Now your friend asks, “well, how do you know the law of contradiction is always true?” What can you say? That it just wouldn’t make any sense? Why? From what does that follow? Another logical law? How do you know that law?
Indeed, the only answer that doesn’t beg any questions is to say, simply, that it just seems to us that entailment is a thing and that it follows absolute rules. It’s an intuition – an incredibly strong one, yes, but an intuition nonetheless. Think of it in terms of your experience. Try to contradict a logical law in your mind – perhaps the law of noncontradiction. What happens? Something in the mind resists. A very powerful rejecting feeling kicks in and says that it just doesn’t work. This intuition is the reason we’re so sure that entailment follows absolute laws.
This tells us something important about the study of logic. When we try to determine what the laws of entailment are – and so cannot take them for granted – we use our intuition. Intuition is the data that we use for initially determining what follows and what doesn’t, prior to having any formal system of logic to do that determining for us.
Another definition: A “system of logic” is any codified set of rules of entailment. I can easily create a system of logic in which from any statement it follows that Santa Claus is thin. This wouldn’t be a useful system of logic, nor would it have anything to do with the logic that we intuitively use; it would be a system of logic nonetheless.
So now, in a nutshell: intuition tells us what follows from what; it also tells us that that “following from” is governed by absolute patterns. We can use these insights to codify our logical intuitions into the system of logic that accurately and fully represents intuitive logic.
So then, the obvious question: of the infinitely many possible systems of logic, which is the one that accurately codifies the logic that we intuitively use? To answer it, we have to match our intuitions about what follows against what contender systems of logic tell us follows. If there’s ever a mismatch, we must either question whether our intuition was correct or disqualify the proposed system. This matching process is the process of logic selection.
This might still seem problematic. If we’re not already working from a system of logic – that would be question-begging – what criteria do we use when making our intuitive logical judgments? Can we really pick between systems of logic without already presupposing one? We’ll jump into the details of the logic selection process in part 2.
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