The Foundations of Logic

There aren’t any.

Say you’re talking with someone who fancies himself a rationalist. You ask him why he believes in general relativity, he points you to experimental data. You question the quadratic formula, he supplies you with a proof. You wonder how he makes decisions, he explains Bayesian inference.

But suppose we go a little more fundamental. Why use the scientific method? Why believe mathematical proofs? Why follow Bayesian models? In short: why do you believe in logic?

Many answers exist, with varying degrees of smugness. Possibilities include:

  • “Logic-based decisions tend to be right more often than intuitive leaps.”
  • “The scientific method offers dependable, testable predictions.”
  • “Try building a bridge without math, and see how far you get.”

But guess what all these answers have in common? They all depend on logic.

You can’t give experimental data as a reason for following the scientific method, because it presupposes the validity of the scientific method.

Or, to put it another way: you can’t use logic as a reason for believing in logic.

Fine, says the rationalist, then I’ll start with an illogical intuitive leap to arrive at my rationalist philosophy. “I believe in it because I believe in it, so there.” Nothing logical about that. And then, safely ensconced in my walls of rationality, I can defend against all invaders.

Sure. Go ahead. But now you have to recognize that your vast, impressive rationalist castle stands on irrational quicksand. Fundamentally, you can’t show that your conclusions are any more valid than the conclusions of Miss Cleo and the Psychic Readers Network, because you’re both making an intuitive leap: I believe in this because it feels right.

So what’s the answer to this paradox? The truth is, I don’t know.

Because, after all, I am the rationalist I’ve been poking fun at. I do believe in the scientific method. I don’t think faith alone is a good enough reason for accepting something. Yet here I am, confessing that faith is the only foundation I can concoct for my own worldview.

Don’t misunderstand me. This is not a triumph of religion over cold science. Everyone uses logic, whether they know it or not. As the Catholic Church correctly points out, “We can’t avoid reasoning; we can only avoid reasoning well.” Throwing out the concept of logical inference means throwing out most of the Bible, too. This is everyone’s castle, and we are all sinking in quicksand.

First ethics, now logic. All my foundations are crumbling.

To many of you, this may sound like mere wordplay or idle speculation. And, true, it doesn’t make much difference in my day-to-day life. I’m not going to start sideswiping kindergartners because my philosophy of ethics is shaky; I’m not going to shake hands with a rattlesnake because logic has failed me. I keep both these pillars enshrined in my heart, because anything else is unthinkable.

But I am a dude who likes things to make sense. And if I’m honest about it, this stuff isn’t making much sense right now.

What do you think?

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4 responses to “The Foundations of Logic

  1. Interesting, but in the end it doesn’t mean much to me. The basis for, like, everything we understand, or think we do, comes from our perceptions- which are very, very human.

    And they’re the only things we have to trust.

  2. This is an interesting question!
    I’ve never quite thought about why I follow logic. I just. . .have. Maybe it was from my teacher from last year, yelling “Why!” Or “Defend yourself” from some other teacher who I can’t remember. Either way, I’m afraid I don’t have an answer. i follow logic because I do. I follow logic because I’m used to it, and the known is better than the unknown. Because logic works?
    I don’t know. Let me know if you find an answer!

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