Created from one of our meeting transcripts @BuildCoherence. Hopefully this makes sense to y'all.

Induction, deduction, and abduction are considered the three fundamental ways to logically reason, yet almost no one understands them. They are usually depicted as three distinct modes, but this is misleading. Induction and abduction are better understood in terms of deduction. So let's start there. Deduction is a logically valid argument: P1: Socrates is a human P2: All humans are mammals C: Socrates is a mammal A deductive argument is truth-preserving. That means that if the premises are true, the conclusion must be true. A math theorem is a deductive argument. We also know by the Curry–Howard correspondence that deductive arguments and computer programs are actually the same thing. Induction can be thought of as extrapolating from data and is really a special case of deduction where some premises are left implicit: P1: Tweety is a bird C: Tweety can likely fly As stated, this isn't truth-preserving. Just because Tweety is a bird doesn't mean she is likely to fly. A penguin named Tweety is not likely to fly. We can convert the argument to a deductive argument by making the additional premises explicit: P1: Tweety is a random bird P2: Random birds can likely fly C: Tweety can likely fly This is valid because knowing a bird is a penguin would no longer make it a random bird. Lastly, abduction. This is the one that computers (even AI) are still not good at. Abduction is where we pick new premises or axioms to reason deductively from. Abduction is where a lot of scientific breakthroughs happen. We got general relativity because Einstein asked, “What if we don’t assume time and space are the same everywhere?”

It's hard to know what makes an idea good, but inconsistency ALWAYS makes an idea bad. Axiom provides an arena for ideas where the rules of logic are enforced. Our early access experience will be out in a few days!