Contradiction has nothing to do with logic? What a maroon - Bugs Bunny

Resulting to insults right off the bat? What a moran -Zisteau

Empirical results aren't always clear (see QM). Also actual databases with input from actual humans ... isn't a piece of cake. Most examples of falsifiability ... I think means empirical evidence (as I was relating). But it is also tautology if we mean math. Logic allows that there are tautology, contradiction and contingency. Non-Aristotelian logic expands that a bit ... most things become contingent. Contingent on what? Something outside of logic, empirical data.

Classical logic acknowledges that contradiction is a bad thing that should be avoided. I don't know a single database that is served by allowing contradictory data, which is why there are consistency checks in these systems in the first place. And empirical results are always subject to interpretation.

Through all this, classical logic has always served us well.

Thing is,

*classical logic* is not

*Aristotle's logic.* It cribs a lot of Aristotle's more useful ideas and makes them its own, but it's a separate thing and despite its name, quite modern. Classical logic cannot tell you which atomic propositions are true. It's simply not its concern. Classical logic is a formal system, and does not judge the contents of the propositions. George Boole may have provided the final push for algebratizing logic, but logic has been shedding Aristotle's chaff for centuries.

Making fire with sticks is useful. Dealing with contingency, for most of us, is where it is at. Most of us don't do math proofs. And for 100 years now, there have been problems even in math, regarding what is "rigor". Formalism is the old style ... but now there is Constructivism and Intuitionism. Intuitionism doesn't use Aristotelian logic. In Constructivism, you don't allow proofs that say X must exist. You have to provide an algorithm for generating one or more examples of X. Mathematicians fight over this ... without resolution.

Mathematicians are people too, regardless of what others might say. If people can fight about evolution vs. creationism even though any rational account comes down in favor of evolution, then fights over less clear subjects is not surprising. That said, I do not see how Constructivism and Intuitionism have earned their keep, and the fact that they are not formal is actually a great detriment to them and severely limits their use. The higher maths are so complicated that it takes careful formalization to get anywhere without tying yourself up in knots.

A pure liar states that he always lies... Contradiction.

Since a pure liar always lies, such a person claiming that they are a pure liar would be telling the absolute truth β therefore, the pure liar cannot say that he is a pure liar, because he only lies. On the other hand, because a pure liar can never claim to be a pure liar, any person claiming to be a pure liar is not; they tell the truth sometimes, just not here.

The key here is just because you're able to articulate a thought, doesn't mean that the thought describes a logically coherent situation. Your brain is not a logical system, but an evolutionary one. While it can emulate a logical system with training, you can entertain thoughts that are contradictory. It is, after all, why we have peer review.