What? There's no variety in triangles.Blood Brain Barrier said:What empirical evidence lets us establish that the angles of all triangles add up to 360? If we had to demonstrate that rule empirically we would have to catalogue every single variety of triangle in existence, an impossible task and in any case one which we haven't deemed necessary to consider the proposition a true one.
It's a binary thing. Either something is a triangle or it's not.
A triangle is defined by a strict set of observable properties. Either an observable object matches all those properties, in which case it's a triangle. Or it does not, in which case it's not a triangle.
Every triangle we can observe is has those exact properties. If it hadn't then it wouldn't be a triangle.
Those properties are rooted in reality, in observation. That's our axiom. That defines what a triangle is.
Based on that axiom we can use reasoning, logic to establish that the angles of all triangles add up to 360 degrees.
You treat science as a static thing. Where if a theory is considered valid if and only if it'll be valid for all time.Blood Brain Barrier said:And besides, we cannot establish by empirical induction that something ALWAYS leads to something. If we find that the boiling temperature of water is 100 degrees celsius by testing it a million times, we still can't be sure that on the million-and-one attempt the result will be the same.
Science isn't static. Science is dynamic. Theories change all the time as new observations and new lines of reasoning become available. That doesn't make previous theories invalid, it merely makes them based on outdated observations.
That's how science works. We make observations. We come up with theories, through logical reasoning, that explain those observations. We make more observations. We come up with new theories and alter existing ones, again through logical reasoning, that explain those new observations. Repeat infinitely.
Logic is based on axioms. Axioms which originated from reality.Blood Brain Barrier said:That's partly true but what I'm saying is that empirical results wouldn't even make sense if there wasn't some pre-existing basis on which to assess them. The statements we are making right now in this thread are not 'based on observation', but a logic based on asserted truths we hold to as more fundamental.
Some philosopher didn't have a wacky dream at one point in which all those axioms magically came to him.
Those axioms were established through observation of undeniable patterns in reality.
And based on those axioms we started reasoning. And from that reasoning came statements, such as you're making in this thread.
Where do you think those asserted truth we hold to as more fundamental came from? You think they came from visions special people had? You think they're ingrained in our brains so that everyone knows them?
Then how do we know that they're actual truths? We know because we can test them. And we can test them against reality.