Hi all, i found by chance this forum, and i can’t resist to give my opinion on this :p
1. What, if anything, can we know with absolute, infallible certainty?
The first thought i had on this (long time ago) is :
Naturally, no conclusion from inductive reasoning is certain, but the frustrating things, is that we also make error with deductive reasonings. We are relatively certain of some conclusions, because we verified them many time, and they are simple.
But verification and simplicity will only diminish uncertainty, it will diminish it greatly, but never make it zero, because if N verifications would diminish the uncertainty to zero, only one of the verifications would diminish uncertainty to zero.
Then, no "constructed knowledge" are certain.
But then, some of the things we thought not to be constructed knowledge, we thought to be "basic/fundamental truths", was in fact constructed knowledge.
It seem that the differentiation between a "constructed knowledge", and a "basic truth", is a constructed knowledge, and then we can’t be sure that something is a basic truth or not,
And then the conclusion is that, nothing is certain.
But rapidly you could see that "nothing is certain", is sort of "self contradictory": If "nothing is certain", then "nothing is certain" is uncertain, and then maybe there are some certainties.
And yes, in fact, all reasonings i saw to prove that "nothing is certain", including my own, rely on a lot of (not very well defined) deductions, and a lot of time, rely also on some inductions.
The thing is, "nothing is certain" rely on a lot more uncertain things, that something like basics logics, or even most of mathematical reasonings.
This is why i will give more weight to "(1+1=2 and 1+2=3) ⇒ (1+(1+1)=3)", than to "nothing is certain".
2. What does it mean for us if we cannot know something with absolute, infallible certainty? How does/should doubt affect our actions?
It mean total self-referential madness.
Some people think that "Nothing is certain, but we could still reason on uncertain things, and give a level of certainty", or something like it.
They just don’t give it enough thought, they don’t really draw the consequences.
First it is uncertain that we could reason on uncertain things, it is also uncertain that we could give level of certainty.
If we give a level of certainty, it is uncertain that this level of certainty is useful, or that we could use it to act.
Worst, it is uncertain that "even if it is uncertain it could be true", and it is also uncertain that "if it is true it can’t be false", and that every words i could or you could say, mean something. And it is not because it doesn’t mean something that it could not be true, and we are also uncertain that it is not absolutely true and certain…
This break every reasonings, even itself.
3. Is radical Cartesian doubt even possible? For instance I may not know for certain that jumping off a particular window ledge of a tall building will kill me but that is not going to prevent me from avoiding said window ledge regardless.
It depend how you define it, but if it is about doubting all your beliefs, it is impossible, because "I doubt A", is a particular believe, that you will need to doubt, and you will even need to doubt the believe that "whatever N, I doubt that i doubt that…N time…that i doubt A"
This sort of construction is self-referential in the worst way, you can’t doubt all your believes because you are "finite", but even if you was "infinite", you still couldn’t do it.