Philosophy/What can we know?
Recently I have been wracked by global scepticism, are we brains in vats, were the world and all our memories created last Thursday etc. I found that with the use of certain logical tools like Ockham's razor and abductive reasoning that I could dispel some of these sceptical doubts. But how do I know that my reasoning is valid? How do I know that there isn't, say, a 100% probability that we are brains in vats?
Excellent question Will. You've stumbled upon a perennial and fundamental philosophical question that comprises the branch of philosophy known as epistemology. What is constitutes knowledge? How does it differ from opinion? What are the limits of knowledge? These are some of the questions epistemology wrestles with.
Your line of thinking resembles that of Descartes (17th century French philosopher who is credited with being the father of modern philosophy).
You might want to take a look at his Meditations, readily available on the internet or in college bookstores.
As far as verification, there are a host of possible approaches. Karl Popper ("Science: Conjectures and refutations") and A.J. Ayer (Language, Truth, and Logic) have written several very readable works dealing with verification of knowledge.