OK, so I know I recently posted a statement about the inability to "know" anything. I have been getting scads of inquiries about my exact intention. Well, maybe not scads -- one guy in a Craigslist forum criticized me for it. So let me clarify.
Here are some categories of stuff we encounter in real life:
1. Things true systemically or by definition. 1+1 is 2 because we create a system which defines 1 and defines two and gives a property of two that relates to the value we set up for 1. Mathematical proofs are about showing identity or property. Two triangles are congruent if they possess certain qualities which can be listed and which satisfy the definition of "congruent."
1A. Things that can be measured by a standardized measure. The temperature is an example. The property of the air might be "68 degrees" because that is ascertained by an external measurement (thermometer). That property is also not about "knowing" but about assigning a quality.
2. Certain things are perceived/sensed. These things are subjectively "true" but the senses are, to a large extent, standardized, so what I think of as "burning" you think of as burning. While there are levels to values (hot, hotter, hottest) all are based in the individual perception and labeling, not about knowing a transcendent truth/quality. Some of this is empirically based and dependent on whether we trust the senses. Does a chair I am sitting on "exist" because I feel it? Can I know that my memory reflects reality?
3. Certain inferences or conclusions which we draw about our world -- causal links, which allow us to make predictions about the world. This is the kind of "knowledge" which I was referring to when I said that we can't "know" anything. These inferences, while very often accurate and based in probability and repeated positive correlations are not true knowledge, but simply reasonable guesses. We don't "know" that the sun will rise tomorrow but science lets us see that odds are it will. We don't "know" that smoking causes cancer but we have some scientific studies which lead us to conclude a causal link. But we can't KNOW that link, only infer it and ignore variables.
So now you can see what I meant about knowledge.