Epistemology is the field of philosophy that deals with knowledge and belief.
Traditionally, knowledge has been held to be a true, justified, belief, where justification means any number of things typically having to do with some form of causal relationship that leads to the belief.
Justification is a minefield of assumptions about reality and whether or not we can be justified in believing anything about anything beyond our immediate sensory perception is questionable.
What we know and what we believe are possibly very distinct from each other.
Ultimately, how can we check the truth of a particular belief about the world? We would, in some sense, have to have absolute knowledge of the world in order to know if our beliefs about it are true. But, this depends heavily on what we take to be our understanding of truth.
The only thing that I think is certainly true and justified and a belief that we can not doubt is that something is thinking. This is a similar concept to that of Rene Descartes who wrote, "Cogito Ergo Sum" or, "I think, therefore, I am".
All other beliefs other than this primary knowledge that, basically, something exists and that something is thinking, are assumptions that can possibly be false. Perhaps that, right now, I am seeing red, is something that can not possibly be false and that I have immediate reason to believe and be justified in believing.
It is important to look at different beliefs and examine how well we can be said to know such beliefs. For example, that the Earth is a sphere is knowledge if it is true that the earth is round.
We could imagine a universe where, though the earth is actually flat, the particular simulation machine we are in indicates that it is round. But, this possibility does not, at least on the surface, appear true because we have no evidence that we are in such a machine.
Perhaps, for humans, as well as artificial intelligent systems, we can rank knowledge.
If truth can be fuzzy, then why too can't knowledge be fuzzy? We can know some things without much thought- things like our current emotional state or that something exists and thoughts are happening here in our consciousness.
But, then we can move outward from ourselves and begin to know things about the immediate environment in terms of what we see, smell, hear, touch, and taste.
These things do not indicate some absolute reality but one can not doubt, whilst smelling strawberries, that the sensation of the smell exists- even if the smell is a hallucination or in a dream. Perhaps someone who has a stroke begins to smell oranges where there are none. We can be sure that the person in question knows they smell oranges.
Epistemology and 9-11:
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One of the main reasons the government's attempt to cover up 9-11 is so transparent is the simple logic and scientific evidentiarry chain we can form using elementary physics and chemistry.
Beliefs about perception and beliefs about the actual state of the world and its history are quite different.
We can know, for example, that explosive residue found in the dust from the rubble of the World Trade Center complex indicate one of two things: Either (a) there were explosives in the World Trade Center buildings or (b) the chemists are mistaken or they are lying.
Now, I also know that the two towers fell at near or at freefall speed and World Trade Center 7 collapsed immediately and without resistance.
This means that, especially in building 7's case, that the world trade center buildings fell in a way that could not have happened without the removal of underlying support. How is underlying support removed in buildings made of steel?
Explosives destabilize and cut support girders unanimously. So, this evidence lends support to the evidence of explosives.
And, both of these facts, are indicative of a controlled demolition. Then, when one traces the possible culprits in the case one finds that the executive branch was involved first and foremost.
We can be less certain of other players, but Richard (Dick) Cheney must have been central to the plot because he was the one standing down a proper response from the air force. How certain can we be that the World Trade Centers were demolished? As certain as we are that the Titanic sank.
While we can not know, in some absolute sense, that either happened, we can be as sure as we are about any observable or recorded event with solid physical evidence- evidence like that of the wreckage of a rather large vessel at the bottom of the Atlantic ocean.