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Knowledge is supposed to be having information, or an experience of something that is real or true. ? Then after having that knowledge a person in good faith should believe that their knowledge is true knowledge, right? Do we believe what our eyes can see unconditionally? Or should be believe in logic and reason? Is there such a thing as having sacred knowledge and in turn should that lead us to further believe? Scientific rationale, cause and effect, are these really the elements of understanding our purpose as humans on this rock? Should we believe in instincts? or (women's) intuition? I have knowledge of my own experiences, yet somehow that is not something that can be equally shared with others after the experience is had. Sometimes all we have are words and an understanding that we too pass though situations that are unreal. whether it's real or not, we all hope to believe in what we consider to be the truth. Some just reach farther than others.
Some personal experiences provide knowledge, but some its better to be skeptical about.
A lot of the methods of knowing you mention are testable - is women's intuition statistically better than guesses?
Everyday experience and logic/math reliably provide some knowledge - but we can be mistaken about some personal experiences and should be skeptical that they happened.
Exceptional/extraordinary experiences or claims(leprechauns in the garden, sacred knowledge) are probably unreliable/nonveridical, so we shouldn't trust that such claims are true/experiences happened.
interesting points. knowledge is most often taken as something empirical. but as the history of ideas has shown us, empiricism = reificaction. the deification of concepts. to KNOW something is to BELIEVE something is true. to believe something rests upon our impulses and perceptions. we define our perceptions using a finite resource, our mind. the language that we use in order to understand the world that we live in is beyond limited. the very act of communicating is a negation of the substance of things. the idea that things are of a substance is logical, but removed from the substance themselves.
this leaves us with a conundrum. shall we acknowledge the void and continue to speak using objective terms, or do we communicate on a more vague, disconnected level. i personally believe it is a combination of the two. a true dialogue can only occur when the problem of interpretation is agreed on and the terms are settled. e.g., if one believes that it is possible to know not only that things ARE, but WHAT they are, they will be unable to come to a consensus concerning a matter with one who believes that at best we can describe what it APPEARS that things are.
in my opinion, certain words serve no real good, e.g., to know. the word implies more than we are capable of. The word believe is also shallow and leaves room for those who want to justify their belief in a god or anything super natural. this has been done for quite some time now and honestly gets under my skin.
so we are stuck with limited language and an impossible situation. in the end we can only be responsible for our own beliefs and this is where many are frustrated and seek a more objective language. i frustrate a lot of people because i contradict myself often. the reason is that many positions are equally tenable.
ok, im rambling. back to the atheist/agnostic question.
according to modern usage, we should all be agnostics in the sense that no one knows anything for sure. even dawkins acknowledged the possibility (marginal as it is) of the existence of a god. an atheist is not only someone who says "there IS NO god" but also one who maintains that "there might be a god, but i am not sure." now, if they say "there might be a god, but i am not sure, but i believe in one" they are a theist with reservations, not a theistic agnostic.