It possible to look at the world optimistically or pessimistically without sacrificing accuracy?

As commonly understood and reinforced here, 2 + 2 = 4 is taken as meeting the test for absolute certainty. This appears to be true in a formal or symbolic sense but is it true in reality? When we count two things as being the same and add them to two other same things do we really get four identical things? Perhaps, perhaps not; it may depend on one's identity theory. Do we know with absolute certainty when we have one thing and not two? What am I missing?

Is there any kind of knowledge that could be called certain?

Who can direct me to the philosopher whose work addresses the relationship between knowledge and emotion?

I have a question about Descartes' response in Med. VI to the dreaming argument. It seems to me that his knowledge that he is not dreaming any set of beliefs is based upon the knowledge that his current experiences are consistent with reality, which relies upon the knowledge that he is not dreaming his set of beliefs about reality. Would it be accurate to accuse the response of circularity?

I have a question about Cartesian skepticism. One of the premises of the argument is something to the effect of: (1) I don't know that I'm not dreaming. My question is: What justifies this proposition? My intuition is that the evidence for (1) cannot possibly be empirical; for the upshot of the skeptical argument is precisely that all empirical claims are dubious. (Maybe it's helpful to rephrase (1) as "It's possible that I'm dreaming," if that is legitimate.)

It is well understood that we are prone to have certain "biases" in our perception of the world, which are caused by some form of highly relative sociocultural conditioning or another. With that in mind, how could we be sure that we can trust our perception of objective reality? Wouldn't that "complete perspective" always out of reach, because with all our sophisticated science and knowledge we are still just human subjects experiencing the world as members of a particular set of social conditions? Also, what about the bias of human perception itself, compared to animal forms of perception which might rely on completely different systems of space and time? Like, the fly that only lives for a day or two, or giant squids who live at extreme temperatures and pressures for 100 years or more. The point is that it seems like a truly comprehensive system for understanding and categorizing objective reality into workable concepts would have to account for the fact that we are limited to our experience as...

"In expanding the field of knowledge we but increase the horizon of ignorance” (Henry Miller). Is this true?

Can reflection destroy knowledge? Is it plausible to say that people's sense of social and moral direction can depend on not asking too many questions? Should one always justify conceptual and moral foundations of this world? Do you risk ending up in a situation where the reasons guiding your actions lose their power to guide? By demanding reasons for reasons, can reflection destroy practical knowledge?

During discussions with one of my friends (who is an undergraduate biologist) we often enter into the empiricism vs. rationalism debate. In support of empiricism as the best route to true knowledge my friend often cites the many practical achievements made throughout history resulting from a scientific/empirical approach. In response to this I find it difficult to cite any significant advancements or examples of knowledge which can be credited to the side of rationalism. Indeed it seems to me the invocation of science's great 'utility' is often used as a defence of its (sometimes questionable) actions as well as its assumed superiority as a means to true knowledge. Therefore my question is how can one most effectively challenge science's monopoly on truth and knowledge (particularly in today's 'science worshipping society') in the face of its great practical achievements?