Does language shape our understanding of what we call reality (or, maybe, our perceptions of reality), or does reality shape our language? Is there, significantly, a German world, a French world and an English world, each of them different from one another in important or trivial ways?

Here is a simple response, which I think is true: Language shapes our understanding and our perception of reality (different words will cause us to focus on different aspects of the world around us) and reality shapes our language (different environments will cause us to adopt different words). Speakers of different languages all belong to the same world, however, for there is only one world. Here is a more complicated response that may do a better job of addressing your concern: When people use different words to refer to the very same objects -- a bug, a chair, a curtain -- the differences in their view of the world can seem trivial. But when different languages focus on entirely different things (even the words for objects such as bugs and chairs can have importantly different associations in different languages), they are bound to reflect important differences in the worldviews of the relevant speakers. In some cases, the different views may be quite compatible because they simply attend...

Is there a difference between the words and expressions a person uses to say what he/she believes, and the beliefs themselves? Is one more important than the other?

Certainly, there is a difference between saying "Harry is rude" and believing that Harry is rude since we can say things that we don't believe and we can believe things that we don't say. But I think your (first) question is about how closely the content of our words matches the content of our beliefs in cases where we do our best to say what we believe. Here are a few cases where the content of my sincere words and the content of my beliefs may diverge: 1. I may say "Harry is rude" without really understanding the difference between being rude and being obnoxious, in which case the content of what I say may be somewhat different than the content of my belief -- if what I really believe, without having the right word to express it, is that he is obnoxious. Once someone explains the difference to me, I would recognize that I believe Harry is obnoxious rather than rude. 2. I may say "Harry is rude", knowing that this is a rather simplified expression of my belief yet being unwilling...

Is there anything to the idea that someone only really understands a concept if she can explain it to someone else? Sometimes I think that the things we know most certainly (such as that 1+1=2) are actually the most difficult to explain.

Most concepts get their meaning, at least in part, from their relations to other concepts. The concept of a contract, for example, gets its meaning from its relations to other concepts such as the concept of a promise, the concept of an obligation, the concept of a free agent, and so on. Likewise, the concept of the number two, and the concept of addition, get their meanings from their relations to the concepts of other numbers and other mathematical functions. So understanding what a concept means seems to depend on understanding how it relates to certain other concepts. We can be a competent user of a concept, using it appropriately in relation to other concepts, without being able to explain our usage to someone else -- at least not easily, and without extensive prompting. You might be able to enter into contracts, and to do mathematics, for example, without being able to explain what you are doing. In these cases, you have knowledge that you have difficulty explaining. Whether you...

What is forgiveness? If I forgive someone for some misdeed, does that mean they are no longer obligated to correct that deed? Or is forgiveness simply an attitude change, when one chooses not to remain angry? Also when I say "I forgive you", is that a performative speech act? Or is it possible to forgive someone without saying it (or contrarily, to say you forgive someone when not really forgiving them).

The topic of forgiveness has recently received quite a bit of philosophical attention, which means quite a bit of philosophical disagreement as well. In particular: Charles Griswold, Pamela Hieronymi, Jacques Derrida have written in different ways about this topic. There seems to be agreement about the answers to most of your questions, however. Forgiveness is a change in attitude whereby one no longer holds a grudge or demands remediation from a wrongdoer -- despite continuing to view that person as responsible for their wrongdoing. This is not just a matter of ceasing to be angry; it is a matter of relinquishing the demand for recourse. A person who is forgiven by someone she has wronged may still be obliged to correct or compensate for her misdeed insofar as she continues to have obligations to herself, to society at large, or to a higher power. On the other hand, insofar as one is forgiven by oneself, one's society, or one's god, these obligations cease. Forgiveness may or may not be...