What do you make of empiricism's claim that all of our knowledge is based on the use of our senses? What areas of knowledge do you think support this theory? Are there any types of knowledge (mathematical knowledge, for example?) that you think are a problem for this theory?

I disagree with the claim that all of our knowledge is based on the use of our senses. I mean senses are really how we acquire useful verifiable knowledge. This would be great to describe knowledge based on experience. To me it falls apart when you are trying to use it to explain math. Math is facts 2 plus 2 is 4 everywhere. I also discussed this briefly in my pervious post. Check it out.

What do you think about methodological skepticism? Do we ever follow this procedure in our daily lives, or do we do the opposite. In other words, do we tend to believe things until it becomes impossible to believe them, rather than doubting everything we can? If so, does this suggest that methodological skepticism is not a good strategy?

I think methodological skepticism is something that is hard to accept at first, but can be used effectively to prove skepticism. I am one of the types of people that clings onto my belief until it is evident that whatever it is, is not true. For example, when I was younger I read a children's book that said corn grew on trees. I loved that book. There was no way you could convince me that corn did not grow on trees. Eventually as I got older, I visited a corn field and was in shock. I doubted my eyes. When I realized that corn did indeed grow from the ground, it made me question all my other childhood assumptions. So I can see how skeptics relate everything back to beliefs. When you truly wholehearted believe in something and then you find out its not true, it makes you question everything around you. Even though I do see where skeptics are coming from. I do not agree about some things. The early Greek skeptics stated "Don't worry about what you cannot know". Isn't questioning beliefs in itself, apart of philosophy? So if we never question and worry, how will we ever know? Is this to say we should be the horses with the blinders on? knowledge. I think that we have came a long way as a people. So 2+2 does not equal 4? Some things are undoubtable. Facts equal Facts until proven otherwise. But even though I do not agree with methodological skepticism, I believe it has interesting points and can be a good strategy to disprove beliefs of others.

In the Allegory of the Cave, Socrates suggests that, without philosophical education, we are all like the prisoners in the cave. What are your thoughts on this? How is philosophy supposed to be liberating? Do you think Socrates is right to be so pessimistic about life without philosophy?

I agree with Socrates. We truly are like prisoners in the cave. We would be walking around like horses with blinders on. The thing that makes us one up from animals is our power of thought. Us humans like to wonder about "why?" and "what"  we are curious creatures by nature. Without philosophy we would be stuck in a world I would rather not live in. I am thankful for philosophers like Martin Luther King Jr. and Malcolm X that changed our views for the better. We needed these "gadflies".

I think philosophy is liberating when it comes to your thoughts and ways of thinking. It frees your mind from captivity of common basic thoughts and allows you to explore thoughts you never had. You question your thoughts over and over. 

Yes I do think Socrates has a right to feel this way. Can you imagine a world with no philosophy? No one questioning truth or beliefs of others? A lot of great things has come from people standing up and questioning others beliefs. Can you think of any?