response essay

Choose one question to write 700 words in response to. The follow up questions in each prompt are not necessary to answer, but will help you structure what a good response to the question most likely includes! 
This need not be a classic essay-formatted assignment, but be clear about your arguments before you are fancy! 

Does knowing something is true necessitate believing that it is true?
In Plato’s Allegory of the Cave, Socrates argues that facts about both empirical objects (like chairs) and non empirical concepts (like mathematical equations) are true for the same reasons—the truth is a priori, defined by the Forms. Do you agree with this (lack of) distinction? Why or why not?
Is a priori knowledge possible? Either: What is an example of a priori knowledge, or what makes it impossible?
Imagine that there are two complete theories of why something is true, both seemingly logically argued but they are mutually incompatible. Does this incompatibility mean that one or both of them are wrong? (This is both a question about how we know that something is true and about Wittgensteinian language games)

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