• It is sometimes said that mathematical reasoning is a process of logical deduction. If this is true, and if the conclusion of a proof must always be implied by (contained in) its premises, how can there
ever be new mathematical knowledge? • We can use mathematics successfully to model real-world processes. Is this because we create mathematics to mirror the world or because the world is intrinsically mathematical? • In the light of the questions above, is mathematics invented or discovered? • Are all mathematical statements either true or false? • It has been argued that we come to know the number 3 through examples such as three oranges or three cups. Does this support the independent existence of the number 3 and, by extension, numbers in general? If so, what of numbers such as 0, -1, i (the square root of -1) and a trillion? If not, in what sense do numbers exist? • Can mathematics be characterized as a universal language?
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Answer ONE of the following questions in a blog post.
1) Is faith an emotion? 2) To what degree can emotion be used as a moral jusitification? 3) Should be emotion play a role in evaluating knowledge claims? • To what degree is emotion biological or “hard-wired”, and hence universal to all human beings? To what extent is it shaped by culture and hence displayed differently in different societies?
• What sorts of things count as emotions? Are emotions and feelings the same thing? • Can feelings have a rational basis? Is “emotional intelligence” an oxymoron? Robert Solomon says that emotions are “systems of judgments”, and that “virtually all of our experience is to some degree ‘affective’, and even our most dispassionate judgments…can be adequately understood only within some larger emotional context”. Is he correct in claiming that virtually all sense perception, and reasoning, must involve emotion? • Is it possible to experience an emotion, a feeling, an attitude or sensibility that cannot be expressed in language? Can an emotion, such as love or grief, have its origins in, or be shaped by, language? • Can emotions be trained? To what extent can we control our emotions, not in terms of how we act on them, but what we actually feel? Do cultures select emotions to foster and use? • Are concepts such as solidarity, patriotism and racism examples of collective emotions? • Is faith an emotion, a feeling, or neither? Pick ONE of these questions and respond in a blog post by April 22 |
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May 2013
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