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Wednesday, 16 June 2010


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Dan Hicks

A handful of philosophers of math (Lakatos, Kitcher, I think someone named Tymoczko) have argued that the method mathematicians practice is basically the same as the method other scientists use: by investigating an array of particular cases, a general hypothesis is formulated; they then attempt to provide evidence (in some sense) in support the hypothesis; usually there's some back-and-forth as the hypothesis has to be modified in light of the new evidence; and eventually the evidence is sufficient to support the final version of the hypothesis (to some appropriate degree).

1. This may not be anything like what Myers had in mind by `a narrowly defined scientific method'.

2. `Evidence' probably needs to be context-dependent for this story to be plausible. Empirical observations (or the data sets generated based on them, or something in the vicinity) need to count as strong evidence in chemistry, but only weak evidence at best in math. Note that this might drive a wedge into your inference from `follow[ing] the scientific method' to `adduc[ing] scientific evidence' in the last post.

3. I take it to be highly plausible that this method, presented at this or a slightly higher level of generality, is either the best or the only way of producing robust, systematic knowledge. `Systemic' here is meant to suggest a distinction between individual beliefs about, eg, the presence of craisins in this particular bowl of oatmeal and whole sets of related beliefs about, eg, the properties of 3-manifolds in general.

4. Theologians, theistic apologists, and philosophers of religion might use another specification of this method for producing systematic theology and reasons sufficient to support belief in god. That, I take it, is a sociological claim best supported by someone familiar with the work of these sorts of intellectuals and popular intellectuals. I am not so familiar. I suspect Myers is not either.

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