Last time we examined Robert Batterman’s idea that the concept of emergence can be made  more precise by the fact that emergent phenomena such as phase transitions can be described by models that include mathematical singularities (such as infinities). According to Batterman, the type of qualitative step that characterizes emergence is handled nicely by way of mathematical singularities, so that there is no need to invoke metaphysically suspect “higher organizing principles.” Still, emergence would remain a genuine case of ontological (not just epistemic) non-reducibility, thus contradicting fundamental reductionism.
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