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Metaphysical Optimism
Published online by Cambridge University Press: 03 July 2018
Abstract
This paper seeks to identify and defend an approach to inquiry dubbed ‘metaphysical optimism’, particularly as it is evidenced at crisis points in the fields of physics, mathematics and logic. That the practice of metaphysical optimism at such moments, wherein it has appeared that there is no clear way to proceed or understand where we have arrived, is both reasonable and useful suggests it is to be taken seriously as capable of progressing fields and increasing knowledge. Given this, the paper then looks in more depth at what such an approach involves and why it might be useful both as a methodological approach in general and to help clarify positions along the realism/anti-realism spectrum in philosophy. From here, the paper arrives at a possible argument in defence of the realist attitude to transcendence.
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References
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5 Just a note: in order to get at the attitude or strategy of metaphysical optimism, I do gloss over almost all of the technical details in each of the examples. The references give some places you might like to look for the technical details, and more discussion on each, for those interested in delving further.
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31 The California school is looking quite specifically for new axioms to decide CH one way or the other.
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53 As a bit of an aside, Heidegger asks: ‘is [this sort of] unthinking (“Alethia”) less than truth, or more’? This of course invites the question of whether what we can hope for via this sort of ‘letting be’ approach, can be anything that looks like, or be best described as, knowledge or even ‘truth’. And, perhaps after all, or in some cases, it cannot, quite. But even granting this (i.e. even granting that what we gain/receive via such approach might not fit so easily into our epistemological categories) need not run counter to optimism – a metaphysically optimistic approach here would simply hope Alethia, if not ‘truth’, is indeed ‘more’ than truth, rather than ‘less’ – allowing that, when something does not quite fit our epistemological categories, it may be because what is gained is more than those categories can contain – (rather than less, or in some way still essentially out of our reach).
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55 For all that, I do not think we should rule out the more arrogant, extreme ends of either attitude as (sometimes) workable strategies in some contexts. What I'm calling ‘unchecked’ humility can play a crucial role in developing constructive solutions. But, equally, unchecked optimism can provide solutions – perhaps more surprising solutions. We can offer up examples of rigorously (or ‘constructively’) won scientific progress, as well as examples of insight and progress that seem to have come from no-where like where they're meant to, and so too from the allowing of the possibility that they might. Ramanujan might be one such: his insight didn't come from a rigorous understanding of mathematical formalisms. Einstein's ‘gedanken’ and Gödel's ‘intuition’ might be others. These insights can't always be reduced to sudden leaps within a system of thought. At times they seem genuinely to look at that system from an entirely other angle. And at those times the image of an explorer may be far more apt than that of a constructive or even a necessarily ‘rational’ thinker.
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61 Wilson, Wandering Significance, 79.
62 Wilson, Wandering Significance, 80.