[Fis] Concluding Comments?

[Carlos Gershenson]

Dear Pedro and colleagues,

Thank you very much for the lively discussions and commentaries. I have learned a lot.

I would not say these are concluding comments, as all questions remain open, but perhaps "summarizing comments".

I think that efforts to “fix” formal systems to go beyond or around their limits (à la Hilbert’s program) are doomed to fail. We still need to accept them or find a better way of dealing with them. Perhaps an alternative would be not to see them as something negative, but as something we can exploit/benefit from. I mean, just hypothetically imagine if mathematics was consistent, complete, and decidable. Yes, we would have absolute truths, we could have certainty. But would we have creativity? Innovation? Serendipity? In other words, we could eliminate many problems we suffer from, but perhaps we would have many more. Even worse, perhaps we would not even be here. For how could human culture evolve in a consistent, complete, and decidable world?

Of course, this does not mean that we should abandon science or formal methods. But by acknowledging their limits, we should be able to use different narratives to explore beyond them.

Best (albeit incomplete) wishes,

Carlos

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