Summary

This was my submission to the MITx philosophy award. I got invited to submit an essay after scoring highly on MIT’s “paradox and infinity” online course. The course covered formalising infinities within maths and explored the consequences and paradoxes caused by it. My essay looked into uncomputable numbers, more specifically Chaitin’s constant, and probability functions. I learnt a lot about writing philosophical essays and found it a very nuanced and difficult process compared to other essays I had previously written. We were recommended Stephen Yablo’s “Guidelines on Writing a Philosophy Paper” which I remember finding very helpful as someone who had never written a philosophy essay before. Overall, I really enjoyed the course and trying to write this essay!

Hindsight

After coming back to this with a better understanding of discrete maths, I think that my argument is wrong. I think my misunderstanding was about what a function is. I seem to make the assumption that for a function to be defined as a function, all its outputs must be able to be evaluated by some algorithm, e.g. must produce a computable numbers. In practice I believe this isn’t the case. As a result, the rational agent function I define is perfectly ok to be represented as a probability function. Therefore the argument is flawed and doesn’t pose a valid critique of objective probabilty or rationality.