My Current Research Programs

It has been over a year since I last posted in this blog. 

My absence has not been due to a decline in philosophical interests – quite the opposite in fact. Thus, the purpose of this entry is to simply provide an update on the philosophical problems that I am currently working on, and the way I expect the research to go:

1. Leibniz, Everettian Quantum Theory, and Free Will

In this paper, I aim to show that the philosophy of Leibniz (particularly, his idea of the complete notion of individual substances) is capable of illuminating, alongside Everettian quantum theory, a way of making free will possible under fully deterministic laws of physics. The paper focuses on the possibility of formulating 'emergent' laws of physics (that is, laws of physics at level of macroscopic entities) that refer to entities with general intelligence. The approach is similar in spirit to Deutsch and Marletto's constructor theory programme, for it seeks to formulate laws of physics in terms other than mere initial conditions and deterministic laws of motion. 

As of March 2025, progress on this topic has been minimal. 

2. Calibration of Betting Markets and its Epistemological Implications                    
This is probably the paper where I have made the most progress. It aims to show that betting markets are not calibrated. To say that betting markets are calibrated is to say that if we take all markets stating that an event has an x% chance of happening, and we calculate the proportion of them in which the event happened, the proportion will be close to x%. 

Intellectuals persuaded by Bayesian epistemology have presented several reports in which betting markets are indeed calibrated, leading them to assert that if prediction markets state that a certain event has an 80% chance of happening, our subjective strength of belief that the event will take place should also be set to 80%. Given that I adhere to a view of epistemology that focuses on good explanations, rather than subjective degrees of belief, I am skeptical of these reports. 

My findings, for now, suggest that all these reports follow a very flawed methodology. I am currently in the process of preparing a report of my own based on what I hold to be the correct methodology – but given the size of the datasets, it is taking longer than I initially anticipated. Nevertheless, some preliminary results seem to reveal that betting markets are indeed not calibrated. 

3. Mathematical Proofs Under Different Laws of Physics

Another research project I am undertaking is that of describing universes in which different laws of physics hold. The purpose of this task is to find universes in which certain mathematical propositions that we find very easy to prove become unprovable. This research is inspired in David Detusch's formulation of an environment with different laws of physics in which the twin primes conjecture could easily be proved/disproven.

As of now, my progress has been almost non-existent. I managed to find some additional conjectures that could be easily examined in the environment Deutsch proposed, but environments where easily-provable theorems become impossible to prove keep eluding me. 

4. An Everettian Account of the Delayed-Choice Quantum Eraser
This is my newest reserch project. After spending over a week trying to understand the famous delayed-choice quantum eraser (which is often claimed to prove that retrocausality – the present affecting the past – is possible), and failing to find even one explanation that made sense, I concluded that a fully Everettian explanation of the experiment is needed. Everettian quantum theory is simply quantum theory without the collapse postulate, and is also known as unitary quantum theory. 

This research began two days ago, so the only progress I have made is that of modeling the experiment in quantum flytrap: a virtual lab that allows users to create experimental setups to learn more about quantum theory. I believe describing the experiment without collapse will present no major challenges, and I expect that the final product will reveal that the claims of retrocausality are simply misguided.