Essay Abstract
1. From the lens of ontology, I begin by defining and distinguishing physical truths and mathematical proofs, prioritising Kurt Gödel's incompleteness theorems. 2. I then develop an expanded version of John Barrows Gödelian chess game, illustrating the crossroads of these kinds of claims of reality and introducing the possibility of mathematical truths, which I subsequently address. 3. From this threefold landscape, I apply Gödel's incompleteness theorems across ontologies, which I term amalgamated sleuths. These applications serve as failures to ground initial axioms within (or between) mathematics and/or physics in a clear, consistent ontological framework. I ultimately refer to this as the misalignment problem. 4. I reanimate this problem in a more traditional, adversarial way: a question between missing physics or metaphysics? I reinforce that to arrive at what is missing we will need to temper mathematical and physical theories in consistent ontological frameworks. If we do not, then either alone or together we cannot say what they mean of reality. This misalignment problem is the direct cause of current undecidability, uncomputability and unpredictability. 5. I conclude that with collaboration, from the lens of ontology, these issues can likely be resolved or quarantined. On this basis, I hold out that David Hilbert's formalist ambition for mathematics may well make a return.
Author Bio
I received a PhD in Philosophy from the University of New England, Australia in 2018. I am 35 years old. I have spent the last two years researching in the philosophy of science (not within academia), whilst working. I have previously worked for mutlinational corporations then as a Crown prosecutor in criminal law. I am now seeking new work.