Ad hoc Ruminations About the Foundations of Mathematics

Intuitionism, Formalism and Realism all have strengths and weaknesses; no one has been able to find common ground. What if the common ground is simply that the ontological and the epistemological are intertwined and interrelated (which does not mean that they are interdependent), and mathematics is virtual in nature? It is about, and is originally derived from measuring quantities, yet, through its formalisation, transcendent and independent from the qualities of the universe (its „fine-tunedness“) and therein stronger and seemingly residing „above“ all physical universes. That is its hard reality. The hard reality of infinite mathematics is it (necessarily) being virtual (since infinite quantities are nowhere to be found in the physical universe). Since it is infinite, it necessarily contains paradoxes, as formalised in the incompleteness theorem. The harder pill to swallow than the incompleteness theorem is abandoning infinity from mathematics, since many calculations only make sense from assuming that infinite sets do exist; which then brings about that mathematics is synthetic, by such a „choice“. Yet, the mathematical untertaking is also analytic and finding a priori truths. As concerns the question whether mathematical truths are a priori and analytic or synthetic, philosopher Willard Van Orman Quine came up with the analyic and the synthetic in the Kantian sense actually not being so easily distinguishable anyway decades ago. With finding out mathematical truths and employing them in technology, humans are then able to alter the „quality“ within the universe, which then might call for a more profound mathematics and new mathematical truths. Are they, then, analytic or synthetic in nature? I am happy that I am more or less through with reading Heidegger, so that I can soon start writing about him. Maybe I can also work my dilettante ruminations about the foundations of mathematics out later this year. That will feel good.

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