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Introduction to Ontological Mathematics

The possibility of a foundational mathematical synthesis such as Ontological Mathematics has been doubted for many years. It will be difficult to grasp the fact that the non-denumerable fuzzy-continuous is absolutely dependent upon the denumerable crisp-discrete; not the other way round.

If an individual has little background in both philosophy and mathematics, and yet is still faced with a choice of selecting one of these two dimensions to elicit metaphysical guidance relative to the other, selecting Mathematics over Philosophy is, given the very advanced stage of human advance concerning the pure ontological implications inherent in the study of the objects alphabeticity or number, is ironically the more rational option.

Although mathematics is not a “science,” it is still capable of exhibiting, exploring, and expressing true descriptions of nature.

In this article, we are using the term Ontological Mathematics to refer to qualitatively extensive foundational Pure Mathematics which, relative to ordinary “formal mathematics,” is inherently and unapologetically profoundly indiscrete.

It must be both qualitatively and quantitatively comprehensive. Humans are qualitative beings, and our mathematical foundations should inherently resonate with these qualitative aspects. In formal mathematics, the discrete is the quantitatively and qualitatively inferior recourse option that is often used when everything else fails. Ontological Mathematics is the complete opposite. When we use ordinary mathematical notation, we will mostly use formal mathematics, with any required new notation built from the formal mathematics under foundations we provide in order to capture the new foundational mathematics based upon this fully extended set theory. We do this to keep representations practical.

Exploring Ontological Mathematics Further!

Amongst the many how and what questions mathematicians may ask themselves, an important one is to inquire as to the workings of mathematical cognition. In general, mathematics seems to be more than just a set of axioms and processes.

That is, mathematics seems to have some kind of independent existence – mathematical concepts and relationships appear to be objective features of some kind of reality. While the nature of this independent mathematical reality is still much debated, with its acknowledged existence commonly referred to as Platonism in the philosophy of mathematics, the central notion that it is explored in an axiomatic-deductive framework with conceptual and practical implications is uncontroversial.

It’s a common idea that mathematics exists as a kind of symbiosis between our consciousness and some kind of objective reality having a mathematical foundation.

This is a brief introduction to the fascinating ideas of Dr. Romanini’s ontological mathematics. While none of what follows should be taken as an exposition of Dr. Romanini’s ideas and arguments, it should hopefully give a flavour of the concepts and perspectives suggested by her theories. Centrally, Romanini suggests that ontological mathematics may be a more fundamental construct than our universe itself.

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