From the realism in ontology, we have the existence of mathematical objects. It would appear that these objects are abstract, in the sense that they are causally inert, not located in space and time, and so on. Moreover, from the realism in truth-value, it would appear that assertions like the twin-prime conjecture and the continuum hypothesis are either true or false, independently of the mind, language, or convention of the mathematician. Thus, we are led to a view much like traditional Platonism, and the notorious epistemological problems that come with it. If mathematical objects exist outside the causal nexus, how can we know anything about them? How can we have any confidence in what the mathematicians say about mathematical objects? Under the suggested realism, this requires epistemic access to an acausal, eternal, and detached mathematical realm. This is the most serious problem for realism.
The main question I have, and that runs counter to the worldview of Via Mathesis, is this: Are we really detached from the World of Mathematical Objects? This big assumption is the real heart of why the "epistemological problems" that come with Platonism are seen as so intractable. Who says we're detached from the mathematical realm, or from Plato's World of Ideas / Forms? Why has this always been assumed without investigating the possibility that we might not be detached from this higher world?
The epistemic problem that philosophers face when considering the existence of mathematical objects could be greatly clarified by looking into the structure of the mind. We begin by positing a three-component system to the overall mind:
- Higher Mind - the 'conceiver'
- Physical Mind - the 'receiver'
- Physical Brain - the 'perceiver'
We create philosophical accounts of reality as a way of clarifying our worldview, so we can orient our thoughts to a structure of beliefs. For those who remain skeptical of a higher mind, they cannot perceive its functioning because their beliefs are such that it is not part of their worldview. So we content ourselves with providing a limited account of the interaction between higher mind and physical mind, aware that this could all be doubted. But knowing that it is more important to have our beliefs consistent with our worldview, we proceed with the premise that those who with an open heart will find all the evidence they need for the existence of a higher mind.
The higher mind is what apprehends mathematical objects, and comprehends them by unifying with them. Its comprehension of these objects gives rise to concepts which are projected into the physical mind, and then filter down into the structuring of the physical brain. So the brain must go through various stages of development to build a neurological network that can receive these types of thoughts from the higher mind.
Our beginnings of acquiring mathematical concepts arise from interacting with physical objects at a young age. Playing with shapes and drawing pictures in kindergarten, we are reminded of the pure mathematical objects that exist above the physical world and prepared to receive concepts of them. The higher mind can have encounters with pure mathematical objects whenever it wants to, but we are not able to receive thoughts from the higher mind about these objects until we have prepared the physical brain to receive such thoughts.
Every mathematician has had an experience of receiving an instantaneous 'download' of thought-information from the higher mind. These are what are classically described as those 'Eureka!' moments when we see the solution to a problem in a flash of insight. There are many stories of mathematicians who said they 'solved' a problem they'd been working on for years at very unexpected moments, such as in the shower, getting on a bus. But it is misleading to think that they solved the problem 'in an instant' in these situations. It is more like the work that was done leading up to that experience is what prepared the neurological circuitry of their brain to be able to receive a 'download' from the higher mind.
In our work as mathematicians, we do not work directly with the pure mathematical objects; instead we work with their projected concepts. But the concepts are accurate enough so that mathematical statements expressed in the concept-language can be true or false statement about the real mathematical objects that exist in the higher world. The concepts are accurate because the objective substance of mathematical objects is thought-substance.
Via Mathesis is a path of spiritual self-knowledge, which is attained by way of mathematical knowledge, hence the name via mathesis. These mathematical studies transform our physical mind to be able to communicate more easily with the higher mind. The higher mind is to be valued much more than simply because it can apprehend pure mathematical objects, but because the higher mind guides our spiritual development and the evolution of our soul, leading us towards those things which we are meant to do. Even if you're not excited by mathematical work, it is still a powerful means by which to build a relationship with the higher mind. Of course, here on Via Mathesis we are exploring the full spectrum of spiritual mathematics, and will have much more interest in developing the connection between physical mind and higher mind.
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