Since Aristotle rejected Heraclitus’s both-and Hidden Harmony about 2,350 years ago, when establishing the either-or foundations of Western logic, it has been assumed that for reasoning to be valid, it must reject self-contradictions.

There is a well-known mathematical joke that illustrates the reason why conventional mathematicians and logicians do not allow paradoxes in their axioms:

The analyst G. H. Hardy once made this remark at dinner, and was asked by a sceptic to justify it: ‘Given that 2 + 2 = 5, prove that McTaggart is the Pope’. Hardy thought briefly, and replied, ‘We know that 2 + 2 = 4, so that 5 = 4. Subtracting 3 we get 2 = 1. McTaggart and the Pope are two, hence McTaggart and the Pope are one.

So, if mathematical proofs are to be valid in linear systems of thought, their axioms must not be contradictory; they must be consistent.

Yet, paradoxes are ubiquitous in the Universe. So, if we reject them—perhaps because they make us feel uncomfortable, questioning our precious sense of identity—we are led into a fragmented view of the world with split psyches.

The spiritual philosopher Tim Freke coined the term paralogical thinking in 2012 to help us become free from our delusions. As Tim says in The Mystery Experience: A Revolutionary Approach to Spiritual Awakening, “We see the paradoxity of something when we understand it from two opposite perspectives at once.” He aptly uses the simple word WOW to denote such an awakened state of being, for there is nothing more wonderful in human experience. Not surprising, this is something “everyone is searching for,” as Tim says.

This means that if we are to unify mysticism and mathematics, we must look at the latter in a quite new way: as the universal art and science of patterns and relationships, emerging directly from the Divine Origin of the Universe. The unproven Cosmic Equation is the basic axiom for our reasoning, which then progresses holographically in the vertical dimension of time, like all other creative processes.

The resulting Integral Relational Logic, as a meta-algebra, is paralogical, entirely logical in this revised definition of logic, just as ‘supernatural’ experiences are quite natural. This does not mean that we should turn mathematics into an experimental science, even though this is sometimes quite useful to gain an intuitive understanding.

For sometimes exceptions to rules do not happen until after billions of repetitions. So, we still need conventional proof methods to establish theorems as universal truths within the specialist discipline of mathematics.

However, Integral Relational Logic is transcultural and transdisciplinary, like the Internet. So, by standing outside ourselves in Gnosis, with Self-reflective Intelligence, we can ground our paralogical reasoning on the Truth, within the Cosmic Context of Satchitānanda, as the union of spiritual and scientific worldviews.