The Magic of Paradox

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“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.” ― Niels Bohr

Introduction

Paradox, ambiguity, uncertainty; these are the sort of concepts which, if you think about them for long enough, will probably start to make you feel a little giddy, a little uncomfortable, perhaps even a little queasy. Almost by definition they are confusing, contradictory, non-logical ideas; portals to the fathomless realms of the unknown. And, as H.P. Lovecraft observed in the introduction to his 1927 essay, Supernatural Horror, “the oldest and strongest emotion of mankind is fear, and the oldest and strongest kind of fear is fear of the unknown.” [^1]

In a 2016 psychology review and research synthesis about fundamental fears, R. Nicholas Carleton supports Lovecraft by positing that fear of the unknown, or ‘FOTU’ is quite possibly the fundamental fear. He notes that, ‘FOTU tautologically does not require a priori learning; indeed, the first thing that could be feared would be “the perceived absence of information at any level of consciousness.”’ [^2]

From the abyss of the unknown out of the very fabric of our fears, we conjure demons, fiends and nameless horrors; they are legion. We learned this as children when, without conscious effort, we materialised monsters under our beds, in our cupboards, in the darkened doorways of our rooms. Of course as we grew up we learned to dispel such childish fears with reason. Relax. There’s nothing to be afraid of. Ah yes sweet logic is the light which banishes the darkness of the unknown. And so when ideas like paradox pop up, ideas which defy coherent rationale, it’s no wonder we almost always pull ourselves away with a slightly unsettled shudder.

So settle in, if you’re game, while we explore that uncomfortable little idea that is paradox. Paradox which seems to characterize so many of the big problems at the forefront of modern science; paradox which has fascinated and confounded philosophers for millennia; paradox, without which mathematics could not have solved the problems on which all modern technology relies.

But, I entreat you, dear reader, to proceed with caution. I’m no academic and this is far from a rigorous exposition. Question every assertion, examine each scrap of evidence, take only that which works for you.

Far from seeking to untangle the profound mysteries of paradox, I hope instead to outline how certain engagements with the concept of paradox can re-pattern the warp and weft of the unfolding Now of your life in strange and marvelous ways. The nature of such mysteries, however, avoids direct scrutiny and is diminished through attempts at explanation. And so the words written here are mostly just the sketchy field notes from my own tentative steps, flickering lantern in hand, into that vast antechamber which holds in its dark embrace the entrance to the bottomless caverns of eternal mystery. There in that yawning vestibule, between the realm of the known and the unknowable, neither in one place nor the other, yet both and neither all at once; there in the liminal twilight, blooms paradox.

But what is a paradox? Well somewhat fittingly it’s a hard idea to pin down. Etymologically it means an idea which is contrary to (παρά, ‘para-’) general opinion (δόξα, ‘doxa’). Often though the word paradox is used to mean something surprising and/or nonsensical. In more formal terms, paradox has been defined as “a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.” [^3]

In A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind, Roy Sorensen describes paradoxes as “questions (or in some cases, pseudoquestions) that suspend us between too many good answers…Typically, the case for one solution to a paradox looks compelling in isolation. The question is kept alive by the tug of war between evenly matched contestants.” [^4]

The High Priestess or The Popess in the Rider–Waite Tarot

Formally paradoxes play an important role in philosophy and mathematics where they are sometimes divided into logical and semantic paradoxes. [^5]

In philosophy paradoxes played a central role in the development of dialectic and logic in the 4th and 5th centuries BCE and are still important today because they help one “become aware of forms of argument that are deceptively convincing yet logically fallacious.” [^6]

Paradoxes have played such a crucial role in the evolution of mathematics in general and number theory in particular that it can confidently be asserted that without paradoxes the modern world, which is so vitally dependent on mathematics, simply would not exist without them. [^7]

[

[] Physics

Consciousness

‘Well well’, I hear you say, 'this is all very interesting and thanks for the potted history lessen and yes yes the footnotes are a nice touch, very… reassuring, but what about magic? Isn’t this supposed to be about magic and? or? of? paradox?’

What is magic?

Crowley’s definition always trotted out. Somewhat priapic view. Not wrong. In fact everyone of you who has had genuine results, especially those undeniable times that, for one reason or another, you’ve never told others about, or at least just to a limited few; each of you knows that your system, your approach, your model is “correct”. you’ve witnessed the proof with your own eyes!

What I’m saying is that is a functioning and correct system of magic, but it is not the only system.

RAT!

Philosophy – obsessed with the binary dominance of logic, fixated on semantics, finds what at it’s heart? Paradox.

Maths – provided a significant lesson into the nature of paradox bu

Paradoxes in Art – e.g. M.C. Escher – the pleasure we feel when beholding a piece of art like Escher’s – impossible geometries and imaginary shapes – symmetry and dissonance held together in harmony – this has a lot in common with the idea of holding two (or more) contradictory ideas in one’s head simultaneously while not engaging with the desire to find resolution; holding them in balance, without judgement.

…perhaps because, “Western thinking is only just emerging from the straightjacket [sic] of the scientific revolution. We have become over-dependent on scientific rationalism and we have been indoctrinated to fear the irrational and the unproven.” [^9]

From our dominant contemporary rationalist vantage point it’s hard to imagine that we could ever have thought another way, ever have experienced existence differently. Yet when considered in relation to the vast 200,000 year or so sweep of modern human history, the scientific revolution, heralded less than half a millennia ago with the publication of Nicolaus Copernicus’ De revolutionibus orbiumdate coelestium in 1543, is but yesterday. [^10]

As the scientific revolution got under way and was beginning to transform disciplines like mathematics, astronomy, physics, and biology, in France, in the village of La Haye en Touraine, on Sunday 31 March 1596, a little baby boy was born. A baby who would grow up to be a philosopher, mathematician and scientist; a man who would change not just the world, but the very fabric of reality, by defining the dominant human perspective from then until now. This man was of course, René Descartes.

To be edited —> However at the heart of every scientific discipline lie great unanswered questions; mysteries which challenge the theoretics: black holes, dark matter, the arrow of time, the nature of being, gravity, to name just a few.

As science slices ever finer, new inexplicable questions bloom. Indeed the quest to unravel these mysteries could be said to be what drives science.

To be continued…

’But is a paradox just a puzzle? I would think a good, interesting paradox is more. Some ‘paradoxes’ (scare quotes) are just fallacies, some are real dilemmas, some perhaps even antinomies. Horwich gives a better characterisation: “a philosophical paradox is a battery of a priori considerations that engenders conflicting epistemic inclinations”.

Paradoxes are useful tools of philosophising because they narrow down the dialectic possibilities to three:

More generally, a paradox presents us with two jobs:

End Notes

[1]. Lovecraft, H.P., Supernatural Horror, 1927, available at Project Gutenberg of Australia, https://gutenberg.net.au/ebooks06/0601181h.html

[2]. Carleton, R. Nicholas, “Fear of the unknown: One fear to rule them all?”, Journal of Anxiety Disorders, Volume 41, 2016, Pages 5-21, https://doi.org/10.1016/j.janxdis.2016.03.011.

[3]. Wikipedia, 2022, Paradox, citing Oxford English Dictionary and Bolander, Thomas, “Self-Reference”, The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), https://en.wikipedia.org/wiki/Paradox

[4]. Sorensen, Roy, A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind. 2005, Oxford University Press USA. p. xii

[5]. MacBride, Fraser, Mathieu Marion, María José Frápolli, Dorothy Edgington, Edward Elliott, Sebastian Lutz, and Jeffrey Paris, Frank Ramsey, The Stanford Encyclopedia of Philosophy (Winter 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.), https://plato.stanford.edu/entries/ramsey/#FounLogiMath

[6]. Philosophy Talk, 3 April 2023, https://www.philosophytalk.org/shows/paradoxes

[7]. Kleiner, Israel & Movshovitz-Hadar, Nitsa. (1994). The Role of Paradoxes in the Evolution of Mathematics. The American Mathematical Monthly. 101. https://doi.org/10.2307/2975163.

[9]. Ozaniec, 1994, p. xv.

[10]. Wikipedia, 2022, Scientific Revolution, citing Juan Valdez, The Snow Cone Diaries: A Philosopher's Guide to the Information Age, p 367

[11]. Blum, Philipp, Paradox Philosophy, Course Notes, February 2020, Course at Akita International University, https://philipp.philosophie.ch/handouts/paradoxes.pdf

References

https://iep.utm.edu/par-log/

Cantini, Andrea and Riccardo Bruni, “Paradoxes and Contemporary Logic”, The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/fall2021/entries/paradoxes-contemporary-logic/

Medieval Philosophy

#philosophy #science #paradox #magic #metaphysics

~ last draft 3 April 2023 ~