10  Ontological vs Epistemic Extremes

Why FAT_BINARY Events Are Neither Black Swans Nor Power Laws

Status: Planned — target journal: Synthese

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NoteChapter forthcoming

10.1 Motivation

Taleb (2007) distinguishes Black Swans — high-impact, unpredictable events — from ordinary risks. The distinction is primarily epistemic: Black Swans are outside the observer’s model, not necessarily outside the true distribution.

Colander (2010) argues further that Taleb’s Black Swan is epistemological (limited information) rather than ontological (inherently indeterminate reality). Knight (1921) introduced the foundational distinction between measurable risk and unmeasurable uncertainty.

Neither framework has been formally operationalized using extreme value theory applied to the specific case of binary-event-driven fat tails.

10.2 The Claim

FAT_BINARY extreme returns occupy a distinct ontological category from both:

1. Gaussian extremes — which are epistemically uncertain (low probability, small magnitude, known distribution)
2. Power-law extremes — which are ontologically fat-tailed (heavy distributional tail, known generating process)

FAT_BINARY extremes are structurally predictable in their event space (the trial succeeds or fails; the FDA approves or rejects) but epistemically uncertain in direction. They are not black swans — the event is announced in advance, the magnitude is approximately known, the probability structure is binary. Yet they produce the same \(\hat{\alpha}\) as genuine power-law tails.

This constitutes a third category that existing typologies do not accommodate: the known-structure, unknown-direction extreme. Formalizing this category using EVT and the mixture process of Chapter 3 is the contribution of this chapter.

10.3 Key prior work

• Knight (1921) — risk vs uncertainty
• Colander (2010) — epistemic vs ontological black swans
• Hansen and Sargent (2008) — robust control as formal Knightian uncertainty
• Taleb et al. (2014) — precautionary principle under fat tails
• Gap: no formal EVT operationalization of the ontological/epistemic distinction. Novelty: HIGH.

Colander, David. 2010. “Black Swans and Knight’s Epistemological Uncertainty.” Journal of Post Keynesian Economics 32 (4): 567–70.

Hansen, Lars Peter, and Thomas J. Sargent. 2008. Robustness. Princeton University Press.

Knight, Frank H. 1921. Risk, Uncertainty and Profit. Houghton Mifflin.

Taleb, Nassim Nicholas. 2007. The Black Swan: The Impact of the Highly Improbable. Random House.

Taleb, Nassim Nicholas, Rupert Read, Raphael Douady, Joseph Norman, and Yaneer Bar-Yam. 2014. The Precautionary Principle (with Application to the Genetic Modification of Organisms).