Ackermans, Lennart B. (2025) Four Formal Versions of The Two-Envelope Paradox. [Preprint]

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Abstract

Philosophical discussion of the Two-Envelope Paradox has suffered from a lack of formal precision. I discuss various versions of the paradoxical argument using modern probability theory, which helps to make diagnoses that are simpler, more insightful, and provably correct. Paradoxical arguments are revealed to be fallacious for one of three reasons: (1) the argument makes a formal mistake such as an equivocation fallacy; (2) the argument disregards relevant uncertainty about or variability in a unit of measurement; (3) the argument uses an invalid decision rule. I improve upon various existing diagnoses and discuss what kind of philosophical and decision-theoretic import the paradox has.

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Item Type:	Preprint
Creators:	Creators Email ORCID Ackermans, Lennart B. philosophy@ackermans.ch 0000-0003-0071-2270
Keywords:	two-envelope paradox, decision theory, paradoxes, probability theory, bayesianism, expected utility
Subjects:	General Issues > Decision Theory Specific Sciences > Probability/Statistics
Depositing User:	Lennart Ackermans
Date Deposited:	02 Jun 2025 13:07
Last Modified:	02 Jun 2025 13:07
Item ID:	25509
Subjects:	General Issues > Decision Theory Specific Sciences > Probability/Statistics
Date:	31 May 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25509

Available Versions of this Item

• Four Formal Versions of The Two-Envelope Paradox. (deposited 07 May 2025 12:35)
  • Four Formal Versions of The Two-Envelope Paradox. (deposited 02 Jun 2025 13:07) [Currently Displayed]

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