No Outside The Limits of Mathematics and Logic From Any First-Person Perspective
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- Englisch ausgewählt
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Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
19.10.2026
Verlag
Independently PublishedSeitenzahl
210
Maße (L/B/H)
22,9/15,2/1,1 cm
Gewicht
289 g
Sprache
Englisch
EAN
9798163705009
Every observer is part of the world it describes. This book works out what follows for mathematics and logic.
A brain that models the world models a world that contains the brain. It runs on fewer resources than the whole, and it cannot represent, as a whole, the apparatus that produces its own representations. No Outside argues that the familiar limits of formal thought follow from this position: incompleteness and undecidability, the uncomputable continuum, the impossibility of certifying from inside an experiment the independence on which certified randomness rests, the inability to sort structure in the world from structure added to keep a formalism running, and the failure of first-person evidence to decide between hypotheses about one's own origin.
One principle connects them. The generator never appears completely in what it generates. It can appear in part, even largely: a program can print its own text (Kleene, 1938). It cannot appear whole.
The argument builds on Lawvere's fixed-point unification of Cantor, Russell, Gödel and Tarski. It departs from that lineage where two of its limits have no diagonal form, and where Priest accepts a contradiction it counts a refutation.
Along the way it treats Einstein's cosmological constant as a patch that later returned as a fitted parameter, the Müller-Lyer lines that still look unequal after measuring, cellular automata in which time is the update, and a simulated worm stored as a static file on a disk. Does the file have an inside?
The closing chapter turns to what embedded observers can share. Refutations travel between perspectives where positive claims do not. Relational structure travels where encoding does not. Every theory, the author's own included, rests on cuts it cannot fully sustain, and using a cut is legitimate as long as it is not mistaken for the world.
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