No Outside

Every observer is a proper part of what it describes. That holds for a human, an animal, a machine, and a creature inside a structure laid out statically on a disk. The book asks what follows for mathematics and logic when nobody gets to stand outside.

From this and two related facts the familiar limits follow, each under the conditions it needs: incompleteness and undecidability, the uncomputable continuum, the impossibility of certifying randomness from inside an experiment, and the failure of first-person evidence to decide between hypotheses about one’s own origin. The second half of the book asks what still passes between perspectives. Refutations do, and so does relational structure, which makes mathematics the most shareable part of a world-model.

The argument covers its author. He looked for an exemption and did not find one.

Contents

• Part I — Mathematics as a Language of Models
• Part II — Logic Seen From Inside
• Part III — Physics From Inside
• Part IV — The Inside of a Structure

The book builds on the Four-Model Theory of consciousness, told for general readers in The Simulation You Call “I”.

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