The Significance of Relativistic Computation for the Philosophy of Mathematics

DOI10.1007/978-3-030-64187-0_7zbMath1478.00017OpenAlexW3168733394MaRDI QIDQ5015969

Krzysztof Wójtowicz

Publication date: 10 December 2021

Published in: Hajnal Andréka and István Németi on Unity of Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-64187-0_7

zbMATH Keywords

set theoryhypercomputationrelativistic computationmathematical explanationindispensability argumentmathematical realismexplanatory proofabstract explanationsprogram explanations

Mathematics Subject Classification ID

Philosophy of mathematics (00A30)

Cites Work

• Optimisation and mathematical explanation: doing the Lévy walk
• A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer
• On the epistemological significance of the Hungarian project
• Energy conservation and supertasks
• General relativistic hypercomputing and foundation of mathematics
• The wave equation with computable initial data such that its unique solution is not computable
• Undecidability and incompleteness in classical mechanics
• A notion of mechanistic theory
• Every planar map is four colorable. I: Discharging
• Every planar map is four colorable. II: Reducibility
• The phenomenology of mathematical proof
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• Quantum algorithm for Hilbert's tenth problem
• Hypercomputation: Philosophical issues
• Measurable cardinals and the continuum hypothesis
• Gödel's square axioms for the continuum
• A proof of the Kepler conjecture
• Why there is no such discipline as hypercomputation
• The case for hypercomputation
• Relativistic computers and the Turing barrier
• Three counterexamples refuting Kieu's plan for ``quantum adiabatic hypercomputation; and some uncomputable quantum mechanical tasks
• A note on ‘Einstein's special relativity beyond the speed of light by James M. Hill and Barry J. Cox’
• The hyperuniverse program
• CLOSED TIMELIKE CURVES IN RELATIVISTIC COMPUTATION
• DECIDABILITY, UNDECIDABILITY, AND GÖDEL'S INCOMPLETENESS IN RELATIVITY THEORIES
• Existence of Faster than Light Signals Implies Hypercomputation already in Special Relativity
• THE SET-THEORETIC MULTIVERSE
• What Makes a Scientific Explanation Distinctively Mathematical?
• Using Mathematics to Explain a Scientific Theory
• IS WAVE PROPAGATION COMPUTABLE OR CAN WAVE COMPUTERS BEAT THE TURING MACHINE?
• Alan Turing: Life and Legacy of a Great Thinker
• Mathematical Explanation in Science
• Hypercomputation
• The Explanatory Power of Phase Spaces
• A computable ordinary differential equation which possesses no computable solution
• Undecidable diophantine equations
• Why Do We Prove Theorems?
• The Wave Equation with Computable Initial Data Whose Unique Solution Is Nowhere Computable
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Hypercomputation and the Physical Church‐Turing Thesis
• Predicting the future in relativistic spacetimes
• Infinite time Turing machines
• Machines, Logic and Quantum Physics
• MATHEMATICAL INFERENCE AND LOGICAL INFERENCE
• Meaning, Truth, and Physics
• Is Cantor's Continuum Problem Inherently Vague?
• The Physical Church–Turing Thesis: Modest or Bold?
• Indexing and Mathematical Explanation
• A Universal Ordinary Differential Equation
• What properties of numbers are needed to model accelerated observers in relativity?
• Definitions by Abstraction in the Peano School
• Theory of Quantum Computation and Philosophy of Mathematics. Part II
• Why Do Mathematicians Re-prove Theorems?
• The Extent of Computation in Malament–Hogarth Spacetimes
• Quantum speedup of Monte Carlo methods
• Powers of regular cardinals
• Does Mathematics Need New Axioms?
• Defending the Axioms
• Mathematical explanation: problems and prospects.
• Non-Turing computations via Malament--Hogarth space-times
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