Fanelli Daniele. A Mathematical Theory of Knowledge, Science, Bias and Pseudoscience

Meta-Research Innovation Center at Stanford (METRICS), Stanford University, 2017. — 96 p.Postulate 1: Information is finite
Postulate 2: Knowledge is information compression
Mathematization of knowledge
The K function
Operations on information
Cumulating
Expanding
Meaning and content of
Properties of K
Property 1: Ockham's razor
Property 2: Optimal accuracy
Property 3: Ignorance about the future
Knowledge
Knowledge gained per experience
Knowledge growth
Science
Verification vs. falsification
Scientific progress
Reproducibility
Soft science
Bias
Post-hoc methodological choices
Fabrication
Ante-hoc methodological choices
Oddity and discrepancy of methods
Pseudoscience
Extreme post-hoc bias
Extreme ante-hoc bias
Extreme methodological discrepancy
Hierarchy of the sciences (and pseudosciences)
Discussion
Summary of findings
Predictions
Predictions about scientific fields
Predictions about knowledge in general
Meta-predictions
Discussion
Validity of the theory
Implications and applications
Conclusions
Derivation of the K function
Complexity as information
Random probability and total information of an object
Knowledge and total information
Abstraction
Operations on information
Generalized formulation of the K function
Objects and meanings of the K function
Classic random variables
Objects, i.e. sequences
Biological adaptation and animal behaviour
Logic and inference
Language, concepts and thought
Statistical interpretation
Bayesian interpretation
Frequentist interpretation
Akaike information criterion
Minimum Description Length principle
SP theory
Explanatory and causal K
Knowledge progress curve