# Précis of epistemology

- The foundations of ethics
- What is knowledge?
- The search for reason
- Why is reality intelligible?
- How the spirit works

Applications and complements :

- The pedagogy of autonomy
- Instinct, learning and memory
- Logical principles
- The incompleteness of mathematical principles
- The truth of relativistic principles
- Why is entropy real?
- Quantum theory of multiple destinies
- The origin and evolution of life and spirit

**Detailed contents**

- The foundations of ethics
- A good will is to will the good
- Emotions for a good life
- The good knowledge
- Living for the good of all spirits
- Virtue
- Is it the dream of an enlightened?

- What is knowledge?
- Rational knowledge must be public and proven
- Conclusive justifications
- Justification of principles
- Justification of observations
- Foundationalism or coherentism?
- Knowing without knowing that we know
- Fallible justifications and the Gettier problem
- Justification of knowledge about knowledge

- The search for reason
- Knowing what to look for without having found it
- Searching without knowing what to look for
- Theoretical problems
- The touchstones of reason
- The discovery of reason
- The unity of reason
- The authority of reason
- What can we hope?

- Why is reality intelligible?
- What is a concept?
- Individuals and the binding of concepts
- The whole being of a being is its being in the whole
- The nature of matter and the truth of perception
- Logically possible worlds
- Explanation
- Nothing new under the sun
- Does Nature really obey laws?
- Naturally possible worlds
- The power of natural properties

- How the spirit works
- The connection between sensors and effectors
- Brain modules and routine activities
- Decision and will
- Attention and consciousness
- The imagination of the present
- The imagination of the absent
- Introspection
- Emotions
- Beliefs
- The invention of perception
- To put oneself in the other's shoes
- What is speech?
- Meaning through imagination
- Understanding words means knowing how to use them
- Mutual understanding
- Theoretical truth
- Thought

Applications and complements

- The pedagogy of autonomy
- The arguments of authority
- The authority of reason
- The foundationalist error
- Becoming a teacher for oneself

- Instinct, learning and memory
- What is learning?
- The instinct to learn
- Neural plasticity
- The development of instincts
- Procedural memory
- A neural model for episodic memory: the convergence-divergence zones
- Learning to perceive

- Logical principles
- Necessary consequence and logical possibility
- The truth of compound statements
- The interdefinability of logical connectors
- The fundamental rules of deduction
- The rule of particularization
- The rule of generalization
- The detachment rule
- The rule of hypothesis incorporation
- The principle of reduction to absurdity
- The rule of double negation suppression
- The rule of analysis
- The rule of synthesis
- The rule of thesis weakening
- The elimination rule for a disjunction
- The rule of direct proof of existence
- The elimination rule for the existential quantifier

- Reasoning without hypothesis and the logical laws
- The derivation of logical consequences
- Why does reasoning enable us to acquire knowledge?
- Justification of logic
- The paradox of Lewis Caroll
- Mathematical knowledge

- The incompleteness of mathematical principles
- The first incompleteness theorem of Gödel
- The uncountable infinite
- Tarski's theorem of the undefinability of truth
- How to prove the unprovable?
- Consistency proofs
- The second incompleteness theorem of Gödel
- The science of everything that can be imagined
- Zermelo's theory of sets
- Russell's paradox
- The truth of Peano's axioms
- The truth of Zermelo's axioms
- The axiom of choice
- Are consistency proofs caught in a vicious circle?
- The independence of the continuum hypothesis
- Theories, software and recursively enumerable sets
- Undecidable sets and problems
- Universal machines and theories
- The undecidability of the halting problem
- The undecidability of the set of all logical laws
- Universality is the cause of undecidability

- The truth of relativistic principles
- The principle of general relativity
- What is a tensor?
- A misunderstanding about the relativity of truth
- Newtonian physics and Galileo's principle of relativity
- Minkowski space-time
- The constancy of the velocity of light
- The relativity of simultaneity
- Spatio-temporal measurement devices
- All lightlike intervals are equal
- Minkowski's metric and the tensors of space-time
- Why is Newtonian physics nevertheless true?

- The curvature of space-time and gravitation
- Free fall and the orbits of planets
- Einstein's great idea
- The equality of inertial and gravitational mass
- Special relativity and general relativity

- Relativistic principles are confirmed by their fruits

- Why is entropy real?
- The reality of thermodynamic entropy
- The three definitions of statistical entropy
- The reality of accessibility entropy
- Statistical ensembles, ergodicity and time averages
- The principle of polls and the Monte Carlo method
- Quantum decoherence
- Microscopic entropy
- The independence of microscopic constituents
- Lack of information, laisser-faire and equilibrium

- The difference between thermodynamic entropy and accessibility entropy
- Information as fuel
- Maxwell's demon
- Amount of information and work

- Why can not Maxwell's demon reduce total entropy?
- The conservation of the subjective entropy of an isolated system
- Why can entropy increase?
- Do irreversible computations always reduce the thermodynamic entropy of a computer?
- Maxwell's demon and the impossibility of a perpetual motion of the second kind
- Thermodynamics is a physics of observation
- Complements
- The perpetual motion of the second kind
- Entropy increase and the microcanonical distribution
- The reality of entropy increase
- Entropy is an extensive quantity when the parts are statistically independent
- The Szilard's engine

- Quantum theory of multiple destinies
- Taking the Schrödinger equation seriously
- The existence theorem of multiple destinies is empirically verifiable
- One space-time for all parallel worlds
- Everett's theory is unified quantum theory

- The origin and evolution of life and spirit
- Evolution through natural selection
- The molecules of heredity
- The spontaneous generation of life in the primitive ocean
- Autocatalytic networks
- Amphiphilic molecules and vesicles
- The first living cells
- The origin of DNA
- How to know if this theory is true?

- Life is at home in the universe
- Cooperation is more fundamental than competition
- The infinite tolerance of life
- The origin of spirit