# Précis of epistemology

Science (or knowledge) is to give good proofs, with good principles, good observations, and logically correct reasoning. Good principles are recognized by their fruits. With this definition of science, even philosophy is a science. Ethics, epistemology and metaphysics are sciences.

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

Good scientists do not say "I know more than you". They say "you can know as much as me, and more". Science is always to raise spirits. If we do not know how to teach science in a way that makes it accessible to all those who want to understand it, this is because we have not really understood it.

To become scientists, we must never forget our beginner's experience. It is the most fundamental experience for understanding science and making discoveries, because real knowledge must answer a beginner's questions and hesitations. To advance on the path of science, we must play by the imagination both the role of the beginner and the role of the scientist, because we recognize real science by its capacity to raise beginners. The hesitations of the beginning provide the criterion for the recognition of the most important knowledge, they germinate all the force of science.

This book is written to help beginners understand the most fundamental principles of science.

Applications and complements :

- Logical principles
- ZFC is false
- 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
- Principles of psychiatry

**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

- 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