Combining Texts

All the ideas for 'Philosophy of Mathematics', 'works' and 'Perpetual Peace'

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16 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
14. Science / B. Scientific Theories / 1. Scientific Theory
You have only begun to do real science when you can express it in numbers [Kelvin]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
The state of nature always involves the threat of war [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
Kant made the social contract international and cosmopolitan [Kant, by Oksala]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
The a priori general will of a people shows what is right [Kant]
24. Political Theory / B. Nature of a State / 3. Constitutions
Each nation should, from self-interest, join an international security constitution [Kant]
A constitution must always be improved when necessary [Kant]
25. Social Practice / B. Equalities / 3. Legal equality
Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant]
25. Social Practice / C. Rights / 1. Basis of Rights
There is now a growing universal community, and violations of rights are felt everywhere [Kant]
There are political and inter-national rights, but also universal cosmopolitan rights [Kant]
25. Social Practice / E. Policies / 1. War / c. Combatants
Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant]
25. Social Practice / E. Policies / 1. War / e. Peace
Some trust in the enemy is needed during wartime, or peace would be impossible [Kant]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]