Combining Philosophers

All the ideas for Kenelm Digby, Mirabeau and committee and Gerhard Gentzen

expand these ideas     |    start again     |     specify just one area for these philosophers

16 ideas

5. Theory of Logic / A. Overview of Logic / 2. History of Logic
11022 Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11065 The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]
11023 The logical connectives are 'defined' by their introduction rules [Gentzen]
11213 Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]
5. Theory of Logic / H. Proof Systems / 4. Natural Deduction
13832 Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10067 Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16597 Quantity is the capacity to be divided [Digby]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
19855 The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
19856 The law expresses the general will, and all citizens can participate [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 3. Constitutions
19861 There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee]
25. Social Practice / A. Freedoms / 2. Freedom of belief
19858 No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee]
25. Social Practice / A. Freedoms / 3. Free speech
19859 Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee]
25. Social Practice / B. Equalities / 2. Political equality
19857 All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee]
25. Social Practice / C. Rights / 4. Property rights
19862 Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee]
25. Social Practice / E. Policies / 4. Taxation
19860 Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
16731 Colours arise from the rarity, density and mixture of matter [Digby]