Combining Philosophers

All the ideas for Celsus, T.H. Green and John Mayberry

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60 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead]
2. Reason / D. Definition / 2. Aims of Definition
Definitions make our intuitions mathematically useful [Mayberry]
2. Reason / E. Argument / 6. Conclusive Proof
Proof shows that it is true, but also why it must be true [Mayberry]
3. Truth / D. Coherence Truth / 1. Coherence Truth
Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry]
There is a semi-categorical axiomatisation of set-theory [Mayberry]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of size is part of the very conception of a set [Mayberry]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic only has its main theorems because it is so weak [Mayberry]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]
Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]
'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]
5. Theory of Logic / K. Features of Logics / 6. Compactness
No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
Greek quantities were concrete, and ratio and proportion were their science [Mayberry]
Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry]
Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
If proof and definition are central, then mathematics needs and possesses foundations [Mayberry]
The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry]
Foundations need concepts, definition rules, premises, and proof rules [Mayberry]
Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry]
We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry]
Set theory is not just another axiomatised part of mathematics [Mayberry]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead]
Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
The good life aims at perfections, or absolute laws, or what is absolutely desirable [Green,TH]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead]
23. Ethics / A. Egoism / 2. Hedonism
Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
States only have full authority if they heed the claims of human fellowship [Green,TH]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH]
24. Political Theory / B. Nature of a State / 4. Citizenship
The ideal is a society in which all citizens are ladies and gentlemen [Green,TH]
Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
The good is identified by the capacities of its participants [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
People are improved by egalitarian institutions and habits [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
All talk of the progress of a nation must reduce to the progress of its individual members [Green,TH]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead]
The highest political efforts express our deeper social spirit [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 9. Communism
Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead]
Original common ownership is securing private property, not denying it [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 14. Nationalism
National spirit only exists in the individuals who embody it [Green,TH, by Muirhead]
25. Social Practice / C. Rights / 4. Property rights
The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead]
Property is needed by all citizens, to empower them to achieve social goods [Green,TH]
25. Social Practice / F. Life Issues / 6. Animal Rights
The world was made as much for animals as for man [Celsus]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
If something develops, its true nature is embodied in its end [Green,TH]
28. God / A. Divine Nature / 1. God
God is the ideal end of the mature mind's final development [Green,TH]
28. God / C. Attitudes to God / 4. God Reflects Humanity
God is the realisation of the possibilities of each man's self [Green,TH]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus]