Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'The Architecture of Mathematics' and 'The Need for Roots'

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31 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
Truth is not a object we love - it is the radiant manifestation of reality [Weil]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
From the axiomatic point of view, mathematics is a storehouse of abstract structures [Bourbaki]
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
Creation produced a network or web of determinations [Weil]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
The aesthete's treatment of beauty as amusement is sacreligious; beauty should nourish [Weil]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
Beauty is the proof of what is good [Weil]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
Respect is our only obligation, which can only be expressed through deeds, not words [Weil]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
The most important human need is to have multiple roots [Weil]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
The need for order stands above all others, and is understood via the other needs [Weil]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
Obligations only bind individuals, not collectives [Weil]
24. Political Theory / B. Nature of a State / 4. Citizenship
A citizen should be able to understand the whole of society [Weil]
Even the poorest should feel collective ownership, and participation in grand display [Weil]
24. Political Theory / B. Nature of a State / 5. Culture
Culture is an instrument for creating an ongoing succession of teachers [Weil]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
A lifelong head of society should only be a symbol, not a ruler [Weil]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
Party politics in a democracy can't avoid an anti-democratic party [Weil]
24. Political Theory / D. Ideologies / 8. Socialism
Socialism tends to make a proletariat of the whole population [Weil]
24. Political Theory / D. Ideologies / 11. Capitalism
The capitalists neglect the people and the nation, and even their own interests [Weil]
25. Social Practice / B. Equalities / 1. Grounds of equality
By making money the sole human measure, inequality has become universal [Weil]
25. Social Practice / C. Rights / 1. Basis of Rights
People have duties, and only have rights because of the obligations of others to them [Weil]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
To punish people we must ourselves be innocent - but that undermines the desire to punish [Weil]
25. Social Practice / E. Policies / 1. War / d. Non-combatants
The soldier-civilian distinction should be abolished; every citizen is committed to a war [Weil]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
Education is essentially motivation [Weil]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion should quietly suffuse all human life with its light [Weil]