Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'Relations' and 'The Human Condition'

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41 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / A. Relations / 1. Nature of Relations
We want the ontology of relations, not just a formal way of specifying them [Heil]
Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
Truthmaking is a clear example of an internal relation [Heil]
If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
If properties are powers, then causal relations are internal relations [Heil]
10. Modality / B. Possibility / 7. Chance
'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
An action may be intended under one description, but not under another [Kekes]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
To control our actions better, make them result from our attitudes, not from circumstances [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
Values are an attempt to achieve well-being by bringing contingencies under control [Kekes]
Values help us to control life, by connecting it to what is stable and manageable [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes]
Practical reason is not universal and impersonal, because it depends on what success is [Kekes]
If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
We are bound to regret some values we never aspired to [Kekes]
There are far more values than we can pursue, so they are optional possibilities [Kekes]
Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes]
Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes]
The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes]
Unconditional commitments are our most basic convictions, saying what must never be done [Kekes]
Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes]
22. Metaethics / B. Value / 2. Values / j. Evil
Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Control is the key to well-being [Kekes]
Well-being needs correct attitudes and well-ordered commitments to local values [Kekes]
23. Ethics / F. Existentialism / 4. Boredom
Boredom destroys our ability to evaluate [Kekes]
Boredom is apathy and restlessness, yearning for something interesting [Kekes]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
Society is alienating if it lacks our values, and its values repel us [Kekes]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes]
Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes]
25. Social Practice / B. Equalities / 4. Economic equality
Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes]