Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'The Symposium' and 'Abstraction Reconsidered'

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33 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
The finest branch of wisdom is justice and moderation in ordering states and families [Plato]
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 / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik]
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]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
True opinion without reason is midway between wisdom and ignorance [Plato]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible [Geach]
16. Persons / E. Rejecting the Self / 1. Self as Indeterminate
We call a person the same throughout life, but all their attributes change [Plato]
Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
18. Thought / E. Abstraction / 8. Abstractionism Critique
The abstractionist cannot explain 'some' and 'not' [Geach]
Only a judgement can distinguish 'striking' from 'being struck' [Geach]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Love of ugliness is impossible [Plato]
Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato]
Beauty and goodness are the same [Plato]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato]
Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
Music is a knowledge of love in the realm of harmony and rhythm [Plato]
22. Metaethics / B. Value / 2. Values / g. Love
Love assists men in achieving merit and happiness [Plato]
Love is desire for perpetual possession of the good [Plato]
Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato]
22. Metaethics / C. The Good / 1. Goodness / d. Good as virtue
If a person is good they will automatically become happy [Plato]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Happiness is secure enjoyment of what is good and beautiful [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
The only slavery which is not dishonourable is slavery to excellence [Plato]
The first step on the right path is the contemplation of physical beauty when young [Plato]
28. God / A. Divine Nature / 3. Divine Perfections
Gods are not lovers of wisdom, because they are already wise [Plato]