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All the ideas for 'works', 'Letters from a Stoic' and 'Structures and Structuralism in Phil of Maths'

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75 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb]
Wisdom does not lie in books, and unread people can also become wise [Seneca]
1. Philosophy / A. Wisdom / 2. Wise People
Wise people escape necessity by willing it [Seneca]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims at happiness [Seneca]
What philosophy offers humanity is guidance [Seneca]
1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
That something is a necessary condition of something else doesn't mean it caused it [Seneca]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Even philosophers have got bogged down in analysing tiny bits of language [Seneca]
2. Reason / A. Nature of Reason / 2. Logos
For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
2. Reason / D. Definition / 4. Real Definition
Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
2. Reason / D. Definition / 5. Genus and Differentia
Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
4. Formal Logic / G. Formal Mereology / 1. Mereology
Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
The notion of a priori truth is absent in Aristotle [Aristotle, by Politis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
14. Science / B. Scientific Theories / 1. Scientific Theory
Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
To the four causes Plato adds a fifth, the idea which guided the event [Seneca]
Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
If everything can be measured, try measuring the size of a man's soul [Seneca]
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji]
19. Language / B. Reference / 1. Reference theories
Referring to a person, and speaking about him, are very different [Seneca]
19. Language / E. Analyticity / 2. Analytic Truths
The notion of analytic truth is absent in Aristotle [Aristotle, by Politis]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
Trouble in life comes from copying other people, which is following convention instead of reason [Seneca]
22. Metaethics / B. Value / 2. Values / d. Health
Humans acquired the concept of virtue from an analogy with bodily health and strength [Seneca, by Allen]
22. Metaethics / B. Value / 2. Values / e. Death
We know death, which is like before birth; ceasing to be and never beginning are the same [Seneca]
Living is nothing wonderful; what matters is to die well [Seneca]
It is as silly to lament ceasing to be as to lament not having lived in the remote past [Seneca]
22. Metaethics / B. Value / 2. Values / g. Love
Is anything sweeter than valuing yourself more when you find you are loved? [Seneca]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Selfishness does not produce happiness; to live for yourself, live for others [Seneca]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
A man is as unhappy as he has convinced himself he is [Seneca]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Life is like a play - it is the quality that matters, not the length [Seneca]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
We are scared of death - except when we are immersed in pleasure! [Seneca]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
The whole point of pleasure-seeking is novelty, and abandoning established ways [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / b. Living naturally
Nature doesn't give us virtue; we must unremittingly pursue it, as a training and an art [Seneca]
Living contrary to nature is like rowing against the stream [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
Character is ruined by not looking back over our pasts, since the future rests on the past [Seneca]
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
It's no good winning lots of fights, if you are then conquered by your own temper [Seneca]
Excessive curiosity is a form of intemperance [Seneca]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
To govern used to mean to serve, not to rule; rulers did not test their powers over those who bestowed it [Seneca]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius]
25. Social Practice / E. Policies / 5. Education / c. Teaching
One joy of learning is making teaching possible [Seneca]
Both teachers and pupils should aim at one thing - the improvement of the pupil [Seneca]
25. Social Practice / F. Life Issues / 4. Suicide
Suicide may be appropriate even when it is not urgent, if there are few reasons against it [Seneca]
If we control our own death, no one has power over us [Seneca]
Sometimes we have a duty not to commit suicide, for those we love [Seneca]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins]
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Does time exist on its own? Did anything precede it? Did it pre-exist the cosmos? [Seneca]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]