Combining Texts

All the ideas for 'Cratylus', 'Speaking of Objects' and 'Elements of Set Theory'

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34 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom is called 'beautiful', because it performs fine works [Plato]
1. Philosophy / A. Wisdom / 2. Wise People
Good people are no different from wise ones [Plato]
2. Reason / C. Styles of Reason / 1. Dialectic
A dialectician is someone who knows how to ask and to answer questions [Plato]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
Truths say of what is that it is, falsehoods say of what is that it is not [Plato]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
We can only define functions if Choice tells us which items are involved [Enderton]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
A name-giver might misname something, then force other names to conform to it [Plato]
A name is a sort of tool [Plato]
Things must be known before they are named, so it can't be the names that give us knowledge [Plato]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Anyone who knows a thing's name also knows the thing [Plato]
7. Existence / B. Change in Existence / 1. Nature of Change
How can beauty have identity if it changes? [Plato]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
"No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia]
7. Existence / E. Categories / 2. Categorisation
We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato]
8. Modes of Existence / B. Properties / 12. Denial of Properties
There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Our conceptual scheme becomes more powerful when we posit abstract objects [Quine]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
Doesn't each thing have an essence, just as it has other qualities? [Plato]
9. Objects / D. Essence of Objects / 3. Individual Essences
Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Is the being or essence of each thing private to each person? [Plato]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
There can't be any knowledge if things are constantly changing [Plato]
15. Nature of Minds / A. Nature of Mind / 2. Psuche
Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine]
Translation of our remote past or language could be as problematic as alien languages [Quine]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
'Arete' signifies lack of complexity and a free-flowing soul [Plato]
27. Natural Reality / G. Biology / 5. Species
The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato]
28. God / A. Divine Nature / 2. Divine Nature
Even the gods love play [Plato]