Combining Texts

All the ideas for 'Cratylus', 'The Metaphysics of Modality' and 'Russell's Mathematical Logic'

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53 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]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G]
2. Reason / C. Styles of Reason / 1. Dialectic
A dialectician is someone who knows how to ask and to answer questions [Plato]
2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
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 / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G]
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]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / B. Change in Existence / 1. Nature of Change
How can beauty have identity if it changes? [Plato]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G]
7. Existence / E. Categories / 2. Categorisation
We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
In all instances of identity, there must be some facts to ensure the identity [Forbes,G]
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 / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G]
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]
Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P]
An individual essence is a set of essential properties which only that object can have [Forbes,G]
Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Essential properties depend on a category, and perhaps also on particular facts [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Essential properties are those without which an object could not exist [Forbes,G]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
Artefacts have fuzzy essences [Forbes,G]
Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Is the being or essence of each thing private to each person? [Plato]
9. Objects / E. Objects over Time / 12. Origin as Essential
An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato]
10. Modality / A. Necessity / 4. De re / De dicto modality
De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G]
The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
Possible worlds are points of logical space, rather like other times than our own [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Transworld identity concerns the limits of possibility for ordinary things [Forbes,G]
The problem of transworld identity can be solved by individual essences [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterpart theory is not good at handling the logic of identity [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G]
We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G]
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]
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]