Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Philosophy of Logic' and 'Naming and Necessity notes and addenda'

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29 ideas

3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Asserting first-order validity implicitly involves second-order reference to classes [Putnam]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Unfashionably, I think logic has an empirical foundation [Putnam]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
We can identify functions with certain sets - or identify sets with certain functions [Putnam]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Having a valid form doesn't ensure truth, as it may be meaningless [Putnam]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism only makes sense if it is materialist [Putnam]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Physics is full of non-physical entities, such as space-vectors [Putnam]
9. Objects / A. Existence of Objects / 5. Simples
We might fix identities for small particulars, but it is utopian to hope for such things [Kripke]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke]
9. Objects / F. Identity among Objects / 5. Self-Identity
A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke]
9. Objects / F. Identity among Objects / 9. Sameness
A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke]
10. Modality / A. Necessity / 7. Natural Necessity
What many people consider merely physically necessary I consider completely necessary [Kripke]
What is often held to be mere physical necessity is actually metaphysical necessity [Kripke]
10. Modality / B. Possibility / 1. Possibility
Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
The a priori analytic truths involving fixing of reference are contingent [Kripke]
14. Science / A. Basis of Science / 4. Prediction
Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam]
15. Nature of Minds / A. Nature of Mind / 1. Mind / a. Mind
I regard the mind-body problem as wide open, and extremely confusing [Kripke]
19. Language / B. Reference / 3. Direct Reference / c. Social reference
A description may fix a reference even when it is not true of its object [Kripke]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]