Combining Texts

All the ideas for 'Counterpart theory and Quant. Modal Logic', 'Introduction to the Theory of Logic' and 'The World'

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28 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 7. Natural Necessity
Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
Counterparts are not the original thing, but resemble it more than other things do [Lewis]
If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
Essential attributes are those shared with all the counterparts [Lewis]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Our sensation of light may not be the same as what produces the sensation [Descartes]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
The Hot, Cold, Wet and Dry of the philosophers need themselves to be explained [Descartes]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
Descartes said there was conservation of 'quantity of motion' [Descartes, by Papineau]