Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'In Defense of Absolute Essentialism' and 'Intro to 'The Reason's Proper Study''

expand these ideas     |    start again     |     specify just one area for these texts

26 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
10631 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10626 Objects just are what singular terms refer to [Hale/Wright]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
13804 A property is essential iff the object would not exist if it lacked that property [Forbes,G]
13805 Properties are trivially essential if they are not grounded in a thing's specific nature [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13808 A relation is essential to two items if it holds in every world where they exist [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / c. Essentials are necessary
13806 Trivially essential properties are existence, self-identity, and de dicto necessities [Forbes,G]
9. Objects / D. Essence of Objects / 9. Essence and Properties
13807 A property is 'extraneously essential' if it is had only because of the properties of other objects [Forbes,G]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
13809 One might be essentialist about the original bronze from which a statue was made [Forbes,G]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
13810 The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10630 Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
19. Language / E. Analyticity / 2. Analytic Truths
10627 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]