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All the ideas for 'What is Logic?st1=Ian Hacking', 'Lectures on Aesthetics' and 'Plural Quantification'

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30 ideas

2. Reason / D. Definition / 3. Types of Definition
A decent modern definition should always imply a semantics [Hacking]
2. Reason / D. Definition / 12. Paraphrase
'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
3. Truth / A. Truth Problems / 2. Defining Truth
Genuine truth is the resolution of the highest contradiction [Hegel]
3. Truth / A. Truth Problems / 3. Value of Truth
What I hold true must also be part of my feelings and character [Hegel]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
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
The various logics are abstractions made from terms like 'if...then' in English [Hacking]
A pure logic is wholly general, purely formal, and directly known [Linnebo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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
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
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
Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
Plural plurals are unnatural and need a first-level ontology [Linnebo]
Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
Second-order quantification and plural quantification are different [Linnebo]
Traditionally we eliminate plurals by quantifying over sets [Linnebo]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
Ordinary speakers posit objects without concern for ontology [Linnebo]
19. Language / C. Assigning Meanings / 3. Predicates
Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
Nineteenth century aesthetics focused on art rather than nature (thanks to Hegel) [Hegel, by Scruton]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Hegel largely ignores aesthetic pleasure, taste and beauty, and focuses on the meaning of artworks [Hegel, by Pinkard]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
Natural beauty is unimportant, because it doesn't show human freedom [Hegel, by Pinkard]
21. Aesthetics / B. Nature of Art / 6. Art as Institution
For Hegel the importance of art concerns the culture, not the individual [Hegel, by Eldridge]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
The purpose of art is to reveal to Spirit its own nature [Hegel, by Davies,S]
The main purpose of art is to express the unity of human life [Hegel]
Art forms a bridge between the sensuous world and the world of pure thought [Hegel]