Combining Texts

All the ideas for 'To be is to be the value of a variable..', 'What is Logic?' and 'The Unimportance of Identity'

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30 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
2. Reason / E. Argument / 7. Thought Experiments
5515 Imaginary cases are good for revealing our beliefs, rather than the truth [Parfit]
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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
7785 The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10699 Does a bowl of Cheerios contain all its sets and subsets? [Boolos]
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]
10225 Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro]
10736 Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo]
10780 Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10697 Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
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 / G. Quantification / 5. Second-Order Quantification
13671 Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10267 We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
10698 Plural forms have no more ontological commitment than to first-order objects [Boolos]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
7806 Boolos invented plural quantification [Boolos, by Benardete,JA]
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]
7. Existence / C. Structure of Existence / 2. Reduction
5516 Reduction can be by identity, or constitution, or elimination [Parfit, by PG]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
10700 First- and second-order quantifiers are two ways of referring to the same things [Boolos]
16. Persons / D. Continuity of the Self / 1. Identity and the Self
5514 Psychologists are interested in identity as a type of person, but philosophers study numerical identity [Parfit]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
5521 If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity [Parfit]
5522 Over a period of time what matters is not that 'I' persist, but that I have psychological continuity [Parfit]
16. Persons / D. Continuity of the Self / 4. Split Consciousness
5519 It is fine to save two dying twins by merging parts of their bodies into one, and identity is irrelevant [Parfit]
5520 If two humans are merged surgically, the new identity is a purely verbal problem [Parfit]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
5518 It doesn't matter whether I exist with half my components replaced (any more than an audio system) [Parfit]