Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Philosophical Remarks' and 'works'

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

20 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
3. Truth / A. Truth Problems / 2. Defining Truth
10153 In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19141 Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
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]
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048 There is no clear boundary between the logical and the non-logical [Tarski]
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 / B. Logical Consequence / 4. Semantic Consequence |=
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
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]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157 Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
9. Objects / A. Existence of Objects / 3. Objects in Thought
22320 An 'object' is just what can be referred to without possible non-existence [Wittgenstein]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
18283 Language pictures the essence of the world [Wittgenstein]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
18282 You can't believe it if you can't imagine a verification for it [Wittgenstein]