Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Truth by Convention' and 'What is Logic?'

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

22 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
8996 If if time is money then if time is not money then time is money then if if if time is not money... [Quine]
2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
2. Reason / D. Definition / 7. Contextual Definition
8995 Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
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 / C. Ontology of Logic / 3. If-Thenism
10064 Quine quickly dismisses If-thenism [Quine, by Musgrave]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
20296 Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
8998 Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
8999 Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
9000 If a convention cannot be communicated until after its adoption, what is its role? [Quine]
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 / A. Nature of Mathematics / 2. Geometry
8994 If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
8997 There are four different possible conventional accounts of geometry [Quine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8993 If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]