Combining Texts

All the ideas for 'works', 'A History of God' and 'What is Logic?'

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19 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]
28. God / A. Divine Nature / 4. Divine Contradictions
7602 In the Bible God changes his mind (repenting of creating humanity, in the Flood) [Armstrong,K]
28. God / C. Attitudes to God / 1. Monotheism
7605 Monotheism introduced intolerance into religious thinking [Armstrong,K]
29. Religion / A. Polytheistic Religion / 3. Hinduism
7599 Around 800 BCE teachers superseded gods in India [Armstrong,K]
29. Religion / B. Monotheistic Religion / 2. Judaism
7597 There is virtually no sign of monotheism in the Pentateuch [Armstrong,K]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
7606 The idea that Jesus was God was only settled in the fourth century [Armstrong,K]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
7596 Faith is not just belief in propositions, but also putting trust in them [Armstrong,K]
6610 I believe because it is absurd [Tertullian]