Combining Texts

All the ideas for 'fragments/reports', 'Summa totius logicae' and 'What is Logic?'

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22 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
9108 From an impossibility anything follows [William of Ockham]
2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
9107 A proposition is true if its subject and predicate stand for the same thing [William of Ockham]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
16300 Ockham had an early axiomatic account of truth [William of Ockham, by Halbach]
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
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 / G. Quantification / 1. Quantification
9106 The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham]
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 / C. Sources of Mathematics / 5. Numbers as Adjectival
9113 Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham]
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
9110 The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
15388 Universals are single things, and only universal in what they signify [William of Ockham]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
9109 If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham]
19. Language / D. Propositions / 4. Mental Propositions
9105 Some concepts for propositions exist only in the mind, and in no language [William of Ockham]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]