Combining Texts

All the ideas for 'Logical Consequence', 'Against the Ethicists (one book)' and 'Course of Positive Philosophy'

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13 ideas

1. Philosophy / G. Scientific Philosophy / 2. Positivism
The phases of human thought are theological, then metaphysical, then positivist [Comte, by Watson]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Reasoning is impossible without a preconception [Sext.Empiricus]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
Saying the good is useful or choiceworth or happiness-creating is not the good, but a feature of it [Sext.Empiricus]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Like a warming fire, what is good by nature should be good for everyone [Sext.Empiricus]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
If a desire is itself desirable, then we shouldn't desire it, as achieving it destroys it [Sext.Empiricus]