Combining Texts

All the ideas for 'Logical Consequence', 'Axioms for the Part Relation' and 'What is Justified Belief?'

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13 ideas

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]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
In the military, persons are parts of parts of large units, but not parts of those large units [Rescher]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
A belief can be justified when the person has forgotten the evidence for it [Goldman]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman]
16. Persons / C. Self-Awareness / 1. Introspection
Introspection is really retrospection; my pain is justified by a brief causal history [Goldman]