Combining Texts

All the ideas for 'Logical Consequence', 'Letter to Frege 29.12.1899' and 'Apriority as an Evaluative Notion'

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16 ideas

2. Reason / F. Fallacies / 4. Circularity
Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
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]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
People vary in their epistemological standards, and none of them is 'correct' [Field,H]
14. Science / C. Induction / 1. Induction
If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H]