Combining Texts

All the ideas for 'Logical Consequence', 'On Second-Order Logic' and 'Explanation - Opening Address'

expand these ideas     |    start again     |     specify just one area for these texts

27 ideas

2. Reason / A. Nature of Reason / 6. Coherence
17070 Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart]
17072 We need comprehensiveness, as well as self-coherence [Smart]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688 '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
10690 Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691 Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689 A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696 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
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10692 Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
17073 I simply reject evidence, if it is totally contrary to my web of belief [Smart]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
17077 The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart]
17078 Universe expansion explains the red shift, but not vice versa [Smart]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
17061 Explanation of a fact is fitting it into a system of beliefs [Smart]
17074 Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart]
17076 Deducing from laws is one possible way to achieve a coherent explanation [Smart]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
17071 An explanation is better if it also explains phenomena from a different field [Smart]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
17062 If scientific explanation is causal, that rules out mathematical explanation [Smart]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
17075 Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
17063 Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart]