Combining Texts

All the ideas for 'Logical Consequence', 'Utopia' and 'Ontology and Mathematical Truth'

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21 ideas

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]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9967 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien]
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 / 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 / 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
9968 A model is 'fundamental' if it contains only concrete entities [Jubien]
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
9965 There couldn't just be one number, such as 17 [Jubien]
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 / 7. Mathematical Structuralism / a. Structuralism
9966 The subject-matter of (pure) mathematics is abstract structure [Jubien]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
9962 How can pure abstract entities give models to serve as interpretations? [Jubien]
9963 If we all intuited mathematical objects, platonism would be agreed [Jubien]
9964 Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
9969 The empty set is the purest abstract object [Jubien]
24. Political Theory / D. Ideologies / 3. Conservatism
7257 All modern social systems seem to be conspiracies of the rich [More,T]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
7254 If you try to get elected, you should be permanently barred from seeking office [More,T]
25. Social Practice / E. Policies / 1. War / a. Just wars
7255 Only Utopians fail to see glory in warfare [More,T]
25. Social Practice / F. Life Issues / 2. Euthanasia
7253 In Utopia, legal euthanasia is considered honourable [More,T]
28. God / C. Attitudes to God / 2. Pantheism
7256 In Utopia, the Supreme Being is identical with Nature [More,T]