Combining Texts

All the ideas for 'Logical Consequence', 'On the Introduction of Transfinite Numbers' and 'On Human Nature'

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25 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]
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
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
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 / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
7. Existence / C. Structure of Existence / 3. Levels of Reality
5311 If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
5312 A child first sees objects as distinct, and later as members of groups [Wilson,EO]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
5309 Beliefs are really enabling mechanisms for survival [Wilson,EO]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
5310 Philosophers study the consequences of ethics instead of its origins [Wilson,EO]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
5313 The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO]
22. Metaethics / B. Value / 2. Values / f. Altruism
5316 We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO]
5318 Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO]
23. Ethics / B. Contract Ethics / 1. Contractarianism
5317 The actor is most convincing who believes that his performance is real [Wilson,EO]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
5308 The only human purpose is that created by our genetic history [Wilson,EO]
27. Natural Reality / G. Biology / 3. Evolution
5314 Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO]
5315 Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
5320 It is estimated that mankind has produced 100,000 religions [Wilson,EO]