Combining Texts

All the ideas for 'Logical Consequence', 'Building Blocks of Mathematical Logic' and 'The Reasons of Love'

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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 / E. Structures of Logic / 4. Variables in Logic
17699 Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]
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 / 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]
10. Modality / A. Necessity / 9. Normative Necessity
9240 Love creates a necessity concerning what to care about [Frankfurt]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
9228 Ranking order of desires reveals nothing, because none of them may be considered important [Frankfurt]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
9238 Morality isn't based on reason; moral indignation is quite unlike disapproval of irrationality [Frankfurt]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
9232 It is by caring about things that we infuse the world with importance [Frankfurt]
9234 If you don't care about at least one thing, you can't find reasons to care about anything [Frankfurt]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
9229 What is worthwhile for its own sake alone may be worth very little [Frankfurt]
9233 Our criteria for evaluating how to live offer an answer to the problem [Frankfurt]
22. Metaethics / B. Value / 2. Values / g. Love
9235 Rather than loving things because we value them, I think we value things because we love them [Frankfurt]
9236 Love can be cool, and it may not involve liking its object [Frankfurt]
9237 The paradigm case of pure love is not romantic, but that between parents and infants [Frankfurt]
9239 I value my children for their sake, but I also value my love for them for its own sake [Frankfurt]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
9227 We might not choose a very moral life, if the character or constitution was deficient [Frankfurt]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
9230 People want to fulfill their desires, but also for their desires to be sustained [Frankfurt]
23. Ethics / A. Egoism / 1. Ethical Egoism
9241 Loving oneself is not a failing, but is essential to a successful life [Frankfurt]
23. Ethics / F. Existentialism / 4. Boredom
9300 Boredom is serious, not just uncomfortable; it threatens our psychic survival [Frankfurt]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
9231 Freedom needs autonomy (rather than causal independence) - embracing our own desires and choices [Frankfurt]