Combining Texts

All the ideas for 'Protagoras', 'Mathematical Intuition' and 'Logical Consequence'

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22 ideas

2. Reason / B. Laws of Thought / 4. Contraries
192 Only one thing can be contrary to something [Plato]
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 / 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 / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
190 If asked whether justice itself is just or unjust, you would have to say that it is just [Plato]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
20184 The only real evil is loss of knowledge [Plato]
20185 The most important things in life are wisdom and knowledge [Plato]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
191 Everything resembles everything else up to a point [Plato]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
203 Courage is knowing what should or shouldn't be feared [Plato]
22. Metaethics / B. Value / 2. Values / j. Evil
202 No one willingly and knowingly embraces evil [Plato]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
193 Some things are good even though they are not beneficial to men [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
197 Some pleasures are not good, and some pains are not evil [Plato]
200 People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
188 Socrates did not believe that virtue could be taught [Plato]
204 Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato]
189 If we punish wrong-doers, it shows that we believe virtue can be taught [Plato]