Combining Texts

All the ideas for 'works', 'Higher-Order Logic' and 'works'

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48 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
23890 For Plato true wisdom is supernatural [Plato, by Weil]
1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / b. Pre-Socratic philosophy
3060 Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius]
2. Reason / C. Styles of Reason / 1. Dialectic
23891 Two contradictories force us to find a relation which will correlate them [Plato, by Weil]
3. Truth / A. Truth Problems / 2. Defining Truth
10153 In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19141 Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10048 There is no clear boundary between the logical and the non-logical [Tarski]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10694 Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
10479 Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10157 Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / A. Relations / 3. Structural Relations
14502 Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
17948 Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas]
20906 Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle]
3039 When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
556 If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
563 If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato]
8. Modes of Existence / D. Universals / 6. Platonic Forms / d. Forms critiques
557 A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato]
565 The Forms cannot be changeless if they are in changing things [Aristotle on Plato]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
9607 The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
13263 We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
13261 Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki]
13265 Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
593 Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
13260 Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki]
9. Objects / D. Essence of Objects / 2. Types of Essence
11237 Only universals have essence [Plato, by Politis]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
11238 Plato and Aristotle take essence to make a thing what it is [Plato, by Politis]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
17085 A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
1651 Plato wanted to somehow control and purify the passions [Vlastos on Plato]
19. Language / F. Communication / 1. Rhetoric
3324 Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
7503 Plato never refers to examining the conscience [Plato, by Foucault]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
2173 As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
9274 Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray]
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
94 Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
17947 Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
6015 Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut]
23. Ethics / F. Existentialism / 4. Boredom
2912 Plato is boring [Nietzsche on Plato]
27. Natural Reality / D. Time / 3. Parts of Time / a. Beginning of time
1526 Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle]