Combining Texts

All the ideas for 'fragments/reports', 'The Establishment of Scientific Semantics' and 'Elements of Geometry'

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20 ideas

2. Reason / E. Argument / 6. Conclusive Proof
8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
13338 '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
13907 If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
13337 A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
13335 Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski]
13336 A language containing its own semantics is inconsistent - but we can use a second language [Tarski]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
13339 A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski]
13340 Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski]
5. Theory of Logic / K. Features of Logics / 2. Consistency
13341 Using the definition of truth, we can prove theories consistent within sound logics [Tarski]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
6297 Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9603 An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
9894 A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
8738 Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
22278 Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
8673 Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
10250 Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
14157 Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
1600 Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
467 A virtue is a combination of intelligence, strength and luck [Ion]