### All the ideas for Alexander, Euclid and Alexius Meinong

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19 ideas

###### 2. Reason / E. Argument / 6. Conclusive Proof
 8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
###### 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]
###### 4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
 8250 So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra]
###### 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
 10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
 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]
 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]
###### 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
 8719 There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend]
###### 9. Objects / A. Existence of Objects / 3. Objects in Thought
 8971 There are objects of which it is true that there are no such objects [Meinong]
 8718 Meinong says an object need not exist, but must only have properties [Meinong, by Friend]
###### 9. Objects / A. Existence of Objects / 4. Impossible objects
 7756 Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan]
 15781 The objects of knowledge are far more numerous than objects which exist [Meinong]
###### 26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / g. Atomism
 20919 How can things without weight compose weight? [Alexander]