Combining Philosophers

All the ideas for Alexander, Euclid and Alexius Meinong

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19 ideas

2. Reason / E. Argument / 6. Conclusive Proof
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
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
So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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
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
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
Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
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
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
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
There are objects of which it is true that there are no such objects [Meinong]
Meinong says an object need not exist, but must only have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 4. Impossible objects
Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan]
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
How can things without weight compose weight? [Alexander]