Combining Texts

All the ideas for 'Properties and Predicates', 'Elements of Geometry' and 'Towards a Critique of Hegel's Philosophy'

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24 ideas

1. Philosophy / C. History of Philosophy / 1. History of Philosophy
19441 All philosophies presuppose their historical moment, and arise from it [Feuerbach]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
19442 I don't study Plato for his own sake; the primary aim is always understanding [Feuerbach]
2. Reason / C. Styles of Reason / 1. Dialectic
19444 Each proposition has an antithesis, and truth exists as its refutation [Feuerbach]
19445 A dialectician has to be his own opponent [Feuerbach]
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 / A. Truth Problems / 3. Value of Truth
19443 Truth forges an impersonal unity between people [Feuerbach]
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]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
19446 To our consciousness it is language which looks unreal [Feuerbach]
8. Modes of Existence / B. Properties / 2. Need for Properties
8568 A property is merely a constituent of laws of nature; temperature is just part of thermodynamics [Mellor]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
8564 There is obviously a possible predicate for every property [Mellor]
8. Modes of Existence / D. Universals / 2. Need for Universals
8566 We need universals for causation and laws of nature; the latter give them their identity [Mellor]
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
8565 If properties were just the meanings of predicates, they couldn't give predicates their meaning [Mellor]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
19447 The Absolute is the 'and' which unites 'spirit and nature' [Feuerbach]
26. Natural Theory / C. Causation / 8. Particular Causation / e. Probabilistic causation
8567 Singular causation requires causes to raise the physical probability of their effects [Mellor]