Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Spreading the Word' and 'The Intelligence of Evil'

expand these ideas     |    start again     |     specify just one area for these texts


34 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
There is no longer anything on which there is nothing to say [Baudrillard]
2. Reason / A. Nature of Reason / 5. Objectivity
The task of philosophy is to unmask the illusion of objective reality [Baudrillard]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Drunken boat pilots are less likely to collide than clearly focused ones [Baudrillard]
2. Reason / C. Styles of Reason / 1. Dialectic
Instead of thesis and antithesis leading to synthesis, they now cancel out, and the conflict is levelled [Baudrillard]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / D. Theories of Reality / 3. Reality
Without God we faced reality: what do we face without reality? [Baudrillard]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
Nothing is true, but everything is exact [Baudrillard]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
10. Modality / A. Necessity / 11. Denial of Necessity
Asserting a necessity just expresses our inability to imagine it is false [Blackburn]
16. Persons / F. Free Will / 5. Against Free Will
There is no need to involve the idea of free will to make choices about one's life [Baudrillard]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
In modern times, being useless is the essential aesthetic ingredient for an object [Baudrillard]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Good versus evil has been banefully reduced to happiness versus misfortune [Baudrillard]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
Whole populations are terrorist threats to authorities, who unite against them [Baudrillard]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
People like democracy because it means they can avoid power [Baudrillard]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Only in the last 200 years have people demanded the democratic privilege of being individuals [Baudrillard]
25. Social Practice / E. Policies / 5. Education / d. Study of history
The arrival of the news media brought history to an end [Baudrillard]
25. Social Practice / F. Life Issues / 4. Suicide
Suicide is ascribed to depression, with the originality of the act of will ignored [Baudrillard]
28. God / B. Proving God / 2. Proofs of Reason / d. Pascal's Wager
Pascal says secular life is acceptable, but more fun with the hypothesis of God [Baudrillard]