Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Paper of December 1676' and 'Unpublished Notebooks 1872-74'

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49 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom prevents us from being ruled by the moment [Nietzsche]
1. Philosophy / A. Wisdom / 2. Wise People
Unlike science, true wisdom involves good taste [Nietzsche]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Suffering is the meaning of existence [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Philosophy ennobles the world, by producing an artistic conception of our knowledge [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
The first aim of a philosopher is a life, not some works [Nietzsche]
You should only develop a philosophy if you are willing to live by it [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / f. Philosophy as healing
Philosophy is pointless if it does not advocate, and live, a new way of life [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Philosophy is more valuable than much of science, because of its beauty [Nietzsche]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
It would better if there was no thought [Nietzsche]
Why do people want philosophers? [Nietzsche]
Philosophy is always secondary, because it cannot support a popular culture [Nietzsche]
1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
Kant has undermined our belief in metaphysics [Nietzsche]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
If philosophy controls science, then it has to determine its scope, and its value [Nietzsche]
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 / A. Overview of Logic / 3. Value of Logic
Logic is just slavery to language [Nietzsche]
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 / C. Structure of Existence / 6. Fundamentals / c. Monads
If some sort of experience is at the root of matter, then human knowledge is close to its essence [Nietzsche]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Belief matters more than knowledge, and only begins when knowledge ceases [Nietzsche]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
It always remains possible that the world just is the way it appears [Nietzsche]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Our knowledge is illogical, because it rests on false identities between things [Nietzsche]
The most extreme scepticism is when you even give up logic [Nietzsche]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
If we find a hypothesis that explains many things, we conclude that it explains everything [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
Our primary faculty is perception of structure, as when looking in a mirror [Nietzsche]
15. Nature of Minds / C. Capacities of Minds / 9. Perceiving Causation
We experience causation between willing and acting, and thereby explain conjunctions of changes [Nietzsche]
17. Mind and Body / A. Mind-Body Dualism / 7. Zombies
It's impossible, but imagine a body carrying on normally, but with no mind [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
It is just madness to think that the mind is supernatural (or even divine!) [Nietzsche]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
The shortest path to happiness is forgetfulness, the path of animals (but of little value) [Nietzsche]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Education is contrary to human nature [Nietzsche]
25. Social Practice / E. Policies / 5. Education / d. Study of history
We should evaluate the past morally [Nietzsche]
25. Social Practice / F. Life Issues / 6. Animal Rights
Protest against vivisection - living things should not become objects of scientific investigation [Nietzsche]
26. Natural Theory / C. Causation / 3. Final causes
We do not know the nature of one single causality [Nietzsche]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Laws of nature are merely complex networks of relations [Nietzsche]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The Greeks lack a normative theology: each person has their own poetic view of things [Nietzsche]