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All the ideas for 'Philosophy of Mathematics', 'Notebooks' and 'Philosophy of Logic'

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33 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Seek wisdom rather than truth; it is easier [Joubert]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
We must think with our entire body and soul [Joubert]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
The love of certainty holds us back in metaphysics [Joubert]
2. Reason / A. Nature of Reason / 9. Limits of Reason
The truths of reason instruct, but they do not illuminate [Joubert]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
3. Truth / A. Truth Problems / 1. Truth
Truth consists of having the same idea about something that God has [Joubert]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
For scientific purposes there is a precise concept of 'true-in-L', using set theory [Putnam]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Before the late 19th century logic was trivialised by not dealing with relations [Putnam]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Asserting first-order validity implicitly involves second-order reference to classes [Putnam]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Unfashionably, I think logic has an empirical foundation [Putnam]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
We can identify functions with certain sets - or identify sets with certain functions [Putnam]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Having a valid form doesn't ensure truth, as it may be meaningless [Putnam]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism only makes sense if it is materialist [Putnam]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Physics is full of non-physical entities, such as space-vectors [Putnam]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
To know is to see inside oneself [Joubert]
14. Science / A. Basis of Science / 4. Prediction
Most predictions are uninteresting, and are only sought in order to confirm a theory [Putnam]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
The imagination has made more discoveries than the eye [Joubert]
18. Thought / A. Modes of Thought / 1. Thought
A thought is as real as a cannon ball [Joubert]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
Where does the bird's idea of a nest come from? [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
He gives his body up to pleasure, but not his soul [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
What will you think of pleasures when you no longer enjoy them? [Joubert]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
Virtue is hard if we are scorned; we need support [Joubert]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
In raising a child we must think of his old age [Joubert]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
We can't exactly conceive virtue without the idea of God [Joubert]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
We cannot speak against Christianity without anger, or speak for it without love [Joubert]