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All the ideas for 'Commentary on 'De Anima'', 'What Required for Foundation for Maths?' and 'Truth'

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48 ideas

1. Philosophy / F. Analytic Philosophy / 3. Analysis of Preconditions
In "if and only if" (iff), "if" expresses the sufficient condition, and "only if" the necessary condition [Engel]
2. Reason / D. Definition / 2. Aims of Definition
Definitions make our intuitions mathematically useful [Mayberry]
2. Reason / E. Argument / 6. Conclusive Proof
Proof shows that it is true, but also why it must be true [Mayberry]
3. Truth / A. Truth Problems / 5. Truth Bearers
Are truth-bearers propositions, or ideas/beliefs, or sentences/utterances? [Engel]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
The redundancy theory gets rid of facts, for 'it is a fact that p' just means 'p' [Engel]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
We can't explain the corresponding structure of the world except by referring to our thoughts [Engel]
3. Truth / D. Coherence Truth / 1. Coherence Truth
The coherence theory says truth is an internal relationship between groups of truth-bearers [Engel]
3. Truth / D. Coherence Truth / 2. Coherence Truth Critique
Any coherent set of beliefs can be made more coherent by adding some false beliefs [Engel]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflationism seems to block philosophers' main occupation, asking metatheoretical questions [Engel]
Deflationism cannot explain why we hold beliefs for reasons [Engel]
3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Maybe there is no more to be said about 'true' than there is about the function of 'and' in logic [Engel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry]
There is a semi-categorical axiomatisation of set-theory [Mayberry]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of size is part of the very conception of a set [Mayberry]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
The mainstream of modern logic sees it as a branch of mathematics [Mayberry]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
First-order logic only has its main theorems because it is so weak [Mayberry]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Only second-order logic can capture mathematical structure up to isomorphism [Mayberry]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Deflationism must reduce bivalence ('p is true or false') to excluded middle ('p or not-p') [Engel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry]
Axiomatiation relies on isomorphic structures being essentially the same [Mayberry]
'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry]
5. Theory of Logic / K. Features of Logics / 6. Compactness
No logic which can axiomatise arithmetic can be compact or complete [Mayberry]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / b. Quantity
Greek quantities were concrete, and ratio and proportion were their science [Mayberry]
Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry]
Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
If proof and definition are central, then mathematics needs and possesses foundations [Mayberry]
The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry]
Foundations need concepts, definition rules, premises, and proof rules [Mayberry]
Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry]
We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry]
Set theory is not just another axiomatised part of mathematics [Mayberry]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
The Humean theory of motivation is that beliefs may be motivators as well as desires [Engel]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
Our beliefs are meant to fit the world (i.e. be true), where we want the world to fit our desires [Engel]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
'Evidentialists' say, and 'voluntarists' deny, that we only believe on the basis of evidence [Engel]
12. Knowledge Sources / D. Empiricism / 3. Pragmatism
Pragmatism is better understood as a theory of belief than as a theory of truth [Engel]
13. Knowledge Criteria / C. External Justification / 5. Controlling Beliefs
We cannot directly control our beliefs, but we can control the causes of our involuntary beliefs [Engel]
17. Mind and Body / C. Functionalism / 1. Functionalism
Mental states as functions are second-order properties, realised by first-order physical properties [Engel]
22. Metaethics / B. Value / 2. Values / e. Death
The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus]