Combining Texts

All the ideas for 'Realism in Mathematics', 'Explanation - Opening Address' and 'Idea for a Universal History'

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21 ideas

2. Reason / A. Nature of Reason / 3. Pure Reason
Reason enables the unbounded extension of our rules and intentions [Kant]
2. Reason / A. Nature of Reason / 6. Coherence
Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart]
We need comprehensiveness, as well as self-coherence [Smart]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
I simply reject evidence, if it is totally contrary to my web of belief [Smart]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart]
Universe expansion explains the red shift, but not vice versa [Smart]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
Explanation of a fact is fitting it into a system of beliefs [Smart]
Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart]
Deducing from laws is one possible way to achieve a coherent explanation [Smart]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
An explanation is better if it also explains phenomena from a different field [Smart]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
If scientific explanation is causal, that rules out mathematical explanation [Smart]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart]
16. Persons / F. Free Will / 2. Sources of Free Will
The manifest will in the world of phenomena has to conform to the laws of nature [Kant]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
Our aim is a constitution which combines maximum freedom with strong restraint [Kant]
The vitality of business needs maximum freedom (while avoiding harm to others) [Kant]
25. Social Practice / D. Justice / 1. Basis of justice
The highest ideal of social progress is a universal cosmopolitan existence [Kant]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart]