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All the ideas for 'Thinking About Mathematics', 'works' and 'Introduction of 'Essence of Christianity''

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25 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
'Impredicative' definitions refer to the thing being described [Shapiro]
9. Objects / D. Essence of Objects / 5. Essence as Kind
Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach]
26. Natural Theory / C. Causation / 4. Naturalised causation
The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley]
27. Natural Reality / G. Biology / 5. Species
Consciousness is said to distinguish man from animals - consciousness of his own species [Feuerbach]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach]
28. God / C. Attitudes to God / 4. God Reflects Humanity
The nature of God is an expression of human nature [Feuerbach]
28. God / C. Attitudes to God / 5. Atheism
If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion is the consciousness of the infinite [Feuerbach]
Today's atheism will tomorrow become a religion [Feuerbach]