Combining Texts

All the ideas for 'Thinking About Mathematics', 'Declaration of the Rights of Man' and 'The Upanishads'

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41 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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
16. Persons / A. Concept of a Person / 3. Persons as Reasoners
Self is the rider, intellect the charioteer, mind the reins, and body the chariot [Anon (Upan)]
16. Persons / C. Self-Awareness / 2. Knowing the Self
We have an apparent and a true self; only the second one exists, and we must seek to know it [Anon (Upan)]
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
Without speech we cannot know right/wrong, true/false, good/bad, or pleasant/unpleasant [Anon (Upan)]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
The wise prefer good to pleasure; the foolish are drawn to pleasure by desire [Anon (Upan)]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
The purpose of society is to protect the rights of liberty, property, security and resistance [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
The law expresses the general will, and all citizens can participate [Mirabeau/committee]
24. Political Theory / B. Nature of a State / 3. Constitutions
There is only a constitution if rights are assured, and separation of powers defined [Mirabeau/committee]
25. Social Practice / A. Freedoms / 2. Freedom of belief
No one should be molested for their opinions, if they do not disturb the established order [Mirabeau/committee]
25. Social Practice / A. Freedoms / 3. Free speech
Free speech is very precious, and everyone may speak and write freely (but take responsibility for it) [Mirabeau/committee]
25. Social Practice / B. Equalities / 2. Political equality
All citizens are eligible for roles in the state, purely on the basis of merit [Mirabeau/committee]
25. Social Practice / C. Rights / 4. Property rights
Property is a sacred right, breached only when essential, and with fair compensation [Mirabeau/committee]
25. Social Practice / E. Policies / 4. Taxation
Everyone must contribute to the state's power and administration, in just proportion [Mirabeau/committee]
25. Social Practice / E. Policies / 5. Education / c. Teaching
Let your teacher be a god to you [Anon (Upan)]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
By knowing one piece of clay or gold, you know all of clay or gold [Anon (Upan)]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
Originally there must have been just Existence, which could not come from non-existence [Anon (Upan)]
28. God / A. Divine Nature / 1. God
Brahma, supreme god and protector of the universe, arose from the ocean of existence [Anon (Upan)]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
Brahman is the Uncaused Cause [Anon (Upan)]
28. God / C. Attitudes to God / 2. Pantheism
Earth, food, fire, sun are all forms of Brahman [Anon (Upan)]
29. Religion / A. Polytheistic Religion / 3. Hinduism
The gods are not worshipped for their own sake, but for the sake of the Self [Anon (Upan)]
A man with desires is continually reborn, until his desires are stilled [Anon (Upan)]
Damayata - be self-controlled! Datta - be charitable! Dayadhwam - be compassionate! [Anon (Upan)]
Those ignorant of Atman return as animals or plants, according to their merits [Anon (Upan)]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Charity and ritual observance distract from the highest good of religion [Anon (Upan)]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
Do not seek to know Brahman by arguments, for arguments are idle and vain [Anon (Upan)]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The immortal in us is the part that never sleeps, and shapes our dreams [Anon (Upan)]
The immortal Self and the sad individual self are like two golden birds perched on one tree [Anon (Upan)]