Combining Texts

All the ideas for 'The Upanishads', 'Alfred Tarski: life and logic' and 'The Good State'

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39 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
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 / A. Basis of a State / 3. Natural Values / c. Natural rights
Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling]
24. Political Theory / C. Ruling a State / 1. Social Power
Politics is driven by power cliques [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
It is essential for democracy that voting is free and well informed [Grayling]
Democracies should require a supermajority for major questions [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
A cap on time of service would restrict party control and career ambitions [Grayling]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
Majority decisions are only acceptable if the minority interests are not vital [Grayling]
25. Social Practice / B. Equalities / 1. Grounds of equality
Liberty and equality cannot be reconciled [Grayling]
25. Social Practice / D. Justice / 1. Basis of justice
The very concept of democracy entails a need for justice [Grayling]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
There should be separate legislative, executive and judicial institutions [Grayling]
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)]