Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Prisoner's Dilemma' and 'Intro to Non-Classical Logic (1st ed)'

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35 ideas

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
Free logic is one of the few first-order non-classical logics [Priest,G]
     Full Idea: Free logic is an unusual example of a non-classical logic which is first-order.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], Pref)
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / a. Symbols of ST
X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets [Priest,G]
     Full Idea: X1 x X2 x X3... x Xn indicates the 'cartesian product' of those sets, the set of all the n-tuples with its first member in X1, its second in X2, and so on.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.0)
<a,b&62; is a set whose members occur in the order shown [Priest,G]
     Full Idea: <a,b> is a set whose members occur in the order shown; <x1,x2,x3, ..xn> is an 'n-tuple' ordered set.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10)
a ∈ X says a is an object in set X; a ∉ X says a is not in X [Priest,G]
     Full Idea: a ∈ X means that a is a member of the set X, that is, a is one of the objects in X. a ∉ X indicates that a is not in X.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
{x; A(x)} is a set of objects satisfying the condition A(x) [Priest,G]
     Full Idea: {x; A(x)} indicates a set of objects which satisfy the condition A(x).
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
{a1, a2, ...an} indicates that a set comprising just those objects [Priest,G]
     Full Idea: {a1, a2, ...an} indicates that the set comprises of just those objects.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
Φ indicates the empty set, which has no members [Priest,G]
     Full Idea: Φ indicates the empty set, which has no members
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
{a} is the 'singleton' set of a (not the object a itself) [Priest,G]
     Full Idea: {a} is the 'singleton' set of a, not to be confused with the object a itself.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
X⊂Y means set X is a 'proper subset' of set Y [Priest,G]
     Full Idea: X⊂Y means set X is a 'proper subset' of set Y (if and only if all of its members are members of Y, but some things in Y are not in X)
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
X⊆Y means set X is a 'subset' of set Y [Priest,G]
     Full Idea: X⊆Y means set X is a 'subset' of set Y (if and only if all of its members are members of Y).
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
X = Y means the set X equals the set Y [Priest,G]
     Full Idea: X = Y means the set X equals the set Y, which means they have the same members (i.e. X⊆Y and Y⊆X).
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
X ∩ Y indicates the 'intersection' of sets X and Y, the objects which are in both sets [Priest,G]
     Full Idea: X ∩ Y indicates the 'intersection' of sets X and Y, which is a set containing just those things that are in both X and Y.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
X∪Y indicates the 'union' of all the things in sets X and Y [Priest,G]
     Full Idea: X ∪ Y indicates the 'union' of sets X and Y, which is a set containing just those things that are in X or Y (or both).
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
Y - X is the 'relative complement' of X with respect to Y; the things in Y that are not in X [Priest,G]
     Full Idea: Y - X indicates the 'relative complement' of X with respect to Y, that is, all the things in Y that are not in X.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
The 'relative complement' is things in the second set not in the first [Priest,G]
     Full Idea: The 'relative complement' of one set with respect to another is the things in the second set that aren't in the first.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
The 'intersection' of two sets is a set of the things that are in both sets [Priest,G]
     Full Idea: The 'intersection' of two sets is a set containing the things that are in both sets.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
The 'union' of two sets is a set containing all the things in either of the sets [Priest,G]
     Full Idea: The 'union' of two sets is a set containing all the things in either of the sets
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.8)
The 'induction clause' says complex formulas retain the properties of their basic formulas [Priest,G]
     Full Idea: The 'induction clause' says that whenever one constructs more complex formulas out of formulas that have the property P, the resulting formulas will also have that property.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.2)
A 'singleton' is a set with only one member [Priest,G]
     Full Idea: A 'singleton' is a set with only one member.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
A 'member' of a set is one of the objects in the set [Priest,G]
     Full Idea: A 'member' of a set is one of the objects in the set.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order [Priest,G]
     Full Idea: An 'ordered pair' (or ordered n-tuple) is a set with its members in a particular order.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10)
A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets [Priest,G]
     Full Idea: A 'cartesian product' of sets is the set of all the n-tuples with one member in each of the sets.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.10)
A 'set' is a collection of objects [Priest,G]
     Full Idea: A 'set' is a collection of objects.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
The 'empty set' or 'null set' has no members [Priest,G]
     Full Idea: The 'empty set' or 'null set' is a set with no members.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.4)
A set is a 'subset' of another set if all of its members are in that set [Priest,G]
     Full Idea: A set is a 'subset' of another set if all of its members are in that set.
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
A 'proper subset' is smaller than the containing set [Priest,G]
     Full Idea: A set is a 'proper subset' of another set if some things in the large set are not in the smaller set
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
The empty set Φ is a subset of every set (including itself) [Priest,G]
     Full Idea: The empty set Φ is a subset of every set (including itself).
     From: Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.6)
23. Ethics / B. Contract Ethics / 1. Contractarianism
Self-interest can fairly divide a cake; first person cuts, second person chooses [Poundstone]
     Full Idea: To fairly divide a cake between two children, the first divides it and the second chooses. …Even division is best, as it anticipates the second child will take the largest piece. Fairness is enforced by the children's self-interests.
     From: William Poundstone (Prisoner's Dilemma [1992], 03 'Cake')
     A reaction: [compressed] This is introduced as the basic principle of game theory. There is an online video of two cats sharing a dish of milk; each one drinks a bit, then pushes the dish to the other one. I'm sure two children could manage that.
23. Ethics / B. Contract Ethics / 6. Game Theory
Formal game theory is about maximising or minimising numbers in tables [Poundstone]
     Full Idea: At the most abstract level, game theory is about tables with numbers in them - numbers that entities are are efficiently acting to maximise or minimise.
     From: William Poundstone (Prisoner's Dilemma [1992], 03 'Curve')
     A reaction: A brilliant idea. The question is the extent to which real life conforms to the numberical tables. The assumption that everyone is entirely self-seeking is blatantly false. Numbers like money have diminishing marginal utility.
The minimax theorem says a perfect game of opposed people always has a rational solution [Poundstone]
     Full Idea: The minimax theorem says that there is always a rational solution to a precisely defined conflict between two people whose interests are completely opposite.
     From: William Poundstone (Prisoner's Dilemma [1992], 03 'Minimax')
     A reaction: This is Von Neumann's founding theorem of game theory. It concerns maximising minimums, and minimising maximums. Crucially, I would say that it virtually never occurs that two people have completely opposite interests. There is a common good.
23. Ethics / B. Contract Ethics / 7. Prisoner's Dilemma
Two prisoners get the best result by being loyal, not by selfish betrayal [Poundstone]
     Full Idea: Prisoners A and B can support or betray one another. If both support, they each get 1 year in prison. If one betrays, the betrayer gets 0 and the betrayed gets 3. If they both betray they get 2 each. The common good is to support each other.
     From: William Poundstone (Prisoner's Dilemma [1992], 06 'Tucker's')
     A reaction: [by Albert Tucker, highly compressed] The classic Prisoner's Dilemma. It is artificial, but demonstrates that selfish behaviour gets a bad result (total of four years imprisonment), but the common good gets only two years. Every child should study this!
The tragedy in prisoner's dilemma is when two 'nice' players misread each other [Poundstone]
     Full Idea: The tragedy is when two 'nice' players defect because they misread the other's intentions. The puzzle of the prisoner's dilemma is how such good intentions pave the road to hell.
     From: William Poundstone (Prisoner's Dilemma [1992], 11 'Howard's')
     A reaction: I really wish these simple ideas were better known. They more or less encapsulate the tragedy of the human race, with its inability to prioritise the common good.
23. Ethics / B. Contract Ethics / 8. Contract Strategies
TIT FOR TAT says cooperate at first, then do what the other player does [Poundstone]
     Full Idea: The successful TIT FOR TAT strategy (for the iterated prisoner's dilemma) says cooperate on the first round, then do whatever the other player did in the previous round.
     From: William Poundstone (Prisoner's Dilemma [1992], 12 'TIT')
     A reaction: There are also the tougher TWO TITS FOR A TAT, and the more forgiving TIT FOR TWO TATS. The one-for-one seems to be the main winner, and is commonly seen in animal life (apparently). I recommend this to school teachers.
Do unto others as you would have them do unto you - or else! [Poundstone]
     Full Idea: TIT FOR TAT threatens 'Do unto others as you would have them do unto you - or else!'.
     From: William Poundstone (Prisoner's Dilemma [1992], 12 'TIT')
     A reaction: Essentially human happiness arises if we are all nice, but also stand up firmly for ourselves. 'Doormats' (nice all the time) get exploited. TIT FOR TAT is weak, because it doesn't exploit people who don't respond at all.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').