12 ideas
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| Full Idea: The 'undetected' or 'veiled' paradox of Eubulides says: if you know your father, and don't know the veiled person before you, but that person is your father, you both know and don't know the same person. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: Essentially an uninteresting equivocation on two senses of "know", but this paradox comes into its own when we try to give an account of how linguistic reference works. Frege's distinction of sense and reference tried to sort it out (Idea 4976). |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| Full Idea: The liar paradox of Eubulides says 'if you state that you are lying, and state the truth, then you are lying'. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.95) Don't say it, then. These kind of paradoxes of self-reference eventually lead to Russell's 'barber' paradox and his Theory of Types. |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| Full Idea: The 'sorites' paradox of Eubulides says: if you take one grain of sand from a heap (soros), what is left is still a heap; so no matter how many grains of sand you take one by one, the result is always a heap. | |
| From: report of Eubulides (fragments/reports [c.390 BCE]) by R.M. Dancy - Megarian School | |
| A reaction: (also Cic. Acad. 2.49) This is a very nice paradox, which goes to the heart of our bewilderment when we try to fully understand reality. It homes in on problems of identity, as best exemplified in the Ship of Theseus (Ideas 1212 + 1213). |
| 16643 | Accidents always remain suited to a subject [Bonaventura] |
| Full Idea: An accident's aptitudinal relationship to a subject is essential, and this is never taken away from accidents….for it is true to say that they are suited to a subject. | |
| From: Bonaventura (Commentary on Sentences [1252], IV.12.1.1.1c) | |
| A reaction: This is the compromise view that allows accidents to be separated, for Transubstantiation, while acknowledging that we identify them with their subjects. |
| 16696 | Successive things reduce to permanent things [Bonaventura] |
| Full Idea: Everything successive reduces to something permanent. | |
| From: Bonaventura (Commentary on Sentences [1252], II.2.1.1.3 ad 5), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.2 | |
| A reaction: Avicenna first took successive entities seriously, but Bonaventure and Aquinas seem to have rejected them, or given reductive accounts of them. It resembles modern actualists versus modal realists. |
| 22717 | 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. |
| 22718 | 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. |
| 22719 | 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. |
| 22720 | 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! |
| 22721 | 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. |
| 22722 | 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. |
| 22723 | 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. |