17 ideas
| 13536 | Skolem did not believe in the existence of uncountable sets [Skolem] |
| Full Idea: Skolem did not believe in the existence of uncountable sets. | |
| From: Thoralf Skolem (works [1920], 5.3) | |
| A reaction: Kit Fine refers somewhere to 'unrepentent Skolemites' who still hold this view. |
| 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. |
| 8388 | Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley] |
| Full Idea: The main approaches to causation I shall refer to as direct realism, Humean reductionism, non-Humean reductionism, and indirect or theoretical realism. | |
| From: Michael Tooley (Causation and Supervenience [2003], 2) | |
| A reaction: The first simply observes causation (Anscombe), the second reduces it to regularity (Hume), the third reduces it to other natural features (Fair, Salmon, Dowe), the fourth takes an instrumental approach (Armstrong, Tooley). I favour the third approach. |
| 8389 | Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley] |
| Full Idea: The three main distinctions concerning causation are between reductionism and realism; between Humean and non-Humean states of affairs; and between states that are immediately observable and those that are not. | |
| From: Michael Tooley (Causation and Supervenience [2003], 2) | |
| A reaction: I favour reductionism over realism, because I like the question 'If x is real, what is it made of?' I favour non-Humean states of affairs, because I think constant conjunction is very superficial. I presume the existence of non-observable components. |
| 8393 | We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley] |
| Full Idea: A reductionist can hold that the direction of causation is to be defined in terms of the direction of time; but this response is only available if one is prepared to adopt a realist view of the direction of time. | |
| From: Michael Tooley (Causation and Supervenience [2003], 4.2.1.2) | |
| A reaction: A nice illustration of the problems that arise if we try to be reductionist about everything. Personally I prefer my realism to be about time rather than about causation. Time, I would say, makes causation possible, not the other way around. |
| 8390 | Causation is directly observable in pressure on one's body, and in willed action [Tooley] |
| Full Idea: The arguments in favour of causation being observable appeal especially to the impression of pressure upon one's body, and to one's introspective awareness of willing, together with the perception of the event which one willed. | |
| From: Michael Tooley (Causation and Supervenience [2003], 3) | |
| A reaction: [He cites Evan Fagels] Anscombe also cites words which have causality built into their meaning. This would approach would give priority to mental causation, and would need to demonstrate that similar things happen out in the world. |
| 8392 | Probabilist laws are compatible with effects always or never happening [Tooley] |
| Full Idea: If laws of causation are probabilistic then the law does not entail any restrictions upon the proportion of events that follow a cause: ...it can have absolutely any value from zero to one. | |
| From: Michael Tooley (Causation and Supervenience [2003], 4.1.3) | |
| A reaction: This objection applies to an account of laws of nature, and also to definitions of causes as events which increase probabilities. One needn't be fully committed to natural necessity, but it must form some part of the account. |
| 8399 | The actual cause may not be the most efficacious one [Tooley] |
| Full Idea: A given type of state may be causally efficacious, but not as efficacious as an alternative states, so it is not true that even a direct cause need raise the probability of its effect. | |
| From: Michael Tooley (Causation and Supervenience [2003], 6.2.4) | |
| A reaction: My intuition is that explaining causation in terms of probabilities entirely misses the point, which mainly concerns explaining the sense of necessitation in a cause. This idea give me a good reason for my intuition. |
| 8391 | In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley] |
| Full Idea: If a counterfactual holds in a possible world, that is presumably because a law holds in that world, which means there could be basic causal laws that lack all instances. But then causal laws cannot be totally supervenient on the history of the universe. | |
| From: Michael Tooley (Causation and Supervenience [2003], 4.1.2) | |
| A reaction: A nice argument, which sounds like trouble for Lewis. One could deny that the laws have to hold in the counterfactual worlds, but then we wouldn't be able to conceive them. |
| 8394 | Explaining causation in terms of laws can't explain the direction of causation [Tooley] |
| Full Idea: The most serious objection to any account of causation in terms of nomological relations alone is that it can't provide any account of the direction of causation. | |
| From: Michael Tooley (Causation and Supervenience [2003], 5.1) | |
| A reaction: Cf. Idea 8393. I am not convinced that there could be an 'account' of the direction of causation, so I am inclined to take it as given. If we take 'powers' (active properties) as basic, they would have a direction built into them. |
| 8398 | Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley] |
| Full Idea: Against the view that causation is a particular physical process, might it not be argued that the concept of causation is the concept of a relation that possesses a certain intrinsic nature, so that causation must be the same in all possible worlds? | |
| From: Michael Tooley (Causation and Supervenience [2003], 5.4) | |
| A reaction: This makes the Humean assumption that laws of nature might be wildly different. I think it is perfectly possible that physical processes are the only way that causation could occur. Alternatively, the generic definition of 'cause' is just very vague. |