14 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 15148 | Powers give explanations, without being necessary for some class membership [Chakravartty] |
| Full Idea: Powers explain behaviours regardless of whether they are necessary for membership in a particular class of things. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 3) | |
| A reaction: This seems right, and is important for driving a wedge between powers and essences. If there are essences, they are not simply some bunch of powers. |
| 15145 | A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty] |
| Full Idea: The modern concept of a kind essence is a set of intrinsic properties that are individually necessary and jointly sufficient for the membership of something in a class of things, or 'kind'. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 2) | |
| A reaction: I am always struck by the problem that the kind itself is constructed from the individuals, so circularity always seems to loom. |
| 15147 | Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty] |
| Full Idea: The fact that members of some cluster kinds are subjects of causal generalizations reflects the degree to which they share causally efficacious properties, not the fact that they may be composed of essence kinds per se. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 2) | |
| A reaction: I think this is right. I am a fan of individual essences, but not of kind essences. I take kinds, and kind explanations, to be straightforward inductive generalisations from individuals. Extreme stabilities give the illusion of a kind essence. |
| 15144 | Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty] |
| Full Idea: Scientific practices such as prediction and explanation regarding causal phenomena are concerned not merely with kinds having essences, but also with kinds lacking them. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 1) | |
| A reaction: Not quite clear what he has in mind, but explanation should certainly involve a coherent picture, and not just the citation of some underlying causal mechanism. |
| 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. |
| 15146 | Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty] |
| Full Idea: Many of the kinds we theorize about and experiment on today simply do not have essences. We can distinguish 'essence kinds', such as electrons, and 'cluster kinds', such as biological species. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 2) | |
| A reaction: This is an important point for essentialists. He offers a strict criterion, in Idea 15145, for mind membership, but we might allow species to have essences by just relaxing the criteria a bit, and acknowledging some vagueness, especially over time. |
| 15151 | Many causal laws do not refer to kinds, but only to properties [Chakravartty] |
| Full Idea: Causal laws often do not make reference to kinds of objects at all, but rather summarize relations between quantitative, causally efficacious properties of objects. | |
| From: Anjan Chakravarrty (Inessential Aristotle: Powers without Essences [2012], 3) | |
| A reaction: This would only be a serious challenge if it was not possible to translate talk of properties into talk of kinds, and vice versa. |