*From*: Jlsperanza@xxxxxxx*To*: lit-ideas@xxxxxxxxxxxxx*Date*: Sun, 7 Jun 2009 13:46:21 EDT

In a message dated 6/7/2009 1:30:35 P.M. Eastern Daylight Time, wokshevs@xxxxxx writes: I take it that few of us would make love, or go fishing, or see the sunset (even in NL) or walk the dog, or any combination of the above, at a time when we recognize that a loved one or a stranger is in dire need of our aid. Many of our maxims are not consciously formulated priot to action. All of our rational actions, however, are maxim-guided (oder?) and all maxims remain open to moral assessment. Did Asha borrow the term from Jack (Rawls) ? ---- I would guess so. Asha Kasher is interested in the double force operating in the principle as a whole. BE COOPERATIVE. Notably for one of the categories -- the first: quantity (of information), Grice provides two: 1. MAXI -- be as informative as is required. 2. MINI do not be more informative than is required. Kasher thinks he can simplify things by appealing to a maximin redux that springs directly from rationality considerations. The same strategy followed by Hintikka in PGRICE, "Philosophical Grounds of Rationality: Intentions, Categories, Ends", but more in terms of game-theory. Stalnaker (MIT) has done even the same but along what he calls UTILITARIAN principles (and so closest to Jack Rawls). For some quotes in the OED: 1949 Econometrica 17 184 The policy of ‘minimax regret’..may..be a plausible description of the actual behaviour of some individuals. But individuals of different temperaments might follow different policies: e.g. ‘maximin complacency’. 1954 D. BLACKWELL & M. A. GIRSHICK Theory Games & Statist. Decisions i. 27 0 is called a maximin strategy for player I. 1957 R. D. LUCE & H. RAIFFA Games & Decisions iv. 81 A strategy which dictates choices c and g on moves 2 and 4, respectively, cannot be maximin for this game. 1972 J. RAWLS Theory of Justice §26. 152 The maximin rule tells us to rank alternatives by their worst possible outcomes. 1999 Nature 8 July 129/1 In a way, von Neumann was right. On the other hand, his own celebrated maximin theorem reduces to a corollary of Nash's existence proof. 1953 Amer. Econ. Rev. 43 399 The player is maximizing the minimum pay off, or ‘playing the maximin’. 1958 Engineering 21 Mar. 369/2 Player A will thus determine the smallest value in each row and choose the largest of these minima, the ‘maximin’. 1970 G. S. G. BEVERIDGE & R. S. SCHECHTER Optimization xii. 656 This result represents the mini-max theorem of von Neumann and Morgenstein [sic] (1953), which states that A's expected gain is at least P, and B's expected loss is at worst L, where P = L... The value of P (and L) lies between the row maxi-min and the column mini-max. [1928 J. VON NEUMANN in Mathematische Annalen C. 307 (heading) Beweis des Satzes Max Min = Min Max.] 1949 Bell Syst. Techn. Jrnl. 28 704 A ‘max min’ type of problem. 1955 Q. Jrnl. Econ. 69 103 Max-min Rule. Assume that whatever alternative is chosen, the worst possible outcome will ensue. 1961 Which? Nov. 277 (caption) Max-min speed switch. 1994 Proc. IEEE Internat. Conf. Neural Networks 7 4273 The FAM introduced by Kosko, which involves Max-Min composition units, is one of the most useful and important paradigms. 1950 Amer. Math. Monthly 57 511 The main theorem for such games is that there always exist optimal strategies for the two players, a strategy for the one player that maximizes his minimum expectation, and a strategy for the second player that minimizes his maximum risk, the max-min equaling the min-max. 1952 J. C. C. MCKINSEY Introd. Theory Games i. 19 Find the max min and min max of the two-finger Morra. 1991 Trans. Amer. Math. Soc. 325 492 The ‘ max-min’..is achieved for Fi := span{1.., i} and u := i. 1962 Ecology 43 543 Differences between the psychometric dry bulb thermometer and the *max-min thermometer inside the shelter are sometimes relatively great. 1985 Gardening from ‘Which?’ Dec. 388 (heading) Max/Min thermometer. 1990 Garden Answers Nov. 67/2 (advt.) A Max-Min thermometer is used all the year round, allowing you to keep an eye on the peaks of heat and depths of cold. 1917 Trans. Amer. Math. Soc. 18 240 If J0 is the value of J at a point P0 and if the inequality J < J0 - where is small and positive defines more than one region near the point P0, then P0 will be called a point of minimax. 1931 Amer. Jrnl. Math. 53 169 It has been proved..that (x,y) possesses a minimax at each of the libration points L1, L2 and L3 and it accordingly follows that (x,y) must have an absolute minimum at L4 and L5. 1958 Engineering 21 Mar. 369/2 Player B, on the other hand, will determine the largest value in each column, and the smallest of these, the ‘minimax’ . 1962 Sci. Amer. Dec. 114/2 Both firms were guided by the principle of the minimax, choosing the best of the worst outcomes. 1968 Brit. Med. Bull. 24 232/2 This would be the Bayesian Strategy of decision theory.., but other strategies, such as minimax or restricted Bayes, could also be used. 1970 G. S. G. BEVERIDGE & R. S. SCHECHTER Optimization xii. 656 The value of P (and L) lies between the row maxi-min and the column mini-max. 1996 Economist 30 Mar. 96/2 At the other extreme, a hypercautious government would prefer ‘minimax’the minimum of maximums. 1917 G. D. BIRKHOFF in Proc. National Acad. Sci. U.S.A. 3 315 Another method may be employed to find a large class of stable periodic orbits which I call of minimax type. 1935 Amer. Jrnl. Math. 57 930 The minimum and minimax methods..establish immediately the existence of an infinite number of closed periodic orbits. 1945 Ann. Math. 41 419 The critical limits, such as absolute minima, relative minima, minimax values, etc., are in general infinite in number. 1938 Amer. Jrnl. Math. 60 831 Let r be any integer such that H(r + 1) assumes the maximum of H(m). The R(n)-block [r + 1, r + R(n)] will then be termed a minimax n-covering in (a). 1940 Amer. Jrnl. Math. 62 237 Let sn denote a value of s for which the maximum diameter of the sets Gs[te(n)] is a minimum,..and let this minimax diameter be d(n). 1951 Ann. Math. Statistics 22 466 The minimax risk is (1 - a). 1990 Glasgow Math. Jrnl. 32 267 If G is a finitely generated soluble-by-finite group of finite rank, then G is a finite extension of a soluble minimax group. 1952 Ann. Math. Statistics 23 587 For such weight functions the supremum of the risk over all is infinite for every decision function, so that every decision function is minimax. 1970 R. B. ASH Basic Probability Theory viii. 250 It is immediate from the definition of admissibility that an admissible test with constant risk (i.e., = ) is minimax. 1947 A. WALD in Econometrica 15 283 An element a0 in A is said to be a minimax strategy of player 1 if InfbK(a, b) takes its maximum value with respect to a for a = a0. 1949 Econometrica 17 230 Often Nature's strategy is completely unknown. In that case Wald suggests that the statistician play a minimax strategy: that is, the statistician should select that decision procedure which minimizes the maximum risk. 1957 R. D. LUCE & H. RAIFFA Games & Decisions i. 2 Although Borel gave a clear statement of an important class of game theoretic problems and introduced the concepts of pure and mixed strategies, von Neumann points out that he did not obtain one crucial resultthe minimax theoremwithout which no theory of games can be said to exist. 1978 M. JEVONS Murder at Margin xiv. 138 If two people are charged with a crime and are separated by the police with no chance of their communicating, there are certain circumstances in which it would be rational for them to confesseven if they did not commit the crime. In economics this is called a minimax strategy. 1993 Personal Computer World July 539/1 Many of the best cognitive games programs have a mini-max algorithm lurking somewhere or other in their innards. 1957 Jrnl. Soc. Industr. & Appl. Math. 5 109 Our formulation of the problem includes the possibility of minimaxing some measure of inaccuracy. 1957 Jrnl. Soc. Industr. & Appl. Math. 5 121 The loss L which is to be minimaxed is the number of observations required before stopping. 1964 J. GOULD & W. L. KOLB Dict. Social Sci. 573/2 The goal may be assumed to take the form of maximizing (or, in game theory, minimaxing) the expected value, over some time interval, of a utility function. 1985 Ann. Statistics 13 1094 The statistical problem of minimaxing V(,f) over r × is meaningless unless the least informative member F0 has positive information. 1949 Amer. Econ. Rev. 39 205 Minimaxing the loss or, as I would prefer to put it, maximining profits. 1953 Amer. Econ. Rev. 43 402 The Nash definition yields the same saddle-point solution that is implied by the von Neumann-Morgenstern solution concept (i.e., it corresponds to both players maximining). 1973 Philos. Q. 23 248 He thinks that POPs would, in choosing their principles, ‘maximin’that is to say, choose which has the best worst outcome. 1949 Econometrica 17 183 Maximining of income..implies the ‘pessimistic’ expectation that nature will always tend to produce the situation most adverse to the operator and the ‘cautious’ unwillingness to take a chance about it. 1973 Philos. Q. 23 184 This maximining approach often has authoritarian results, coercion being justified where this secures a higher lowest. 1977 Jrnl. Econ. Lit. 15 512 Hare writes that ‘this justifies only insurance, not maximining’. 1957 Rev. Econ. Stud. 25 2 In the two-person zero-sum game the process called minimaxing ensures a payoff of a certain size. 1973 Nature 23 Feb. 507/1 The fundamental mechanism underlying all this work [on machines designed to play games] has been a cycle of processes: lookahead, evaluation and minimaxing. 1984 P. H. WINSTON Artificial Intelligence (ed. 2) iv. 117 Note that the whole idea of minimaxing rests on the translation of board goodness into a single number, the static value. 1968 Listener 4 Apr. 438/1 Just like that 50-50 combination of heads and tails, the minimaxing peasant might pick a 40-60 combination of wheat and millet. Cheers, J. L. Speranza Buenos Aires, Argentina **************We found the real ‘Hotel California’ and the ‘Seinfeld’ diner. What will you find? Explore WhereItsAt.com. 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