PDF Archive search engine
Last database update: 17 October at 15:17 - Around 76000 files indexed.
Fool Me Once: Can Indifference Vindicate Induction? Roger White (2015) sketches an ingenious new solution to the problem of induction. It argues on a priori grounds that the world is more likely to be inductionfriendly than inductionunfriendly. The argument relies primarily on the principle of indifference, and, somewhat surprisingly, assumes little else. If inductive methods could be vindicated in anything like this way, it would be quite a groundbreaking result. But there are grounds for pessimism about the envisaged approach. This paper shows that in the crucial test cases White concentrates on, the principle of indifference actually renders induction no more accurate than random guessing. It then diagnoses why the indifferencebased argument seems so intuitively compelling, despite being ultimately unsound. 1 An IndifferenceBased Strategy White begins by imagining that we are “apprentice demons” tasked with devising an inductionunfriendly world – a world where inductive methods tend to be unreliable. To simplify, we imagine that there is a single binary variable that we control (such as whether the sun rises over a series of consecutive days). So, in essence, the task is to construct a binary sequence such that – if the sequence were revealed one bit at a time – an inductive reasoner would fare poorly at predicting its future bits. This task, it turns out, is surprisingly difficult. To see this, it will be instructive to consider several possible strategies for constructing a sequence that would frustrate an ideal inductive predictor. Immediately, it is clear that we should avoid uniformly patterned sequences, such as: 00000000000000000000000000000000 or 01010101010101010101010101010101. 1 Sequences like these are quite kind to induction. Our inductive reasoner would quickly latch onto the obvious patterns these sequences exhibit. A more promising approach, it might seem, is to build an apparently patternless sequence: 00101010011111000011100010010100 But, importantly, while induction will not be particularly reliable at predicting the terms of this sequence, it will not be particularly unreliable here either. Induction would simply be silent about what a sequence like this contains. As White puts it, “ In order for... induction to be applied, our data must contain a salient regularity of a reasonable length” (p. 285). When no pattern whatsoever can be discerned, presumably, induction is silent. (We will assume that the inductive predictor is permitted to suspend judgment whenever she wishes.) The original aim was not to produce an inductionneutral sequence, but to produce a sequence that elicits errors from induction. So an entirely patternless sequence will not suffice. Instead, the inductionunfriendly sequence will have to be more devious, building up seeming patterns and then violating them. As a first pass, we can try this: 00000000000000000000000000000001 Of course, this precise sequence is relatively friendly to induction. While our inductive predictor will undoubtedly botch her prediction of the final bit, it is clear that she will be able to amass a long string of successes prior to that point. So, on balance, the above sequence is quite kind to induction – though not maximally so. In order to render induction unreliable, we will need to elicit more errors than correct predictions. We might try to achieve this as follows: 00001111000011110000111100001111 2 The idea here is to offer up just enough of a pattern to warrant an inductive prediction, before pulling the rug out – and then to repeat the same trick again and again. Of course, this precise sequence would not necessarily be the way to render induction unreliable: For, even if we did manage to elicit an error or two from our inductive predictor early on, it seems clear that she would eventually catch on to the exceptionless higherorder pattern governing the behavior of the sequence. The upshot of these observations is not that constructing an inductionunfriendly sequence is impossible. As White points out, constructing such a sequence should be possible, given any complete description of how exactly induction works (p. 287). Nonetheless, even if there are a few special sequences that can frustrate induction, it seems clear that such sequences are fairly few and far between. In contrast, it is obviously very easy to corroborate induction (i.e. to construct a sequence rendering it thoroughly reliable). So induction is relatively unfrustrateable. And it is worth noting that this property is fairly specific to induction. For example, consider an inferential method based on the gambler’s fallacy, which advises one to predict whichever outcome has occurred less often, overall. It would be quite easy to frustrate this method thoroughly (e.g. 00000000…). So far, we have identified a highly suggestive feature of induction. To put things roughly, it can seem that: * Over a large number of sequences, induction is thoroughly reliable. * Over a large number of sequences, induction is silent (and hence, neither reliable nor unreliable). * Over a very small number of sequences (i.e. those specifically designed to thwart induction), induction is unreliable (though, even in these cases, induction is still silent much of the time). 3 Viewed from this angle, it can seem reasonable to conclude that there are a priori grounds for confidence that an arbitrary sequence is not inductionunfriendly. After all, there seem to be far more inductionfriendly sequences than inductionunfriendly ones. If we assign equal probability to every possible sequence, then the probability that an arbitrary sequence will be inductionfriendly is going to be significantly higher than the probability that it will be inductionunfriendly. So a simple appeal to the principle of indifference seems to generate the happy verdict that induction can be expected to be more reliable than not, at least in the case of binary sequences. Moreover, as White points out, the general strategy is not limited to binary sequences. If we can show a priori that induction over a binary sequence is unlikely to be inductionunfriendly, then it’s plausible that a similar kind of argument can be used to show that we are justified in assuming that an arbitrary world is not inductionunfriendly. If true, this would serve to fully vindicate induction. 2 Given Indifference, Induction Is not Reliable However, there are grounds for pessimism about whether the strategy is successful even in the simple case of binary sequences. Suppose that, as a special promotion, a casino decided to offer Fair Roulette. The game involves betting $1 on a particular color – black or red – and then spinning a wheel, which is entirely half red and half black. If wrong, you lose your dollar; if right, you get your dollar back and gain another. If it were really true that induction can be expected to be more reliable than not over binary sequences, it would seem to follow that induction can serve as a winning strategy, over the long term, in Fair Roulette. After all, multiple spins of the wheel produce a binary sequence of reds and blacks. And all possible sequences are 4 equally probable. Of course, induction cannot be used to win at Fair Roulette – past occurrences of red, for example, are not evidence that the next spin is more likely to be red. This suggests that something is amiss. Indeed, it turns out that no inferential method – whether inductive or otherwise – can possibly be expected to be reliable at predicting unseen bits of a binary sequence, if the principle of indifference is assumed. This can be shown as follows. Let S be an unknown binary sequence of length n. S is to be revealed one bit at a time, starting with the first. S: ? ? ? ? ? ? … ? :S n bits Let f be an arbitrary predictive function that takes as input any initial subsequence of S and outputs a prediction for the next bit: ‘0’, ‘1’, or ‘suspend judgment’. A predictive function’s accuracy is measured as follows: +1 for each correct prediction; 1 for each incorrect prediction; 0 each time ‘suspend judgment’ occurs. (So the maximum accuracy of a function is n; the minimum score is –n.) Given a probability distribution over all possible sequences, the expected accuracy of a predictive function is the average of its possible scores weighted by their respective probabilities. Claim: If we assume indifference (i.e. if we assign equal probability to every possible sequence), then – no matter what S is – each of f’s predictions will be expected to contribute 0 to f’s accuracy. And, as a consequence of this, f has 0 expected accuracy more generally. Proof: For some initial subsequences, f will output ‘suspend judgment’. The contribution of such predictions will inevitably be 0. So we need consider only those cases where f makes a firm prediction (i.e. ‘0’ or ‘1’; not ‘suspend judgment’). Let K be a klength initial subsequence for which f makes a firm prediction about the bit in 5
1) deliberate indifference and clearly unreasonable acts and omissions that created a hostile educational environment for students before a sexual assault by a fellow student by conduct and policies making a student more vulnerable to sexual assault itself;
29 June/ 12 July 2010 memory of the Holy Apostles Peter and Paul Presbyter Fr. Pedro Luiz Anacleto dos Santos Junior Tel. +30 6988 975 751 Email : email@example.com To: His Eminence Metropolitan (G.O.C.) Kyr kyr Kirykos. Your Eminence, It is to my great sorrow to note that until now You have not answered my letter from 28 Feb. (O.C.)/ 13 Mar. (N.C.), which shows Your Eminence’s indifference and contempt towards my humbleness. For which reasons You display such indifference, the Lord knows. Since, however, the themes and problems, which I set forth in my above‐ mentioned letter to You, arise in Your letter to my humbleness and touch upon issues concerning the Faith of the Orthodox Church handed down and sealed by the Holy Fathers and because Your teachings, positions, views and actions deviate from this, for this reason, I am obligated to not silence myself, but to mention and clarify the below: 1.
devoid of humane feelings.” And digging deeper, “Humane” is described by Merriam-Webster as “marked by compassion, sympathy, or consideration for humans or animals.” Google.com defines Cruelty as, “Callous indifference to or pleasure in causing pain and suffering” and “behavior that causes physical or mental harm to another… whether intentionally or not.” So, combining these definitions we can fully define a cruel person as:
- Indifference to native people shows again;
Many of the issues identified appear to be a result of in-experience or indifference and certainly a lack of any desire to perform even average workmanship.
Anaka has conveyed her political position, and it is one of indifference. As long as her principles are followed in general within the socioeconomic frameworks humanity organizes itself into, then she has no objections to such systems.
A Life of Metropolitan Philaret of New York Written by Vladimir Moss Early Years Metropolitan Philaret, in the world George Nikolayevich Voznesensky, was born in the city of Kursk on March 22 / April 4, 1903, into the family of Protopriest Nicholas. In 1909 the family moved to Blagoveschensk‐on‐Amur in the Far East, where the future hierarch finished high school. In a sermon at his nomination as Bishop of Brisbane, the future metropolitan said: “There is hardly anything specially worthy of note in my life, in its childhood and young years, except, perhaps, a recollection from my early childhood years, when I as a small child of six or seven years in a childishly naïve way loved to ‘play service’ – I made myself a likeness of a Church vestment and ‘served’. And when my parents began to forbid me to do this, Vladyka Evgeny, the Bishop of Blagoveschensk, after watching this ‘service’ of mine at home, to their amazement firmly stopped them: ‘Leave him, let the boy “serve” in his own way. It is good that he loves the service of God.’” In this way was the saint’s future service in the Church foretold in a hidden way already in his childhood. In 1920 the family was forced to flee from the revolution into Manchuria, to the city of Harbin. There, in 1921, George’s mother, Lydia Vasilievna, died, after which his father, Fr. Nicholas, took the monastic tonsure with the name Demetrius and became Archbishop of Hailar. Vladyka Demetrius was a learned theologian, the author of a series of books on the history of the Church and other subjects. In 1927 George graduated from the Russo‐Chinese Polytechnical institute and received a specialist qualification as an engineer‐electrical mechanic. Later, when he was already First Hierarch of the Russian Church Outside Russia (ROCOR), he did not forget his friends at the institute. All those who had known him, both at school and in the institute, remembered him as a kind, affectionate comrade. He was distinguished by his great abilities and was always ready to help. After the institute he got a job as a teacher; he was a good instructor, and his pupils loved and valued him. But his instructions for the young people went beyond the bounds of the school programme and penetrated every aspect of human life. Many of his former pupils and colleagues after meeting him retained a high estimate of him for the rest of their lives. Living in the family of a priest, the future metropolitan naturally became accustomed, from his early years, to the church and the Divine services. But, as he himself said later, at the beginning there was in this “almost nothing deep, inwardly apprehended and consciously accepted”. “But the Lord knows how to touch the human soul!” he recalled. “And I undoubtedly see this caring touch of the Father’s right hand in the way in which, during my student years in Harbin, I was struck as if with a thunderclap by the words of the Hierarch Ignatius Brianchaninov which I read in his works: ‘My grave! Why do I forget you? You are waiting for me, waiting, and I will certainly be your inhabitant; why then do I forget you and behave as if the grave were the lot only of other men, and not of myself?’ Only he who has lived through this ‘spiritual blow’, if I can express myself thus, will understand me now! There began to shine before the young student as it were a blinding light, the light of a true, real Christian understanding of life and death, of the meaning of life and the significance of death – and new inner life began… Everything secular, everything ‘worldly’ lost its interest in my eyes, it disappeared somewhere and was replaced by a different content of life. And the final result of this inner change was my acceptance of monasticism…” In 1931 George completed his studies in Pastoral Theology in what was later renamed the theological faculty of the Holy Prince Vladimir Institute. In this faculty he became a teacher of the New Testament, pastoral theology and homiletics. In 1936 his book, Outline of the Law of God, was published in Harbin. In 1930 he was ordained to the diaconate, and in 1931 – to the priesthood, serving as the priest George. In the same year he was tonsured into monasticism with the name Philaret in honour of Righteous Philaret the Merciful. In 1933 he was raised to the rank of igumen, and in 1937 ‐ to the rank of archimandrite. “Man thinks much, he dreams about much and he strives for much,” he said in one of his sermons, “and nearly always he achieves nothing in his life. But nobody will escape the Terrible Judgement of Christ. Not in vain did the Wise man once say: ‘Remember your last days, and you will not sin to the ages!’ If we remember how our earthly life will end and what will be demanded of it after that, we shall always live as a Christian should live. A pupil who is faced with a difficult and critical examination will not forget about it but will remember it all the time and will try to prepare him‐ or herself for it. But this examination will be terrible because it will be an examination of our whole life, both inner and outer. Moreover, after this examination there will be no re‐examination. This is that terrible reply by which the lot of man will be determined for immeasurable eternity… Although the Lord Jesus Christ is very merciful, He is also just. Of course, the Spirit of Christ overflows with love, which came down to earth and gave itself completely for the salvation of man. But it will be terrible at the Terrible Judgement for those who will see that they have not made use of the Great Sacrifice of Love incarnate, but have rejected it. Remember your end, man, and you will not sin to the ages.” In his early years as a priest, Fr. Philaret was greatly helped by the advice of the then First‐Hierarch of ROCOR, Metropolitan Anthony (+1936), with whom he corresponded for several years. He also studied the writings of the holy fathers, and learned by heart all four Gospels. One of his favourite passages of Scripture was the passage from the Apocalypse reproaching the lukewarmness of men, their indifference to the truth. Thus in a sermon on the Sunday of All Saints he said: “The Orthodox Church is now glorifying all those who have pleased God, all the saints…, who accepted the holy word of Christ not as something written somewhere to someone for somebody, but as written to himself; they accepted it, took it as the guide for the whole of their life and fulfilled the commandments of Christ. “… Of course, their life and exploit is for us edification, they are an example for us, but you yourselves know with what examples life is now filled! Do we now see many good examples of the Christian life?!…. When you see what is happening in the world,… you involuntarily think that a man with a real Orthodox Christian intention is as it were in a desert in the midst of the earth’s teeming millions. They all live differently… Do you they think about what awaits them? Do they think that Christ has given us commandments, not in order that we should ignore them, but in order that we should try to live as the Church teaches. “…. We have brought forward here one passage from the Apocalypse, in which the Lord says to one of the servers of the Church: ‘I know your works: you are neither cold nor hot. Oh if only you were cold or hot!” We must not only be hot, but must at least follow the promptings of the soul and fulfil the law of God. “But there are those who go against it… But if a man is not sleeping spiritually, is not dozing, but is experiencing something spiritual somehow, and if he does not believe in what people are now doing in life, and is sorrowful about this, but is in any case not dozing, not sleeping – there is hope that he will come to the Church. Do we not see quite a few examples of enemies and deniers of God turning to the way of truth? Beginning with the Apostle Paul… “In the Apocalypse the Lord says: ‘Oh if only thou wast cold or hot, but since thou art neither cold nor hot (but lukewarm), I will spew thee out of My mouth’… This is what the Lord says about those who are indifferent to His holy work. Now, in actual fact, they do not even think about this. What are people now not interested in, what do they not stuff into their heads – but they have forgotten the law of God. Sometimes they say beautiful words. But what can words do when they are from a person of abominable falsehood?!… It is necessary to beseech the Lord God that the Lord teach us His holy law, as it behoves us, and teach us to imitate the example of those people have accepted this law, have fulfilled it and have, here on earth, glorified Almighty God.” Fr. Philaret was very active in ecclesiastical and pastoral‐preaching work. Already in the first years of his priesthood he attracted many people seeking the spiritual path. The Divine services which he performed with burning faith, and his inspired sermons brought together worshippers and filled the churches. Multitudes pressed to the church in which Fr. Philaret was serving. All sections of the population of Harbin loved him; his name was also known far beyond the boundaries of the Harbin diocese. He was kind and accessible to all those who turned to him. Queues of people thirsting to talk with him stood at the doors of his humble cell; on going to him, people knew that they would receive correct advice, consolation and help. Fr. Philaret immediately understood the condition of a man’s soul, and, in giving advice, consoled the suffering, strengthened the despondent and cheered up the despairing with an innocent joke. He loved to say: “Do not be despondent, Christian soul! There is no place for despondency in a believer! Look ahead – there is the mercy of God!” People went away from him pacified and strengthened by his strong faith. In imitation of his name‐saint, Fr. Philaret was generous not only in spiritual, but also in material alms, and secretly gave help to the needy. Many
since the female sex were fared for by the men they had chivalrously enslaved, of course, r-selection (associated with such traits as the low-grade, low-distribution pre-psychopathy seen in women, callousness, indifference, obliviousness, and a tendency to overexaggerate out of narcissism their perceptiveness and overstate the importance of their feelings based on intensity alone, rather than actual significance;
Even though initially the USA showed a certain indifference about it, in a matter of days, the press reflected the concern of the Americans in relation to the launch of the Sputnik.