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CanIndifferenceVindicateInduction 100%

    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 

https://www.pdf-archive.com/2017/02/19/canindifferencevindicateinduction/

19/02/2017 www.pdf-archive.com

FoolMeOnce 99%

Can Indifference Vindicate Induction?

https://www.pdf-archive.com/2017/02/19/foolmeonce/

19/02/2017 www.pdf-archive.com

Household Induction Cooktops Market 99%

Executive Summary (1/2) Knowledge Based Value (KBV) Research Household Induction Cooktops Market Full Report:

https://www.pdf-archive.com/2017/09/06/household-induction-cooktops-market/

06/09/2017 www.pdf-archive.com

DMSUnit4 99%

7 Hours  Mathematical Induction  The Well Ordering Principle  Mathematical Induction  Recursive Definitions Page 39 DISCRETE MATHEMATICAL STRUCTURES UNIT IV 10CS34 6 H ours Properties of the Integers MATHEMATICAL INDUCTION:

https://www.pdf-archive.com/2015/08/23/dmsunit4/

23/08/2015 www.pdf-archive.com

Global Induction Cookware Industry 99%

2017 Market Research Report on Global Induction Cookware Industry www.orbisresearch.com;

https://www.pdf-archive.com/2017/11/15/global-induction-cookware-industry/

15/11/2017 www.pdf-archive.com

to james anderson 98%

(I have plenty of excess time over winter break.) I have first read your paper, “Secular Responses to the Problem of Induction,” and I find it both helpful and largely agreeable.

https://www.pdf-archive.com/2010/12/18/to-james-anderson/

18/12/2010 www.pdf-archive.com

debate response 98%

Bolt’s claim that the existence of a supernatural creator-deity is the only satisfactory solution to the infamous problem of induction.

https://www.pdf-archive.com/2010/10/21/debate-response/

21/10/2010 www.pdf-archive.com

debate response 98%

Bolt’s claim that the existence of a supernatural creator-deity is the only satisfactory solution to the infamous problem of induction.

https://www.pdf-archive.com/2010/10/21/debate-response-1/

21/10/2010 www.pdf-archive.com

Bottle, Induction Cap and Heat Sealer Machine - Enerconind 98%

Latest News a +44 (0) 1296 330 542 f Introducing Enercon Our Products Find Out More Our Distributors Contact Us Induction Cap Sealer Machines Our Products Induction Cap Sealers c Top Belt Sealing c Sentri System c Adjustable Stand c An induction cap sealer creates hermetic seals to prevent leaks, preserve product freshness and provide tamper evident packaging.

https://www.pdf-archive.com/2015/05/23/bottle-induction-cap-and-heat-sealer-machine-enerconind/

23/05/2015 www.pdf-archive.com

industrial process induction heating furnaces1025 97%

industrial process induction heating furnaces Industrial process induction heating furnaces are insulated enclosures designed to deliver heat to loads for many forms of induction heating processing.

https://www.pdf-archive.com/2014/08/28/industrial-process-induction-heating-furnaces1025/

28/08/2014 www.pdf-archive.com

why choose induction melting furnace1718 96%

why choose induction melting furnace If you are using an Induction Melting Furnace, you are already facing all the benefits it is to deal.

https://www.pdf-archive.com/2014/08/27/why-choose-induction-melting-furnace1718/

27/08/2014 www.pdf-archive.com

high frequency induction heating treatment1035 96%

high frequency induction heating treatment Solid state converters for induction heating are built with different types of switches depending on frequency range:

https://www.pdf-archive.com/2014/08/28/high-frequency-induction-heating-treatment1035/

28/08/2014 www.pdf-archive.com

38I16-IJAET0916903 v6 iss4 1775to1787 95%

In this paper, assessments of interconnection of Doubly-Fed Induction Generator (DFIG), Self-Excited Induction Generator (SEIG) and Hydro-Governor Synchronous Generator with various loads like R, L, C, RL, RLC are discussed.

https://www.pdf-archive.com/2014/07/04/38i16-ijaet0916903-v6-iss4-1775to1787/

04/07/2014 www.pdf-archive.com

IJETR2166 94%

2321-0869 (O) 2454-4698 (P), Volume-7, Issue-5, May 2017 The Amalgamation Performance Analysis of the LCI and VSI Fed Induction Motor Drive Shashank Kumar Singh, Mr.

https://www.pdf-archive.com/2017/09/09/ijetr2166/

09/09/2017 www.pdf-archive.com

the fast and clean induction1490 94%

the fast and clean induction We are blessed with a number of improved and useful devices and systems that have changed our life.

https://www.pdf-archive.com/2014/08/27/the-fast-and-clean-induction1490/

27/08/2014 www.pdf-archive.com

NFMUSICHOF 2019 INDUCTION CRITERIA 93%

Selected inductees are announced, inducted and awarded at NFMusicHOF’s Induction Gala to be held annually.      Nomination Criteria The NFMusicHOF encourages nominations/applications from all genres of music, as well as, businesses and individuals that have had a significant impact on both the local music scene and the music industry in general.

https://www.pdf-archive.com/2019/03/04/nfmusichof-2019-induction-criteria/

04/03/2019 www.pdf-archive.com

33I17-IJAET1117374 v6 iss5 2253-2261 93%

22311963 SPEED CONTROL OF INDUCTION MOTORS USING HYBRID PI PLUS FUZZY CONTROLLER Gauri V.

https://www.pdf-archive.com/2014/07/04/33i17-ijaet1117374-v6-iss5-2253-2261/

04/07/2014 www.pdf-archive.com

40I14-IJAET0514312 v6 iss2 920to931 93%

2231-1963 PERFORMANCE OF INDUCTION MOTOR USING HYSTERESIS BAND PWM CONTROLLER Srinivasa Rao Jalluri1 and B.

https://www.pdf-archive.com/2013/05/13/40i14-ijaet0514312-v6-iss2-920to931/

13/05/2013 www.pdf-archive.com

Induction Cooking Options 93%

Induction Cooking Options The traditional cooking styles available are fire, gas, electric and microwave.

https://www.pdf-archive.com/2018/05/02/induction-cooking-options/

02/05/2018 www.pdf-archive.com

induction 93%

000.3 - Mathematical Induction c 2010 Treasure Trove of Mathematics Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers (non-negative integers).1 It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.

https://www.pdf-archive.com/2011/07/28/induction/

28/07/2011 www.pdf-archive.com

ind1 93%

Recall that mathematical induction reaches infinity within two steps:

https://www.pdf-archive.com/2015/11/08/ind1/

08/11/2015 www.pdf-archive.com

Math in CS 93%

22 Induction I 23 2.1 A Warmup Puzzle .

https://www.pdf-archive.com/2014/10/14/math-in-cs/

14/10/2014 www.pdf-archive.com

27I18-IJAET0118634 v6 iss6 2548-2555 92%

22311963 PERFORMANCE ANALYSIS OF OPERATING CHARACTERISTIC OF SINGLE PHASE INDUCTION MOTOR WITH BLOWER APPLICATION Atul Gajare1 and Nitin Bhasme2 1 PG Student, 2Associate Professor Department of Electrical Engineering, Government College of Engineering, Aurangabad, India ABSTRACT The single phase induction motor is used in wide variety of industrial, commercial, workshop area and domestic applications.

https://www.pdf-archive.com/2014/07/04/27i18-ijaet0118634-v6-iss6-2548-2555/

04/07/2014 www.pdf-archive.com