what is ampliative inductive inference?
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Inductive inference\n\nAround 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations. Given is the beginning of some sequence of symbols. Which symbol will be next? Solomonoff's theory provides an answer that is optimal in a certain sense. Unlike Karl Popper's informal theory of inductive inference, Solomonoff's is mathematically sound.\n\nFundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion.\n\nSee also\nAlgorithmic probability \nKolmogorov complexity \nConfirmation bias \nLanguage identification in the limit
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Extrapolation is a process of logical induction.  You take a trend from observations, and assume a trend holds in order to predict the outcome of a hypothetical observation.
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milkyway: \nI think your answer is incomplete. Unfortunately, I don't have my own proof, but let me criticize yours. \nSorry.:-)\n\nWhat is definitely proven by induction in your post is that you are able to construct an acceptable set of N points. However, in my view, your reasoning does not prove the statement for a given set.\n\n1. From the very beginning, you have N points. How can one realize the induction scheme in this case? Perhaps, you mean that you can temporarily erase N-3 points (keeping in mind their positions) and start with 3 points forming a triangle, or "3 couples" in your terms. Then you restore the erased points one by one at their positions.  I believe this should be explained in your proof. \n\n2. Note that if you start with 3 aligned points, by "restoring" the 4th point, you can generate an allowed set of N+1 points out of the prohibited set of N points. This is missing in your proof, where you deal only with allowed N-sets.  \n\nBut this is not the most serious flaw there.\n\n3. You write: "now, this way there always are the old two couples, plus two new couples (new point-non aligned point of each of such two couples). So going from N to N+1, the number of acceptable couples is always >=3."  \n\nI disagree with this statement. \n\nIndeed, imagine that the three couples, which work at the stage N, form a triangle. Aligning the newly "restored" point with one side of the triangle, you kill one working couple. Still you have the two remaining old couples and get a possibly working new couple (new point -- non aligned point of the triangle). However, it is not at all guaranteed that there is no other point lying on the line going through this new possibly working couple. If such point exists, the number of working couples in this case gets reduced from 3 to 2 when going from N to N+1. At the next step, this way I will reduce the number of working couples from 2 to 1 and so on.\n\nThe transition from N to N+1 is therefore not justified.\n\n4. A general question. For N=infinity the statement is false for points located at nodes of a regular \n(say, square) lattice. Doesn't it contradict to the very idea of proving this statement by induction?\n\n\n------------------------------\n\n\n\n\nHere is my proof.\n\nGiven a set of N points, the number of all possible couples is M=N(N-1)/2.\n\nFor each couple draw a straight line going through it. We get M lines.\n\nLet us assume that the statement we are going to prove is false: i.e., none of those M lines goes through ONLY TWO points.\n\nThen, of course, each of those M lines coincides with at least the two other lines, so the actual number of distinguishable lines K < M.\n\nWe have N points and K different lines.\n\nEach of the NK pairs (point + line) is characterised by a distance S(n,k) between  the point n and the line k. \n\nThis distance S(n,k) is defined as a length of a segment perpendicular to the line k with one of the ends lying on the line k and the other end coinciding with the point n.\n\nLet us list all the NK distances S(n,k). Since NK is a finite integer number, one can find the shortest value (or several equal shortest values) of S(n,k). \n\nTake a closer look at the point P and the line L with the shortest S(n=P,k=L).\n\nBy assumption, there are at least three points (L1,L2, and L3) lying on the line L. Therefore, at least two of these three points (say, L1 and L2) can be found to the one side (say, to the right) of the point A where the perpendicular to the line L starting at the point P hits the line L. The case when one of the three points (say, L1) coincides with the point A is treated in exactly the same way.\n\nNow we have a triangle (P-L1-L2), with two vertices L1 and L2 lying on the line L to the right of A in the order A,L1,L2 from left to right. \n\nSince L1 lies to the right of A (or coincides with A), the angle between P-L1 and L1-L2 is greater than (or equal to) pi/2.\n\nTherefore t
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I'm not sure if I understood correctly but check out the pigeonhole principle
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Anything's possible.  This is where Occam's Razor comes in quite handy.
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maksing weak or incorrect arguments with eloquent language.
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I can't help you justify generalizations, however, I can type about use of it in logic.  \n\nFallacies:\n\n1.)  Accident:  When one applies a generalization to an individual case that it does not properly govern. \n\n2.)  Converse Accident:   When one moves carelessly or too quickly from a single case to an indefensibly broad generalizaiton.\n\nAssumptions:\n\n1.)  An assumption is an induction.  Its like assuming the sun will rise tomorrow.  We assume its going to happen because it has for millions of years.   \n\n2.) The bad thing about assumption is that you are using probabilities to create a conclusion.
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THE ACT OR RESULT OF AMPLIFYING ,ENLARGING OR EXTENDING
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conditional statement and its inverse
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SHUSHANUFALUFAGUS VON FUKEDAHSHITHEAD CLUELESBUTTLICKER DEARABIANPUSSIES
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"Inference" is a presumption, to "infer" something.  So, for example, you hit someone in the face.  "Assault" is defined as defendant's physical contact with a person with the intent to cause harm. A jury can "infer" that you intended the reasonable consequences of your actions. Thus, if the evidence is that you swung your fist at the guy's face, the jury can make the "inference" that you did so with the intent to harm, and convict you of assault.
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:}\nchance without cause is a logical impossibility
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Relational algebra is the mathematical treatment of set theory.\nSQL is an implementation of a subset of set theory in order to work with relational databases.\nAn understanding of relational algebra is not required ofr SQL and vice versa.
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The internet:\nhttp://www.valuebasedmanagement.net/methods_contingency_theory.html
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Inductive reasoning is the process of arriving at a conclusion based on a set of observations. \n  In itself, it is not a valid method of proof. Just because a person observes a number of situations in which a pattern exists doesn't mean that that pattern is true for all situations. \n   For example, after seeing many people outside walking their dogs, one may observe that every dog that is a poodle is being walked by an elderly person. The person observing this pattern could inductively reason that poodles are owned exclusively by elderly people. This is by no means a method of proof for such a suspicion; in fact, in the real world it is a means by which people and things are stereotyped.\n  A hypothesis based on inductive reasoning, can, however, lead to a more careful study of a situation. \n  By inductive reasoning, in the example above, a viewer has formed a hypothesis that poodles are owned exclusively by elderly people. The observer could then conduct a more formal study based on this hypothesis and conclude that his hypothesis was either right, wrong, or only partially wrong.
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Newton advanced it as an axiom, by virtue of which it wouldn't be "proven", only tested (the resulting predictions tested.) If I say "suppose I assume a space where all parallel lines converge", I don't "prove" my assumption - it's an assumption. You work outward from it and see what you get. If what you get is impossible (or wrong), it was a bad assumption.
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Well, I'm not sure about a workshop. However, there is a great book called Being Logical: A guide to good thinking by D.Q. McInerny. It's only a 129 pages, but they are power packed.\n\n Here is a review:\n"Highly readable...D.Q. McInerny offers an introduction to symbolic logic in plain English, so you can finally be clear on what is deductive reasoning and what is inductive. And you'll see how deductive arguments are constructed."\n- Detroit Free Press