what is a inductive reasoning?
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"Inductive reasoning" (not to be confused with "mathematical induction" or and "inductive proof", which is something quite different) is the process of reasoning that a general principle is true because the special cases you've seen are true. For example, if all the people you've ever met from a particular town have been very strange, you might then say "all the residents of this town are strange". That is inductive reasoning: constructing a general principle from special cases. It goes in the opposite direction from deductive reasoning.
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No.  Deductive proofs start from a "given", that is, a fact accepted as true or a theorem previously proven to be true.  But other kinds of proofs start with an assumption that the theorem to be proved is not true, and from that assumption derive some contradiction, thus proving that the theorem itself is true.\n\nAn example would be the proof that there is no highest prime number, which goes like this. Assume that there is a highest prime number.  Call it x.  Now consider the number x! + 1.  (X! is X times X-1 times X-2 all the way down to 1.)  Since x! is divisible by 2, x! + 1, being just 1 more than x!, is not divisible by 2.  Similarly, x! + 1 is not divisible by 3, 4, or any other integer up to and including x.  Since x! + 1 is not divisible by any number up to x, either it is prime, or it's prime factors are larger than x.  But that contradicts our assumption that x is the largest prime.  Thus, our assumption is false.  QED.
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Logical Fallacy. The best practice is to draw conclusions from irrefutable evidence (which any lawyer can tell you doesn't exist). Best not to draw conclusions at all if you can help it.
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Definitions of the terms. The axioms for the natrual numbers are as follows:\n\n1) 0 is a natural number,\n2) The successor of a natural number is a natural number,\n3) No two numbers have the same successor\n4) 0 is not the successor of any natural number\n5) If P(x) is a property of natural numbers such that P(0) is true and such that P(n) true implies P(succ n) is true, then P(n) is true for all natural numbers (Mathematical Induction)\n\nUse S(n) to denote the successor of n and *define*\n1=S(0) and 2=S(1).\n\nNow *define* addition inductively by\nn+0=n and\nn+Sm=S(n+m).\n\nThen,\n1+1=1+S(0)\n=S(1+0)=S(1)=2.
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I think you might find that engagement in logic and reasoning is an activity that is undertaken voluntarily, when it suits a particular purpose. The proportion of one's time spent in these activities is not related specifically to intelligence, but to other social factors. For instance, if one doesn't agree with the opinions or beliefs of a particular group of people, it might simply be easier and faster to assume that these people are of lower intelligence, rather than provide any evidence whatsoever of their potential motives for holding those beliefs or opinions, or evidence that they are, in fact, of lower intelligence.\n\nThis doesn't mean that the person him/herself is of lower intelligence for jumping to an easy assumption (in this case, that this particular group of people is of lower average intelligence). This person could have abandoned logic and reason for a variety of reasons. This person could simply be lazy, or heavily biased. In any case, it would be in this person's argument's best interest to actually bring statistical evidence to the table, otherwise there is no real way the claim might be supported (though it might be superficially supported in its current form by those who happen to share the person's particular opinion, for whatever reason). This is not the hallmark of true inquiry; rather, it is the hallmark of true rhetoric. While rhetoric has its place in inquiry and the search for truth, all too often it is passed off AS the truth, an activity which is in no one's best interests except those trying to espouse and spread an opinion that is not based on accepted facts (in this case, that this particular group of people are of lower average intelligence).\n\nSadly, such tactics can at times be construed to be intentional. Sometimes a person might take a personal belief, no matter how erroneous, and pass it off as fact to support an argument motivated by any number of dubious motives, from malice to simple jealousy. This is a true hallmark or racial propaganda, for instance.\n\nAt the core of the matter may be a simple concept: both the humanist and Christian (I won't comment of other schools of thought or religions, though they exist) ideas that the individual human has intrinsic value. Basing an argument on the idea that one person or group of people has some negative quality, like low intellignce, does a great disservice to the discourse. Arguments that contain such personal motivations invariably end up being beside the point anyway.
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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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All people think. Some do it with greater success than others. \n\nYou can teach logic and you can teach patterns of inquiry, but I don't believe you can "teach" synthesis or evaluation. Some forms of analysis maybe because they can be pattern based. What a good teacher can do though is create situations where challenge and practice are possible.
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Deduction starts with general principles and moves to specific conclusions.  Induction starts with specific observations and moves to general principles.\n\nHere's a link that may help.\n\nhttp://www.socialresearchmethods.net/kb/dedind.htm
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a hypothesis is an educated guess on a problem or experiment.
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The discovery method is a teaching technique that encourages students to take a more active role in their learning process by answering a series of questions or solving problems designed to introduce a general concept.  In this teaching approach, the instructor guides the student’s thought process by posing a series of questions whose responses would lead to the understanding of a concept before it is explicitly stated. “Children act as detectives as they solve concept-attainment activities in stimulating learning environments. In doing so, they place a newly introduced object in a category that they have previously discovered or identified.” This teaching method is believed to increase retention of material because the student organizes the new information and integrates it with information that has already been stored.
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i am intrigued by your idea of LOGIC!!! interesting
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hav u ever heard of the Principle of Mthematical Induction ?\nthat could solve ur problem in a jiffy!!\n\nHowever if u havn't, dont worry!!\n\nNote that, the sum in ur series(i.e. 1+1/2+1/3+...+1/n),where n>=2, is always less than 2, but greater than 1. so it can't b an integer.\nwanna know why?\ntry cramming up some theorems about Sequence & series of real numbers!! its a regulation part of any under-graduate level Real analysis course.
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It's easy, no one can dispute the fact that I don't know something when I in fact don't. Admitting you do not know a thing when you don't is the highest form of truth there is. Assumption of truth with out proof is irrational.
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If we imagine a line continuum between machine and man, and place Induction, Deduction & Analogy on it. Induction will probably be closer to the machine and Analogy will be closer to man, with Deduction probably in the center.
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Logic is A=B, B=C, therefore A=C. (sees the steps in a process, understands cause and effect, etc)\n\nCritical thinking says.... "okay, that is true, but why? and what can I do with that knowledge? and how will affect/effect me now and in the future?"
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What a pity that you cannot answer your own question! I'm getting curious...\n\nIt seems to be a question in pure logics rather than arithmetics: as you don't know me you cannot give me any apple (first proposition: False) \nBut canaries don't have teeth (second proposition: false)\n\nSo the implication is true... \n\nOtherwise, being the postulate contradictory, any proposition can be logically proven: including "lower than 3 and higher than 5"\n\nI'm giving numbers?
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Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. It can be thought as the application side of fuzzy set theory dealing with well thought out real world expert values for a complex problem. (Klir 1997).\n\nDegrees of truth are often confused with probabilities. However, they are conceptually distinct; fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition. To illustrate the difference, consider this scenario: Bob is in a house with two adjacent rooms: the kitchen and the dining room. In many cases, Bob's status within the set of things "in the kitchen" is completely plain: he's either "in the kitchen" or "not in the kitchen". What about when Bob stands in the doorway? He may be considered "partially in the kitchen". Quantifying this partial state yields a fuzzy set membership. With only his little toe in the dining room, we might say Bob is 99% "in the kitchen" and 1% "in the dining room", for instance. No event (like a coin toss) will resolve Bob to being completely "in the kitchen" or "not in the kitchen", as long as he's standing in that doorway. Fuzzy sets are based on vague definitions of sets, not randomness.\n\nFuzzy logic allows for set membership values between and including 0 and 1, shades of gray as well as black and white, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Prof. Lotfi Zadeh at the University of California, Berkeley.\n\nFuzzy logic is controversial in some circles, despite wide acceptance and a broad track record of successful applications. It is rejected by some control engineers for validation and other reasons, and by some statisticians who hold that probability is the only rigorous mathematical description of uncertainty. Critics also argue that it cannot be a superset of ordinary set theory since membership functions are defined in terms of conventional sets.