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Inductive vs. Deductive Writing

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❶Spectral density estimation Fourier analysis Wavelet Whittle likelihood. Having once had the phenomena bound together in their minds in virtue of the Conception, men can no longer easily restore them back to detached and incoherent condition in which they were before they were thus combined".

Understanding Inductive Reasoning

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Rarely spotted by Whewell's predecessors, such mental inventions rapidly evade notice. Having once had the phenomena bound together in their minds in virtue of the Conception, men can no longer easily restore them back to detached and incoherent condition in which they were before they were thus combined". These "superinduced" explanations may well be flawed, but their accuracy is suggested when they exhibit what Whewell termed consilience —that is, simultaneously predicting the inductive generalizations in multiple areas—a feat that, according to Whewell, can establish their truth.

Perhaps to accommodate prevailing view of science as inductivist method, Whewell devoted several chapters to "methods of induction" and sometimes said "logic of induction"—and yet stressed it lacks rules and cannot be trained. Originator of pragmatism , C S Peirce who, as did Gottlob Frege independently, in the s performed vast investigations that clarified the basis of deductive inference as mathematical proof, recognized induction but continuously insisted on a third type of inference that Peirce variously termed abduction or retroduction or hypothesis or presumption.

Having highlighted Hume's problem of induction , John Maynard Keynes posed logical probability as its answer—but then figured not quite. The principle of induction, as applied to causation, says that, if A has been found very often accompanied or followed by B , then it is probable that on the next occasion on which A is observed, it will be accompanied or followed by B.

If the principle is to be adequate, a sufficient number of instances must make the probability not far short of certainty.

If this principle, or any other from which it can be deduced, is true, then the casual inferences which Hume rejects are valid, not indeed as giving certainty, but as giving a sufficient probability for practical purposes. If this principle is not true, every attempt to arrive at general scientific laws from particular observations is fallacious, and Hume's skepticism is inescapable for an empiricist.

The principle itself cannot, of course, without circularity, be inferred from observed uniformities, since it is required to justify any such inference. It must therefore be, or be deduced from, an independent principle not based on experience. To this extent, Hume has proved that pure empiricism is not a sufficient basis for science. But if this one principle is admitted, everything else can proceed in accordance with the theory that all our knowledge is based on experience.

It must be granted that this is a serious departure from pure empiricism, and that those who are not empiricists may ask why, if one departure is allowed, others are forbidden. These, however, are not questions directly raised by Hume's arguments. What these arguments prove—and I do not think the proof can be controverted—is that the induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle, science is impossible".

In a paper, Gilbert Harman explained that enumerative induction is not an autonomous phenomenon, but is simply a masked consequence of inference to the best explanation IBE. Inductive reasoning has been criticized by thinkers as far back as Sextus Empiricus. Although the use of inductive reasoning demonstrates considerable success, its application has been questionable. Recognizing this, Hume highlighted the fact that our mind draws uncertain conclusions from relatively limited experiences.

In deduction, the truth value of the conclusion is based on the truth of the premise. In induction, however, the dependence on the premise is always uncertain. As an example, let's assume "all ravens are black. However, the assumption becomes inconsistent with the fact that there are white ravens. Therefore, the general rule of "all ravens are black" is inconsistent with the existence of the white raven.

Hume further argued that it is impossible to justify inductive reasoning: Since this is circular he concluded that our use of induction is unjustifiable with the help of Hume's Fork. However, Hume then stated that even if induction were proved unreliable, we would still have to rely on it.

So instead of a position of severe skepticism , Hume advocated a practical skepticism based on common sense , where the inevitability of induction is accepted. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure". By now, inductive inference has been shown to exist, but is found rarely, as in programs of machine learning in Artificial Intelligence AI.

Inductive reasoning is also known as hypothesis construction because any conclusions made are based on current knowledge and predictions. Examples of these biases include the availability heuristic , confirmation bias , and the predictable-world bias. The availability heuristic causes the reasoner to depend primarily upon information that is readily available to them. People have a tendency to rely on information that is easily accessible in the world around them.

For example, in surveys, when people are asked to estimate the percentage of people who died from various causes, most respondents would choose the causes that have been most prevalent in the media such as terrorism, and murders, and airplane accidents rather than causes such as disease and traffic accidents, which have been technically "less accessible" to the individual since they are not emphasized as heavily in the world around them.

The confirmation bias is based on the natural tendency to confirm rather than to deny a current hypothesis. Research has demonstrated that people are inclined to seek solutions to problems that are more consistent with known hypotheses rather than attempt to refute those hypotheses.

Often, in experiments, subjects will ask questions that seek answers that fit established hypotheses, thus confirming these hypotheses. For example, if it is hypothesized that Sally is a sociable individual, subjects will naturally seek to confirm the premise by asking questions that would produce answers confirming that Sally is in fact a sociable individual.

The predictable-world bias revolves around the inclination to perceive order where it has not been proved to exist, either at all or at a particular level of abstraction. Gambling, for example, is one of the most popular examples of predictable-world bias. Gamblers often begin to think that they see simple and obvious patterns in the outcomes and, therefore, believe that they are able to predict outcomes based upon what they have witnessed. In reality, however, the outcomes of these games are difficult to predict and highly complex in nature.

However, in general, people tend to seek some type of simplistic order to explain or justify their beliefs and experiences, and it is often difficult for them to realise that their perceptions of order may be entirely different from the truth. A generalization more accurately, an inductive generalization proceeds from a premise about a sample to a conclusion about the population. There are 20 balls—either black or white—in an urn. To estimate their respective numbers, you draw a sample of four balls and find that three are black and one is white.

A good inductive generalization would be that there are 15 black and five white balls in the urn. How much the premises support the conclusion depends upon a the number in the sample group, b the number in the population, and c the degree to which the sample represents the population which may be achieved by taking a random sample. The hasty generalization and the biased sample are generalization fallacies.

Two dicto simpliciter fallacies can occur in statistical syllogisms: Simple induction proceeds from a premise about a sample group to a conclusion about another individual. This is a combination of a generalization and a statistical syllogism, where the conclusion of the generalization is also the first premise of the statistical syllogism.

The basic form of inductive inference , simply induction , reasons from particular instances to all instances, and is thus an unrestricted generalization. As this reasoning form 's premises, even if true, do not entail the conclusion's truth, this is a form of inductive inference.

The conclusion might be true, and might be thought probably true, yet it can be false. Questions regarding the justification and form of enumerative inductions have been central in philosophy of science , as enumerative induction has a pivotal role in the traditional model of the scientific method.

The process of analogical inference involves noting the shared properties of two or more things, and from this basis inferring that they also share some further property: Analogical reasoning is very frequent in common sense , science , philosophy and the humanities , but sometimes it is accepted only as an auxiliary method. A refined approach is case-based reasoning.

A causal inference draws a conclusion about a causal connection based on the conditions of the occurrence of an effect. Premises about the correlation of two things can indicate a causal relationship between them, but additional factors must be confirmed to establish the exact form of the causal relationship. As a logic of induction rather than a theory of belief, Bayesian inference does not determine which beliefs are a priori rational, but rather determines how we should rationally change the beliefs we have when presented with evidence.

We begin by committing to a prior probability for a hypothesis based on logic or previous experience, and when faced with evidence, we adjust the strength of our belief in that hypothesis in a precise manner using Bayesian logic. Around , Ray Solomonoff founded the theory of universal inductive inference , the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols.

This is a formal inductive framework that combines algorithmic information theory with the Bayesian framework. Universal inductive inference is based on solid philosophical foundations, [31] and can be considered as a mathematically formalized Occam's razor. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. From Wikipedia, the free encyclopedia. For the technique in mathematical proof, see Mathematical induction.

Thinking portal Logic portal. Abductive reasoning Algorithmic probability Analogy Bayesian probability Counterinduction Deductive reasoning Explanation Failure mode and effects analysis Falsifiability Grammar induction Inductive inference Inductive logic programming Inductive probability Inductive programming Inductive reasoning aptitude Inductivism Inquiry Kolmogorov complexity Lateral thinking Laurence Jonathan Cohen Logic Logical positivism Machine learning Mathematical induction Mill's Methods Minimum description length Minimum message length New riddle of induction Open world assumption Raven paradox Recursive Bayesian estimation Retroduction Solomonoff's theory of inductive inference Statistical inference Stephen Toulmin Marcus Hutter.

Essentials of Logic Second ed. Upper Saddle River, NJ: While this usage is still sometimes found even in philosophical and mathematical contexts, for the most part, it is outdated. International Journal of General Systems. The Problem of Induction. The Stanford Encyclopedia of Philosophy.

Kant's account of reason". Fundamentals of Discrete Mathematical Structures 3rd ed. Retrieved 1 December Rationality without Foundations New York: Routledge , , ch. Cambridge University Press , , pp , — A fairly recent debate has arisen over the merits of strict inductivism.

Some philosophers have argued that there are other forms of nondeductive inference that do not fit the model of enumerative induction. Peirce describes a form of inference called ' abduction ' or ' inference to the best explanation '. This form of inference appeals to explanatory considerations to justify belief. One infers, for example, that two students copied answers from a third because this is the best explanation of the available data—they each make the same mistakes and the two sat in view of the third.

Alternatively, in a more theoretical context, one infers that there are very small unobservable particles because this is the best explanation of Brownian motion. Let us call 'liberal inductivism' any view that accepts the legitimacy of a form of inference to the best explanation that is distinct from enumerative induction. For a defense of liberal inductivism, see Gilbert Harman 's classic paper.

Harman defends a strong version of liberal inductivism according to which enumerative induction is just a disguised form of inference to the best explanation ". Routledge , , pp 63— Routledge , , "The validity of inference"], pp —64, quote on p Which should the writer use?

It depends on content, the intended audience , and your overall purpose. If you want your audience to discover new things with you , then inductive writing might make sense. Here is n example:. My dog Max wants to chase every non-human living creature he sees, whether it is the cats in the house or rabbits and squirrels in the backyard. Sources indicate that this is a behavior typical of Jack Russell terriers. While Max is a mixed breed dog, he is approximately the same size and has many of the typical markings of a Jack Russell.

From these facts along with his behaviors, we surmise that Max is indeed at least part Jack Russell terrier. Purposes for this kind of writing include creative writing and perhaps some persuasive essays, although much academic work is done in deductive form.

If your audience is not likely going to read the entire written piece, then deductive reasoning might make more sense, as the reader can look for what he or she wants by quickly scanning first sentences of each paragraph. Here is an example:. My backyard is in dire need of cleaning and new landscaping. The Kentucky bluegrass that was planted there five years ago has been all but replaced by Creeping Charlie, a particularly invasive weed.

The stone steps leading to the house are in some disrepair, and there are some slats missing from the fence. Perennials were planted three years ago, but the moles and rabbits destroyed many of the bulbs, so we no longer have flowers in the spring. The reader knows from the very first sentence that the backyard is a mess! Purposes for this kind of writing include business letters and project documents, where the client is more likely to skim the work for generalities or to hunt for only the parts that are important to him or her.

Again, scientific writing tends to follow this format as well, and research papers greatly benefit from deductive writing. Whether one method or another is chosen, there are some other important considerations. Perform research carefully and from appropriate sources; make sure ideas are cited properly. Try not to write questions: Lastly, avoid quotes in thesis statements or conclusions, because they are not your own words — and thus undermine your authority as the paper writer.


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In some quarters, inductive reasoning is referred to as the scientific method which consists of six steps namely; problem statement, evaluation of the problem, hypothesis statement, hypothesis testing, result analysis, stating the findings and lastly revision.

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(This for of inductive reasoning proceeds from a generalization to a conclusion about an individual or sample.) All policemen who are at least 40 years of age have apprehended at least 2 traffic violators. Thomas is a policeman who is 43 years of age.

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Writing the Inductive Essay. Going from examples to conclusions. Inductive Writing. Looks at specific instances and culminates in the conclusion. Understand that inductive reasoning does not necessarily. prove. anything. Conclusion: Cloning Should Not be Encouraged (Writer’s Position). The term "inductive reasoning" refers to reasoning that takes specific information and makes a broader generalization that is considered probable, allowing for the fact that the conclusion may not be sportwallpaper.tktanding Inductive Reasoning. There are varying degrees of strength and weakness in inductive reasoning, and various types including statistical syllogism, arguments .

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Reasoning Reasoning is a method of coming to conclusions by the use of logical argument. There are three basic form of reasoning: inductive, deductive and the combination of both called inductive/deductive (Walliman & Baiche, ). Inductive reasoning does not result with a definite conclusion like deductive reasoning does, but rather is based on past opinion and observations of others. Deductive reasoning applies what is known. 3/5(5).