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Deductive Reasoning

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In Peirce made a three-way distinction between probability, verisimilitude, and plausibility, and defined plausibility with a normative "ought": The phrase "inference to the best explanation" not used by Peirce but often applied to hypothetical inference is not always understood as referring to the most simple and natural hypotheses such as those with the fewest assumptions. However, in other senses of "best", such as "standing up best to tests", it is hard to know which is the best explanation to form, since one has not tested it yet.

Still, for Peirce, any justification of an abductive inference as good is not completed upon its formation as an argument unlike with induction and deduction and instead depends also on its methodological role and promise such as its testability in advancing inquiry. At the methodeutical level Peirce held that a hypothesis is judged and selected [18] for testing because it offers, via its trial, to expedite and economize the inquiry process itself toward new truths, first of all by being testable and also by further economies, [20] in terms of cost, value, and relationships among guesses hypotheses.

Here, considerations such as probability, absent from the treatment of abduction at the critical level, come into play. Norwood Russell Hanson , a philosopher of science , wanted to grasp a logic explaining how scientific discoveries take place. He used Peirce's notion of abduction for this. In other words, deduction derives the consequences of the assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion.

For example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. Indeed, it turns out that some swans are black. For example, in a billiard game, after glancing and seeing the eight ball moving towards us, we may abduce that the cue ball struck the eight ball. The strike of the cue ball would account for the movement of the eight ball.

It serves as a hypothesis that explains our observation. Given the many possible explanations for the movement of the eight ball, our abduction does not leave us certain that the cue ball in fact struck the eight ball, but our abduction, still useful, can serve to orient us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduce a single explanation or a few explanations for this process in the expectation that we can better orient ourselves in our surroundings and disregard some possibilities.

Properly used, abductive reasoning can be a useful source of priors in Bayesian statistics. Criteria for picking out a member representing "the best" explanation include the simplicity , the prior probability , or the explanatory power of the explanation. The methods are sound and complete and work for full first order logic, without requiring any preliminary reduction of formulae into normal forms.

These methods have also been extended to modal logic. Abductive logic programming is a computational framework that extends normal logic programming with abduction. A different formalization of abduction is based on inverting the function that calculates the visible effects of the hypotheses. If this condition is met, abduction can be seen as a form of set covering. Abductive validation is the process of validating a given hypothesis through abductive reasoning.

This can also be called reasoning through successive approximation. Under this principle, an explanation is valid if it is the best possible explanation of a set of known data. The best possible explanation is often defined in terms of simplicity and elegance see Occam's razor. Abductive validation is common practice in hypothesis formation in science ; moreover, Peirce claims that it is a ubiquitous aspect of thought:. Looking out my window this lovely spring morning, I see an azalea in full bloom.

I don't see that; though that is the only way I can describe what I see. That is a proposition, a sentence, a fact; but what I perceive is not proposition, sentence, fact, but only an image, which I make intelligible in part by means of a statement of fact.

This statement is abstract; but what I see is concrete. I perform an abduction when I so much as express in a sentence anything I see. The truth is that the whole fabric of our knowledge is one matted felt of pure hypothesis confirmed and refined by induction. Not the smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step.

It was Peirce's own maxim that "Facts cannot be explained by a hypothesis more extraordinary than these facts themselves; and of various hypotheses the least extraordinary must be adopted. Abductive validation is a method for identifying the assumptions that will lead to your goal. Probabilistic abductive reasoning is a form of abductive validation, and is used extensively in areas where the probability distribution over possible hypotheses needs to be derived, such as for making diagnoses from medical tests.

For example, a pharmaceutical company that develops a test for a particular infectious disease will typically determine the reliability of the test by hiring a group of infected and a group of non-infected people to undergo the test. The interpretations of the conditionals are: The problem with applying these conditionals in a practical setting is that they are expressed in the opposite direction to what the practitioner needs. The conditionals needed for making the diagnosis are: Unfortunately the required conditionals are usually not directly available to the medical practitioner, but they can be obtained by applying Bayes' theorem if the base rate aka.

These two instances of Bayes' theorem are. Probabilistic abduction can thus be described as a method for probabilistic deduction that uses Bayes' theorem. While this reasoning error often can produce a relatively good approximation of the correct hypothesis probability value, it can lead to a completely wrong result and wrong conclusion in case the base rate is very low and the reliability of the test is not perfect.

An extreme example of the base rate fallacy is to conclude that a male person is pregnant just because he tests positive in a pregnancy test. Obviously, the base rate of male pregnancy is zero, and assuming that the test is not perfect, it would be correct to conclude that the male person is not pregnant or the person is not biologically male.

The expression for probabilistic abduction can be generalised to multinomial cases, [44] i. Subjective logic generalises probabilistic logic by including degrees of uncertainty in the input arguments, i. Abduction in subjective logic is thus a generalization of probabilistic abduction described above. The equality between the different expressions for subjective abduction is given below:. The advantage of using subjective logic abduction compared to probabilistic abduction is that uncertainty about the input argument probabilities can be explicitly expressed and taken into account during the analysis.

It is thus possible to perform abductive analysis in the presence of uncertain arguments, which naturally results in degrees of uncertainty in the output conclusions. Applications in artificial intelligence include fault diagnosis , belief revision , and automated planning.

The most direct application of abduction is that of automatically detecting faults in systems: In medicine , abduction can be seen as a component of clinical evaluation and judgment. Abduction can also be used to model automated planning. In intelligence analysis , analysis of competing hypotheses and Bayesian networks , probabilistic abductive reasoning is used extensively.

Similarly in medical diagnosis and legal reasoning, the same methods are being used, although there have been many examples of errors, especially caused by the base rate fallacy and the prosecutor's fallacy. Belief revision , the process of adapting beliefs in view of new information, is another field in which abduction has been applied. The main problem of belief revision is that the new information may be inconsistent with the corpus of beliefs, while the result of the incorporation cannot be inconsistent.

This process can be done by the use of abduction: This use of abduction is not straightforward, as adding propositional formulae to other propositional formulae can only make inconsistencies worse. Instead, abduction is done at the level of the ordering of preference of the possible worlds. Preference models use fuzzy logic or utility models. In the philosophy of science , abduction has been the key inference method to support scientific realism , and much of the debate about scientific realism is focused on whether abduction is an acceptable method of inference.

In historical linguistics , abduction during language acquisition is often taken to be an essential part of processes of language change such as reanalysis and analogy.

In anthropology , Alfred Gell in his influential book Art and Agency defined abduction after Eco [51] as "a case of synthetic inference 'where we find some very curious circumstances, which would be explained by the supposition that it was a case of some general rule, and thereupon adopt that supposition ' ".

That is, abduction can explain how works of art inspire a sensus communis: Abduction is the answer to this conundrum because the tentative nature of the abduction concept Peirce likened it to guessing means that not only can it operate outside of any pre-existing framework, but moreover, it can actually intimate the existence of a framework. As Gell reasons in his analysis, the physical existence of the artwork prompts the viewer to perform an abduction that imbues the artwork with intentionality.

A statue of a goddess, for example, in some senses actually becomes the goddess in the mind of the beholder; and represents not only the form of the deity but also her intentions which are adduced from the feeling of her very presence. Therefore, through abduction, Gell claims that art can have the kind of agency that plants the seeds that grow into cultural myths. The power of agency is the power to motivate actions and inspire ultimately the shared understanding that characterizes any given society.

It allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect; and thus many hypotheses may seem at first glance to be excluded by the pragmatical maxim that are not really so excluded. The text in this article is licensed under the Creative Commons-License Attribution 4. You can use it freely with some kind of link , and we're also okay with people reprinting in publications like books, blogs, newsletters, course-material, papers, wikipedia and presentations with clear attribution.

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A deductive approach is concerned with “developing a hypothesis (or hypotheses) based on existing theory, and then designing a research strategy to test the hypothesis” It has been stated that “deductive means reasoning from the particular to the general.

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Deductive reasoning works from the more general to the more specific. Sometimes this is informally called a "top-down" approach. We might begin with thinking up a theory about our topic of interest.

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The main difference between inductive and deductive approaches to research is that whilst a deductive approach is aimed and testing theory, an inductive approach is concerned with the generation of new theory emerging from the data. Deductive reasoning and inductive reasoning are two different approaches to conducting scientific research. Using deductive reasoning, a researcher tests a theory by collecting and examining empirical evidence to see if the theory is true. Using inductive reasoning, a researcher first gathers and.

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The procedure followed by deductive research can be summarized as follows: Theory, starting with existing knowledge or assumptions. Hypothesis, formulating a research question or hypothesis based on existing knowledge, theories or assumptions. Observation, or data collection. Deductive definition is - of, relating to, or provable by deriving conclusions by reasoning: of, relating to, or provable by deduction. but resisted what seemed to them the blinkered reliance on deductive reasoning and empirical research enforced by encroaching science.