Jul 03, · Of course, this doesn't mean that you have to restrict yourself to trivial issues or to ones that you care nothing about. Rather, it means that you should consider topics you know something about and are prepared to deal with thoughtfully in a short essay of or words. A well-supported argument on the need for a campus child-care center, for instance, would probably be more effective The Evidential Problem of Evil. The evidential problem of evil is the problem of determining whether and, if so, to what extent the existence of evil (or certain instances, kinds, quantities, or distributions of evil) constitutes evidence against the existence of God, that is to say, a being perfect in power, knowledge and blogger.comtial arguments from evil attempt to show that, once we Nov 14, · Test taking strategies for essays bebe qui essaye de faire caca. Essay about lgbt, essay on journey by train in pakistan example of essay about covid vous essays examples Que @yale supplemental essayez. Bilingual essay topics vous @yale
Inductive Logic (Stanford Encyclopedia of Philosophy)
An inductive logic is a logic of evidential support, inductive essays. In a deductive logic, the premises of a valid deductive argument logically entail the conclusion, where logical entailment means that every logically possible state of affairs that makes the premises true must make the conclusion true as well.
Thus, the premises of a valid deductive argument provide total support for the conclusion, inductive essays. An inductive logic extends this idea to weaker arguments. In a good inductive argument, the truth of the premises provides some degree of support for the truth of the conclusion, inductive essays, where this degree-of-support might be measured via some numerical scale.
By analogy with the notion of deductive entailment, inductive essays, the notion of inductive degree-of-support might mean something like this: among the logically possible states of affairs that make the premises true, the conclusion must be true in at least proportion r of them—where r is some numerical measure of the support strength. If a logic of good inductive arguments is to inductive essays of any real value, the measure of support it articulates should be up to the task.
Presumably, the logic should at least satisfy the following condition:. The CoA stated here may strike some readers as surprisingly strong. Given a specific logic of evidential support, how might it be shown to satisfy such a condition?
Section 4 will show precisely how this condition is satisfied by the logic of evidential support articulated in Sections 1 through 3 of this article. This article will focus on the kind of the approach to inductive logic most widely studied by epistemologists and logicians in recent years. This approach employs conditional probability functions to represent measures of the degree to which evidence statements support hypotheses.
Presumably, hypotheses should be empirically evaluated based on what they say or imply about the likelihood that evidence claims will be true, inductive essays. Thus, this approach to the logic of evidential support is often called a Bayesian Inductive Logic or a Bayesian Confirmation Theory. This article will first provide a detailed explication of a Bayesian inductive essays to inductive logic, inductive essays.
It will then examine the extent to which this logic may pass muster as an adequate inductive essays of evidential support for hypotheses.
In particular, we will inductive essays how such a logic may be shown to satisfy the Criterion inductive essays Adequacy stated above. Sections 1 through 3 present all of the main ideas underlying the Bayesian probabilistic logic of evidential support. These three sections should suffice to provide an adequate inductive essays of the subject. Section 5 extends this account to cases where the implications of hypotheses about evidence claims called likelihoods are vague or imprecise.
After reading Sections 1 through 3, the reader may safely skip directly to Section 5, bypassing the rather technical account in Section 4 of how inductive essays the CoA is satisfied. Section 4 is for the more advanced reader who wants an understanding of how this logic may bring about convergence to the true hypothesis as evidence accumulates, inductive essays.
This result shows that the Criterion of Adequacy is indeed satisfied—that as evidence accumulates, false hypotheses will very probably come to have evidential support values as measured by their posterior probabilities that approach 0; and inductive essays this happens, a true hypothesis may very probably acquire evidential support values as measured by its posterior probability that approaches 1. Let us begin by considering some common kinds of examples of inductive arguments.
Consider the following two arguments:, inductive essays. Example 1. Every raven in a random sample of ravens is black. This strongly supports the following conclusion: All ravens are black. Example 2, inductive essays.
Bush for President in the Inductive essays election. This supports with a probability of at least. This kind of argument is often called an induction by enumeration. It is closely related to the technique of statistical estimation, inductive essays. We may represent the logical form of such arguments semi-formally as follows:. Premise: In random sample S consisting of n members of population B inductive essays, the proportion of members that have attribute A is r. The premise breaks down into three separate statements: [ 1 ].
Any inductive logic that treats such arguments should address two challenges. In particular, it should tell us how to determine the appropriate degree p to which such premises inductively support the conclusion, for a given margin of error q.
That is, it should be provable as a metatheorem that if a conclusion expressing the approximate proportion for an attribute in a population is true, then it is very likely that sufficiently numerous random samples of the population will provide true premises for good inductive arguments that confer degrees of support inductive essays approaching 1 for that true conclusion—where, on pain of triviality, these sufficiently numerous samples inductive essays only a tiny fraction of a large population.
The supplement on Enumerative Inductions: Bayesian Estimation and Inductive essaysshows precisely how a a Bayesian account of enumerative induction may meet these two challenges. Enumerative induction is, however, rather limited in scope.
This form of induction is only applicable to the support of claims involving simple universal conditionals i. But, many important empirical hypotheses are not reducible to this simple form, and the evidence for these hypotheses is not composed of an enumeration of such instances.
Consider, for example, the Newtonian Theory of Mechanics:. All objects remain at rest or in uniform motion unless acted upon by some external force. If an object exerts a force on another object, the second inductive essays exerts an equal amount of force on the first object, but in the opposite direction to the force exerted by the first object, inductive essays. The evidence for and against this theory is not gotten by examining a randomly selected subset of objects and the forces acting upon them.
Rather, the theory is tested by calculating what this theory says or implies about observable phenomena in a wide variety of specific situations—e. This approach to testing hypotheses and theories is ubiquitous, inductive essays, and should be captured by an adequate inductive logic. More generally, for a wide range of cases where inductive reasoning is important, enumerative induction is inadequate.
Rather, the kind of evidential reasoning that judges the likely truth inductive essays hypotheses on the basis of what they say or imply about the evidence is more appropriate. Consider the kinds of inferences jury members are supposed to make, based on the evidence presented at inductive essays murder trial.
The inference to probable guilt or innocence is based on a patchwork of evidence of various kinds. It almost never involves consideration of a randomly selected sequences of past situations when people like the accused committed similar murders, inductive essays. Or, consider how a doctor diagnoses her patient on the basis of his symptoms.
Although the frequency of occurrence of various diseases when inductive essays symptoms have been present may play inductive essays role, this is clearly not the whole story. Diagnosticians commonly employ a form of hypothesis evaluation —e. Thus, a fully adequate account of inductive logic should explicate the logic of hypothesis evaluationthrough which a hypothesis or theory may be tested on inductive essays basis of what it says or "predicts" about observable phenomena.
In Section 3 we will see how a kind of probabilistic inductive logic called "Bayesian Inference" or "Bayesian Confirmation Theory" captures such reasoning. The full logical structure of such arguments will be spelled out in that section, inductive essays.
Perhaps the oldest and best understood way of representing partial belief, uncertain inference, inductive essays, and inductive essays support is in terms of probability and the equivalent notion odds.
Mathematicians have studied probability for over years, but inductive essays concept is certainly much older, inductive essays. In recent times a number of other, related representations of partial belief and uncertain inference have emerged. Some of these approaches have found useful application in computer based artificial intelligence systems that perform inductive inferences in expert domains such as medical diagnosis.
Nevertheless, probabilistic representations have predominated in such application domains, inductive essays. So, in this article we will focus exclusively on probabilistic representations of inductive support, inductive essays.
A brief comparative description of some of the most prominent alternative inductive essays of uncertainty and support-strength can be found in the supplement Some Prominent Approaches to the Representation of Uncertain Inference. The mathematical study of probability originated with Blaise Pascal and Pierre de Fermat in the mid th century.
From that time through the early 19 th century, as the mathematical theory continued to develop, probability theory was primarily applied to the assessment of risk in games of chance and to drawing simple statistical inferences about characteristics of large populations—e.
In the early 19 th century Pierre de Laplace made further theoretical advances and showed how to apply probabilistic reasoning to a much wider range of scientific and practical problems, inductive essays. Since that time probability has become an indispensable tool in the sciences, inductive essays, business, and many other areas of modern life.
Throughout the development of probability theory various researchers appear to have thought of it as a kind of logic. John Venn followed two decades later with an alternative empirical frequentist account of probability in The Logic of Chance Not long after that the whole discipline of inductive essays was transformed by new developments in deductive logic, inductive essays.
In the inductive essays 19 th and early 20 th century Frege, followed by Russell and Whitehead, showed how deductive logic may be represented in the kind of rigorous formal system we now call quantified predicate logic.
For the first time logicians had a fully formal deductive logic powerful enough to represent all valid deductive arguments inductive essays arise in mathematics and the sciences. In this logic the validity of deductive arguments depends only on the logical structure of the sentences involved.
This development in deductive logic spurred some inductive essays to attempt to apply a similar approach to inductive reasoning. The idea was to extend the deductive entailment relation to a notion of probabilistic entailment for cases where premises provide less than conclusive support for conclusions. Attempts to develop such a logic vary somewhat with regard to the ways in which they attempt to emulate the paradigm of formal deductive logic. Some inductive logicians have tried to follow the deductive paradigm by attempting to specify inductive support probabilities solely in terms of the syntactic structures of premise and conclusion sentences, inductive essays.
In deductive logic the syntactic structure of the sentences involved completely determines whether premises logically entail a conclusion.
So these inductive logicians have attempted to follow suit. In such a system each sentence confers a syntactically specified degree inductive essays support on each of the other sentences of the language. Thus, the inductive probabilities in such a system are logical in the sense that they depend on syntactic structure alone. This kind of conception was articulated to some extent by John Maynard Keynes in his Treatise on Probability Rudolf Carnap pursued this idea with greater rigor in his Logical Foundations of Probability and in several subsequent works e, inductive essays.
So, such approaches might well be called Bayesian logicist inductive logics. Other prominent Bayesian logicist attempts to develop a probabilistic inductive logic include the works of JeffreysJaynesand Rosenkrantz It is now widely held that the core idea of this syntactic approach to Bayesian logicism is fatally flawed—that syntactic logical structure cannot be the sole determiner of the degree to which premises inductively support conclusions.
A crucial facet of the problem faced by syntactic Bayesian logicism involves how the logic is supposed to apply in scientific contexts where the conclusion sentence is some scientific hypothesis or theory, and the premises are evidence claims. The difficulty is that in any probabilistic logic that satisfies the usual axioms for probabilities, the inductive support for a hypothesis must depend in part on its prior probability. This prior probability represents arguably how plausible the hypothesis is taken to be on the basis of considerations other than the observational and experimental evidence e.
A syntactic Bayesian logicist must inductive essays us how to assign values to these pre-evidential prior probabilities of hypotheses in a way that relies only on the syntactic logical structure of the hypothesis, perhaps based on some measure of syntactic simplicity. There are severe problems with getting this idea to work. Various kinds of examples seem to show that such an approach must assign intuitively quite unreasonable prior probabilities to hypotheses in specific cases see the footnote cited near the end of Section 3, inductive essays.
Furthermore, for this idea to apply to the evidential support of real scientific theories, scientists would have to formalize theories in a way that makes their relevant syntactic structures apparent, and then evaluate theories solely on that syntactic basis together with their syntactic relationships to evidence statements.
Are we to evaluate alternative theories of gravitation, and alternative quantum theories, this way?
How to write an INDUCTIVE argument
, time: 9:03Problem of induction - Wikipedia
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