In *The Stanford Encyclopedia of Philosophy*. Winter 2014 edition, 2014.

Paper abstract bibtex

Paper abstract bibtex

An inductive logic is a system of evidential support that extendsdeductive logic to less-than-certain inferences. For valid deductivearguments the premises logically entail the conclusion, wherethe entailment means that the truth of the premises provides aguarantee of the truth of the conclusion. Similarly, in a good inductive argument the premises should provide some degree of support for the conclusion, where such support means that the truth of the premises indicates with some degree of strength that the conclusion is true. Presumably, if the logic of good inductive arguments is to be of any real value, the measure of support it articulates should meet the following condition: , This article will focus on the kind of the approach to inductive logic most widely studied by philosophers and logicians in recent years. These logics employ conditional probability functions to represent measures of the degree to which evidence statements support hypotheses. This kind of approach usually draws on Bayes' theorem, which is a theorem of probability theory, to articulate how the implications of hypotheses about evidence claims influences the degree to which hypotheses are supported by those evidence claims. We will examine the extent to which this kind of logic may pass muster as an adequate logic of evidential support, especially in regard to the testing of scientific hypotheses. In particular, we will see how such a logic may be shown to satisfy the Criterion of Adequacy., Sections 1 through 3 present all of the main ideas behind the probabilistic logic of evidential support. For most readers these three sections will suffice to provide an adequate understanding of the subject. Those readers who want to know more about how the logic applies when the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise may, after reading sections 1-3, skip down to section 6., Sections 4 and 5 are for the more advanced reader who wants a detailed understanding of some telling results about how this logic may bring about convergence to the truth. These results show 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 as this happens, a true hypothesis will very probably acquire evidential support values (as measured by their posterior probabilities) that approach 1.

@incollection{hawthorne_inductive_2014, edition = {Winter 2014}, title = {Inductive {Logic}}, url = {http://plato.stanford.edu/archives/win2014/entries/logic-inductive/}, abstract = {An inductive logic is a system of evidential support that extendsdeductive logic to less-than-certain inferences. For valid deductivearguments the premises logically entail the conclusion, wherethe entailment means that the truth of the premises provides aguarantee of the truth of the conclusion. Similarly, in a good inductive argument the premises should provide some degree of support for the conclusion, where such support means that the truth of the premises indicates with some degree of strength that the conclusion is true. Presumably, if the logic of good inductive arguments is to be of any real value, the measure of support it articulates should meet the following condition: , This article will focus on the kind of the approach to inductive logic most widely studied by philosophers and logicians in recent years. These logics employ conditional probability functions to represent measures of the degree to which evidence statements support hypotheses. This kind of approach usually draws on Bayes' theorem, which is a theorem of probability theory, to articulate how the implications of hypotheses about evidence claims influences the degree to which hypotheses are supported by those evidence claims. We will examine the extent to which this kind of logic may pass muster as an adequate logic of evidential support, especially in regard to the testing of scientific hypotheses. In particular, we will see how such a logic may be shown to satisfy the Criterion of Adequacy., Sections 1 through 3 present all of the main ideas behind the probabilistic logic of evidential support. For most readers these three sections will suffice to provide an adequate understanding of the subject. Those readers who want to know more about how the logic applies when the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise may, after reading sections 1-3, skip down to section 6., Sections 4 and 5 are for the more advanced reader who wants a detailed understanding of some telling results about how this logic may bring about convergence to the truth. These results show 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 as this happens, a true hypothesis will very probably acquire evidential support values (as measured by their posterior probabilities) that approach 1.}, urldate = {2016-02-04}, booktitle = {The {Stanford} {Encyclopedia} of {Philosophy}}, author = {Hawthorne, James}, editor = {Zalta, Edward N.}, year = {2014}, keywords = {Bayes' Theorem, epistemology: Bayesian, probability, interpretations of}, }

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