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- Robert C. Cummins (1992). Cross Domain Inference and Problem Embedding. In Robert E. Cummins & John L. Pollock (eds.), Philosophy and AI: Essays at the Interface. MIT Press.I.1. Two reasons for studying inference. Inference is studied for two distinct reasons: for its bearing on justification and for its bearing on learning. By and large, philosophy has focused on the role of inference in justification, leaving its role in learning to psychology and artificial intelligence. This difference of role leads to a difference of conception. An inference based theory of learning does not require a conception of inference according to which a good inference is one that justifies its conclusion, whereas, obviously, an inference based theory of justification does require such a conception.1 Because of its focus on normative issues of justification, philosophy has taken a retrospective approach to inference, whereas a focus on learning naturally leads to a prospective approach. A focus on learning leads us to ask, "Given what is known, what should be inferred? How can what is known lead, via inference, to new knowledge?" A focus on justification has led philosophers to concentrate instead on a retrospective question: "Given a belief, can it be validly inferred from what is known? How can what is known justify, via inference, a new belief?" Thus, for philosophy, inference can be regarded as permissive: one needn't worry about what to infer, only about whether what has been arrived at somehow or other is or can be inferentially justified. A theory of learning, on the other hand, requires a conception of inference that is directive, for the problem of inference based learning is precisely the problem of what to infer.Reading list | Discuss | Edit | Categorize |My bibliography
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I argue that Goodman's puzzle of grue at least poses no real challenge about inductive inference. By drawing on Stove's characterisation of Hume's characterisation of inductive inference, we see that the premises in an inductive inference report experienced impressions; and Goodman can be interpreted as posing a real challenge about inductive inference only if we treat an epistemic subject's observations more as logical contents and less as experienced impressions. So, even though the grue puzzle was effective against its stated logicist targets, it is not thereby an enduring difficulty regarding experience's ability to impart epistemic justification via inductive evidence.
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| | Other links: journals.cambridge.org jstor.org dx.doi.org | Scholar | At my library | More options ... For some authors, at least in some contexts,1 the distinction between inference and consequence is minimal. An inference can then be regarded as an ordered pair 〈Γ,φ〉, where Γ is a set of sentences or propositions and φ is a sentence or proposition.2 And then an inference 〈Γ,φ〉 can be said to valid just in case φ is a consequence of Γ (analogously for logically valid and logical consequence). For some other authors, the distinction between inference and consequence..
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| | Other links: people.su.se | Scholar | More options ... What is the connection between justification and the kind of consequence relations that are studied by logic? In this essay, I shall try to provide an answer, by proposing a general conception of the kind of inference that counts as justified or rational.
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| | Other links: users.ox.ac.uk usc.edu dx.doi.org springerlink.com | Scholar | At my library | More options ... Non-monotonic inference is inference that is defeasible: in contrast with deductive inference, the conclusions drawn may be withdrawn in the light of further information, even though all the original premises are retained. Much of our everyday reasoning is like this, and a non-monotonic approach has applications to a number of technical problems in artificial intelligence. Work on formalizing non-monotonic inference has progressed rapidly since its beginnings in the 1970s, and a number of mature theories now exist – the most important being default logic, autoepistemic logic, and circumscription.
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| | Other links: oro.open.ac.uk elsevier.com | Scholar | More options ... Second, there is a form of ampliative inference that has come to be called ‘inference to the best explanation,’ or more briefly ‘explanatory inference.’ Roughly: From the fact that a certain hypothesis would explain the data at hand better than any other available hypothesis, we infer with some degree of confidence that that leading hypothesis is correct. There is no question but that this inference is often performed. Arguably, every human being performs it many times in a day, perhaps without letup.
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| | Scholar | More options ... It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.
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| | Other links: informaworld.com dx.doi.org | Scholar | At my library | More options ... Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction.
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| | Other links: philsci-archive.pitt.edu journals.uchicago.edu dx.doi.org | Scholar | At my library | More options ... I argue that Richard Fumerton’s controversial “Principle of Inferential Justification” (PIJ) can be satisfactorily defended against several charges that have been leveled against it, namely, that it leads to skepticism, that it confuses different levels of justification, and that it involves a fallacy of “misconditionalization.”The basis of my defense of PIJ is a distinction between two theories of the nature of inference—an internalist conception (IC), according to which inferring requires that the reasoner have a conscious perspective on the evidential relation between premises and conclusion, and an externalist conception (EC), which does not require any such perspective. Given IC, the above charges against PIJ fail, and PIJ emerges as a plausible thesis. Given EC, however, the above charges stick, and PIJ is untenable. An internalist position on inferential justification is tenable, therefore, if and only if it is held in conjunction with an internalist conception of inference.
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| | Scholar | At my library | More options ... This paper aims to be a friendly introduction to formal learning theory. I introduce key concepts at a slow pace, comparing and contrasting with other approaches to inductive inference such as con…rmation theory. A number of examples are discussed, some in detail, such as Goodman’s Riddle of Induction. I outline some important results of formal learning theory that are of philosophical interest. Finally, I discuss recent developments in this approach to inductive inference.
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| | Scholar | More options ... Knowledge can be transmitted by a valid deductive inference. If I know that p, and I know that if p then q, then I can infer that q, and I can thereby come to know that q. What feature of a valid deductive inference enables it to transmit knowledge? In some cases, it is a proof of validity that grounds the transmission of knowledge. If the subject can prove that her inference follows a valid rule, then her inference transmits knowledge. However, this only pushes the question back to the inference that was made in this proof. What feature of that inference enables it to transmit knowledge? A vicious regress looms here. Every proof requires a valid inference, and every valid inference must follow at least one rule of inference. So every proof must follow at least one rule of inference. Therefore not every valid inference that transmits knowledge can acquire this power through a proof, on pain of vicious infinite regress. So it must be possible to transmit knowledge by making an inference that follows an underived rule. A deductive inference that follows an underived rule is what I will call a basic deductive inference. It must be possible to transmit knowledge by making a basic deductive inference. But how is this possible? What feature of a basic deductive inference gives it this power to transmit knowledge?
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| | Scholar | More options ... Discussion of Robert C. Cummins, Cross domain inference and problem embedding
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