Direct Inference and the Problem of Induction

McGrew, Timothy

doi:10.5840/monist200184211

Cited by 13 publications

(11 citation statements)

References 3 publications

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“…Williams 1947, Kyburg 1974, Stove 1986, McGrew 2001, Thorn 2014. The following result, reported by McGrew (2001), illustrates the described combinatorial fact:…”

Section: Imprecise Frequencies Based On Samplingmentioning

confidence: 54%

Direct Inference from Imprecise Frequencies

Thorn

2017

European Studies in Philosophy of Science

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Abstract:It is well known that there are, at least, two sorts of cases where one should not prefer a direct inference based on a narrower reference class, in particular: cases where the narrower reference class is gerrymandered, and cases where one lacks an evidential basis for forming a precise-valued frequency judgment for the narrower reference class. I here propose (1) that the preceding exceptions exhaust the circumstances where one should not prefer direct inference based on a narrower reference class, and (2) that minimal frequency information for a narrower (non-gerrymandered) reference class is sufficient to yield the defeat of a direct inference for a broader reference class. By the application of a method for inferring relatively informative expected frequencies, I argue that the latter claim does not result in an overly incredulous approach to direct inference. The method introduced here permits one to infer a relatively informative expected frequency for a reference class R, given frequency information for a superset of R and/or frequency information for a sample drawn from R.

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“…Williams 1947, Kyburg 1974, Stove 1986, McGrew 2001, Thorn 2014. The following result, reported by McGrew (2001), illustrates the described combinatorial fact:…”

Section: Imprecise Frequencies Based On Samplingmentioning

confidence: 54%

Direct Inference from Imprecise Frequencies

Thorn

2017

European Studies in Philosophy of Science

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“…There are other approaches to justifying inheritance inference that appeal to combinatorial facts that relate the relative frequency of a characteristic among a set (such as C) to the relative frequencies of the characteristic among the subsets of the set (such as SC). One such approach appeals to combinatorial variants of the Law of Large Numbers, which tell us that the vast majority of the subsets of C of sufficient size differ from C by no more than a small amount regarding the frequency of any given property φ (McGrew, 2001; Thorn, 2014, 2017). In making an inheritance inference, this approach proceeds by treating SC as if it were a randomly selected subset of C, as a basis for concluding that it is very probable that the frequency of φ among SC is very similar to the frequency of φ among C. A significant problem with this approach is to justify the treatment of SC as if it were a randomly selected subset of C. Beyond such worries, one might regard the described approach to justifying inheritance inference as too limited, because it cannot be applied as a basis for justifying inheritance inference in the case of so‐called “exceptional subclasses,” which we will now briefly describe.…”

Section: Cautious Monotony and Inheritance In The Case Of Exceptional Subclassesmentioning

confidence: 99%

How Category Selection Impacts Inference Reliability: Inheritance Inference From an Ecological Perspective

Thorn

Schurz

2021

Cognitive Science

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This article presents results from a simulation‐based study of inheritance inference, that is, inference from the typicality of a property among a “base” class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of “exceptional subclasses” (i.e., subclasses that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses.

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“…Like the Reichenbachian justification, the Williams-Stove justification persists in the more recent literature on induction: some recent proponents include Timothy McGrew (2001) as well as Campbell and Franklin (2004). Like the Reichenbachian justification, there are many possible objections to both the bold Williams and modest Stove versions of this justification of induction (Hempel 1960); (Indurkhya 1990); (Maher 1996); (Lange 2011).…”

Section: The Robust Significance Of Armstrongian Universalsmentioning

confidence: 99%

What Can Armstrongian Universals Do for Induction?

Peden

2020

Philosophia

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David Armstrong (1983) argues that necessitation relations among universals are the best explanation of some of our observations. If we consequently accept them into our ontologies, then we can justify induction, because these necessitation relations also have implications for the unobserved. By embracing Armstrongian universals, we can vindicate some of our strongest epistemological intuitions and answer the Problem of Induction. However, Armstrong’s reasoning has recently been challenged on a variety of grounds. Critics argue against both Armstrong’s usage of inference to the best explanation and even whether, by Armstrong’s own standards, necessitation relations offer a potential explanation of this explanandum, let alone the best explanation. I defend Armstrong against these particular criticisms. Firstly, even though there are reasons to think that Armstrong’s justification fails as a self-contained defence of induction, it can usefully complement several other answers to Hume. Secondly, I argue that Armstrong’s reasoning is consistent with his own standards for explanation.

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Direct Inference and the Problem of Induction

Cited by 13 publications

References 3 publications

Direct Inference from Imprecise Frequencies

Direct Inference from Imprecise Frequencies

How Category Selection Impacts Inference Reliability: Inheritance Inference From an Ecological Perspective

What Can Armstrongian Universals Do for Induction?

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