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The Problem of Induction throughout the Philosophy of Science
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The Problem of Induction throughout the Philosophy of Science

A special issue of Philosophies (ISSN 2409-9287).

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 18089

Special Issue Editor

Dr. Benjamin Jantzen

E-Mail Website
Guest Editor
Department of Philosophy, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Interests: algorithmic discovery; machine learning; philosophy of science; philosophy of physics; philosophy of biology

Special Issue Information

Dear Colleagues,

Any inference from current observations to observations not yet made or to generalizations that entail facts not yet in evidence is widely conceded to invite a Problem of Induction. Some view this as a problem of justification: How can we justify such ampliative inferences? This invites a focus on the relation of justification between theory and evidence, typically deploying the tools of conceptual analysis. Insofar as methodology is relevant, these analyses of justification tend to elevate existing scientific practices to the status of ideals. However, the focus on justification can also invite radical rejections of methodological conventions, such as the defense of non-empirical methods of theory evaluation in theoretical physics. In either case, there is a presumption that a logic of discovery is either impossible or irrelevant.

Others have framed the Problem of Induction in terms of the failure to obtain truth: Going beyond our observations entails the risk of error, and the problem is to ascertain how or if this risk can be eliminated, mitigated, or circumscribed. This invites a focus on method. Proposed solutions to this version of the problem include formal learning theory (logical reliability), meta-inductivism, and probably approximately correct (PAC) learnability. These proposals and their focus on method reopen the door to a non-trivial logic of discovery and are especially salient to the rise of machine learning in science and debates over its foundations and scope. Can machines carry out novel scientifically significant induction of theory from observation? What are the normative constraints on such algorithms? These more recent methodological approaches to the problem of induction have also given rise to the development of new domains of scientific practice, chief among them the burgeoning field of causal discovery.

How have these divergent interpretations of the Problem of Induction and the consequent strategies introduced to resolve or dissolve the problem shaped the recent philosophy of science? What should a philosophy of the new sciences of inductive learning look like? This Special Issue aims to bring to the fore the ways in which the Problem of Induction continues to drive the philosophy of science, and to evaluate the impact of proposed solutions to the problem of induction on both science and its philosophy.

Prof. Benjamin Jantzen
Guest Editor

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Keywords

  • problem of induction
  • confirmation
  • inductive skepticism
  • meta-induction
  • formal learning theory
  • logical reliability
  • theory choice
  • ampliative inference
  • machine learning
  • logic of discovery

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Published Papers (5 papers)

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24 pages, 1631 KiB  
Article
On Falsifiable Statistical Hypotheses
by Konstantin Genin
Philosophies 2022, 7(2), 40; https://doi.org/10.3390/philosophies7020040 - 2 Apr 2022
Cited by 1 | Viewed by 4489
Abstract
Popper argued that a statistical falsification required a prior methodological decision to regard sufficiently improbable events as ruled out. That suggestion has generated a number of fruitful approaches, but also a number of apparent paradoxes and ultimately, no clear consensus. It is still [...] Read more.
Popper argued that a statistical falsification required a prior methodological decision to regard sufficiently improbable events as ruled out. That suggestion has generated a number of fruitful approaches, but also a number of apparent paradoxes and ultimately, no clear consensus. It is still commonly claimed that, since random samples are logically consistent with all the statistical hypotheses on the table, falsification simply does not apply in realistic statistical settings. We claim that the situation is considerably improved if we ask a conceptually prior question: when should a statistical hypothesis be regarded as falsifiable. To that end we propose several different notions of statistical falsifiability and prove that, whichever definition we prefer, the same hypotheses turn out to be falsifiable. That shows that statistical falsifiability enjoys a kind of conceptual robustness. These notions of statistical falsifiability are arrived at by proposing statistical analogues to intuitive properties enjoyed by exemplary falsifiable hypotheses familiar from classical philosophy of science. That demonstrates that, to a large extent, this philosophical tradition was on the right conceptual track. Finally, we demonstrate that, under weak assumptions, the statistically falsifiable hypotheses correspond precisely to the closed sets in a standard topology on probability measures. That means that standard techniques from statistics and measure theory can be used to determine exactly which hypotheses are statistically falsifiable. In other words: the proposed notion of statistical falsifiability both answers to our conceptual demands and submits to standard mathematical techniques. Full article
(This article belongs to the Special Issue The Problem of Induction throughout the Philosophy of Science)
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15 pages, 347 KiB  
Article
Causal Emergence: When Distortions in a Map Obscure the Territory
by Frederick Eberhardt and Lin Lin Lee
Philosophies 2022, 7(2), 30; https://doi.org/10.3390/philosophies7020030 - 9 Mar 2022
Cited by 3 | Viewed by 2826
Abstract
We provide a critical assessment of the account of causal emergence presented in Erik Hoel’s 2017 article “When the map is better than the territory”. The account integrates causal and information theoretic concepts to explain under what circumstances there can be causal descriptions [...] Read more.
We provide a critical assessment of the account of causal emergence presented in Erik Hoel’s 2017 article “When the map is better than the territory”. The account integrates causal and information theoretic concepts to explain under what circumstances there can be causal descriptions of a system at multiple scales of analysis. We show that the causal macro variables implied by this account result in interventions with significant ambiguity, and that the operations of marginalization and abstraction do not commute. Both of these are desiderata that, we argue, any account of multi-scale causal analysis should be sensitive to. The problems we highlight in Hoel’s definition of causal emergence derive from the use of various averaging steps and the introduction of a maximum entropy distribution that is extraneous to the system under investigation. Full article
(This article belongs to the Special Issue The Problem of Induction throughout the Philosophy of Science)
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16 pages, 356 KiB  
Article
Induction, Experimentation and Causation in the Social Sciences
by Lars-Göran Johansson
Philosophies 2021, 6(4), 105; https://doi.org/10.3390/philosophies6040105 - 16 Dec 2021
Cited by 1 | Viewed by 3515
Abstract
Inductive thinking is a universal human habit; we generalise from our experiences the best we can. The induction problem is to identify which observed regularities provide reasonable justification for inductive conclusions. In the natural sciences, we can often use strict laws in making [...] Read more.
Inductive thinking is a universal human habit; we generalise from our experiences the best we can. The induction problem is to identify which observed regularities provide reasonable justification for inductive conclusions. In the natural sciences, we can often use strict laws in making successful inferences about unobserved states of affairs. In the social sciences, by contrast, we have no strict laws, only regularities which most often are conditioned on ceteris paribus clauses. This makes it much more difficult to make reliable inferences in the social sciences. In particular, we want knowledge about general causal relations in order to be able to determine what to do in order to achieve a certain state of affairs. Knowledge about causal relations that are also valid in the future requires experiments or so called ‘natural experiments’. Only knowledge derived from such experiences enable us to draw reasonably reliable inferences about how to act in order to achieve our goals. Full article
(This article belongs to the Special Issue The Problem of Induction throughout the Philosophy of Science)
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26 pages, 12663 KiB  
Article
Scientific Variables
by Benjamin C. Jantzen
Philosophies 2021, 6(4), 103; https://doi.org/10.3390/philosophies6040103 - 13 Dec 2021
Cited by 1 | Viewed by 2453
Abstract
Despite their centrality to the scientific enterprise, both the nature of scientific variables and their relation to inductive inference remain obscure. I suggest that scientific variables should be viewed as equivalence classes of sets of physical states mapped to representations (often real numbers) [...] Read more.
Despite their centrality to the scientific enterprise, both the nature of scientific variables and their relation to inductive inference remain obscure. I suggest that scientific variables should be viewed as equivalence classes of sets of physical states mapped to representations (often real numbers) in a structure preserving fashion, and argue that most scientific variables introduced to expand the degrees of freedom in terms of which we describe the world can be seen as products of an algorithmic inductive inference first identified by William W. Rozeboom. This inference algorithm depends upon a notion of natural kind previously left unexplicated. By appealing to dynamical kinds—equivalence classes of causal system characterized by the interventions which commute with their time evolution—to fill this gap, we attain a complete algorithm. I demonstrate the efficacy of this algorithm in a series of experiments involving the percolation of water through granular soils that result in the induction of three novel variables. Finally, I argue that variables obtained through this sort of inductive inference are guaranteed to satisfy a variety of norms that in turn suit them for use in further scientific inferences. Full article
(This article belongs to the Special Issue The Problem of Induction throughout the Philosophy of Science)
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19 pages, 2284 KiB  
Article
The Impact of Meta-Induction: From Skepticism to Optimality
by Gerhard Schurz
Philosophies 2021, 6(4), 95; https://doi.org/10.3390/philosophies6040095 - 26 Nov 2021
Viewed by 2937
Abstract
In the first section, five major attempts to solve the problem of induction and their failures are discussed. In the second section, an account of meta-induction is introduced. It offers a novel solution to the problem of induction, based on mathematical theorems about [...] Read more.
In the first section, five major attempts to solve the problem of induction and their failures are discussed. In the second section, an account of meta-induction is introduced. It offers a novel solution to the problem of induction, based on mathematical theorems about the predictive optimality of attractivity-weighted meta-induction. In the third section, how the a priori justification of meta-induction provides a non-circular a posteriori justification of object-induction, based on its superior track record, is explained. In the fourth section, four important extensions and refinements of the method of meta-induction are presented. The final section, summarizes the major impacts of the program of meta-induction for epistemology, the philosophy of science and cognitive science. Full article
(This article belongs to the Special Issue The Problem of Induction throughout the Philosophy of Science)
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