# Naturalizing Logic: How Knowledge of Mechanisms Enhances Inductive Inference

## Abstract

**:**

## 1. Introduction

## 2. Mechanisms

## 3. Inductive Generalization

Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a little way towards establishing an universal proposition? Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients, and has solved the problem of Induction.

## 4. Inference to the Best Explanation

## 5. Causality and Counterfactuals

- (1)
- There is a known mechanism by which C produces E.
- (2)
- There is a plausible mechanism by which C produces E.
- (3)
- There is no known mechanism by which C produces E.
- (4)
- There is no plausible mechanism by which C produces E.

## 6. Probability

## 7. Evaluating Mechanisms

## 8. Conclusions

## Funding

## Conflicts of Interest

## References

- Thagard, P. Natural Philosophy: From Social Brains to Knowledge, Reality, Morality, and Beauty; Oxford University Press: New York, NY, USA, 2019. [Google Scholar]
- Johnson-Laird, P.N.; Byrne, R.M. Deduction; Lawrence Erlbaum Associates: Hillsdale, NJ, USA, 1991. [Google Scholar]
- Rips, L.J. The Psychology of Proof: Deductive Reasoning in Human Thinking; MIT Press: Cambridge, MA, USA, 1994. [Google Scholar]
- Holland, J.H.; Holyoak, K.J.; Nisbett, R.E.; Thagard, P.R. Induction: Processes of Inference, Learning, and Discovery; MIT Press: Cambridge, MA, USA, 1986. [Google Scholar]
- Thagard, P. The Cognitive Science of Science: Explanation, Discovery, and Conceptual Change; MIT Press: Cambridge, MA, USA, 2012. [Google Scholar]
- Goodfellow, I.; Bengio, Y.; Courville, A. Deep Learning; MIT Press: Cambridge, MA, USA, 2016. [Google Scholar]
- Thagard, P. Bots and Beasts: What Makes Machines, Animals, and People Smart? MIT Press: Cambridge, MA, USA, 2021. [Google Scholar]
- Bechtel, W. Mental Mechanisms: Philosophical Perspectives on Cognitive Neuroscience; Routledge: New York, NY, USA, 2008. [Google Scholar]
- Craver, C.F.; Darden, L. In Search of Mechanisms: Discoveries across the Life Sciences; University of Chicago Press: Chicago, IL, USA, 2013. [Google Scholar]
- Craver, C.F.; Tabery, J. Mechanisms in Science. In Stanford Encyclopedia of Philosophy; Stanford University: Stanford, CA, USA, 2015. [Google Scholar]
- Glennan, S. The New Mechanical Philosophy; Oxford University Press: Oxford, UK, 2017. [Google Scholar]
- Ranney, M.A.; Clark, D. Climate change conceptual change: Scientific information can transform attitudes. Top. Cogn. Sci.
**2016**, 8, 49–75. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dimitrov, D.S. Virus entry: Molecular mechanisms and biomedical applications. Nat. Rev. Microbiol.
**2004**, 2, 109–122. [Google Scholar] [CrossRef] [PubMed] - Mill, J.S. A System of Logic, 8th ed.; Longman: London, UK, 1970. [Google Scholar]
- Connell, L.; Keane, M.T. A model of plausibility. Cogn. Sci.
**2006**, 30, 95–120. [Google Scholar] [CrossRef] [PubMed][Green Version] - Thagard, P. Explanatory coherence. Behav. Brain Sci.
**1989**, 12, 435–467. [Google Scholar] [CrossRef] - Nisbett, R.E.; Krantz, D.; Jepson, C.; Kunda, Z. The use of statistical heuristics in everyday inductive reasoning. Psychol. Rev.
**1983**, 90, 339–363. [Google Scholar] [CrossRef] - Thagard, P.; Nisbett, R.E. Variability and confirmation. Philos. Studies
**1982**, 42, 379–394. [Google Scholar] [CrossRef] - Hempel, C.G. Aspects of Scientific Explanation; The Free Press: New York, NY, USA, 1965. [Google Scholar]
- Goodman, N. Fact, Fiction and Forecast, 2nd ed.; Bobbs-Merrill: Indianapolis, IN, USA, 1965. [Google Scholar]
- Bird, A.; Tobin, E. Natural Kinds. In Stanford Encyclopedia of Philosophy; Stanford University: Stanford, CA, USA, 2017. [Google Scholar]
- Boyd, R. Realism, anti-foundationalism and the enthusiasm for natural kinds. Philos. Studies Int. J. Philos. Anal. Trad.
**1991**, 61, 127–148. [Google Scholar] [CrossRef] - Harman, G. Thought; Princeton University Press: Princeton, NJ, USA, 1973. [Google Scholar]
- Lipton, P. Inference to the Best Explanation, 2nd ed.; Routledge: London, UK, 2004. [Google Scholar]
- Thagard, P. The best explanation: Criteria for theory choice. J. Philos.
**1978**, 75, 76–92. [Google Scholar] [CrossRef] - Josephson, J.R.; Josephson, S.G. (Eds.) Abductive Inference: Computation, Philosophy, Technology; Cambridge University Press: Cambridge, UK, 1994. [Google Scholar]
- Magnani, L. Abductive Cognition: The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning; Springer: Berlin, Germany, 2009. [Google Scholar]
- Peirce, C.S. Collected Papers; Hartshorne, W.P., Burks, A., Eds.; Harvard University Press: Cambridge, MA, USA, 1958. [Google Scholar]
- Harman, G. Change in View: Principles of Reasoning; MIT Press/Bradford Books: Cambridge, MA, USA, 1986. [Google Scholar]
- Laudan, L. A confutation of convergent realism. Philos. Sci.
**1981**, 48, 19–49. [Google Scholar] [CrossRef] - Thagard, P. Coherence, truth, and the development of scientific knowledge. Philos. Sci.
**2007**, 74, 28–47. [Google Scholar] [CrossRef][Green Version] - Van Fraassen, B. The Scientific Image; Clarendon Press: Oxford, UK, 1980. [Google Scholar]
- Thagard, P. Coherence in Thought and Action; MIT Press: Cambridge, MA, USA, 2000. [Google Scholar]
- Hume, D. A Treatise of Human Nature; Selby-Bigge, L.A., Ed.; Clarendon Press: Oxford, UK, 1888. [Google Scholar]
- Hill, A.B. The environment and disease: Association or causation? Proc. R. Soc. Med.
**1965**, 58, 295–300. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hennekens, C.H.; Buring, J.E. Epidemiology in Medicine; Little, Brown and Co.: Boston, MA, USA, 1987. [Google Scholar]
- Dammann, O. Etiological Explanations; CRC Press: Boca Raton, FL, USA, 2020. [Google Scholar]
- Dammann, O.; Poston, T.; Thagard, P. How do Medical Researchers Make Causal Inferences? In What Is Scientific Knowledge? An Introduction to Contemporary Epistemology of Science; McCain, K., Kampourakis, K., Eds.; Routledge: New York, NY, USA, 2019; pp. 33–51. [Google Scholar]
- Thagard, P. How Scientists Explain Disease; Princeton University Press: Princeton, NJ, USA, 1999. [Google Scholar]
- Pearl, J. The algorithmization of counterfactuals. Ann. Math. Artif. Intell.
**2011**, 61, 29–39. [Google Scholar] [CrossRef] - Gentner, D. Structure-mapping: A theoretical framework for analogy. Cogn. Sci.
**1983**, 7, 155–170. [Google Scholar] [CrossRef] - Howson, C.; Urbach, P. Scientific Reasoning: The Bayesian Tradition; Open Court: Lasalle, IL, USA, 1989. [Google Scholar]
- Olsson, E. Against Coherence: Truth, Probability, and Justification; Oxford University Press: Oxford, UK, 2005. [Google Scholar]
- Hájek, A. Interpretations of Probability. In Stanford Encyclopedia of Philosophy; Stanford University: Stanford, CA, USA, 2019. [Google Scholar]
- Hájek, A.; Hitchcock, C. The Oxford Handbook of Probability and Philosophy; Oxford University Press: Oxford, UK, 2016. [Google Scholar]
- Kahneman, D.; Tversky, A. (Eds.) Choices, Values, and Frames; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Kuhn, J. Part 2: Why does glass break? Corning Museum of Glass. 2015. Available online: https://blog.cmog.org/2015/06/03/part-2-why-does-glass-break/ (accessed on 18 June 2021).
- Abrams, M. Mechanistic probability. Synthese
**2012**, 187, 343–375. [Google Scholar] [CrossRef] - Popper, K.R. The propensity interpretation of probability. Br. J. Philos. Sci.
**1959**, 10, 25–42. [Google Scholar] [CrossRef] - Thagard, P. Causal inference in legal decision making: Explanatory coherence vs. Bayesian networks. Appl. Artif. Intell.
**2004**, 18, 231–249. [Google Scholar] [CrossRef][Green Version] - Kwisthout, J.; Wareham, T.; van Rooij, I. Bayesian intractability is not an ailment that approximation can cure. Cogn. Sci.
**2011**, 35, 779–784. [Google Scholar] [CrossRef] [PubMed] - Pearl, J.; Mackenzie, D. The Book of Why: The New Science of Cause and Effect; Basic Books: New York, NY, USA, 2018. [Google Scholar]
- Johnson, G.S.; Ahn, W.K. Causal networks or causal Islands? The representation of mechanisms and the transitivity of causal judgment. Cogn. Sci.
**2015**, 39, 1468–1503. [Google Scholar] [CrossRef] [PubMed] - Keil, C.F.; Lockhart, K.L. Beyond cause: The development of clockwork cognition. Curr. Dir. Psychol. Sci.
**2021**, 30, 167–173. [Google Scholar] [CrossRef] - Thagard, P. Mechanisms of misinformation: Getting COVID-19 wrong and right. Forthcoming.

Combination (Whole, System, Structure) | Parts (Entities, Components) | Interactions (Activities, Operations) | Changes | Results (Behaviors, Functions, Phenomena) | |
---|---|---|---|---|---|

Global warming | Solar system including Earth | Sun, solar radiation, Earth’s atmosphere, Earth’s surface, greenhouse gas molecules | Earth absorbs sunlight. Earth emits energy as infrared light. Greenhouse gases absorb light, retaining energy. Energy heats up the Earth. | Earth warms. | Earth’s temperature is permanently increasing. Severe weather and flooding are increasingly common. |

Viral epidemic | Human population | Bodies, cells, viruses | Viruses infect cells and reproduce. Viruses spread to other bodies. | Infections spread among bodies | Epidemics and pandemics occur. |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Thagard, P.
Naturalizing Logic: How Knowledge of Mechanisms Enhances Inductive Inference. *Philosophies* **2021**, *6*, 52.
https://doi.org/10.3390/philosophies6020052

**AMA Style**

Thagard P.
Naturalizing Logic: How Knowledge of Mechanisms Enhances Inductive Inference. *Philosophies*. 2021; 6(2):52.
https://doi.org/10.3390/philosophies6020052

**Chicago/Turabian Style**

Thagard, Paul.
2021. "Naturalizing Logic: How Knowledge of Mechanisms Enhances Inductive Inference" *Philosophies* 6, no. 2: 52.
https://doi.org/10.3390/philosophies6020052