Abstract
In this chapter we go beyond Peirce by studying the role of abduction in the weak justification or confirmation of hypotheses. Section 6.1 deals with qualitative confirmation, or its special cases of inductive and abductive confirmation as identified by Howard Smokler. Section 6.2 treats quantitative abductive confirmation within the setting of Bayesian epistemic probabilities. The basic theorem of abductive confirmation shows that contingent evidence E is positively relevant (PR) to consistent hypothesis H if H logically entails E. More generally, if H deductively or inductively explains E, then E PR-confirms H. This result shows that abduction is generally credence-increasing, and refutes the GW-thesis that abduction is ignorance-preserving. In Sect. 6.3 we show comparatively that better explanations with higher explanatory power receive stronger degrees of confirmation. Thus, it is useful to follow Carl G. Hempel in combining the notions of explanatory and predictive power into one concept of the “systematic power” of a scientific theory. Section 6.4 analyzes the virtues of unification by theories. It is shown that Whewell’s “consilience of inductions” (i.e. a theory entails two independent laws) has to be distinguished from the idea of inductive systematization (i.e. two independent empirical phenomena become relevant to each other relative to a theory). The latter case is covered by Myrvold’s measure of unification.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
Bas van Fraassen’s (1989) “constructive empiricism ” restricts the empirical basis to observations by our “naked” senses.
- 3.
In all sciences, statements already in the empirical level are conceptually laden interpretations of reality. In the human and social sciences, the situation is even more complex, since the empirical basis typically concerns human agents and their actions which are meaningful to the agents themselves. Thus, the researcher has to impose a second-order meaning to the first-order discourse of the agents. For an application of Peirce’s semiotics to this problem of meaning construction, see Tavory and Timmermans (2014) .
- 4.
Lawlike statements, including probabilistic laws, make assertions about counterfactual situations. The doctrine that there are real possibilities beyond the domain of actuality was important for Peirce’′s later realist versions of his pragmatism (see Peirce 1901). This inferential problem has to combine the method of abduction with experimental operations which also realize counterfactual possibilities.
- 5.
This idea goes back to Plato’s Academy and Greek astronomy, and was hotly debated during the time of the Copernican Revolution. An excellent history, with sympathies on the side of the instrumentalists, is given by Duhem (1969) .
- 6.
Carnap called this concept “Bewährung” following Popper , but Popper’s “Bewährungsgrad” was later translated as “the degree of corroboration” (see Popper 1959), to distinguish it from the inductivist notion of “confirmation”.
- 7.
Note that the notion of confirmation or support is weaker than the notion of acceptance , where a hypothesis is so strongly supported by evidence that it is rational to tentatively accept it as true, i.e. to include it in the body of what is currently taken to be scientific knowledge. See Chap. 7 for the stronger notion of justification by IBE .
- 8.
We shall see below that this was not Whewell’s own interpretation, as consilience for him provided an argument in favour of the unifying theory H.
- 9.
The concept of conditional deductive confirmation of H by E can be defined by the requirement that there is an observational statement C such that H achieves deductive systematization between C and E, i.e. H&C├ E. To avoid the trivial choice of C as H → E, one should require that C is logically independent of H (see Kuipers 2000, 36) .
- 10.
Laudan (1990) also argues that hypotheses are not confirmed by all of their observational consequences.
- 11.
- 12.
More precisely, in a simple NP-test with null hypothesis Ho and a specific alternative H1, the significance level α is the statistical probability of rejecting Ho when Ho is true, so that 1 – α is the truth-frequency for inferences about Ho. The power of the test is the statistical probability of rejecting H0 (or accepting H1) when H1 is true, so that it is the truth-frequency for inferences about H1. This note corrects a mistake in Niiniluoto (1999b), 447.
- 13.
- 14.
- 15.
Gerhard Schurz (2008a) defends abduction as a mode of inference with some value in justification , but rejects the Bayesian approach as being unable to demarcate scientifically worthwhile hypotheses from pure speculations. To show that Bayesian incremental confirmation is too easy, Schurz (2008b) considers the God’s will hypothesis
(G-E)
God wants E, and whatever God wants, happens.
where E is any empirical phenomenon. As G-E deductively entails E, by (5) E confirms G-E, even though G-E is purely speculative and should not receive any scientific confirmation. This argument raises many issues that belong to the philosophy of religion. All theologians would not accept that evil events happen by God’s wishes. Some religious thinkers, like Richard Swinburne, have applied Bayesian confirmation theory to the hypothesis that God exists. So the Bayesian approach is flexible enough to reconstruct the thinking of a religious person who sees divine providence everywhere and thereby finds confirmation for his or her faith. One may recall that confirmation is a weak epistemic concept which does not yet guarantee that a hypothesis is acceptable as true (Niiniluoto 2008). But I agree with Schurz that G-E should not receive any scientific confirmation. However, this does not require that Bayesianism is rejected, as Schurz pleads, since a Bayesian can block the confirmation of such speculative religious hypothesis by giving them zero prior probability . This move could be justified by arguing that problems with the notion of God’s omnipotence show that G-E is inconsistent. Another line of argument would be to accept that G-E entails E, but deny that G-E explains E, since it includes an ad hoc assumption that God wants E, so that G-E is not supported by the refined result (6).
- 16.
The Basic Theorem gives a Bayesian counterargument to the thesis of Roche and Sober (2013) that “explanatoriness is evidentially irrelevant”. They defend this thesis by claiming that P(H/E&B) = P(H/E), when B states “were H and E true, H would explain E”. But our theorem (6) is expressed as a conditional “if B then P(H/E) > P(H)”. If B is a proposition which can occur as argument of the probability function, then the correct counterpart of (6) is P(H/E&B) > P(H/B), i.e. E is positively relevant to H given B, rather than the equation of Roche and Sober. For a different reply, see Climenhaga (2017) .
- 17.
- 18.
- 19.
- 20.
- 21.
Peirce was aware of this distinction, as one can see in CP 8.231–232.
- 22.
In spite of his doubts about Bayesianism , Psillos (2004) , 90, finds this suggestion interesting.
- 23.
- 24.
For an estimate of the historical record of theoretical abductions , see Douven (2002) .
- 25.
- 26.
As the difficulties in the explication of the notion of complexity show (cf. Foster and Martin 1966) , it is not easy to give a precise account of counting the number of the “logically independent basic assumptions” of a theory. This is illustrated by the debate of Myrvold (2003) and Schurz (2008b) on the comparison of the Ptolemaic and Copernican theories in astronomy.
- 27.
In the special of curve fitting , where the curve is defined by a function of order m and goes though n data points, the relative simplicity is the ratio n/m. Gillies (1989) proposes the difference n-m as a measure of “explanatory surplus”. Currently the most popular approaches to curve fitting or “model selection” are the Akaike Information Criterion AIC and the Bayesian Information Criterion, which give different trade-offs between accuracy and simplicity (see Sober 2008, 82–104) . When model M is a class of functions of order m, and L(M) is the member of M with the highest likelihood relative to data D, AIC gives log P(D/L(M)) – m as an unbiased estimate of the average predictive accuracy of M. Sober argues that this value is an unbiased estimate of the closeness to the truth of L(M), when closeness is measured by the directed divergence (8.15) (ibid., 98).
- 28.
On the other hand, the religious hypothesis G-E (mentioned in footnote 14) would have minimal relative simplicity in Kaila’s sense , since for each empirical statement E it requires the ad hoc premise that God wants E. Kitcher (1981) says that G-E achieves “spurious unification ”, but in fact it does not yield any kind of unification.
- 29.
As an alternative to IS, one may require that H together with E is positively relevant to E′. i.e., 1 > P(E′/H&E) > P(E′). These notions of inductive systematization are motivated by Hempel’s suggestion in 1958 that theoretical concepts could be logically indispensable for inductive systematization. Hempel had noted that deductive systematization by a theory H (i.e. H&E′├ E and not E′├ E) can always be achieved by an observational subtheory of H. As a way out of this “theoretician’s dilemma”, he proposed that inductive systematization might behave differently. Niiniluoto and Tuomela (1973) prove that Hempel’s guess was right.
- 30.
- 31.
See also footnote 9 on conditional deductive confirmation .
- 32.
- 33.
Schupbach (2005) , who otherwise defends Myrworld against Lange , emphasizes the difference between Myrvold’s unification and common cause explanations. However, in his reply to Lange, Myrvold (2017) argues that his measure U of mutual information unification applies to evidence statements which are sequences of values of X and Y, given a hypothesis which posits a common cause.
- 34.
As the third relevant case one should mention examples of misleading similarities (convergence in evolution) and spurious correlations (e.g. between divorce rates and the consumption of margarine), where a common cause explanation is not plausible and should be replaced by separate cause explanations (see Sober 1988) . But note that the search for such separate cause explanations is abductive as well.
Bibliography
Brössel, P. (2013). Correlation and truth. In V. Karakostas and D. Dieks (eds.), EPSA11 Perspectives and foundational problems in philosophy of science (pp. 41-55). Cham: Springer.
Bovens, L., & Hartmann, S. (2003). Bayesian epistemology. Oxford: Oxford University Press.
Carnap, R. (1962). Logical foundations of probability (2nd ed.). Chicago: The University of Chicago Press.
Cleland, C. (2002). Methodological and epistemic differences between historical science and experimental science. Philosophy of Science, 69, 474–496.
Climenhaga, N. (2017). How explanation guides confirmation. Philosophy of Science, 84, 359–368.
Douven, I. (2002). Testing inference to the best explanation. Synthese, 130, 355–377.
Duhem, P. (1969). To save the phenomena: An essay on the idea of physical theory from Plato to Galileo. Chicago: The University of Chicago Press. (Original in French in 1908).
Earman, J. (1992). Bayes or bust? A critical examination of Bayesian confirmation theory. Cambridge, MA: The MIT Press.
Festa, R. (1999). Bayesian confirmation. In M. Galavotti & A. Pagnini (Eds.), Experience, reality, and scientific explanation (pp. 55–87). Dordrecht: Kluwer.
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, 66, S362–S378.
Foster, M. H., & Martin, M. L. (Eds.). (1966). Probability, confirmation, and simplicity: Readings in the philosophy of inductive logic. New York: The Odyssey Press.
Gabbay, D. M., & Woods, J. (2005). The reach of abduction: Insight and trial. Amsterdam: Elsevier.
Gillies, D. (1989). Non-Bayesian confirmation theory and the principle of explanatory surplus. In A. Fine & J. Leplin (Eds.), PSA 1988 (Vol. 2, pp. 373–380). East Lansing: Philosophy of Science Association.
Good, I. J. (1960). Weight of evidence, corroboration, explanatory power, information and the utility of experiments. Journal of the Royal Statistical Society B, 22, 319–322.
Harper, W. L. (2011). Isaac Newton’s scientific method. Oxford: Oxford University Press.
Hempel, C. G. (1965). Aspects of scientific explanation. New York: The Free Press.
Hempel, C. G. (1966). Philosophy of natural science. Englewood Cliffs: Prentice-Hall.
Hesse, M. (1974). The structure of scientific inference. London: Macmillan.
Hintikka, J. (1968). The varieties of information and scientific explanation. In B. van Rootselaar & J. F. Staal (Eds.), Logic, methodology, and philosophy of science III (pp. 151–171). Amsterdam: North-Holland.
Hintikka, J., & Suppes, P. (Eds.). (1966). Aspects of inductive logic. Amsterdam: North-Holland.
Howson, C., & Urbach, P. (1989). Scientific reasoning: The Bayesian approach. La Salle, IL: Open Court.
Iranzo, V. (2007). Abduction and inference to the best explanation. Theoria: An International Journal for Theory, History and Foundations of Science, 60, 339–346.
Kaila, E. (2014). Human knowledge: A classic statement of logical empiricism. La Salle: Open Court.
Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48, 507–531.
Kneale, W. (1949). Probability and induction. Oxford: Oxford University Press.
Kuipers, T. (2000). From instrumentalism to constructive realism: On some relations between confirmation, empirical progress, and truth approximation. Dordrecht: Kluwer.
Lange, M. (2004). Bayesianism and unification: A reply to Wayne Myrvold. Philosophy of Science, 71, 205–215.
Laudan, L. (1990). Science and relativism. Chicago: The University of Chicago Press.
Levi, I. (1967). Gambling with truth. New York: Alfred A. Knopf.
Lipton, P. (2001b). Is explanation a guide to inference? A reply to Wesley C. Salmon. In Hon & Rakover (Eds.), pp. 93–120.
Lipton, P. (2004). Inference to the best explanation. London: Routledge (First edition in 1991).
McGrew, T. (2003). Confirmation, heuristics, and explanatory reasoning. The British Journal for the Philosophy of Science, 54, 553–567.
Milne, P. (1996). Log[P(h/eb)/P(h/b)] is the one true measure of confirmation. Philosophy of Science, 63, 21–26.
Monton, B. (1998). Bayesian agnosticism and constructive empiricism. Analysis, 58, 207–212.
Morrison, M. (2000). Unifying scientific theories: Physical concepts and mathematical structures. Cambridge: Cambridge University Press.
Myrvold, W. C. (1996). Bayesianism and diverse evidence: A reply to Andrew Wayne. Philosophy of Science, 63, 661–665.
Myrvold, W. C. (2003). A Bayesian account of the virtue of unification. Philosophy of Science, 70, 399–423.
Myrvold, W. (2017). On evidential import of unification. Philosophy of Science, 84, 92–114.
Nagel, E. (1961). The structure of science. London: Routledge & Kegan Paul.
Niiniluoto, I. (1983). Novel facts and Bayesianism. The British Journal for the Philosophy of Science, 34, 375–379.
Niiniluoto, I. (1984). Is science progressive? Dordrecht: D. Reidel.
Niiniluoto, I. (1999a). Critical scientific realism. Oxford: Oxford University Press.
Niiniluoto, I. (1999b). Defending abduction. Philosophy of Science (Proceedings), 66, S436–S451.
Niiniluoto, I. (2004). Truth-seeking by abduction. In F. Stadler (Ed.), Induction and deduction in the sciences (pp. 57–82). Dordrecht: Kluwer.
Niiniluoto, I. (2008). Abduction, unification, and Bayesian confirmation: Comment on Schurz. In C. Dégremont, L. Keiff, & H. Rückert (Eds.), Dialogues, logics and other strange things (pp. 365–370). London: College Publications.
Niiniluoto, I. (2011c). The Development of the Hintikka Program. In D. Gabbay, S. Hartmann, & J. Woods (Eds.), Handbook of the History of Logic, vol. 10: Inductive Logic (pp. 311–356). Amsterdam: North-Holland.
Niiniluoto, I. (2016). Unification and confirmation. Theoria: An International Journal for Theory, History and Foundations of Science, 31, 107–124.
Niiniluoto, I., & Tuomela, R. (1973). Theoretical concepts and hypothetico-inductive inference. Dordrecht: D. Reidel.
Nyrup, R. (2015). How explanatory reasoning justifies pursuit: A Peircean view of IBE. Philosophy of Science, 82, 749–760.
Okasha, S. (2000). Van Fraassen’s critique of inference to the best explanation. Studies in History and Philosophy of Science, 31, 691–710.
Olsson, E. (2005). Against coherence: Truth, probability, and justification. Oxford: Oxford University Press.
Peirce, C. S. (1901). Modality, necessary, possibility, probability. In J. M. Baldwin (Ed.), Dictionary of philosophy and psychology. P. Smith: Gloucester, MA.
Popper, K. R. (1959). The logic of scientific discovery. London: Hutchinson.
Popper, K. R. (1963). Conjectures and refutations. London: Hutchinson.
Psillos, S. (2004). Inference to the best explanation and Bayesianism. In F. Stadler (Ed.), Induction and deduction in the sciences (pp. 83–91). Dordrecht: Kluwer.
Roche, W., & Sober, E. (2013). Explanatoriness is evidentially irrelevant; or, inference to the best explanation meets Bayesian confirmation theory. Analysis, 73, 659–668.
Salmon, W. (2001a). Explanation and confirmation: A Bayesian critique of inference to the best explanation. In Hon & Rakover (Eds.), pp. 61–91.
Salmon, W. (2001b). Reflections of a bashful Bayesian: A reply to Peter Lipton. In Hon & Rakover (Eds.), pp. 121–136.
Schupbach, J. N. (2005). On a Bayesian analysis of the virtue of unification. Philosophy of Science, 72, 594–607.
Schurz, G. (1999). Explanation and unification. Synthese, 120, 95–114.
Schurz, G. (2008a). Patterns of abduction. Synthese, 164, 201–234.
Schurz, G. (2008b). Common cause abduction and the formation of theoretical concepts in science. In C. Dégremont, L. Keiff, & H. Rückert (Eds.), Dialogues, logics and other strange things (pp. 337–364). London: College Publications.
Schurz, G. (2015). Causality and unification: How causality unifies statistical regularities. Theoria: An International Journal for Theory, History and Foundations of Science, 30, 73–95.
Shogenji, T. (1999). Is coherence truth conducive? Analysis, 59, 338–345.
Shogenji, T. (2013). Coherence of the contents and the transmission of probabilistic support. Synthese, 190, 2525–2545.
Smokler, H. (1968). Conflicting conceptions of confirmation. The Journal of Philosophy, 65, 300–312.
Snyder, L. J. (1997). Discoverers’ induction. Philosophy of Science, 64, 580–604.
Sober, E. (1988). Reconstructing the past: Parsimony, evolution, and inference. Cambridge, MA: The MIT Press.
Sober, E. (2008). Evidence and evolution: The logic behind the science. Cambridge: Cambridge University Press.
Tavory, I., & Timmermans, S. (2014). Abductive analysis: Theorizing qualitative research. Chicago: The University of Chicago Press.
van Fraassen, B. (1989). Laws and symmetry. Oxford: Oxford University Press.
Whewell, W. (1847). The philosophy of inductive sciences, founded upon their history (2nd ed.). London: John W. Parker and Sons.
Zamora Bonilla, J. P. (1996). Truthlikeness without truth: A methodological approach. Synthese, 93, 343–372.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Niiniluoto, I. (2018). Abduction and Confirmation. In: Truth-Seeking by Abduction. Synthese Library, vol 400. Springer, Cham. https://doi.org/10.1007/978-3-319-99157-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-99157-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99156-6
Online ISBN: 978-3-319-99157-3
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)