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Conditionals, Counterfactuals, and Rational Reasoning: An Experimental Study on Basic Principles

Abstract

We present a unified approach for investigating rational reasoning about basic argument forms involving indicative conditionals, counterfactuals, and basic quantified statements within coherence-based probability logic. After introducing the rationality framework, we present an interactive view on the relation between normative and empirical work. Then, we report a new experiment which shows that people interpret indicative conditionals and counterfactuals by coherent conditional probability assertions and negate conditionals by negating their consequents. The data support the conditional probability interpretation of conditionals and the narrow-scope reading of the negation of conditionals. Finally, we argue that coherent conditional probabilities are important for probabilistic analyses of conditionals, nonmonotonic reasoning, quantified statements, and paradoxes.

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Notes

  1. We thank Hans Rott for stimulating the construction of the rational monotonicity tasks.

References

  • Adams, E. W. (1975). The logic of conditionals. An application of probability to deduction. Dordrecht: Reidel.

    MATH  Google Scholar 

  • Baioletti, M., Capotorti, A., Galli, L., Tognoloni, S., Rossi, F., & Vantaggi, B. (2016). CkC (Check Coherence package; version e6, November 2016). http://www.dmi.unipg.it/~upkd/paid/software.html. Retrieved November 2016

  • Benferhat, S., Dubois, D., & Prade, H. (1997). Nonmonotonic reasoning, conditional objects and possibility theory. Artificial Intelligence, 92, 259–276.

    MathSciNet  Article  MATH  Google Scholar 

  • Bezzazi, H., Makinson, D., & Pérez, R. P. (1997). Beyond rational monotony: Some strong non-horn rules for nonmonotonic inference relations. Journal of Logic and Computation, 7(5), 605–631.

    MathSciNet  Article  MATH  Google Scholar 

  • Biazzo, V., & Gilio, A. (2000). A generalization of the fundamental theorem of de Finetti for imprecise conditional probability assessments. International Journal of Approximate Reasoning, 24(2–3), 251–272.

    MathSciNet  Article  MATH  Google Scholar 

  • BonJour, L. (1985). The structure of empirical knowledge. Cambridge: Harvard University Press.

    Google Scholar 

  • Bonnefon, J.-F., Da Silva Neves, R., Dubois, D., & Prade, H. (2012). Qualitative and quantitative conditions for the transitivity of perceived causation: Theoretical and experimental results. Annals of Mathematics and Artificial Intelligence, 64, 311–333.

    MathSciNet  Article  MATH  Google Scholar 

  • Capotorti, A., Lad, F., & Sanfilippo, G. (2007). Reassessing accuracy rates of median decisions. American Statistician, 61(2), 132–138.

    MathSciNet  Article  Google Scholar 

  • Chater, N., & Oaksford, M. (1999). The probability heuristics model of syllogistic reasoning. Cognitive Psychology, 38, 191–258.

    Article  Google Scholar 

  • Cohen, A. (1999). Generics, frequency adverbs, and probability. Linguistics and Philosophy, 22, 221–253.

    Article  Google Scholar 

  • Cohen, A. (2012). Generics as modals. Recherches linguistiques de Vincennes, 41, 63–82.

    Article  Google Scholar 

  • Coletti, G., & Scozzafava, R. (2002). Probabilistic logic in a coherent setting. Dordrecht: Kluwer.

    Book  MATH  Google Scholar 

  • Coletti, G., Scozzafava, R., & Vantaggi, B. (2015). Possibilistic and probabilistic logic under coherence: Default reasoning and System P. Mathematica Slovaca, 65(4), 863–890.

    MathSciNet  Article  MATH  Google Scholar 

  • Cruz, N., Baratgin, J., Oaksford, M., & Over, D. E. (2015). Bayesian reasoning with ifs and ands and ors. Frontiers in Psychology, 6, Article 192.

  • Cruz, N., Baratgin, J., Oaksford, M., & Over, D. E. (2016). Centering and the meaning of conditionals. In A. Papafragou, D. Grodner, D. Mirman & J. Trueswell (Eds.), Proceedings of the 38th Annual Meeting of the Cognitive Science Society (pp. 1104–1109). Philadelphia, PA: The Cognitive Science Society.

  • Da Silva Neves, R., Bonnefon, J.-F., & Raufaste, E. (2002). An empirical test of patterns for nonmonotonic inference. Annals of Mathematics and Artificial Intelligence, 34, 107–130.

    MathSciNet  Article  MATH  Google Scholar 

  • de Finetti, B. (1931/1993). On the subjective meaning of probability (translation; original work published in Fundamenta Mathematicae, 17, 1931). In P. Monari & D. Cocchi (Eds.), Probabilità e induzione (pp. 291–321). Bolognia: Cooperativa Libraria Universitaria Editrice Bologna.

  • de Finetti, B. (1937/1980). Foresight: Its logical laws, its subjective sources. In H. J. Kyburg & H. E. Smokler (Eds.), Studies in subjective probability (pp. 55–118). Huntington, New York: Robert E. Krieger Publishing Company.

  • de Finetti, B. (1970/1974). Theory of probability (Vols. 1, 2). Chichester: Wiley.

  • Douven, I. (2016). The epistemology of indicative conditionals: Formal and empirical approaches. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Elqayam, S., Bonnefon, J.-F., & Over, D. E. (Eds.). (2016). New paradigm psychology of reasoning: Basic and applied perspectives. London: Routledge.

    Google Scholar 

  • Elqayam, S., & Evans, J. S. B. T. (2011). Substracting “ought” from “is”: Descriptivism versus normativism in the study of human thinking. Behavioral and Brain Sciences, 34, 233–290.

    Article  Google Scholar 

  • Evans, J. S. B. T. (2012). Questions and challenges to the new psychology of reasoning. Thinking & Reasoning, 18(1), 5–31.

    Article  Google Scholar 

  • Evans, J. S. B. T., Newstead, S. E., & Byrne, R. M. J. (1993). Human reasoning. The psychology of deduction. Hove: Lawrence Erlbaum.

    Google Scholar 

  • Evans, J. S. B. T., & Over, D. E. (2004). If. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Evans, J. S. B. T., Thompson, V. A., & Over, D. E. (2015). Uncertain deduction and conditional reasoning. Frontiers in Psychology, 6, Article 398.

  • Ford, M. (2004). System LS: A three-tiered nonmonotonic reasoning system. Computational Intelligence, 20(1), 89–108.

    MathSciNet  Article  Google Scholar 

  • Fugard, A. J. B., Pfeifer, N., Mayerhofer, B., & Kleiter, G. D. (2011). How people interpret conditionals: Shifts towards the conditional event. Journal of Experimental Psychology: Learning, Memory, and Cognition, 37(3), 635–648.

    Google Scholar 

  • Gilio, A. (2002). Probabilistic reasoning under coherence in System P. Annals of Mathematics and Artificial Intelligence, 34, 5–34.

    MathSciNet  Article  MATH  Google Scholar 

  • Gilio, A. (2012). Generalizing inference rules in a coherence-based probabilistic default reasoning. International Journal of Approximate Reasoning, 53(3), 413–434.

    MathSciNet  Article  MATH  Google Scholar 

  • Gilio, A., Over, D. E., Pfeifer, N., & Sanfilippo, G. (2017). Centering and compound conditionals under coherence. In M. B. Ferraro (Ed.), Soft methods for data science (pp. 253–260). Berlin: Springer.

    Chapter  Google Scholar 

  • Gilio, A., Over, D. E., Pfeifer, N., & Sanfilippo, G. (submitted). Centering with conjoined and iterated conditionals under coherence. https://arxiv.org/abs/1701.07785.

  • Gilio, A., Pfeifer, N., & Sanfilippo, G. (2015). Transitive reasoning with imprecise probabilities. In S. Destercke & T. Denoeux (Eds.), Symbolic and quantitative approaches to reasoning with uncertainty (ECSQARU 2015) (pp. 95–105). Dordrecht: Springer LNAI 9161.

  • Gilio, A., Pfeifer, N., & Sanfilippo, G. (2016). Transitivity in coherence-based probability logic. Journal of Applied Logic, 14, 46–64.

    MathSciNet  Article  MATH  Google Scholar 

  • Gilio, A., & Sanfilippo, G. (2011). Coherent conditional probabilities and proper scoring rules. In F. Coolen, G. De Cooman, T. Fetz & M. Oberguggenberger (Eds.), Proceedings of the 7th international symposium on imprecise probability: Theories and applications (pp. 189–198). Innsbruck: SIPTA.

  • Gilio, A., & Sanfilippo, G. (2013a). Conditional random quantities and iterated conditioning in the setting of coherence. In L. C. van der Gaag (Ed.), ECSQARU 2013 (Vol. 7958, pp. 218–229). Berlin: Springer.

    Google Scholar 

  • Gilio, A., & Sanfilippo, G. (2013b). Conjunction, disjunction and iterated conditioning of conditional events. In R. Kruse, B. M. R, C. Moewes, M. A. Gil, P. Grzegorzewski, & O. Hryniewicz (Eds.), Synergies of soft computing and statistics for intelligent data analysis (pp. 399–407). Berlin: Springer.

  • Gilio, A., & Sanfilippo, G. (2013c). Probabilistic entailment in the setting of coherence: The role of quasi conjunction and inclusion relation. International Journal of Approximate Reasoning, 54(4), 513–525.

    MathSciNet  Article  MATH  Google Scholar 

  • Gilio, A., & Sanfilippo, G. (2013d). Quasi conjunction, quasi disjunction, t-norms and t-conorms: Probabilistic aspects. Information Sciences, 245, 146–167. doi:10.1016/j.ins.2013.03.019.

    MathSciNet  Article  MATH  Google Scholar 

  • Gilio, A., & Sanfilippo, G. (2014). Conditional random quantities and compounds of conditionals. Studia Logica, 102(4), 709–729.

    MathSciNet  Article  MATH  Google Scholar 

  • Ginsberg, M. L. (1986). Counterfactuals. Artificial Intelligence, 30, 35–79.

    MathSciNet  Article  MATH  Google Scholar 

  • Grice, H. P. (1975). Logic and conversation. In P. Cole & J. L. Morgan (Eds.), Syntax and semantics (Vol. 3: Speech acts). New York: Seminar Press.

  • Johnson-Laird, P. N., & Tagart, J. (1969). How implication is understood. The American Journal of Psychology, 82(3), 367–373.

    Article  Google Scholar 

  • Khemlani, S., & Johnson-Laird, P. N. (2012). Theories of the syllogisms: A meta-analysis. Psychological Bulletin, 138(3), 427–457.

    Article  Google Scholar 

  • Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.

    MathSciNet  Article  MATH  Google Scholar 

  • Lad, F. (1996). Operational subjective statistical methods: A mathematical, philosophical, and historical introduction. New York: Wiley.

    MATH  Google Scholar 

  • Lehtinen, T. (1983). Suomen konditionaalin morfologisesta ja semanttisesta motivaatiosta. Virittäjä, 87, 482–507.

    Google Scholar 

  • Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.

    MATH  Google Scholar 

  • Lindworsky, J. (1916). Das schlußfolgernde Denken. Experimentellpsychologische Untersuchungen. Freiburg im Breisgau: Herdersche Verlagshandlung.

    Google Scholar 

  • Macnamara, J. (1986). A border dispute. The place of logic in psychology. Cambridge: MIT Press.

    Google Scholar 

  • Marr, D. (1982). Vision. A computational investigation into the human representation and processing of visual information. San Francisco: W. H. Freeman.

    Google Scholar 

  • Mele, A., & Rawling, P. (Eds.). (2004). The Oxford handbook of rationality. New York: Oxford University Press.

    Google Scholar 

  • Milne, P. (2012). Indicative conditionals, conditional probabilities, and the “defective truth-table”: A request for more experiments. Thinking & Reasoning, 18(2), 196–224.

    Article  Google Scholar 

  • Nickerson, R. S. (Ed.). (2008). Aspects of rationality. Reflections on what it means to be rational and whether we are. New York: Psychology Press.

    Google Scholar 

  • Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101, 608–631.

    Article  Google Scholar 

  • Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Oaksford, M., & Chater, N. (2009). Précis of “Bayesian rationality: The probabilistic approach to human reasoning”. Behavioral and Brain Sciences, 32, 69–120.

    Article  Google Scholar 

  • Oaksford, M., Chater, N., & Larkin, J. (2000). Probabilities and polarity biases in conditional inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 883–899.

    Google Scholar 

  • Over, D. E. (2009). New paradigm psychology of reasoning. Thinking and Reasoning, 15, 431–438.

    Article  Google Scholar 

  • Over, D. E., & Baratgin, J. (2017). The “defective” truth table: Its past, present, and future. In N. Galbraith, E. Lucas, & D. E. Over (Eds.), The thinking mind: A Festschrift for Ken Manktelow (pp. 15–28). Hove: Psychology Press.

    Google Scholar 

  • Over, D. E., Hadjichristidis, C., Evans, J. S. B. T., Handley, S. J., & Sloman, S. (2007). The probability of causal conditionals. Cognitive Psychology, 54, 62–97.

    Article  Google Scholar 

  • Pfeifer, N. (2006). Contemporary syllogistics: Comparative and quantitative syllogisms. In G. Kreuzbauer & G. J. W. Dorn (Eds.), Argumentation in Theorie und Praxis: Philosophie und Didaktik des Argumentierens (pp. 57–71). Wien: Lit Verlag.

    Google Scholar 

  • Pfeifer, N. (2008). A probability logical interpretation of fallacies. In G. Kreuzbauer, N. Gratzl, & E. Hiebl (Eds.), Rhetorische Wissenschaft: Rede und Argumentation in Theorie und Praxis (pp. 225–244). Wien: Lit Verlag.  

    Google Scholar 

  • Pfeifer, N. (2011). Systematic rationality norms provide research roadmaps and clarity. Commentary on Elqayam & Evans: Subtracting “ought” from “is”: Descriptivism versus normativism in the study of human thinking. Behavioral and Brain Sciences, 34, 263–264.

    Article  Google Scholar 

  • Pfeifer, N. (2012). Experiments on Aristotle’s Thesis: Towards an experimental philosophy of conditionals. The Monist, 95(2), 223–240.

    Article  Google Scholar 

  • Pfeifer, N. (2013a). The new psychology of reasoning: A mental probability logical perspective. Thinking & Reasoning, 19(3–4), 329–345.

    Article  Google Scholar 

  • Pfeifer, N. (2013b). On argument strength. In F. Zenker (Ed.), Bayesian argumentation. The practical side of probability (pp. 185–193). Dordrecht: Synthese Library (Springer).

  • Pfeifer, N. (2014). Reasoning about uncertain conditionals. Studia Logica, 102(4), 849–866.

    MathSciNet  Article  MATH  Google Scholar 

  • Pfeifer, N. (2016). Experimental probabilistic pragmatics beyond Bayes’ theorem. Zeitschrift für Sprachwissenschaft, 35(1), 89–96.

    Article  Google Scholar 

  • Pfeifer, N., & Douven, I. (2014). Formal epistemology and the new paradigm psychology of reasoning. The Review of Philosophy and Psychology, 5(2), 199–221.

    Article  Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2003). Nonmonotonicity and human probabilistic reasoning. In Proceedings of the 6th workshop on uncertainty processing (pp. 221–234). Hejnice: September 24–27, 2003.

  • Pfeifer, N., & Kleiter, G. D. (2005a). Coherence and nonmonotonicity in human reasoning. Synthese, 146(1–2), 93–109.

    MathSciNet  Article  MATH  Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2005b). Towards a mental probability logic. Psychologica Belgica, 45(1), 71–99.

    Article  Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2006a). Inference in conditional probability logic. Kybernetika, 42, 391–404.

    MathSciNet  MATH  Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2006b). Is human reasoning about nonmonotonic conditionals probabilistically coherent? In Proceedings of the 7th workshop on uncertainty processing (pp. 138–150). Mikulov: September 16–20, 2006.

  • Pfeifer, N., & Kleiter, G. D. (2007). Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedent. In G. De Cooman, J. Vejnarová & M. Zaffalon (Eds.), Proceedings of the 5th international symposium on imprecise probability: Theories and applications (pp. 347–356). Prague: SIPTA.

  • Pfeifer, N., & Kleiter, G. D. (2009a). Framing human inference by coherence based probability logic. Journal of Applied Logic, 7(2), 206–217.

    MathSciNet  Article  MATH  Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2009b). Mental probability logic. Commentary on Oaksford & Chater: Bayesian rationality. Behavioral and Brain Sciences, 32, 98–99.

    Article  Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2010). The conditional in mental probability logic. In M. Oaksford & N. Chater (Eds.), Cognition and conditionals: Probability and logic in human thought (pp. 153–173). Oxford: Oxford University Press.  

    Google Scholar 

  • Pfeifer, N., & Kleiter, G. D. (2011). Uncertain deductive reasoning. In K. Manktelow, D. E. Over, & S. Elqayam (Eds.), The science of reason: A Festschrift for Jonathan St. B.T. Evans (pp. 145–166). Hove: Psychology Press.

    Google Scholar 

  • Pfeifer, N., & Sanfilippo, G. (2017). Square of opposition under coherence. In M. B. Ferraro (Ed.), Soft methods for data science (pp. 407–414). Berlin: Springer.

    Google Scholar 

  • Pfeifer, N., & Sanfilippo, G. (submitted). Probabilistic squares and hexagons of opposition under coherence. https://arxiv.org/abs/1701.07306.

  • Pfeifer, N., & Stöckle-Schobel, R. (2015). Uncertain conditionals and counterfactuals in (non-)causal settings. In G. Arienti, B. G. Bara & S. G. (Eds.), Proceedings of the EuroAsianPacific joint conference on cognitive science (4th European conference on cognitive science; 10th International conference on cognitive science) (Vol. 1419, pp. 651–656). Aachen: CEUR Workshop Proceedings. Retrieved from http://ceur-ws.org/Vol-1419/paper0108.

  • Politzer, G., & Baratgin, J. (2015). Deductive schemas with uncertain premises using qualitative probability expressions. Thinking & Reasoning, 22(1), 78–98.

    Article  Google Scholar 

  • Quine, W. O. (1950). Methods of logic. New York: Holt.

    MATH  Google Scholar 

  • Ramsey, F. P. (1929/1994). General propositions and causality (1929). In D. H. Mellor (Ed.), Philosophical papers by F. P. Ramsey (pp. 145–163). Cambridge: Cambridge University Press.

  • Rott, H. (2014). Unvergleichbarkeit und unabhängige Bedeutung. Zeitschrift für philosophische Forschung, 68, 237–250.

    Article  Google Scholar 

  • Schurz, G. (2005). Non-monotonic reasoning from an evolution-theoretic perspective: Ontic, logical and cognitive foundations. Synthese, 1–2, 37–51.

    MathSciNet  Article  MATH  Google Scholar 

  • Schurz, G., & Thorn, P. D. (2012). Reward versus risk in uncertain inference: Theorems and simulations. The Review of Symbolic Logic, 5(4), 574–612.

    MathSciNet  Article  MATH  Google Scholar 

  • Stanovich, K. E. (1999). Who is rational. Studies of individual differences in reasoning. Mahwah: Erlbaum.

    Google Scholar 

  • Stanovich, K. E., & West, R. F. (2000). Individual differences in reasoning: Implications for the rationality debate? Behavioral and Brain Sciences, 23, 645–726.

    Article  Google Scholar 

  • Störring, G. (1908). Experimentelle Untersuchungen zu einfachen Schlußprozessen. Archiv für die Gesamte Psychologie, 11, 1–127.

    Google Scholar 

  • Walley, P. (1991). Statistical reasoning with imprecise probabilities. London: Chapman and Hall.

    Book  MATH  Google Scholar 

  • Wallmann, C., & Kleiter, G. (2014). Degradation in probability logic: When more information leads to less precise conclusions. Kybernetika, 50(2), 268–283.

    MathSciNet  MATH  Google Scholar 

  • Wason, P. C. (1966). Reasoning. In B. M. Foss (Ed.), New horizons in psychology I (pp. 106–137). Harmandsworth: Penguin.

    Google Scholar 

  • Wason, P. C., & Johnson-Laird, P. N. (1972). The psychology of reasoning: Structure and content. Cambridge: Harvard University Press.

    Google Scholar 

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Acknowledgements

We thank David Over and Giuseppe Sanfilippo as well as three anonymous referees for helpful comments on the work reported in this paper. This research was supported by the DFG Project PF 740/2-2 (awarded to Niki Pfeifer) as part of the DFG Priority Program “New Frameworks of Rationality” (SPP1516).

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Appendix

Appendix

The Appendix contains illustrative examples of Finnish original tasks and their English translations used in different booklets (see also Table 1).

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Pfeifer, N., Tulkki, L. Conditionals, Counterfactuals, and Rational Reasoning: An Experimental Study on Basic Principles. Minds & Machines 27, 119–165 (2017). https://doi.org/10.1007/s11023-017-9425-6

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Keywords

  • Coherence-based probability logic
  • Conditionals
  • Counterfactuals
  • Experimental study
  • Human reasoning
  • Negation
  • Nonmonotonic reasoning
  • Quantification
  • Paradoxes
  • Probabilistic reasoning
  • Rationality