Abstract
Hakkarainen and Sintonen (Sci Educ 11(1):25–43, 2002) praise the descriptive adequacy of Hintikka’s Interrogative Model of Inquiry (imi) to describe children’s practices in an inquiry-based learning context. They further propose to use the imi as a starting point for develo** new pedagogical methods and designing new didactic tools. We assess this proposal in the light of the formal results that in the imi characterize interrogative learning strategies. We find that these results actually reveal a deep methodological issue for inquiry-based learning, namely that educators cannot guarantee that learners will successfully acquire a content, without limiting learner’s autonomy, and that a trade-off between success and autonomy is unavoidable. As a by-product of our argument, we obtain a logical characterization of serendipity.
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
Similar content being viewed by others
Notes
- 1.
A first-order language \(\mathcal{L}\) can express statements about individuals, their properties and relations; combinations of such statements (with Boolean operators not, and, or, and if…then…); and their existential and universal generalizations (with quantifiers there exists …and for all…respectively). A basic sentence of \(\mathcal{L}\) contains only individual names and relations symbols, i.e. no Boolean operator other than (possibly) an initial negation, and no quantifier. In what follows, we implicitly restrict the meaning of ‘deduction’ to ‘first-order deduction’—i.e. relations between premises and conclusions couched in some first-order language.
- 2.
Introducing A s weakens the assumptions that: (a) data streams are always complete in the limit; (b) all predicates (names) of \(\mathcal{L}\) denote observable qualities (identifiable objects); and: (c) a datum needs no analysis. The imi also drops the idealization that: (d) Nature always chooses s in S(T), and: (e) all answers in A s are true in s. Cases where (d–e) hold define the special case of Pure Discovery (cf. Sect. 3.1).
- 3.
An example is the halting problem, in which one must determine whether the current run of a program p, that may execute either finitely many instructions, or loop an instruction indefinitely, is finite or infinite. An ‘impatient’ method that conjectures that p is currently at the beginning of an infinite run, and repeats this conjecture indefinitely unless p stops (in which case the method changes its assessment) solves the problem in the above sense on every possible run. Kelly (2004) discusses in details the relation between the halting problem and empirical inductive problems.
- 4.
Holmes confesses that “[he] could not believe it possible that the most remarkable horse in England could long remain concealed [and] expected to hear that he had been found, and that his abductor was the murderer” (Conan Doyle 1986, p. 522).
- 5.
If A or ϕ(a) include vague terms (or imprecise categories), disambiguation is needed to obtain an answer, but sequence of yes-no questions (further specifying a ‘prototype’ in the current context) will suffice.
- 6.
Because of the possibility of mismatch, the converse of the Deduction Theorem only holds on the condition that elements of A s needed to obtain (interrogatively) q i from T are answers to questions in Inquirer’s range of attention.
- 7.
This understanding eschews the issue of possible mismatch between A s and Inquirer’s range of attention. In the left-to-right direction, every whether-question about A or B, or wh-question about ϕ(⋅ ), that receives (say) answer A or ϕ(a) suffices for the yes-no questions about A or ϕ(a) to enter Inquirer’s range of attention for the purpose of reconstructing an argument. The antecedent of the right-to-left direction holds when the yes-no questions are already in the range of attention (the consequent is satisfied trivially).
- 8.
Inspector Gregory, to whom the case has been committed, is an extremely competent officer. Were he but gifted with imagination he might rise to great heights in his profession. On his arrival he promptly found and arrested the man upon whom suspicion naturally rested. (Conan Doyle 1986, p. 527)
References
Barber, E., & Merton, R. K. (2004). The travels and adventures of serendipity. Princeton: Princeton University Press.
Conan Doyle, A. (1986). Sherlock Holmes: The complete novel and stories (Vol. 1). New York: Bantam Books.
Genot, E. J. (2009). The game of inquiry. The interrogative approach to inquiry and belief revision theory. Synthese, 171, 271–289.
Genot, E. J., & Jacot, J. (2012). How can yes-or-no questions be informative before they are answered? Episteme, 9(2), 189–204.
Hakkarainen, K., & Sintonen, M. (2002). The interrogative model of inquiry and computer-supported collaborative learning. Science & Education, 11(1), 25–43.
Hintikka, J. (1986). Reasoning about knowledge in philosophy: The paradigm of epistemic logic. In TARK ’86: Proceedings of the 1986 conference on theoretical aspects of reasoning about knowledge (pp. 63–80). Monterey: Morgan Kaufmann.
Hintikka, J. (1987). The interrogative approach to inquiry and probabilistic inference. Erkenntnis, 26(3), 429–442.
Hintikka, J. (1988). What is abduction? The fundamental problem of contemporary epistemology. Transactions of the Charles S. Peirce Society, 34, 503–533.
Hintikka, J. (1992). The concept of induction in the light of the interrogative approach to inquiry. In J. Earman (Ed.), Inference, explanation, and other philosophical frustrations (pp. 23–43). Berkeley: University of California Press.
Hintikka, J. (2007). Socratic epistemology. Cambridge: Cambridge University Press.
Hintikka, J., & Halonen, I. (1997). Semantics and pragmatics for why-questions. The Journal of Philosophy, 92, 636–657.
Hintikka, J., Halonen, I., & Mutanen, A. (2002). Interrogative logic as a general theory of reasoning. In D. M. Gabbay, R. H. Johnson, H. J. Ohlbach, & J. Woods (Eds.), Handbook of the logic of argument and inference (Vol. 1, pp. 295–337). Amsterdam: Elsevier.
Kelly, K. T. (2004). Uncomputability: The problem of induction internalized. Theoretical Computer Science, 317(1–3), 227–249.
Martin, E., & Osherson, D. (1998). Elements of scientific inquiry. Cambridge: MIT.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Genot, E.J., Gulz, A. (2016). The Interrogative Model of Inquiry and Inquiry Learning. In: Başkent, C. (eds) Perspectives on Interrogative Models of Inquiry. Logic, Argumentation & Reasoning, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-20762-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-20762-9_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20761-2
Online ISBN: 978-3-319-20762-9
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)