Abstract
Like belief revision, conceptual change has rational aspects. The paper discusses this for predicate change. We determine the meaning of predicates by a set of imaginable instances, i.e., conceptually consistent entities that fall under the predicate. Predicate change is then an alteration of which possible entities are instances of a concept. The recent exclusion of Pluto from the category of planets is an example of such a predicate change. In order to discuss predicate change, we define a monadic predicate logic with three different kinds of lawful belief: analytic laws, which hold for all possible instances; doxastic laws, which hold for the most plausible instances; and typicality laws, which hold for typical instances. We introduce predicate changing operations that alter the analytic laws of the language and show that the expressive power is not affected by the predicate change. One can translate the new laws into old laws and vice versa. Moreover, we discuss rational restrictions of predicate change. These limit its possible influence on doxastic and typicality laws. Based on the results, we argue that predicate change can be quite conservative and sometimes even hardly recognisable.
References
Alchourron, C.E., Gärdenfors, P., Makinson, D. (1985). On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2), 510–530.
Baltag, A., & Renne, B. (2016). Dynamic epistemic logic. In Zalta, EN (Ed.) The stanford encyclopedia of philosophy, winter 2016 edn, metaphysics research lab. Stanford: stanford university.
Baltag, A., Moss, L.S., Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In Proceedings of the 7th conference on Theoretical aspects of rationality and knowledge (pp. 43–56). Burlington: Morgan Kaufmann Publishers.
van Benthem, J. (2004). Belief revision and dynamic logic. Journal of Applied Non-Classical Logics, 14(2), 1–25.
van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.
van Benthem, J., van Eijck, J., Kooi, B. (2006). Logics of communication and change. Information and Computation, 204(11), 1620–1662.
Carey, S. (2009). The origin of concepts. Oxford: Oxford University Press.
Carnap, R. (1928). Der logische Aufbau der Welt. Felix Meiner, Berlin.
Carnap, R. (1947). Meaning and necessity: a study in semantics and modal logic. Chicago: University of Chicago Press.
Carnap, R. (1955). Meaning and synonymy in natural languages. Philosophical studies, 6(3), 33–47.
van Ditmarsch, H., van der Hoek, W., Kooi, B. (2007). Dynamic epistemic logic. Dordrecht: Springer.
Fleck, L. (1979). Genesis and development of a scientific fact. Chicago: University of Chicago Press.
Hall, B.K. (1999). The paradoxical platypus. BicoScience, 49(3), 211–218.
Hampton, J.A. (1987). Inheritance of attributes in natural concept conjunctions. Memory & Cognition, 15(1), 55–71.
Kraus, S., Lehmann, D., Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1-2), 167–207.
Kuhn, T. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
Lewis, C.I. (1943). The modes of meaning. Philosophy and Phenomenological Research, 4(2), 236–250.
Lewis, D. (1969). Convention. a philosophical study. Cambridge: Harvard University Press.
Lewis, D. (1973). Counterfactuals. Cambridge: Harvard University Press.
Linné, C. (1735). Systema naturae 1. http://www.biodiversitylibrary.org.
Linné, C. (1758). Systema naturae 10, pt. 1.http://www.biodiversitylibrary.org, .
Makinson, D., & Hawthorne, J. (2015) In Koslow, A., & Buchsbaum, A. (Eds.), Lossy inference rules and their bounds: a brief review, (pp. 385–407). Birkhäuser: Cham.
Quine, W.V. (1951). Two dogmas of empiricism. The Philosophical Review, 60(1), 20–43.
Rosch, E. (1973). Natural categories. Cognitive Psychology, 4, 328–350.
Rosch, E., & Mervis, C.B. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7, 573–605.
Rott, H. (2009). Shifting priorities: Simple representations for twenty-seven iterated theory change operators. In Makinson, D, Malinowski, J, Wansing, H (Eds.), Towards mathematical philosophy (pp. 269–296). Dordrecht: Springer.
Schurz, G. (2001). What is ‘normal’? An evolution-theoretic foundation for normic laws and their relation to statistical normality. Philosophy of Science, 68, 476–497.
Schurz, G. (2012). Prototypes and their composition from an evolutionary point of view. In Hinzen w, & Machery, E (Eds.) (pp. 530–553). Oxford: The Oxford Handbook of Compositionality, Oxford University Press.
Strößner, C. (2015). Normality and majority: Towards a statistical understanding of normality statements. Erkenntnis, 80(4), 793–809.
Thagard, P. (1992). Conceptual revolutions. Princeton: Princeton University Press.
Veltman, F. (1996). Defaults in update semantics. Journal of philosophical logic, 25(3), 221–261.
Acknowledgments
Open Access funding provided by Projekt DEAL. Work on this paper was funded by the DFG (Deutsche Forschungsgemeinschaft) within the project “The Structure of Representations in Language, Cognition, and Science” (Grant SFB991 D01). I am grateful to two anonymous reviewers, who provided many helpful suggestions.
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Appendix
Appendix
Proposition 1
Any consistent analytic law in dynamic AD (and ADT / ADT 3) can be stipulated by inclusive and exclusive predicate changes.
Proof
We prove by induction, starting with atomic predicates and generalising to complex predicates.
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Base case: Analytic laws with one atomic predicate As said on page 27, the following two formulae are tautological:
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\([\varPhi \uparrow \varPsi ] \mathcal {A}\varPsi \varPhi \)
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\([\varPhi \downarrow \varPsi ] \mathcal {A}\varPhi \varPsi \)
Therefore, if Φ is atomic, then the laws \(\mathcal {A}\varPsi \varPhi \) and \(\mathcal {A}\varPhi \varPsi \) can be generated. Φ ↑Ψ can be called an inclusive change (of Φ) towards \(\mathcal {A}\varPsi \varPhi \) and Φ ↓Ψ an exclusive change (of Φ) towards \(\mathcal {A}\varPhi \varPsi \).
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Induction step Inclusive and exclusive change can be generalised to arbitrary complex predicates Ξ
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1.
Inclusive predicate change towards \(\mathcal {A}\varPsi \varXi \).
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(a)
If Ξ is atomic, include by Ξ ↑Ψ.
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(b)
For Ξ =Φ 1 ∩Φ2, make an inclusive predicate change towards \(\mathcal {A}\varPsi \varPhi _1\) and an inclusive predicate change towards \(\mathcal {A}\varPsi \varPhi _2\).
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(c)
For Ξ =Φ 1 ∪Φ2, make an inclusive predicate change towards \(\mathcal {A}\varPsi \varPhi _1\) or an inclusive predicate change towards \(\mathcal {A}\varPsi \varPhi _2\).
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(d)
For Ξ = −Φ, make an exclusive predicate change of Φ towards \(\mathcal {A}\varPhi -\varPsi \), which is equivalent to \(\mathcal {A}\varPsi -\varPhi \).
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(a)
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2.
Exclusive predicate change towards \(\mathcal {A}\varXi \varPsi \).
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(a)
If Ξ is atomic, exclude by Ξ ↓Ψ.
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(b)
For Ξ =Φ 1 ∪Φ2, make an exclusive predicate change towards \(\mathcal {A}\varPhi _1\varPsi \) and an exclusive predicate change towards \(\mathcal {A}\varPhi _2\varPsi \).
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(c)
For Ξ =Φ 1 ∩Φ2, make an exclusive predicate change towards \(\mathcal {A}\varPhi _1\varPsi \) or an exclusive predicate change towards \(\mathcal {A}\varPhi _2\varXi \).
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(d)
For Ξ = −Φ, make an inclusive predicate change of Φ towards \(\mathcal {A}-\varPsi \varPhi \), which is equivalent to \(\mathcal {A}-\varPhi \varPsi \).
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(a)
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1.
Thus, any (consistent) analytic statements (no matter how complex) can be generated by a series of predicate changes. □
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Strößner, C. Predicate Change. J Philos Logic 49, 1159–1183 (2020). https://doi.org/10.1007/s10992-020-09552-x
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DOI: https://doi.org/10.1007/s10992-020-09552-x
Keywords
- Conceptual change
- Dynamic epistemic logic
- Belief revision
- Analyticity
- Typicality
- Conditional logic