Frege's puzzle, Superman, Clark Kent, Louis, solution, model-based, Marvin Minsky, world model, Niels Bohr, truth, nature

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Frege's Puzzle from a Model-Based Point of View

By Karlis Podnieks

Frege's puzzle about propositional attitude reports can be presented in terms of Superman comics... At the beginning, Lois Lane does not realize that Clark Kent and Superman are the same person, and she concludes from her observations that Superman is strong, but Clark Kent is not strong. Thus, it is true that Lois believes that Superman is strong, and that Lois does not believe that Clark Kent is strong. But since Clark and Superman are the same person, Clark Kent = Superman is true as well.

Now, is the rule F(x) & x=y F(y) valid as a general logical principle? If it is, then, by applying it to true sentences, Lois does not believe that Clark Kent is strong, and Clark Kent = Superman, we should obtain a true sentence: Lois does not believe that Superman is strong. However, the sentence Lois believes that Superman is strong is true as well, which is a contradiction. Thus, as a general logical principle, F(x) & x=y F(y) seems to be wrong.

This kind of disorder has caused more than a century of controversy. Let's try one more approach to solving the puzzle.

The model-based approach used below can be traced to Marvin Minsky (1965: Matter, Mind and Models, Proceedings of IFIP Congress 65, 1: 45-49)...

How does Frege's puzzle look from this point of view? At the beginning, Lois' world model includes the axiom Clark Kent Superman. Thus, in Lois' world model, her conclusions that Superman is strong, but Clark Kent is not strong do not contradict each other. But, as a reader of the Superman comics, I know from the very beginning that Clark and Superman are the same person. Hence, in my world model, Clark Kent is strong, but Lois believes the opposite. At the end of story, Lois is forced to change her world model axioms, and Clark becomes strong in her model, too. No puzzle here!

one can run into puzzles only by confusion of different world models...

The triviality of this solution is due to the purely syntactical character of the approach. Namely, let's regard world models not as “models of the world” with the world itself as their unique “reference”. Let's consider world models simply as the way that people are thinking and talking about the world...

A similar formulation is attributed to Niels Bohr: "There is no quantum world. There is only an abstract quantum physical description. It is wrong to think the task of physics is to find out how nature is. Physics concerns what we can say about nature." – quoted after Aage Petersen (1963: The Philosophy of Niels Bohr. Bulletin of the Atomic Scientists, XIX(7): 8–14)...

Full text:
K. Podnieks.
Frege's Puzzle from a Model-Based Point of View. The Reasoner, Vol. 6, N 1, January 2012, pp. 5-6 (available online).

Frege's puzzle, Superman, Clark Kent, Louis, solution, model-based, Marvin Minsky, world model, Niels Bohr, truth, nature