Abstract
This paper uses Avron’s algebraic semantics for the logic RMI to model some ideas in the philosophy of science. Avron’s relevant disjunctive structures (RDS) are each partitioned into relevance domains. Each relevance domain is a boolean algebra. I employ this semantics to act as a formal framework to represent what Nancy Cartwright calls the “dappled world”. On the dappled world hypothesis, local scientific theories each represent restricted aspects and regions of the universe. I use relevance domains to represent the domains of each of these local theories and I provide a formalisation of the salient relationships between so-called fundamental theories and local theories. I also examine ways in which the paraconsistent nature of RMI can be used to deal with inconsistencies within and between theories adopted by scientists. The paper ends with some suggestions about updating RDS given changes in the theories that science adopts.
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Notes
- 1.
Avron’s relevance relation (Avron 1990a, p. 713ff) is his formalisation of this notion of connection between propositions.
- 2.
For a similar but more protracted defence of intensional disjunction, see Read (1988).
- 3.
In fact, Newton’s laws allow the derivation of laws that are approximately the same as Kepler’s laws. I can adjust my view to claim that Newton’s laws allow the derivation of a theory that is approximately the same as Kelper’s, but this will require the use of a relation of approximate similarity, and this will add rather a lot of complexity to the formalism. So I just make the simplifying assumption that on the fundamentalist theory local theories are straightforwardly derivable from general ones.
- 4.
- 5.
At some places in Galileo’s text, the bodies described are stones, and at others they are a musket ball and a cannon ball.
- 6.
For example, I have heard some physicists say that they like to use the elegant mathematics of string theory, and that it gives the right results, but that they do not believe it. As my student Tim Irwin pointed out to me, in the social sciences it is a platitude that “all theories are false, but some are useful”.
- 7.
In R and stronger systems, \((A\rightarrow B)\circ (B\rightarrow A)\) is equivalent to \((A\rightarrow B)\wedge (B\rightarrow A)\), where \(\wedge \) is extensional conjunction.
- 8.
As one referee helpfully pointed out, in real life theories quantifiers are used. I would be interesting to see what effect the addition of quantifiers has to the theory of relevance domains. My idea is this: extend RDS using Halmos’s theory of polyadic algebras (Halmos 1962). I think relevance domains would remain and would look like little classical polyadic algebras. But I do not have a proof of this yet.
- 9.
The opposite has occurred several times in science. For example, whereas Newton’s theory distinguishes conceptually between gravitational and inertial mass, Einstein’s theory takes them to be the same. One could imagine, however, a future physical theory that once again distinguishes between them.
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Mares, E. (2021). Relevance Domains and the Philosophy of Science. In: Arieli, O., Zamansky, A. (eds) Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Outstanding Contributions to Logic, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-71258-7_10
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