The Joint Russian-Brazilian Colloquium “Inferential Knowledge about Fictions: How We Infer, and How Far These Inferences Go”

What would be the case if P was the case? Counterfactual imagination pervades intelligent life. But how does it work and what’s its epistemic value?

The mainstream way of drawing the distinction between indicative and counterfactual hypothetical thought has it that one can only suppose that P in the former way when one is not certain that P is false. I think that’s wrong. The real difference is that counterfactual imagination can make us lose certainties in ways imagination ‘in the indicative mood’ cannot. This gives counterfactual imagination the power to do something its indicative sibling cannot do – namely, supporting a Ramsey Test: one’s credence in ‘If it were that P, it would be that Q’ just is one’s credence in Q given P, i.e., on the counterfactual supposition of P, when the counterfactual is interpreted à la Stalnaker. We must not read that ‘given’, however, as Bayesian conditioning. Counterfactual hypotheses are governed by a procedure Lewis invented, which he called imaging. So I explore the workings of imaging and outline why having a Ramsey Test for it is epistemically valuable.

In [1] we introduced two logics of fiction, L1 and L2, whose design was guided by the distinction between factual and fictional truth values – in short, the idea that the sentences ‘Allan Pinkerton is a detective’ and ‘Sherlock Holmes is a detective’ are true in quite different senses of ‘truth’. Accordingly, the semantics of L1 and L2 countenance four truth values: T and F , standing for respectively factual truth and factual falsity, and t and f , standing for respectively fictional truth and fictional falsity.

A crucial difference between L1 and L2 concerns the evaluation of mixed sentences, viz., sentences in which both fictional and non-fictional terms occur, for example:

(i) Sherlock Holmes’s observation powers surpass those of Allan Pinkerton

(ii) Allan Pinkerton and Sherlock Holmes are clever people

While in L1 (the formal renderings of) these sentences would count as either fictionally true or fictionally false (due to the fact they are about Sherlock Holmes), in L2 they would count as either factually true or factually false (due to the fact that they are about Allan Pinkerton, a real detective). In this respect, the choice between either system is bound to betray our intuitions about the values of mixed sentences – e.g., while sentence (i) above seems to be fictionally true, the following sentence

(iii) Allan Pinkerton admired Sherlock Holmes 

seems to be factually false (Allan Pinkerton died three years before Conan Doyle published A Study in Scarlet, Holmes’s first story).

In view of this phenomenon, and in spired by the results in [2], we proposed a further development of the framework in [1] that resorts to a non-deterministic evaluation of mixed sentences: sentences such as (i)-(iii) receive an indeterminate value from the sets {T, t} and {F, f}, and the indeterminacy occurring at the atomic level propagates across the connectives and quantifiers.

In this talk we will present the logics L1 and L2, as well as their non-deterministic version, and discuss their philosophical motivations and potential drawbacks.

References

[1] Newton Peron and Henrique Antunes. A Four-Valued Logical Framework for Reasoning About Fiction. Logic and Logical Philosophy, 31(4):579–610, 2022. DOI: 10.12775/LLP.2022.020

[2] Marcelo E. Coniglio. Ivlev-like modal logics of formal inconsistency obtained by fibring swap structures. Studia Logica, 2024. First published online: July 23, 2024. DOI: 10.1007/s11225-024-10127-z