Abstract
How account for the intuitive difference between simply knowing a necessary proposition, and knowing that it is a necessary truth? In the paper it will be shown that two-dimensional semantics does not do the job in an adequate way. A solution is provided which is based on Hintikka’s worldlines. Assuming a slight extension of the syntax, modal epistemic logic can thus deal with classical puzzles like knowledge of identities.
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Notes
- 1.
Technically, standard Kripkean models are extended in order to include worlds where the valuation is no more standard. In such worlds, the value of complex formulas is no more calculated according to that of atoms, but it is just postulated. For instance, the conjunction of p, p → q and \(\neg q\) can obtain at the same world. If such a world is epistemically accessible from some (standard) world w, then at w the agent can be said to know that p and that p → q, while ignoring that q. This makes such non-standard worlds look impossible, even though they are consistent theoretic constructions.
- 2.
A more complete overview of 2D semantics and its various interpretations is provided by the SEP entry (Schroeter 2012).
- 3.
This could be done by an updating of an accessibility relation between possible worlds. However, I will not go into details about the formal implementation of the general idea.
- 4.
According to a more charitable reading, Kripke would mean that once philosophical analysis is done e.g. for natural kind terms in general, every empirical knowledge of, say, identities (like the identity between water and H2O) would automatically lead to a knowledge that these identities are necessary. But it means that the analysis must have been done by the knowing agent herself, and it remains odd to qualify her knowledge about the modal status of a truth as empirical – whereas knowledge of necessary identities can of course be empirical.
- 5.
Such ascriptions do not presuppose any language use by the ascribee. One could also state the following about the Obama family’s pet dog: “Bo knows that Barack Obama is in the kitchen”. This statement could involve either the ascriber’s way of identifying the bearer of the name, or the ascribee’s, which is by no way linguistic.
- 6.
For simplification the domain is supposed to be constant across possible worlds; to get variable domains, D should be defined as a function ascribing a domain of individuals D w to each possible world w ∈ W.
- 7.
KPa as it is used in the present paper is equivalent to the IF formula KP(a ∕K ), and would be unchanged in Wehmeier’s notation; KPa K would correspond to KPa and to KPa s respectively.
- 8.
In what follows, I use the notations of Aloni (2005).
- 9.
I thank a referee for having raised this issue in my original definition.
- 10.
So this is not a matter of scope, and the formula \(\exists x\ (x = a \wedge KPx)\) can be used to ascribe de dicto knowledge – as far as the worldline picked out by the existential quantifier is variable.
- 11.
It is implied by \(\square (h^{K} = p^{K})\), but in general this formula is not true, since the two names are expected to encode two diverging worldlines – two different senses, to put it in Fregean terms.
- 12.
A complete theory would allow worldlines for predicates and not only for names. See Egré (2014) for a proposal in that direction. It would expand my solution to cases with no individual constants, like the ascription of knowledge of “Tigers are mammals”. That this is a necessary truth (after Putnam) does not mean that knowing this truth implies knowing that it is necessary. However, a referee stressed that the inference \((\star )\) would not be blocked in the propositional case. This is true, and it shows that propositional modal logic is not fine-grained enough to handle the distinction between knowledge of a necessary truth and knowledge that this truth is necessary.
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Acknowledgements
Preliminary versions of this paper were presented at conferences in Rennes (France) and Rijeka (Croatia). I wish to thank Filipe Drapeau-Contim, Ghislain Guigon, Pierre Joray, Pascal Ludwig, Claudine Tiercelin, Tero Tulenheimo, and an anonymous reviewer for helpful comments and suggestions.
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Rebuschi, M. (2016). Knowing Necessary Truths. In: Redmond, J., Pombo Martins, O., Nepomuceno Fernández, Á. (eds) Epistemology, Knowledge and the Impact of Interaction. Logic, Epistemology, and the Unity of Science, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-26506-3_10
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