Sensitivity as Dependance or Shiftiness

Back when I was trying to find a modal (also sometimes called "intensional" or "combinatorial", in the literature) definition of intrinsicality, everyone was benign her head against a point discovered by Lewis: that there are two different ways of understanding what it means for some one aspect of reality (a parameter) E to be sensitive to another one F (commonly, a contextual feature, but not necessarily):

1. Dependance: The value of E depends on F.

2. Shiftiness: The value of E changes with F.

One might think that both things are just different aspects of the same phenomenon and that they are, at least, extensionally equivalent. However, a little bit of reflection reveals that this is not so. It is perfectly possible for a parameter to get the same value in different ways depending on different features of its context.

This phenomenon is most easily seen in natural language, as Kaplan clearly showed in his logic of indexicals. Thus, it is perfectly natural for a context sensitive expression E to be sensitive to a contextual feature F in such a way that (3) is true, but (4) is not:

3. Contextual Dependance: The semantic value of expression E depends on contextual feature F.

4. Contextual Shiftiness: The semantic value of expression E changes with contextual feature F.

For example, let E be the sentence "She is female" and F be the gender of the salient person denoted by the relevant occurrence of "She". (4) is false because this context-sensitive sentence  remains true regardless of who "she" refers to in the context.  Nevertheless, we still want to say that E is context-sensitive, because it contains the indexical "She" and therefore (3) is true of it, i.e., who its is about, what fact makes it true or not, depends on who "she" refers to and, in particular, on her gender.

A natural corollary is that (5) and (6) can also diverge in truth value:

5. The semantic value of E does not remain constant through changes in the value of F (for example, where "here" is depends on the location of utterance).

6. The truth value of any sentences where E occurs does not remain constant through changes in the value of F (for example, whether "here is in Mexico" is true or not depends on the location of utterance).

Thus, it is possible for 5 to be true, while 6 is not. This occurs in cases where the change in semantic value of E are indistinct to the meeting of sentence S's truth conditions. In the previous example, "She is female" remains true regardless of who "she" refers to in the context.  

The phenomenon pops up all over philosophy (specially in metaphysics), in discussions of supervinience, causality, responsibility, intrinsically, indexicality, etc. For example, in discussing exrinsicality, it is important to distinguish between:

7. Extrinsic Dependance: Whether an object a has a property P depends on something completely external to a itself.

8. Extrinsic Shiftiness: Whether an object a has a property P can vary with changes happening completely outside of a itself.

Langton and Lewis famous example of a property P that satisfies (7) but not (8) is (9):

9. Being either a lonely positron or an accompanied electron (Langton and Lewis 1998, Marshall 2009)

In the metaphysics of logic, to put another example, there is currently a debate between people who think that logical truths like that it is either raining or it is not, are still about whether it is raining or not (Fine, Berto, etc. and, in general, people into neo-aristotelian metaphysics) and people who (like me, so far, I think, but in general, most traditional philosophers of logic) who think that these truths are, if anything, about the logical operations of disjunction and negation. It is not hard to see that these two views diverge in their understanding of truth making: metaphysicians adopts a view of truth making as dependance, while philosophers of logic adopt a view of truth making as shiftiness:

9. Truth Dependance: Given a true proposition S, fact F makes S true if S's truth depends on the existence of fact F.

10. Truth Shiftiness: Given a true proposition S, fact F makes S true if the truth value of S can vary with changes in the status of F.

Neo-Aristoteleian metaphysicians view this distinction as direct proof of the hyperintensionality of notions like causality, intrinsically, truth-making, responsibility, content, etc. However, there are good reasons to resist this interpretation. Defenders of intensional visions (at least as far back as Platos' Phaedo (Ebrey 2023)) use to appeal to two sorts of reasons when rejecting the validity of dependence conceptions in favor of their intensional conceptions: epistemic and metaphysical. From an epistemic point of view, it is hard to follow dependence relations without appealing to intuitions (McSweeney forthcoming, Schnieder 2016, §2, and Correia 2014) that tend to be many times slippery. From a metaphysical perspective, it is hard to see how something can depend on something else if it makes no actual difference to whether it is the case or not. Thus, cases like the aforementioned logical truth "It is raining or it is not" may seem to be about whether it is raining right now or not, but this appearance is misleading because it does not make a difference to its truth whether it currently rains or not. The same thing applies mutates mutandi to similar examples of allegedly hyperintensional phenomena.

It is not surprising to notice that examples like these are disjunctive and that their working as counter-examples depends on a classical interpretation of their logical behaviour. Thus, some non-classical logicians, conexivists (a radical sort of relevantist), for example, have good reasons to reject them. From a conexivist perspectiuve, Langton and Lewis argument against the intensionality of intinsicality is clearly invalid.

The issue comes up again in Gillian Russell's recent work on what she has called "barriers of entailment", for example, why indexical truths cannot be logically derived from non-contextual truths.

"...the truth-values of indexical sentences vary with .... the context... If [an] indexical sentence followed from [some set of] non-indexical premises ..., it would be a logical consequence of true premises, and so true itself—no matter what the context was. So [it] can [not] be entailed by the premises..." (Russell 2022: 608)

Consider the sentence "If everyone has to pay taxes, I have to pay taxes". This might seem like a counter-example to the general claim that indexical truths cannot be derived from non-indexical truths, because, as Russell herself details, even though the truth of the conclusion depends on the relevant referent of "I", its truth restricted to those models where the premises are true, does not shift in truth value, but remains as true.

However, this sentence is not logically true, for reasons that have already been brought about by critics of Gómez-Torrente's analysis of Tarski's definition of logical consequence, i.e., that "Everyone has to pay taxes" does not require the existence of anyone who has to pay taxes, while "I have to pay taxes" does. This is because, even though the truth of the later is indistinct as to who "I" is, it is not indifferent to at least there being someone to whom the indexical refers.

From a proof-theoretic perspective, it is even more straightforward to notice that "I have to pay taxes" does not follow logically from "Everyone has to pay taxes", since this derivation violates the restriction of application of universal instantiation.

References

Correia, F. (2014) ‘Logical Grounds’. The Review of Symbolic Logic 7(1), 31-59.

Ebrey D. (2023) Socrates’ Autobiography: 95e–102a. In: Plato’s Phaedo: Forms, Death, and the Philosophical Life. Cambridge University Press; 2023:207-247.

McSweeney, Michaela M. 'Grounding Logically Complex Facts'. Forthcoming in Michael Raven (ed.), the Routledge Handbook of Metaphysical Grounding.

Schnieder (2016) ‘In Defence of a Logic for ‘Because’’. Journal of Applied Non-Classical Logics 26(2), 160-171.