Last Thursday I gave a talk at Sydney University's philosophy department about Kipper's bombshell, my old account of necessity, and my new account involving counterfactual invariance deciders. I was asked many good questions and got a lot out of it.
In preparing the talk, I came to realise that I may have been too quick to assume that 'Air is airy' disproves my old account, according to which a proposition is necessarily true iff it is in the deductive closure of the set of propositions which are both true and inherently counterfactually invariant. Because 'There is nothing more to being air than being airy' is plausibly true and ICI, and it does - at least on a rich enough notion of impication - imply 'Air is airy'.
Now, if that's right, what follows? Are my new ideas about abandoning, in the analysis of necessity, the property of ICI for a relation of deciderhood, to be thrown out? I don't think so. Even if I was pushed towards them by the possibly wrong idea that my old account can't be defended from 'Air is airy', they still seem to give us an account which seems better. The old account now seems clumsy, so to speak. Maybe it can be understood in a way - with a rich notion of implication - so that it doesn't go wrong on 'Air is airy'. But this still seems like a kind of lucky break, and it's not clear to me that there aren't more threatening examples in the offing. The new account, on which a proposition is necessary iff it has a true positive counterfactual invariance decider, seems to reveal the notion's workings more faithfully, and seems less hostage to as-yet-unconsidered examples.
(Also note that, with the new account, you can use 'There's nothing more to being air than being airy' as your decider, but it seems like you can also use something like 'Air has no underlying nature' or 'Air is not a natural kind', and these do not seem to imply 'Air is airy' - they do not seem to contain that information. And since it seems you can plug these into the new account and conclude that 'Air is airy' is necessary, but cannot conclude the same on the same basis with the old account, that the new account is superior here, in enabling us to conclude necessity on a sometimes slenderer basis than we can using the old account.)
In the talk I gave, there were a number of questions and examples suggested which could look like they may disprove my account, but I was able to respond to all of them straightforwardly and to my account's credit. (With some elements of the new account, it's hard to see immediately why they're there and are as they are, but working through some examples clarifies things.) I also fielded a question (thanks to N.J.J. Smith) about how my account goes beyond what we already find in Kripke. There too I was able to give what I think is a satisfactory answer: the account isolates a plausibly a priori tractable, maybe broadly semantic, aspect to necessity. Kripke's work doesn't do this. He says a proposition is necessary if it holds in all the ways things could have been, and one of his main points is that we don't in general know a priori what these ways are. True, he also allows that we know by 'a priori philosophical analysis' (this occurs in 'Identity and Necessity') that 'Hesperus is Phosphorus' is necessarily true if true at all, but that isn't true of all examples. You might thus wonder, with respect to examples that don't work that way, what part 'a priori philosophical analysis' might play in our knowledge of their modal status. My account gives us an answer to this.
But another sort of question arose in the talk was how my account relates to two-dimensional semantics, and I was less satisfied with what I had to say on that. The true CI deciding proposition(s) in my account seem to play a role close to the role played by what world is actual in two-dimensional semantics. I worry that some in the audience were beginning to suspect that I've just laboriously re-arrived at two-dimensionalism along a somewhat different path. (And I'm getting a bit suspicious myself.)
So, I think that now, the most pressing task is to clarify the relationship of my new account to two-dimensional semantics, rather than to defend it further from counterexample. (This has always been a background concern, even with my old account, but now it has become urgent.) The notions in my account come up in a different way, and most formulations of two-dimensionalism seem to bring up difficulties which I may be able to avoid. My account seems more minimal and focused on its topic, and thus potentially more instructive.
Such anyway is my hunch, but it remains to make this clear.
Showing posts with label Jens Kipper. Show all posts
Showing posts with label Jens Kipper. Show all posts
Monday, 6 November 2017
Monday, 11 September 2017
A New Account of the Conditions Under Which a Proposition is Necessary
The previous posts were quite raw and had me wrestling with new data. In this post, I try to be clearer and more accessible, and give a first outline of a new account of necessity that has emerged from my research on these topics.
My old account of necessity was:
A proposition is necessarily true iff it is, or is implied by, a proposition which is both inherently counterfactually invariant (ICI) and true.
A proposition P is ICI iff P's negation does not appear in any (genuine) counterfactual scenario description for which P is held true.
(I.e. if you hold P true, then you won't produce (genuine) CSDs in that capacity (of holding P to be true) according to which not-P.)
(You might wonder about what exactly a CSD is and what it takes for one to be genuine, but this will not be our focus here.)
This account nicely handles an example like 'Hesperus is Phosphorus or my hat is on the table'. This proposition isn't itself ICI - after all, you can hold it true by holding it true that my hat is on the table but Hesperus is not Phosphorus, and in that case you'd be prepared to produce CSDs in which it's false. But it is implied by a true ICI proposition, namely 'Hesperus is Phosphorus'.
The account also handles more complicated cases where there is no component ICI proposition (as there happens to be in the last example). It is enough that a true ICI proposition implies the necessary truth we are interested in.
But this account recently fell, due initially to an example from Jens Kipper (discussed in recent posts here). The example is 'Air is airy'. The point of this sentence is that it denotes something which isn't a natural kind - i.e. has no particular underlying nature - and predicates of it its superficial properties. Since, as it turns out, air isn't a natural kind, 'Air is airy' is necessarily true; there couldn't have been non-airy air, since, as it turns out, what is is to be air is just to be airy. If on the other hand air had turned out to have an underlying nature, like water does, we would regard 'Air is airy' as contingent, like we do 'Water is watery'; there could have been non-watery water, i.e. H20 in a situation where it isn't watery.
The problem for my old account is that 'Air is airy' is necessarily true, but it is neither ICI nor is it implied by an ICI true proposition.
(After the Kipper example, I have also come upon an example due to Strohminger and Yli-Vakkuri: 'Dylan is at least as tall as Zimmerman'. Since Dylan is Zimmerman, this is necessary. But it isn't ICI, since you could hold it true while holding that Dylan and Zimmerman are distinct. With this example, you could try to save my account by maintaining that - in a rich sense of 'implies' - this troublesome example is implied by 'Dylan is Zimmerman' (which is true and ICI), so my account gives the right answer after all, provided we have the rich sense of 'implies' on board. But I see little point in this, as this trick doesn't help with 'Air is airy'.)
What I think all this shows is that, in our analysis of necessity, we need, not the notion of implication, but more specialised relevant relationships between propositions. In particular, we need to consider when the truth of a proposition P would make a proposition Q necessary. Or, for a more penetrating analysis, when P would make Q counterfactually invariant.
Let's say that P is a positive counterfactual invariance decider for Q iff Q does not vary across genuine CSDs for which P is held true.
(A proposition P varies across a bunch of CSDs iff it is true according to some of them but not according to others.)
So, for example, 'Hesperus is Phosphorus' is its own positive CI decider; if you hold it true, then, in that capacity of holding it true, you won't produce any genuine CSDs according to which Hesperus is not Phosphorus. ('Hesperus is not Phosphorus' is also a positive CI decider for 'Hesperus is Phosphorus', although it happens to not be true.) But really, these are vacuous cases; since 'Hesperus is Phosphorus' and 'Hesperus is not Phosphorus' are inherently counterfactually invariant, any proposition you like counts (on the above definitions, which may not be optimal) as a positive CI decider for these.
(UPDATE 26/10/2017: This last claim is false. Some random proposition like 'Snow is white' actually doesn't count as a positive CI decider for 'Hesperus is Phosphorus', since you might hold it true but not hold 'Hesperus is Phosphorus' true. If CI deciderhood had been defined by referring to the genuine CSDs in which P (the potential decider) and Q (the potentially decided) are held true, rather than just P. )
The notion comes into its own with non-ICI propositions:
'Hesperus is Phosphorus' a positive CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you won't let the latter vary across CSDs.
'Hesperus is not Phosphorus' is a negative CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you will let the latter vary across CSDs (depending on whether my hat is on the table or not in the scenarios being described).
'Hesperus is Phosphorus' is a negative CI decider for 'Hesperus is not Phosphorus or my hat is on the table', and 'Hesperus is not Phosphorus' is a positive CI decider for 'Hesperus is not Phosphorus or my hat is on the table'.
Furthermore, this apparatus gives us good things to say about Kipper's counterexample to my old account:
'Air is not a natural kind' is a positive CI decider for 'Air is airy'; if you hold the former true, then the latter won't vary across CSDs.
(UPDATE 26/10/17: This last claim may be faulty, because you could perhaps hold 'Air is not a natural kind' true and also hold 'Air is not airy' true. This depends on how 'airy' is defined - is it part of its meaning that to be airy is to have the actual properties that air has, whatever those are? Then maybe you couldn't really coherently hold it false. But if it's defined in terms of a list of properties that we think air has, then you could get all skeptical the way Kripke does with cats and hold it true that air actually doesn't have these properties and it's some elaborate ruse which makes us think it does. This could be gotten around by narrowing our attention in the definition of positive CI deciderhood to genuine CSDs where, not just P (the potential decider) is held true, but also Q (the potentially decided). However, I don't think that this is required to save the analysis as formulated in this post, since we can just give up on 'Air is not a natural kind' itself being a CI decider (at least all by itself) of 'Air is airy' and instead appeal to 'All there is to being air is to be airy' or even just 'Air is airy and is not a natural kind'.)
(Likewise for the Strohminger/Yli-Vakkuri example: 'Dylan is Zimmerman' is a positive CI decider for 'Dylan is at least as tall as Zimmerman'.)
I think a good account of necessity can now be given as follows:
A proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive CI decider.
Note: it seems plausible that CI deciderhood is an a priori tractable matter; whether some P is a CI decider for some Q, and if so whether it is a positive or a negative decider, seem to be the sort of thing we can work out a priori. What we might not be able to know a priori is the truth-values of P and Q.
I will keep working on the best way to present this sort of approach, but I think the essentials are now in place.
My old account of necessity was:
A proposition is necessarily true iff it is, or is implied by, a proposition which is both inherently counterfactually invariant (ICI) and true.
A proposition P is ICI iff P's negation does not appear in any (genuine) counterfactual scenario description for which P is held true.
(I.e. if you hold P true, then you won't produce (genuine) CSDs in that capacity (of holding P to be true) according to which not-P.)
(You might wonder about what exactly a CSD is and what it takes for one to be genuine, but this will not be our focus here.)
This account nicely handles an example like 'Hesperus is Phosphorus or my hat is on the table'. This proposition isn't itself ICI - after all, you can hold it true by holding it true that my hat is on the table but Hesperus is not Phosphorus, and in that case you'd be prepared to produce CSDs in which it's false. But it is implied by a true ICI proposition, namely 'Hesperus is Phosphorus'.
The account also handles more complicated cases where there is no component ICI proposition (as there happens to be in the last example). It is enough that a true ICI proposition implies the necessary truth we are interested in.
But this account recently fell, due initially to an example from Jens Kipper (discussed in recent posts here). The example is 'Air is airy'. The point of this sentence is that it denotes something which isn't a natural kind - i.e. has no particular underlying nature - and predicates of it its superficial properties. Since, as it turns out, air isn't a natural kind, 'Air is airy' is necessarily true; there couldn't have been non-airy air, since, as it turns out, what is is to be air is just to be airy. If on the other hand air had turned out to have an underlying nature, like water does, we would regard 'Air is airy' as contingent, like we do 'Water is watery'; there could have been non-watery water, i.e. H20 in a situation where it isn't watery.
The problem for my old account is that 'Air is airy' is necessarily true, but it is neither ICI nor is it implied by an ICI true proposition.
(After the Kipper example, I have also come upon an example due to Strohminger and Yli-Vakkuri: 'Dylan is at least as tall as Zimmerman'. Since Dylan is Zimmerman, this is necessary. But it isn't ICI, since you could hold it true while holding that Dylan and Zimmerman are distinct. With this example, you could try to save my account by maintaining that - in a rich sense of 'implies' - this troublesome example is implied by 'Dylan is Zimmerman' (which is true and ICI), so my account gives the right answer after all, provided we have the rich sense of 'implies' on board. But I see little point in this, as this trick doesn't help with 'Air is airy'.)
What I think all this shows is that, in our analysis of necessity, we need, not the notion of implication, but more specialised relevant relationships between propositions. In particular, we need to consider when the truth of a proposition P would make a proposition Q necessary. Or, for a more penetrating analysis, when P would make Q counterfactually invariant.
Let's say that P is a positive counterfactual invariance decider for Q iff Q does not vary across genuine CSDs for which P is held true.
(A proposition P varies across a bunch of CSDs iff it is true according to some of them but not according to others.)
So, for example, 'Hesperus is Phosphorus' is its own positive CI decider; if you hold it true, then, in that capacity of holding it true, you won't produce any genuine CSDs according to which Hesperus is not Phosphorus. ('Hesperus is not Phosphorus' is also a positive CI decider for 'Hesperus is Phosphorus', although it happens to not be true.) But really, these are vacuous cases; since 'Hesperus is Phosphorus' and 'Hesperus is not Phosphorus' are inherently counterfactually invariant, any proposition you like counts (on the above definitions, which may not be optimal) as a positive CI decider for these.
(UPDATE 26/10/2017: This last claim is false. Some random proposition like 'Snow is white' actually doesn't count as a positive CI decider for 'Hesperus is Phosphorus', since you might hold it true but not hold 'Hesperus is Phosphorus' true. If CI deciderhood had been defined by referring to the genuine CSDs in which P (the potential decider) and Q (the potentially decided) are held true, rather than just P. )
The notion comes into its own with non-ICI propositions:
'Hesperus is not Phosphorus' is a negative CI decider for 'Hesperus is Phosphorus or my hat is on the table'; if you hold the former true, you will let the latter vary across CSDs (depending on whether my hat is on the table or not in the scenarios being described).
'Hesperus is Phosphorus' is a negative CI decider for 'Hesperus is not Phosphorus or my hat is on the table', and 'Hesperus is not Phosphorus' is a positive CI decider for 'Hesperus is not Phosphorus or my hat is on the table'.
Furthermore, this apparatus gives us good things to say about Kipper's counterexample to my old account:
'Air is not a natural kind' is a positive CI decider for 'Air is airy'; if you hold the former true, then the latter won't vary across CSDs.
(UPDATE 26/10/17: This last claim may be faulty, because you could perhaps hold 'Air is not a natural kind' true and also hold 'Air is not airy' true. This depends on how 'airy' is defined - is it part of its meaning that to be airy is to have the actual properties that air has, whatever those are? Then maybe you couldn't really coherently hold it false. But if it's defined in terms of a list of properties that we think air has, then you could get all skeptical the way Kripke does with cats and hold it true that air actually doesn't have these properties and it's some elaborate ruse which makes us think it does. This could be gotten around by narrowing our attention in the definition of positive CI deciderhood to genuine CSDs where, not just P (the potential decider) is held true, but also Q (the potentially decided). However, I don't think that this is required to save the analysis as formulated in this post, since we can just give up on 'Air is not a natural kind' itself being a CI decider (at least all by itself) of 'Air is airy' and instead appeal to 'All there is to being air is to be airy' or even just 'Air is airy and is not a natural kind'.)
(Likewise for the Strohminger/Yli-Vakkuri example: 'Dylan is Zimmerman' is a positive CI decider for 'Dylan is at least as tall as Zimmerman'.)
I think a good account of necessity can now be given as follows:
A proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive CI decider.
Note: it seems plausible that CI deciderhood is an a priori tractable matter; whether some P is a CI decider for some Q, and if so whether it is a positive or a negative decider, seem to be the sort of thing we can work out a priori. What we might not be able to know a priori is the truth-values of P and Q.
I will keep working on the best way to present this sort of approach, but I think the essentials are now in place.
Wednesday, 30 August 2017
Kipper's Bombshell
In a recent post (and an article I am working on), I arrived at the view that if a proposition can be known to be necessary (i.e. necessarily true or false) then either it or its negation is in the deductive closure of a set of true propositions with a priori necessary character - i.e. propositions which are such that it can be known a priori that they are necessary.
There is a new article by Jens Kipper forthcoming in Analysis, 'On what is apriori about necessities', which seems to make serious trouble for this view (as well as its ancestors). Here is the problem in my own words:
Kipper zeroes in on the fact that with some terms, such as - plausibly - 'air' and 'water', it is not a priori whether they pick out a natural kind or not. It turns out that 'air' doesn't pick out a natural kind, and that 'water' does. Now, let 'airy' be a predicate that applies to a stuff when it exhibits the superficial characteristics that air has in our world, and similarly for 'watery'.
Kipper's bombshell is to point out that 'Air is airy' is plausibly necessary (since air doesn't have some underlying nature which makes it air - rather its being air is basically just a matter of its being airy) but 'Water is watery' is plausibly not necessary (since something with water's underlying nature, i.e. being comprised mainly of H20, could have existed in quite different conditions where it isn't watery). And it definitely seems like these things could not have been known a priori.
I have mixed feelings realising this. I was really happy with my proposed link between necessity and apriority. I still feel inclined to suppose that there is something in the idea. But I cannot deny the simplicity and insightfulness of Kipper's bombshell.
Kipper considers and casts serious doubt on a view that tries to escape the bombshell by claiming that meaning change occurs when we discover whether a term like 'air' doesn't pick out a natural kind. I am pretty sympathetic to Kipper's rebuttal of this, and am inclined to look elsewhere for a way of saving, or repairing, my link. Could I perhaps figure out a way of getting propositions which clearly do have a priori necessary character and which imply propositions like 'Air is airy'?
I will post again on this matter once I get a better view of the situation.
There is a new article by Jens Kipper forthcoming in Analysis, 'On what is apriori about necessities', which seems to make serious trouble for this view (as well as its ancestors). Here is the problem in my own words:
Kipper zeroes in on the fact that with some terms, such as - plausibly - 'air' and 'water', it is not a priori whether they pick out a natural kind or not. It turns out that 'air' doesn't pick out a natural kind, and that 'water' does. Now, let 'airy' be a predicate that applies to a stuff when it exhibits the superficial characteristics that air has in our world, and similarly for 'watery'.
Kipper's bombshell is to point out that 'Air is airy' is plausibly necessary (since air doesn't have some underlying nature which makes it air - rather its being air is basically just a matter of its being airy) but 'Water is watery' is plausibly not necessary (since something with water's underlying nature, i.e. being comprised mainly of H20, could have existed in quite different conditions where it isn't watery). And it definitely seems like these things could not have been known a priori.
I have mixed feelings realising this. I was really happy with my proposed link between necessity and apriority. I still feel inclined to suppose that there is something in the idea. But I cannot deny the simplicity and insightfulness of Kipper's bombshell.
Kipper considers and casts serious doubt on a view that tries to escape the bombshell by claiming that meaning change occurs when we discover whether a term like 'air' doesn't pick out a natural kind. I am pretty sympathetic to Kipper's rebuttal of this, and am inclined to look elsewhere for a way of saving, or repairing, my link. Could I perhaps figure out a way of getting propositions which clearly do have a priori necessary character and which imply propositions like 'Air is airy'?
I will post again on this matter once I get a better view of the situation.
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