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.

Wednesday, 23 August 2017

Notes on Counterfactual Scenario Descriptions, Sources of Modal Error (or Uncertainty), and Deep Puzzles of Modality

One interesting thing about my account of subjunctive necessity is the way it separates two kinds of things that we could be wrong or confused about in our judgements of subjunctive modality: the truth of what we're holding true for the purposes of a counterfactual scenario description (CSD) and the genuineness of that CSD.

For example, I might think 'Hesperus is not Phosphorus' is subjunctively possible because I falsely believe that Hesperus is Phosphorus. Or I might be acquainted with some strange animals I call Toves and then not feel sure whether 'Toves are animals' is necessary simply because I am not sure whether the things I am acquainted with are animals.


By contrast, there are modal questions which do not centre - at least not in any definite way - on the truth or otherwise of what is being held true. For example, granting that I am human, could I have been an animal? Or how about a Neanderthal? Or a bank account?

And cosmic questions about whether there could have been less matter or energy, or perhaps just one atom in a void? And here the question arises: how do you know what you have to know in order to know whether something is necessarily the way it is or not? (In some cases, that seems clear. E.g. you have to know whether Hesperus is in fact Phosphorus in order to know whether it necessarily is. But in others it really doesn't.)

Another puzzling thing stems from the way, in my account, you can have CSDs which aren't possible, since the things held true for them aren't true. For instance, if I think wrongly that Hesperus isn't Phosphorus (or even just grant that for the sake of argument), I will be prepared to produce CSDs involving Hesperus not being Phosphorus, and these may be perfectly genuine. This strikes me as an important virtue of my account - i.e., that it is some sort of advance, giving us a fruitful way of talking and thinking philosophically about modality. It is hard to say exactly why. One thing is that it enables us to bracket off distracting sources of modal uncertainty and error, perhaps allowing us to focus better on the stuff which really bothers us philosophically about modality. 

In any case, this thing - about there being genuine CSDs which, despite being genuine, aren't possible because false things are held true for them - gives rise to some puzzlement in its own right. When we can go different ways on the question of whether Hesperus is Phosphorus or Clark Kent is Superman - questions of the identity or distinctness of things - it seems like our underlying way of thinking about things, our conceptual apparatus, is basically the same. And to a fair, but perhaps lesser extent, going different ways on the question of the underlying nature of cats, or Toves, or water also seems to leave our conceptual apparatus largely the same. (There may be something wrong or lacking in this description.) We get the sense that we can flip the switch either way on these things quite readily, and continue in much the same way in either case when it comes to grasping a range of genuine CSDs which arise on the assumption that things are the one way or the other. On the other hand, what of things which are - in a conceptual sense, I want to say - far from true? 

Things get puzzling very quickly once such questions come into view. If I somehow hold it true that humans are cats, can I then produce genuine CSDs according to which that is true? It is hard to know what to say. One thing is that there might be an issue about whether we can really hold such things true, or perhaps better, whether it makes sense to talk of holding such things true. But to that it may always be replied - OK, but we can sometimes do something here, in these cases where you might worry about whether we can really hold the things in question true or not.

Are there two ways, then, of getting out of the sphere of genuine CSD-hood? One by holding things true which are either true, or not a big deal or problematic to hold true, and then going further and further away from actuality, so to speak, until you say things we might hesitate to call CSDs (e.g. holding it true that I am human, but then talking about a scenario where I'm a cat), and another by holding far-out things true?

Another worry concerns what might be called modal encroachment. The idea that, if we learn more about some things, we might realise that some things aren't possible that we thought were. And there is a question here about whether that could affect what we think about genuineness of a CSD, or whether what we formerly thought were not only genuine CSDs but possibilities (i.e. that the things being held true for those CSDs are the case) can always be retained as genuine CSDs by holding the right false things true.

I feel that with these issues my account, which could seem merely logic-choppy and perhaps trivial in a way, begins to make contact with some of the deeper puzzles surrounding modality. 

In a future post I want to try to explore how our ideas might be prone to shifting and slipping without our realising it when we philosophize about modality. For instance, the obscure way the stakes can seemingly be raised in some way by the question of 'But could that really have happened?'. I also hope to make some progress on puzzles concerning 'whether the ground of modality is in us or the world', by trying to better uncover the thought processes underlying that unsatisfactory question. Perhaps then we will see better what the real issues are in this thicket of philosophy.

Postscript (or seedling for next time):

Dim hypothesis re. Kripkean showing of necessity of identity: it shows that things couldn't have been otherwise in a deep way by showing that they couldn't have been otherwise in a shallow way. 

I.e. in a certain frame of mind, we might think 'What do we know about how, and the extent to which, things really might have been different?'. A frame of mind with a sense of cosmic mystery, open to underlying system we have little or no inkling of. Then the Kripkean arguments come along and say 'Well, whatever the truth is about that, things certainly couldn't have been such that Hesperus isn't Phosphorus'.

It is notable that Kripke's results are necessities, or denials of possibility. This leaves it open that we have a way of thinking, or a concept of modality, on which all the Kripkean necessities are necessary as required, but where there is leeway which then disappears on some deeper view.

Friday, 18 August 2017

Scholarly Attention for the First Ever Sprachlogik Post!

It recently came to my attention that the first ever post here, from back in 2011, is the subject of a journal article by Matheus Silva, a Brazilian philosopher and logician.

Silva has also recently engaged with my argument against the Brogaard-Salerno Stricture, a principle about when it is OK to reason using conditionals.

Tuesday, 1 August 2017

An Adventure in Linking Necessity to Apriority

There is an important link between necessity and apriority which can shed light on our knowledge of the former, but initially plausible attempts to spell out what it is fall victim to counterexamples. Casullo (2003) discusses one such proposal, argues that it fails, and suggests an alternative. In this post, I argue that Casullo’s alternative also fails, suggest another, argue that that fails too, and then suggest another which I hope is correct.

First proposal

Kripke (1980) showed that it is not always knowable a priori whether a proposition is necessarily true. But, you might think, perhaps it is always knowable a priori whether a proposition has whatever truth value it has necessarily or contingently. To use Casullo’s (2003) terminology, while Kripke showed that knowledge of specific modal status (necessarily true, contingently false, etc.) is not always possible a priori, this leaves open the possibility of apriori knowledge of general modal status (necessary or contingent - and on this usage of ‘necessary’ and ‘contingent’, truth value is left open). Perhaps that is the link we are after between necessity and apriority.

The claim that general modal status is always knowable a priori entails the following:

(1) If p is a necessary proposition and S knows that p is a necessary proposition, then S can know a priori that p is a necessary proposition.

(The second conjunct of (1)’s antecedent sidesteps the worry that some necessary propositions may be such that it is unknowable that they are necessary.)

Casullo, following Anderson (1993), argues convincingly that this is false. Consider:

(1X) Hesperus is Phosphorus or my hat is on the table.

This is a necessary proposition, but for all any S could know a priori, it could be necessarily true (if the first disjunct is true), contingently true (if the first disjunct is false but the second true), or contingently false (if both disjuncts are false). So (1) can’t be right.

Second proposal

In an interesting effort to avoid the problem affecting (1), Casullo introduces the notions of conditional modal propositions and conditional modal status:

Associated with each truth functionally simple proposition is a pair of conditional propositions: one provides the specific modal status of the proposition given that it is true; the other provides its specific modal status given that it is false. Associated with each truth functionally compound proposition is a series of conditional propositions, one for each assignment of truth values to its simple components. Each conditional proposition provides the specific modal status of the proposition given that assignment of truth values. Let us call these propositions conditional modal propositions and say that S knows the conditional modal status of p just in case S knows all the conditional modal propositions associated with p. (Casullo (2003), p. 197.)
His proposed link between necessity and apriority is as follows:

(2) If p is a necessary proposition and S knows the conditional modal status of p, then S can know a priori the conditional modal status of p.

Casullo dubs this ‘a version of the traditional account of the relationship between the a priori and the necessary that is immune to Kripke’s examples of necessary a posteriori propositions’ (Casullo (2003), p. 199). It handles (1X) nicely. Calling (1X)’s disjuncts ‘Hesp’ and ‘Hat’, its associated conditional modal propositions will run as follows:

If Hesp is true and Hat is true, (1X) is necessary.
If Hesp is true and Hat is false, (1X) is necessary.
If Hesp is false and Hat is true, (1X) is contingent.
If Hesp is false and Hat is false, (1X) is contingent.

These are plausibly knowable a priori, as required by (2).

But consider:

(2X) Everything is either such that it is either not Hesperus or is Phosphorus, or such that it is either on the table or not my hat.

While it contains connectives, this is not a truth functional compound in the relevant sense, since it does not embed any whole propositions. So on Casullo’s proposal, (2X) will be associated with just a pair of conditional modal propositions. Which ones? A problem here is that there is no very clear positive case for any pair (the account, after all, was probably not formulated with (2X) in mind), but I think it is clear that the only candidate pair which could stand a chance is:

If (2X) is true, it is necessary.
If (2X) is false, it is contingent.

(After all, (2X) is true and necessary, so the other available choice for first member couldn’t be right, and the second member of the pair seems true and knowable a priori.)

Instantiating Casullo’s proposal (2) on (2X), we get:

If (2X) is a necessary proposition and S knows the conditional modal status of (2X), then S can know a priori the conditional modal status of (2X).

But it seems clear that the first conditional modal proposition for (2X), i.e. that if (2X) is true, it is necessary, could not be known a priori. So (2) can’t be right either.

Third proposal

What strikes one initially about the disjunctive counterexample to the first proposal is that it has a component whose general modal status is knowable a priori. But this isn’t true of the counterexample to the second proposal; it has no component propositions at all. What is true about both counterexamples is, not that they have cromponent propositions whose general modal status is knowable a priori, but that they are implied by such propositions.

Let us say that a proposition p possesses a priori necessary character iff it can be known a priori that p is a necessary proposition, i.e. that p has whatever truth value it has necessarily.

Now, I submit that if a proposition whose general modal status is knowable at all is necessarily true, then it is in the deductive closure of a set of true propositions possessing a priori necessary character.

How, though, to generalize this so that it covers all necessary propositions (i.e. necessarily false propositions as well as true ones)? For a few weeks, I thought this would work:

If a proposition whose general modal status is knowable at all is necessary, then it is either in the deductive closure of a set of true propositions possessing a priori necessary character, or it is in the deductive closure of a consistent set of false propositions possessing a priori necessary character.

To cast the point in a form similar to (1) and (2) above:

(3) If p is a necessary proposition and S knows that p is a necessary proposition, then p is either in the deductive closure of a set of true propositions which S can know a priori to be necessary, or it is in the deductive closure of a consistent set of false propositions which S can know a priori to be necessary.

But I have just recently realised that this is false as well.

The problem lies with necessarily false propositions. Requiring consistency of the set of false propositions that implies a putative necessary proposition rules out necessarily false propositions that contradict themselves. E.g. 'It is both raining and not raining' is, and can be known to be, a necessary proposition, but it is not implied by any consistent set of false propositions of apriori necessary character. On the other hand, removing the consistency requirement causes the account to overgenerate, at least on a classical conception of implication; 'I had toast for breakfast' is implied by the set of false propositions of a priori necessary character {'2 + 2 = 4', 'not-(2 + 2 = 4)'}, since that set implies any proposition whatsoever.

Fourth proposal

Now, without wanting to rule out that we could specify a special implication-like relation which behaves as desired, I have nevertheless tentatively given up on bringing in consistency to get a general result which covers not only necessary true propositions but necessarily false ones as well. Instead, I think the thing to do is to exploit the idea that a necessarily false proposition's negation is necessarily true, giving us:

(4) If p is a necessary proposition and S knows that p is a necessary proposition, then either p or its negation is in the deductive closure of a set of true propositions which S can know a priori to be necessary.

Maybe this one is true! Please let me know, by comment or email, if you see a problem.


[UPDATE 31/08/2017: Trouble has arisen.]

Thanks to Albert Casullo for helpful and encouraging correspondence on this topic.

References

Anderson, C. Anthony (1993). Toward a Logic of A Priori Knowledge. Philosophical Topics 21(2):1-20.

Casullo, Albert (2003). A Priori Justification. Oxford University Press USA.

Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.