For a long time I have wondered, with an uneasy feeling that there was something I couldn't see, about the relationship between two-dimensional semantics and my approach to analysing subjunctive necessity de dicto. As I flagged in the previous post, this has become even more urgent in light of my new, relational account involving the notion of a counterfactual invariance (CI) decider.
I think I've finally made a breakthrough here, and found a clear connection. There is more to say, but here it is briefly.
Recall that my account states that a proposition is necessary (i.e. necessarily true or necessarily false) iff it has a true positive counterfactual invariance (CI) decider.
(P is a positive counterfactual invariance decider for Q iff Q does not vary across genuine counterfactual scenario descriptions for which P is held true.)
A close analogue of this account can be stated in terms of two-dimensional semantics: a proposition Q is necessary iff there is a true proposition P such that for every scenario S in which P is true, Q's two-dimensional intension maps, for all W, <S, W> to the same truth-value.
And I think I can maintain, as CI deciderhood is plausibly a priori tractable and arguably a semantic matter, so too is the question whether, given some propositions P and Q, P is such that for every scenario S in which P is true, Q's two-dimensional intension maps, for all W, <S, W> to the same truth-value.
This makes clear one major way in which my analysis goes beyond the normal two-dimensional account of subjunctive necessity in terms of secondary (or C) intension - and this way can then be translated into two-dimensional terms. And looking at necessity this way, as opposed to with just the usual two-dimensional account of subjunctive necessity, gives us a finer grained picture of the role played by what Kripke called 'a priori philosophical analysis' in our knowledge of necessity. You don't have to know which scenario is actual to know that a proposition is necessary - you just need to know that you're in one of some range of scenarios such that, if they were actual, the proposition would be necessary. And such a range can be characterized by a proposition which you can know a priori to be a CI decider for the necessary proposition in question.
Showing posts with label counterfactual scenarios. Show all posts
Showing posts with label counterfactual scenarios. Show all posts
Thursday, 9 November 2017
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.
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.
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