After writing what appears below, I found a treatment-in-passing of the very same issue by von Wright in a rich paper called 'Modal Logic and the Tractatus'.
Discuss: is PC-tautologousness a modal notion?
'Can't come out F'.
But, having a populated abstract space of valuations:
'Doesn't come out F in any row/valuation'.
But then what goes into the conception of 'all valuations'? Isn't this the same as, or tantamount to, 'all possible valuations'?
But what if one tries to gainsay that?
'No, they're all actual.' - One can give non-modal conditions for 'permissible valuation', to be sure. Picking them out of a larger space. But how do we get the notion of the larger space?
We can say: there are valuations. A valuation is a mapping from atoms to {0, 1}. Any mapping from atoms to {0, 1} is a valuation.
We get, as it were, modal effects from a population of abstracta. And it seems we can conceive these abstracta without modal notions. That is, 'mapping from "p" to {0, 1}' doesn't seem like a modal notion.
But what about 'all such mappings'? Is there even any basis for decision? Is there a determinate answer? (Open texture.) Or is there a need to further fix concepts here? More than one legitimate way of going?
If so, we could have something like 'weakly modal' vs. 'strongly modal' so that 'all such mappings' is weakly but not strongly modal. But how do we draw the line?
For can't we, at least superficially, pull the same trick out in all cases, or a great many more than I was dimly thinking of above? The trick, that is, of trading modality - or strong modality - in for abstracta? Isn't ersatzism just such a move? Can we find a principled way of refuting ersatzism but allowing the move in the PC case?
I'm dimly seeing two distinctions:
One:
The case where everything under discussion is abstract, part of the abstract population.
vs.
The case where, as it were 'concrete configurations' are under discussion. So that to be a possible concrete configuration is to correspond to one of the abstract population. E.g. a switchboard.
Another:
The case where the abstract population is well-defined vs. not.
Also:
Abstract population discrete vs. continuous.
Before examining the crossings of these distinctions and trying for examples of each combination: is (1) really about abstract vs. concrete? Or is it rather about whether the object under discussion is itself part of the abstract population? You might, e.g., think of 'actual songs' as non-spatial but temporal and created, and thus hold an actual song to be distinct from its "abstract nature" or whatever, the latter being platonic (uncreated, non-temporal) - a space of "song-patterns".
Showing posts with label varieties of modality. Show all posts
Showing posts with label varieties of modality. Show all posts
Saturday, 10 January 2015
Saturday, 20 September 2014
Modality and 'Epistemic'
...plus a preview of forthcoming analyses of a priority and analyticity.
This is a correspondence-inspired followup to 'Two Concepts of Metaphysical Modality'.
What I there called 'metaphysical modality in the broad sense' should probably be thought of as including what David Chalmers calls the logical or epistemic modality (also sometimes the 'indicative' modality), tied to what is a priori consistent. This despite my characterizing it in part with the term 'non-epistemic'.
What's going on? It may look like there is some disagreement between me and Chalmers about whether some modality has some status which we both call 'epistemic'.
I don't think this is so, however. It seems there are just different uses of 'epistemic' at work here. Chalmers doesn't think that what he calls the logical or epistemic modality depends upon our knowledge or conventions (any more than logic does). Whereas I was using 'epistemic' in 'non-epistemic' (and tend to use it elsewhere) to mean something like 'depending on or having to do with knowledge'.
This also connects with a bit in Chalmers's short piece on the tyranny of the subjunctive, where he fields the objection 'But indicative necessity is epistemic!' and says 'So?'.
For me that always seemed like a bullet that really didn't have to be bitten - in fact, on that ought not to have been. But this is probably because I was reading 'epistemic' to mean something like 'depending on, or having to do with, knowledge'. I now suspect I was reading it contrary to Chalmers's intention. One moral: take care using and interpreting overworked philosophical words!
Now for the preview...
For my part, I think the core notion behind the a priori/a posteriori distinction in propositional typology - which distinction is tied to what Chalmers calls the logical, epistemic or indicative modality - isn't really 'epistemic' in the sense that I tend to give that word. 'A priori' could of course be stipulated to be about knowability without experience or whatever, but what underlies and explains that knowability has to do with the nature of the proposition itself.
I'm working on cashing that out in terms of the internal meaning determining the truth value. And that sounds like analyticity, but to that I reply that it's the full internal meaning in question here, which need not be fully grasped in order to pass as understanding the proposition in question. To define analyticity, I want to use a notion of a 'meaning-radical' - something like a bit of conceptual structure such that having it on board suffices for you to count as understanding the proposition in question - and say that a proposition is analytic iff its meaning-radical determines its truth value. Or one of its meaning-radicals, if there can be more than one. (Meaning-radical/analyticity are pretty vague notions, I think.)
This also provides a nice pithy answer to Kant's big question; the synthetic a priori is possible because full internal meaning can outrun meaning-radicals. This connects to the idea of the linguistic division of labour, and Wittgensteinian points about the widely-scatteredness of the determinants of meaning.
This is a correspondence-inspired followup to 'Two Concepts of Metaphysical Modality'.
What I there called 'metaphysical modality in the broad sense' should probably be thought of as including what David Chalmers calls the logical or epistemic modality (also sometimes the 'indicative' modality), tied to what is a priori consistent. This despite my characterizing it in part with the term 'non-epistemic'.
What's going on? It may look like there is some disagreement between me and Chalmers about whether some modality has some status which we both call 'epistemic'.
I don't think this is so, however. It seems there are just different uses of 'epistemic' at work here. Chalmers doesn't think that what he calls the logical or epistemic modality depends upon our knowledge or conventions (any more than logic does). Whereas I was using 'epistemic' in 'non-epistemic' (and tend to use it elsewhere) to mean something like 'depending on or having to do with knowledge'.
This also connects with a bit in Chalmers's short piece on the tyranny of the subjunctive, where he fields the objection 'But indicative necessity is epistemic!' and says 'So?'.
For me that always seemed like a bullet that really didn't have to be bitten - in fact, on that ought not to have been. But this is probably because I was reading 'epistemic' to mean something like 'depending on, or having to do with, knowledge'. I now suspect I was reading it contrary to Chalmers's intention. One moral: take care using and interpreting overworked philosophical words!
Now for the preview...
For my part, I think the core notion behind the a priori/a posteriori distinction in propositional typology - which distinction is tied to what Chalmers calls the logical, epistemic or indicative modality - isn't really 'epistemic' in the sense that I tend to give that word. 'A priori' could of course be stipulated to be about knowability without experience or whatever, but what underlies and explains that knowability has to do with the nature of the proposition itself.
I'm working on cashing that out in terms of the internal meaning determining the truth value. And that sounds like analyticity, but to that I reply that it's the full internal meaning in question here, which need not be fully grasped in order to pass as understanding the proposition in question. To define analyticity, I want to use a notion of a 'meaning-radical' - something like a bit of conceptual structure such that having it on board suffices for you to count as understanding the proposition in question - and say that a proposition is analytic iff its meaning-radical determines its truth value. Or one of its meaning-radicals, if there can be more than one. (Meaning-radical/analyticity are pretty vague notions, I think.)
This also provides a nice pithy answer to Kant's big question; the synthetic a priori is possible because full internal meaning can outrun meaning-radicals. This connects to the idea of the linguistic division of labour, and Wittgensteinian points about the widely-scatteredness of the determinants of meaning.
Saturday, 2 August 2014
Two Concepts of Metaphysical Modality
Here I want to distinguish two concepts of metaphysical modality and then give two reasons for thinking that this is an important distinction.
One concept, which I will call the concept of metaphysical modality in the narrow sense, crucially involves the subjunctive/indicative contrast, or the contrast between considering a scenario as counterfactual versus considering it as actual, and focuses on the subjunctive/counterfactual side. (This is why Chalmers is able, in 'The Foundations of Two-Dimensional Semantics' and other papers, to choose 'subjunctive necessity' as his preferred term for metaphysical necessity in the narrow sense.) It concerns how things could have been in a very broad sense. And so we can help fix the concept with familiar Kripkean talk like 'To be sure, we don't know a priori that Hesperus is Phosphorus. Given far-out enough empirical revelations, that could turn out to be wrong. But given that we're not mistaken about this - given that Hesperus is Phosphorus - then it could not have been otherwise. It is a necessary truth that Hesperus is Phosphorus'.
The other concept, which I will call the concept of metaphysical modality in the broad sense, doesn't involve this contrast. It may be roughly characterized as modality which is neither epistemic nor somehow conventional. Modal facts which are the way they are irrespective of anything to do with our knowledge, and irrespective of any conventions we might have, are metaphysical modal facts. And we might want to throw in something about the modality not being restricted as well.
To illustrate the difference, consider a proposition like 'This typewriter cannot have two of its keys depressed simultaneously' - or, to avoid the idea that this may be a case of some tacitly restricted modality, 'This typewriter cannot in the course of its proper functioning have two of its keys depressed simultaneously'. This proposition clearly has a modal element. Also, this modal element appears to have little to do with knowledge or some convention we have set up. If the proposition is true, then the typewriter in question has this modal property - that of not being able to have two of its keys depressed simulteneously in the course of its proper functioning - in virtue of the way it is, not in virtue of our state of knowledge or any convention we have set up. And so we might want to say that the modality in question is metaphysical in the broad sense. But it seems not to be an instance of metaphysical modality in the narrow sense. The subjunctive, or the consideration of scenarios as counterfactual, doesn't come into the matter; it is, we might say, about what the typewriter can actually do, not what it might have done had things gone differently (even if, in this case, there is a one-to-one correspondence between actual and counterfactual possibilities).
Another example of a proposition involving a modality which we should say is metaphysical in the broad sense but not in the narrow, is 'It is possible to win a game of chess in five moves'. Here the object of interest is something abstract (the game of chess), whereas in the first example the object of interest was a concrete mechanical thing.
Why is it important to realize that there are these two different concepts of metaphysical modality? One reason is that it seems very likely to be relevant to solving problems about the varieties of modality, a topic whose difficulty has become steadily more apparent in the decades following Naming and Necessity.
Another reason, which has been even closer to my concerns, is its relevance for the project of trying to analyze or give an account of metaphysical modality in the narrower sense. For instance, the account of this which I have been developing involves a notion which clearly has a modal component.
The account, which I will post on soon, says that a proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true. And the notion of inherent counterfactual invariance is cashed out in terms of the counterfactual scenario descriptions producible by the language system to which the proposition in question belongs. Not those which it actually does produce in its career, but those which it can. (A proposition is inherently counterfactually invariant iff its negation does not appear in any of these producible counterfactual scenario descriptions.)
The question now arises: does the presence of this modal element - which should be a good sign to anyone who, like me, is suspicious that there could be any such thing as a reduction of a modal notion to non-modal notions - make the account circular? 'Circular' in this context seems like a dirty word, but note that if the answer is Yes, that wouldn't mean that the account is no good at all; it would still be far from obvious or trivial. It could then perhaps be seen as a recursive definition, presupposing some cases as a base, and explaining the rest in terms of it. But still, Yes might seem like the wrong answer. I suspect it is. Separating metaphysical modality in the broad sense from metaphysical modality in the narrow sense opens up a promising way of supporting a No; the account deals with metaphysical necessity in the narrow sense - subjunctive necessity, necessity when considering-as-counterfactual - and appeals, on the right hand side of the 'iff', to a distinct species of metaphysical modality in the broad sense. On this understanding, there is no circularity - or to put it more politely, recursiveness - in the account at all. Of course, it doesn't supply us with a key for analyzing modality away altogether, as some attempts at analyzing metaphysical necessity in the narrow sense (without perhaps isolating that sense sufficiently clearly) have tried to do, but that should probably be seen as one of its more important virtues.
References
Chalmers, David J. (2006). The foundations of two-dimensional semantics. In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. 55-140.
Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.
One concept, which I will call the concept of metaphysical modality in the narrow sense, crucially involves the subjunctive/indicative contrast, or the contrast between considering a scenario as counterfactual versus considering it as actual, and focuses on the subjunctive/counterfactual side. (This is why Chalmers is able, in 'The Foundations of Two-Dimensional Semantics' and other papers, to choose 'subjunctive necessity' as his preferred term for metaphysical necessity in the narrow sense.) It concerns how things could have been in a very broad sense. And so we can help fix the concept with familiar Kripkean talk like 'To be sure, we don't know a priori that Hesperus is Phosphorus. Given far-out enough empirical revelations, that could turn out to be wrong. But given that we're not mistaken about this - given that Hesperus is Phosphorus - then it could not have been otherwise. It is a necessary truth that Hesperus is Phosphorus'.
The other concept, which I will call the concept of metaphysical modality in the broad sense, doesn't involve this contrast. It may be roughly characterized as modality which is neither epistemic nor somehow conventional. Modal facts which are the way they are irrespective of anything to do with our knowledge, and irrespective of any conventions we might have, are metaphysical modal facts. And we might want to throw in something about the modality not being restricted as well.
To illustrate the difference, consider a proposition like 'This typewriter cannot have two of its keys depressed simultaneously' - or, to avoid the idea that this may be a case of some tacitly restricted modality, 'This typewriter cannot in the course of its proper functioning have two of its keys depressed simultaneously'. This proposition clearly has a modal element. Also, this modal element appears to have little to do with knowledge or some convention we have set up. If the proposition is true, then the typewriter in question has this modal property - that of not being able to have two of its keys depressed simulteneously in the course of its proper functioning - in virtue of the way it is, not in virtue of our state of knowledge or any convention we have set up. And so we might want to say that the modality in question is metaphysical in the broad sense. But it seems not to be an instance of metaphysical modality in the narrow sense. The subjunctive, or the consideration of scenarios as counterfactual, doesn't come into the matter; it is, we might say, about what the typewriter can actually do, not what it might have done had things gone differently (even if, in this case, there is a one-to-one correspondence between actual and counterfactual possibilities).
Another example of a proposition involving a modality which we should say is metaphysical in the broad sense but not in the narrow, is 'It is possible to win a game of chess in five moves'. Here the object of interest is something abstract (the game of chess), whereas in the first example the object of interest was a concrete mechanical thing.
Why is it important to realize that there are these two different concepts of metaphysical modality? One reason is that it seems very likely to be relevant to solving problems about the varieties of modality, a topic whose difficulty has become steadily more apparent in the decades following Naming and Necessity.
Another reason, which has been even closer to my concerns, is its relevance for the project of trying to analyze or give an account of metaphysical modality in the narrower sense. For instance, the account of this which I have been developing involves a notion which clearly has a modal component.
The account, which I will post on soon, says that a proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true. And the notion of inherent counterfactual invariance is cashed out in terms of the counterfactual scenario descriptions producible by the language system to which the proposition in question belongs. Not those which it actually does produce in its career, but those which it can. (A proposition is inherently counterfactually invariant iff its negation does not appear in any of these producible counterfactual scenario descriptions.)
The question now arises: does the presence of this modal element - which should be a good sign to anyone who, like me, is suspicious that there could be any such thing as a reduction of a modal notion to non-modal notions - make the account circular? 'Circular' in this context seems like a dirty word, but note that if the answer is Yes, that wouldn't mean that the account is no good at all; it would still be far from obvious or trivial. It could then perhaps be seen as a recursive definition, presupposing some cases as a base, and explaining the rest in terms of it. But still, Yes might seem like the wrong answer. I suspect it is. Separating metaphysical modality in the broad sense from metaphysical modality in the narrow sense opens up a promising way of supporting a No; the account deals with metaphysical necessity in the narrow sense - subjunctive necessity, necessity when considering-as-counterfactual - and appeals, on the right hand side of the 'iff', to a distinct species of metaphysical modality in the broad sense. On this understanding, there is no circularity - or to put it more politely, recursiveness - in the account at all. Of course, it doesn't supply us with a key for analyzing modality away altogether, as some attempts at analyzing metaphysical necessity in the narrow sense (without perhaps isolating that sense sufficiently clearly) have tried to do, but that should probably be seen as one of its more important virtues.
References
Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.
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