Armstrong claims that truthmakers for causal claims, for Lewis, are entirely this-worldly:
"Lewis's talk of possible worlds here is to a degree miselading. It is important to realize, as I did not originally realize, and I think many others have not realized, that these counterfactuals are supposed to hold solely in virtue of features of the world in which the causal relation holds. As I would put it, the truthmaker for causal truths is to be found solely in the world in which the relation holds. (I think this follows straight from the contingency of the causal relation, a contingency that Lewis does not doubt.) In his theory of causation the possible worlds enter as mere calculational devices. He has given me as an example the way that we might say with truth that a person is a Montague rather than a Capulet, without being being committed to the view that these families are actual. The fictional families are used as no more than a calculational device." ("Going through the Open Door Again: Counterfactual versus Singularist Theories of Causation," p. 445)
I must confess that I don't understand, so perhaps you all can help me understand. If the possible worlds are merely a calculational device, then there should be some way to make the calculation with a different device. (I could explain what was meant by a person being a Montague rather than a Capulet with different concepts if you had never read Shakespeare.) Assume, then that there are no possible worlds. What is it, in this world, that makes causal counterfactuals—had c not occurred, e would not have occurred—true (when they are)? It must have something to do with laws, but I'm not sure how that would go.
(I assume that Armstrong does not mean merely that the possible worlds don't need to be Lewisian worlds, that they might be linguistic constructions or sets of abstract states of affairs. The claim is not that the truthmakers don't have to be other-worldly; it's that they are entirely this-worldy.)
I'm also puzzled by Armstrong's parenthetical remark, that the this-worldy nature of truthmakers for causal claims follows directly from the contingency of causation. How is that argument supposed to go?
Showing posts with label Counterfactuals. Show all posts
Showing posts with label Counterfactuals. Show all posts
Tuesday, January 26, 2010
Monday, October 5, 2009
New Metaphysics Drafts
I've got three new drafts of metaphysics papers up on my (new) website.
They are:
Balls and All
In this paper I lay out a rather unusual combination of views about spacetime, mereology and material objects. The view is coherent, I claim: and if it is coherent it seems to provide a counterexample to a number of assumptions that are made about what sorts of views have to go together. (In particular I use it to argue against a number of Ted Sider's arguments in his Four-Dimensionalism.)
Disposition Impossible, with C.S. Jenkins
In this paper Carrie and I investigate "unmanifestable dispositions": dispositions to PHI in C, where either PHI is impossible or C is. We argue that objects have such dispositions, and it is a non-trivial matter which ones they have. We also argue that these impossible dispositions play, or can play, significant theoretical roles. If we are right, a number of standard styles of theories of dispositions are in trouble.
The third is a piece of "applied metaphysics", I suppose, at least if work on counterfactuals counts as metaphysics. My impression is that it often is counted that way, even though it is at least as much philosophy of language and philosophy of science:
Why Historians (and Everyone Else) Should Care About Counterfactuals.
I discuss eight good reasons historians can usefully concern themselves with counterfatuals: some have been argued for before by others, but even in these cases I either have different characterisations of exactly why conditionals are important, or have different arguments for their importance in historical method.
Any feedback on any of the three papers would of course be welcome. (Obviously not any feedback. But you know what I mean.)
They are:
Balls and All
In this paper I lay out a rather unusual combination of views about spacetime, mereology and material objects. The view is coherent, I claim: and if it is coherent it seems to provide a counterexample to a number of assumptions that are made about what sorts of views have to go together. (In particular I use it to argue against a number of Ted Sider's arguments in his Four-Dimensionalism.)
Disposition Impossible, with C.S. Jenkins
In this paper Carrie and I investigate "unmanifestable dispositions": dispositions to PHI in C, where either PHI is impossible or C is. We argue that objects have such dispositions, and it is a non-trivial matter which ones they have. We also argue that these impossible dispositions play, or can play, significant theoretical roles. If we are right, a number of standard styles of theories of dispositions are in trouble.
The third is a piece of "applied metaphysics", I suppose, at least if work on counterfactuals counts as metaphysics. My impression is that it often is counted that way, even though it is at least as much philosophy of language and philosophy of science:
Why Historians (and Everyone Else) Should Care About Counterfactuals.
I discuss eight good reasons historians can usefully concern themselves with counterfatuals: some have been argued for before by others, but even in these cases I either have different characterisations of exactly why conditionals are important, or have different arguments for their importance in historical method.
Any feedback on any of the three papers would of course be welcome. (Obviously not any feedback. But you know what I mean.)
Thursday, March 26, 2009
The Age of Hyperintensionality
A place in a sentence is extensional if words with the same extension can always be substituted into it without changing the truth-value of the whole sentence. (That definition is a little too crude in about three ways, but bear with me.) A place in a sentence is intensional, in one sense of “intensional”, when words that necessarily share the same extension can always be substituted into it without changing the truth-value of the whole sentence.
It has become increasingly clear since the 1970s that we need to carve meanings more finely than by “intensions” in the sense associated with the specification above. Call the sorts of intensions employed, for example, by Richard Montague possible worlds intensions. Handling belief clauses by insisting that anyone who believes something believes everything necessarily equivalent to it has always caused problems. Once we accept that names are rigid designators, allowing their substitution in all sorts of representational and psychological contexts causes trouble: the Sheriff of Nottingham can be hunting for Robin Hood without hunting for Robin of Locksley, or so it seems.
There seem to be places outside our psychological talk that require hyperintensionality. Talk of entailment in the sense of logical consequence, for example: it does not logically follow from apples being red that all bachelors are unmarried, let alone that water is H2O, even though it does follow that either apples are red or apples are not red. Use of counter-possible conditionals is another example: two conditionals can have necessarily false antecedents but differ in truth-value. Talk about moral obligation and permission seems to be hyperintensional, as anyone struggling with substituting logical equivalents in the scope of deontic operators may have seen. I’m just back from a conference in Colorado where people were insisting that “in virtue of”, “because”, and other explanatory expressions were hyperintensional. (Benjamin Schnieder, Gideon Rosen and Kit Fine were three in particular.) Once you look around you see quite a bit of hyperintensionality.
There’s a piece of rhetoric I associate with Richard Sylvan about this. He was fond of suggesting that there would be a move from using possible-worlds intensions to using hyperintensional resources that would parallel the move made from extensionalism to possible-worlds intensionalism. In the nineteen-sixties, the big goal was to be able to do philosophy of language while treating language extensionally: think of Davidson’s project in particular, though Quine was also a big booster of the extensionalist program. I guess it was typical of that project to assign extensions to categories of expressions, and then have some syncatogramatic expressions that operated on extensions to yield other extensions. (E.g. “all” did not get an extension, but (All x)(Fx) operated on the extension of “F” to yield a sentence-extension, i.e. a truth-value)
There are still people trying to carry out that extensionalist project, but it came under increasingly severe attack since the early 1970s. (And maybe earlier: I think Carnap might be an important precursor here, along with Prior, and perhaps many others). The extensional programme was not very satisfying in its treatment of propositional attitude reports, entailment, normative discourse such as the use of “ought”, and a number of other areas. But the star witness against the extensional programme was modal vocabulary. Treating “necessarily” extensionally does not get you very far, and after Saul Kripke popularised possible-worlds semantics for “necessarily”, the floodgates started to open. Richard Montague and David Lewis were among the vanguard of those arguing for a systematic, intensional treatment of natural language, arguing that it handled all sorts of constructions that extensional treatments faced serious difficulty with.
The intensions that Montague and Lewis relied upon were set-theoretic constructions out of possible worlds and possible individuals. (Not just sets of possibilia or functions from possibilia to possiblia, but also sets of those sets, functions from those functions to other functions, etc. etc.) The Montague project of trying to handle all of language with these possible-worlds intensions is alive and well today: I take Robert Stalnaker to be one of its prominent contemporary philosophical defenders, though I haven’t scrutinised his recent work to see if any weakening has happened.
But I think that project is doomed. There is too much work that needs to be done that requires hyperintensional distinctions, and those trying to hold the line that everything can be done with possible-worlds intensions will look as outdated in thirty years as the extensionalists look to the intensionalists today.
Of course, even if we decided we wanted to do more justice to hyperintensional phenomena than standard possible-worlds semantics, we have several options about how to go on from here. The response that is perhaps closest to the standard possible-worlds tradition is to let the semantic value of a piece of language be a pair of a possible-worlds-intension plus some kind of constituent tree, that serves as a logical form or otherwise conveys information about the internal linguistic structure of the expression. Alternatively, we could let the semantic value of a complex expression be a tree whose nodes are possible-worlds intensions: Lewis discusses this way of going, for example, in OTPW p 49-50.
Another response that is close to the possible-worlds tradition is to use impossible worlds as well as possible ones. Since things that do not vary across possible worlds can vary across impossible worlds, impossible worlds give us finer-grained distinctions. If we allow logically impossible worlds, we can even get the effect of places in sentences where substitution of logical equivalents fail, since for example the worlds where (p or not-p) obtain need not be the ones where (q or not-q) obtain. I take it that semantics using situations instead of worlds is often a close cousin of this.
More radical responses to hyperintensionality include moving to an algebraic semantics, such as the sort advocated by George Bealer. Even these can be seen as successors to the possible-worlds tradition, since the structures of the algebras are often inspired by the structural relationships possible-worlds intensions stand in to each other. No doubt philosophers will come up with other approaches too - some revert to talking about Fregean senses and functions on them, though whether this is much more than a cosmetic difference from algebraic approaches I’m not sure.
Why does this matter for metaphysics? Well, one immediate reason it matters is that the metaphysics of language had better be able to cope with hyperintensionality and hyperintensions. One place that disputes in the philosophy of language often spill over is into the metaphysics of meaning, of truth (or at least truth-conditions), of propositions and so on.
A connected reason is that respect for hyperintensionality might go along with more warmth towards hyperintensional entities. We may be less likely to smile on the demand that properties that necessarily have the same instances are identical, for example. This in turn may motivate rejecting the picture of properties as sets of their actual and possible instances. Indeed, set theory might be of less use in metaphysics in general once we want to individuate things hyperintensionally.
There are other ways the hyperintensional turn could affect metaphysics. It might make us more sympathetic to impossible worlds, for example: I’ve argued elsewhere that counter-possible conditionals give us a good reason to postulate impossible worlds. It might make us think that some relational predicates are not associated with relations, or maybe are associated with finer-grained relata than they appear to be associated with: see Carrie Jenkins’s post about grounding. Modal analyses of hyperintensional pieces of language seem unappealing, since modal analyses are normally only intensional not hyperintensional. I could go on.
So, metaphysicians, join the hyperintensional revolution! You have nothing to lose but your coarse grains!
It has become increasingly clear since the 1970s that we need to carve meanings more finely than by “intensions” in the sense associated with the specification above. Call the sorts of intensions employed, for example, by Richard Montague possible worlds intensions. Handling belief clauses by insisting that anyone who believes something believes everything necessarily equivalent to it has always caused problems. Once we accept that names are rigid designators, allowing their substitution in all sorts of representational and psychological contexts causes trouble: the Sheriff of Nottingham can be hunting for Robin Hood without hunting for Robin of Locksley, or so it seems.
There seem to be places outside our psychological talk that require hyperintensionality. Talk of entailment in the sense of logical consequence, for example: it does not logically follow from apples being red that all bachelors are unmarried, let alone that water is H2O, even though it does follow that either apples are red or apples are not red. Use of counter-possible conditionals is another example: two conditionals can have necessarily false antecedents but differ in truth-value. Talk about moral obligation and permission seems to be hyperintensional, as anyone struggling with substituting logical equivalents in the scope of deontic operators may have seen. I’m just back from a conference in Colorado where people were insisting that “in virtue of”, “because”, and other explanatory expressions were hyperintensional. (Benjamin Schnieder, Gideon Rosen and Kit Fine were three in particular.) Once you look around you see quite a bit of hyperintensionality.
There’s a piece of rhetoric I associate with Richard Sylvan about this. He was fond of suggesting that there would be a move from using possible-worlds intensions to using hyperintensional resources that would parallel the move made from extensionalism to possible-worlds intensionalism. In the nineteen-sixties, the big goal was to be able to do philosophy of language while treating language extensionally: think of Davidson’s project in particular, though Quine was also a big booster of the extensionalist program. I guess it was typical of that project to assign extensions to categories of expressions, and then have some syncatogramatic expressions that operated on extensions to yield other extensions. (E.g. “all” did not get an extension, but (All x)(Fx) operated on the extension of “F” to yield a sentence-extension, i.e. a truth-value)
There are still people trying to carry out that extensionalist project, but it came under increasingly severe attack since the early 1970s. (And maybe earlier: I think Carnap might be an important precursor here, along with Prior, and perhaps many others). The extensional programme was not very satisfying in its treatment of propositional attitude reports, entailment, normative discourse such as the use of “ought”, and a number of other areas. But the star witness against the extensional programme was modal vocabulary. Treating “necessarily” extensionally does not get you very far, and after Saul Kripke popularised possible-worlds semantics for “necessarily”, the floodgates started to open. Richard Montague and David Lewis were among the vanguard of those arguing for a systematic, intensional treatment of natural language, arguing that it handled all sorts of constructions that extensional treatments faced serious difficulty with.
The intensions that Montague and Lewis relied upon were set-theoretic constructions out of possible worlds and possible individuals. (Not just sets of possibilia or functions from possibilia to possiblia, but also sets of those sets, functions from those functions to other functions, etc. etc.) The Montague project of trying to handle all of language with these possible-worlds intensions is alive and well today: I take Robert Stalnaker to be one of its prominent contemporary philosophical defenders, though I haven’t scrutinised his recent work to see if any weakening has happened.
But I think that project is doomed. There is too much work that needs to be done that requires hyperintensional distinctions, and those trying to hold the line that everything can be done with possible-worlds intensions will look as outdated in thirty years as the extensionalists look to the intensionalists today.
Of course, even if we decided we wanted to do more justice to hyperintensional phenomena than standard possible-worlds semantics, we have several options about how to go on from here. The response that is perhaps closest to the standard possible-worlds tradition is to let the semantic value of a piece of language be a pair of a possible-worlds-intension plus some kind of constituent tree, that serves as a logical form or otherwise conveys information about the internal linguistic structure of the expression. Alternatively, we could let the semantic value of a complex expression be a tree whose nodes are possible-worlds intensions: Lewis discusses this way of going, for example, in OTPW p 49-50.
Another response that is close to the possible-worlds tradition is to use impossible worlds as well as possible ones. Since things that do not vary across possible worlds can vary across impossible worlds, impossible worlds give us finer-grained distinctions. If we allow logically impossible worlds, we can even get the effect of places in sentences where substitution of logical equivalents fail, since for example the worlds where (p or not-p) obtain need not be the ones where (q or not-q) obtain. I take it that semantics using situations instead of worlds is often a close cousin of this.
More radical responses to hyperintensionality include moving to an algebraic semantics, such as the sort advocated by George Bealer. Even these can be seen as successors to the possible-worlds tradition, since the structures of the algebras are often inspired by the structural relationships possible-worlds intensions stand in to each other. No doubt philosophers will come up with other approaches too - some revert to talking about Fregean senses and functions on them, though whether this is much more than a cosmetic difference from algebraic approaches I’m not sure.
Why does this matter for metaphysics? Well, one immediate reason it matters is that the metaphysics of language had better be able to cope with hyperintensionality and hyperintensions. One place that disputes in the philosophy of language often spill over is into the metaphysics of meaning, of truth (or at least truth-conditions), of propositions and so on.
A connected reason is that respect for hyperintensionality might go along with more warmth towards hyperintensional entities. We may be less likely to smile on the demand that properties that necessarily have the same instances are identical, for example. This in turn may motivate rejecting the picture of properties as sets of their actual and possible instances. Indeed, set theory might be of less use in metaphysics in general once we want to individuate things hyperintensionally.
There are other ways the hyperintensional turn could affect metaphysics. It might make us more sympathetic to impossible worlds, for example: I’ve argued elsewhere that counter-possible conditionals give us a good reason to postulate impossible worlds. It might make us think that some relational predicates are not associated with relations, or maybe are associated with finer-grained relata than they appear to be associated with: see Carrie Jenkins’s post about grounding. Modal analyses of hyperintensional pieces of language seem unappealing, since modal analyses are normally only intensional not hyperintensional. I could go on.
So, metaphysicians, join the hyperintensional revolution! You have nothing to lose but your coarse grains!
Thursday, February 26, 2009
Laws, Counterfactuals, and Essential Properties
I find it curious that nobody seems to be particularly bothered by the fact that the following three commonly-held and seemingly plausible theses seem to be somewhat at odds:
Now, I'd be curious to hear which one(s) of the above theses (if any) the readers of this blog think should be amended/rejected in order to resolve the conflict and why. (I do have a main suspect, but, in order to avoid skewing my little survey, I'm not going to reveal its identity for the moment).
- Unlike accidental generalizations, nomic generalizations support counterfactual conditionals. (So, for example, if it is a law that copper is a good conductor, then, if this piece of wood was made of copper, it would be a good conductor.)
- Some properties are essential to their bearers (So, for example, it is metaphysically impossible for this piece of wood to be made of anything other than wood and a fortiori to be made of copper).
- Counterfactuals whose antecedent is necessarily false are vacuously true.
Now, I'd be curious to hear which one(s) of the above theses (if any) the readers of this blog think should be amended/rejected in order to resolve the conflict and why. (I do have a main suspect, but, in order to avoid skewing my little survey, I'm not going to reveal its identity for the moment).
Monday, February 23, 2009
Was Lewis wrong or a relativist about counterfactuals?
David Lewis persuasively argued that counterfactuals are sensitive to context. As a consequence, Lewis claimed, counterfactuals don’t obey rules that other types of propositions do, like antecedent strengthening, hypothetical syllogism and contraposition. (From the fact that, were I to strike the match, it would light, it does not follow that, were I to strike the match and were I underwater, it would light.)
Just how is context relevant? Let’s make two distinctions. First, distinguish between a counterfactual sentence, “P > Q”, and a counterfactual proposition, {P > Q}. (I can’t quite figure out how to use the less than sign for some reason, as is typical to denote a proposition, so I’ll use curly brackets.) Second, distinguish between relativism and contextualism. According to relativism, a given proposition {P} might be true in one context, but false in another. (Note: I’m speaking of the proposition; one and the same proposition can be true in one context but false in another.) According to contextualism, a given sentence, “P”, might express one proposition in one context and a different proposition in another context.
I should note two things about these definitions. First, I don’t know if they are the standard uses of the terms “relativist” and “contextualist”. But they sound appropriate to me, so I’ll use them here. Second, relativism and contextualism are independent. One could deny both, accept one but not the other, or accept both.
There are at least two ways context might be relevant to counterfactuals: 1) In determining the truth conditions for a given counterfactual proposition; 2) In determining which counterfactual proposition a given counterfactual sentence asserts.
Suppose that Lewis was a contextualist but not a relativist about counterfactuals. Context determines when a given counterfactual sentence expresses a given counterfactual proposition, but the truth conditions are fixed for counterfactual propositions. Were that Lewis’ view, then he would be wrong about the failure of, say, weakening with respect to counterfactuals. That’s what Berit Brogaard and Joe Solerno argue in “Counterfactuals and Context” (Analysis, 68(1), 2008). After all, when examining an argument for validity, we don’t allow context to shift from premise to premise or between premises and conclusion. Suppose I utter the words “I am hungry,” and you utter the words, “Therefore, I am hungry and tall.” If validity didn’t require us to hold context fixed, we’d have a counterexample to and introduction. Yet all of the supposed counterexamples to, say, antecedent strengthening, involve a shift in context. Moral: If Lewis is a contextualist, he was wrong to think that antecedent strengthening, hypothetical syllogism and contraposition are invalid.
Suppose we hold fixed, then, that Lewis believed these arguments invalid (and that he didn’t hold a false belief!). Then Lewis must have been a relativist about counterfactuals. Or is there some other option?
Just how is context relevant? Let’s make two distinctions. First, distinguish between a counterfactual sentence, “P > Q”, and a counterfactual proposition, {P > Q}. (I can’t quite figure out how to use the less than sign for some reason, as is typical to denote a proposition, so I’ll use curly brackets.) Second, distinguish between relativism and contextualism. According to relativism, a given proposition {P} might be true in one context, but false in another. (Note: I’m speaking of the proposition; one and the same proposition can be true in one context but false in another.) According to contextualism, a given sentence, “P”, might express one proposition in one context and a different proposition in another context.
I should note two things about these definitions. First, I don’t know if they are the standard uses of the terms “relativist” and “contextualist”. But they sound appropriate to me, so I’ll use them here. Second, relativism and contextualism are independent. One could deny both, accept one but not the other, or accept both.
There are at least two ways context might be relevant to counterfactuals: 1) In determining the truth conditions for a given counterfactual proposition; 2) In determining which counterfactual proposition a given counterfactual sentence asserts.
Suppose that Lewis was a contextualist but not a relativist about counterfactuals. Context determines when a given counterfactual sentence expresses a given counterfactual proposition, but the truth conditions are fixed for counterfactual propositions. Were that Lewis’ view, then he would be wrong about the failure of, say, weakening with respect to counterfactuals. That’s what Berit Brogaard and Joe Solerno argue in “Counterfactuals and Context” (Analysis, 68(1), 2008). After all, when examining an argument for validity, we don’t allow context to shift from premise to premise or between premises and conclusion. Suppose I utter the words “I am hungry,” and you utter the words, “Therefore, I am hungry and tall.” If validity didn’t require us to hold context fixed, we’d have a counterexample to and introduction. Yet all of the supposed counterexamples to, say, antecedent strengthening, involve a shift in context. Moral: If Lewis is a contextualist, he was wrong to think that antecedent strengthening, hypothetical syllogism and contraposition are invalid.
Suppose we hold fixed, then, that Lewis believed these arguments invalid (and that he didn’t hold a false belief!). Then Lewis must have been a relativist about counterfactuals. Or is there some other option?
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