The basic idea of premise semantics is roughly this: A counterfactual conditional asserts that it... more The basic idea of premise semantics is roughly this: A counterfactual conditional asserts that its consequent follows from its antecedent when we add some suitable premises. To make it a viable analysis, Kratzer (1981, 1989) introduces the notion of ‘premise sets’ representing suitable ways of adding premises, such that ‘p □q’ is true iff every premise set is a subset of some premise set that logically implies the consequent q. The project, then, is to find appropriate constraints on premise sets that can give us the correct truth-conditions for counterfactuals. Kratzer (1989) proposes invoking the notion of ‘lumping’ to specify the required constraints,on premise sets. The idea is that propositions are sometimes ‘lumped’ together, such that when we add one proposition in our counterfactual reasoning we will thereby add all the propositions it lumps. The lumping relation is then defined under the framework of a situation semantics by some part-whole relation on situations. This approach has the advantage of being able to solve many problems that Kratzer’s previous accounts encounter. But it also suffers from enormous difficulties, as Kanazawa et al. (2005) show in their triviality results. Kratzer herself also abandoned this approach very soon (Kratzer 1990, 2002), reformulating her premise semantics in terms of the notion of ‘natural’ propositions instead of the lumping relations on propositions. In this paper, I will offer a critical defence of Kratzer’s ‘lumping’ semantics in her 1989 version. My proposal is that we understand the notion of lumping in terms of the notion of ‘grounding’ instead of the part-whole relations on situations. More precisely, on my proposal a proposition p lumps a proposition q if and only if p is grounded in q, and accordingly, when we add a proposition into a counterfactual scenario we will thereby add all the propositions that are its grounds. In this way, I argue, we can accommodate all the examples that motivate the lumping semantics, whilst avoiding the triviality results of Kanazawa et al. (2005).
In this paper, I examine Williamson's (2007) counterfactual-based account of modal epistemology. ... more In this paper, I examine Williamson's (2007) counterfactual-based account of modal epistemology. I argue that such an account faces two serious problems | the cotenability problem and the gap problem. As I diagnose it, these problems somehow indicate that our standard way of understanding counterfactuals under the received possible worlds
semantics may have insufficient 'structures' to distinguish various different kinds of constraints on our counterfactual thinking. The remedy, I suggest, is to invoke the 'structural semantics' as developed by Pearl (2009) and Halpern (2000). Based on this semantics, I offer some philosophical elucidation for various kinds of modality, and thereby provide a more satisfactory account of how our modal knowledge can be grounded in our knowledge of counterfactuals.
Many metaphysical controversies can be understood as debates over whether some alleged entities a... more Many metaphysical controversies can be understood as debates over whether some alleged entities are metaphysically possible. (Examples: Are zombies possible? Is atomless gunk possible? Are extended simples possible? etc.) No doubt, with regard to these matters, we may have opinions or theories, commonsensical or sophisticated. But do we have knowledge of them? Can we really know that something is metaphysically possible, and if so, how? Several different answers have been offered in the literature, intending to illustrate how we may have knowledge of metaphysical modality. In this paper, I concentrate on a proposal by Timothy Williamson (2007). On this account, our alleged knowledge of metaphysical modality is justified by and grounded in our capacity to handle ordinary mundane counterfactual conditionals. However, I argue that Williamson’s account fails, mainly because the modality involved in ordinary mundane counterfactuals is causal, and thus our capacity to handle them still falls short of giving us any knowledge of metaphysical modality. In the end of the paper, I also provide my own answer to the question. My answer is a sceptical one: we do not really have knowledge of metaphysical modality. But such ignorance is harmless, or so I argue.
The basic idea of premise semantics is roughly this: A counterfactual conditional asserts that it... more The basic idea of premise semantics is roughly this: A counterfactual conditional asserts that its consequent follows from its antecedent when we add some suitable premises. To make it a viable analysis, Kratzer (1981, 1989) introduces the notion of ‘premise sets’ representing suitable ways of adding premises, such that ‘p □q’ is true iff every premise set is a subset of some premise set that logically implies the consequent q. The project, then, is to find appropriate constraints on premise sets that can give us the correct truth-conditions for counterfactuals. Kratzer (1989) proposes invoking the notion of ‘lumping’ to specify the required constraints,on premise sets. The idea is that propositions are sometimes ‘lumped’ together, such that when we add one proposition in our counterfactual reasoning we will thereby add all the propositions it lumps. The lumping relation is then defined under the framework of a situation semantics by some part-whole relation on situations. This approach has the advantage of being able to solve many problems that Kratzer’s previous accounts encounter. But it also suffers from enormous difficulties, as Kanazawa et al. (2005) show in their triviality results. Kratzer herself also abandoned this approach very soon (Kratzer 1990, 2002), reformulating her premise semantics in terms of the notion of ‘natural’ propositions instead of the lumping relations on propositions. In this paper, I will offer a critical defence of Kratzer’s ‘lumping’ semantics in her 1989 version. My proposal is that we understand the notion of lumping in terms of the notion of ‘grounding’ instead of the part-whole relations on situations. More precisely, on my proposal a proposition p lumps a proposition q if and only if p is grounded in q, and accordingly, when we add a proposition into a counterfactual scenario we will thereby add all the propositions that are its grounds. In this way, I argue, we can accommodate all the examples that motivate the lumping semantics, whilst avoiding the triviality results of Kanazawa et al. (2005).
In this paper, I examine Williamson's (2007) counterfactual-based account of modal epistemology. ... more In this paper, I examine Williamson's (2007) counterfactual-based account of modal epistemology. I argue that such an account faces two serious problems | the cotenability problem and the gap problem. As I diagnose it, these problems somehow indicate that our standard way of understanding counterfactuals under the received possible worlds
semantics may have insufficient 'structures' to distinguish various different kinds of constraints on our counterfactual thinking. The remedy, I suggest, is to invoke the 'structural semantics' as developed by Pearl (2009) and Halpern (2000). Based on this semantics, I offer some philosophical elucidation for various kinds of modality, and thereby provide a more satisfactory account of how our modal knowledge can be grounded in our knowledge of counterfactuals.
Many metaphysical controversies can be understood as debates over whether some alleged entities a... more Many metaphysical controversies can be understood as debates over whether some alleged entities are metaphysically possible. (Examples: Are zombies possible? Is atomless gunk possible? Are extended simples possible? etc.) No doubt, with regard to these matters, we may have opinions or theories, commonsensical or sophisticated. But do we have knowledge of them? Can we really know that something is metaphysically possible, and if so, how? Several different answers have been offered in the literature, intending to illustrate how we may have knowledge of metaphysical modality. In this paper, I concentrate on a proposal by Timothy Williamson (2007). On this account, our alleged knowledge of metaphysical modality is justified by and grounded in our capacity to handle ordinary mundane counterfactual conditionals. However, I argue that Williamson’s account fails, mainly because the modality involved in ordinary mundane counterfactuals is causal, and thus our capacity to handle them still falls short of giving us any knowledge of metaphysical modality. In the end of the paper, I also provide my own answer to the question. My answer is a sceptical one: we do not really have knowledge of metaphysical modality. But such ignorance is harmless, or so I argue.
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Papers by Duen-Min Deng
Kratzer (1989) proposes invoking the notion of ‘lumping’ to specify the required constraints,on premise sets. The idea is that propositions are sometimes ‘lumped’ together, such that when we add one proposition in our counterfactual reasoning we will thereby add all the propositions it lumps. The lumping relation is then defined under the framework of a situation semantics by some part-whole relation on situations. This approach has the advantage of being able to solve many problems that Kratzer’s previous accounts encounter. But it also suffers from enormous difficulties, as Kanazawa et al. (2005) show in their triviality results. Kratzer herself also abandoned this approach very soon (Kratzer 1990, 2002), reformulating her premise semantics in terms of the notion of ‘natural’ propositions instead of the lumping relations on propositions.
In this paper, I will offer a critical defence of Kratzer’s ‘lumping’ semantics in her 1989 version. My proposal is that we understand the notion of lumping in terms of the notion of ‘grounding’ instead of the part-whole relations on situations. More precisely, on my proposal a proposition p lumps a proposition q if and only if p is grounded in q, and accordingly, when we add a proposition into a counterfactual scenario we will thereby add all the propositions that are its grounds. In this way, I argue, we can accommodate all the examples that motivate the lumping semantics, whilst avoiding the triviality results of Kanazawa et al. (2005).
semantics may have insufficient 'structures' to distinguish various different kinds of constraints on our counterfactual thinking. The remedy, I suggest, is to invoke the 'structural semantics' as developed by Pearl (2009) and Halpern (2000). Based on this semantics, I offer some philosophical elucidation for various kinds of modality, and thereby provide a more satisfactory account of how our modal knowledge can be grounded in our knowledge of counterfactuals.
Kratzer (1989) proposes invoking the notion of ‘lumping’ to specify the required constraints,on premise sets. The idea is that propositions are sometimes ‘lumped’ together, such that when we add one proposition in our counterfactual reasoning we will thereby add all the propositions it lumps. The lumping relation is then defined under the framework of a situation semantics by some part-whole relation on situations. This approach has the advantage of being able to solve many problems that Kratzer’s previous accounts encounter. But it also suffers from enormous difficulties, as Kanazawa et al. (2005) show in their triviality results. Kratzer herself also abandoned this approach very soon (Kratzer 1990, 2002), reformulating her premise semantics in terms of the notion of ‘natural’ propositions instead of the lumping relations on propositions.
In this paper, I will offer a critical defence of Kratzer’s ‘lumping’ semantics in her 1989 version. My proposal is that we understand the notion of lumping in terms of the notion of ‘grounding’ instead of the part-whole relations on situations. More precisely, on my proposal a proposition p lumps a proposition q if and only if p is grounded in q, and accordingly, when we add a proposition into a counterfactual scenario we will thereby add all the propositions that are its grounds. In this way, I argue, we can accommodate all the examples that motivate the lumping semantics, whilst avoiding the triviality results of Kanazawa et al. (2005).
semantics may have insufficient 'structures' to distinguish various different kinds of constraints on our counterfactual thinking. The remedy, I suggest, is to invoke the 'structural semantics' as developed by Pearl (2009) and Halpern (2000). Based on this semantics, I offer some philosophical elucidation for various kinds of modality, and thereby provide a more satisfactory account of how our modal knowledge can be grounded in our knowledge of counterfactuals.