This paper calls for a re-appraisal of McGee’s analysis of the semantics, logic and probabilities... more This paper calls for a re-appraisal of McGee’s analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation—built on the principle that the antecedent of a conditional is probabilistically independent of the conditional—and a more transparent method of constructing such measures is provided. McGee’s Dutch book argument is restructured to more clearly reveal that it introduces a novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee’s analysis—generating a rather wide consensus that it yields ‘unintuitive’ or ‘wrong’ probabilities for compounds —fail to strike at the...
Annals of Mathematics and Artificial Intelligence, 2019
This paper is about the statics and dynamics of belief states that are represented by pairs consi... more This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent's credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing one's belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change.
It is argued that the "inner" negation ∼ familiar from 3-valued logic can be interpreted as a for... more It is argued that the "inner" negation ∼ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: ∼A is read 'A is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g.,"If Jim went to the party he had a good time"). It is shown that the logic induced by the semantics shares many familiar properties with classical negation, but is orthogonal to both intuitionistic and classical negation: it differs from both in validating the inference from A → ∼B to ∼(A → B).
A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presen... more A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of 'global' expres-sivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege-Geach problem). The expressivist framework is semantically characterised in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL ('Indicative Conditional Logic'). The expressivist framework extends the AGM framework for belief revision and so provides a categorical ('yes'-'no') epistemology for conditionals that complements McGee's probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives.
It is argued that truth value of a sentence containing free variables in a context of use (or the... more It is argued that truth value of a sentence containing free variables in a context of use (or the truth value of the proposition it expresses in a context of use), just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. On letting, say, x be such that x 2 ¼ 4, the sentence 'Either x ¼ 2 or x ¼ À2' is true but the sentence 'x ¼ 2' has an indeterminate truth value: it is determinate that the variable x refers to either 2 or À2, but it is indeterminate which of the two it refers to, as a result 'x ¼ 2' has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a 'radically' supervaluational (or plurivaluational) semantic framework closely analogous to the treatment of vagueness in
The connectives of classical propositional logic are given an analysis in terms of necessary and ... more The connectives of classical propositional logic are given an analysis in terms of necessary and sufficient conditions of acceptance and rejection, i.e.\ the connectives are analyzed within an expressivist bilateral meaning-is-use framework. It is explained how such a framework differs from standard (bilateral) inferentialist frameworks and it is argued that it is better suited to address the particular issues raised by the expressivist thesis that the meaning of a sentence is determined by the mental state that it is conventionally used to express. Furthermore, it is shown that the classical requirements governing the connectives completely characterize classical logic, are conservative (indeed make the connectives redundant) and separable, are in bilateral harmony, are structurally preservative with respect to the classical coordination requirements and resolve the categoricity problem. These results are taken to show that one can give an expressivist bilateral meaning-is-use analysis of the connectives that confer on them a determinate coherent classical interpretation.
Non-bivalent languages (languages containing sentences that can be true, false or neither) are gi... more Non-bivalent languages (languages containing sentences that can be true, false or neither) are given a probabilitistic interpretation in terms of betting quotients. Necessary and sufficient conditions for avoiding Dutch books-the laws of non-bivalent probability-in such a setting are provided.
It is argued that expressivists can solve their problems in accounting for the unity and autonomy... more It is argued that expressivists can solve their problems in accounting for the unity and autonomy of logic -- logic is topic independent and does not derive from a general `logic' of mental states -- by (1) adopting an analysis of the logical connectives that takes logically complex sentences to express complex combinations of simple attitudes like belief and disapproval and dispositions to form such simple attitudes upon performing suppositional acts, and (2) taking acceptance and rejection of sentences to be the common mental denominator in descriptive and evaluative discourse, and structural requirements governing these to be the basis for logic.
""Preprint. Published in Erkenntnis Volume 78, Issue 6 (2013), Page 1381-1403.
This paper provi... more ""Preprint. Published in Erkenntnis Volume 78, Issue 6 (2013), Page 1381-1403.
This paper provides finitary jointly necessary and sufficient acceptance and rejection conditions for the logical constants of a first order quantificational language. By introducing the notion of an \emph{assignment} as a distinct object level practice (as opposed to a meta-level semantic notion) and combining this with the practice of (hypothetical and categorical) acceptance and rejection and the practice of making suppositions one gains a structure that is sufficiently rich to fully characterize the class of classical first order theories. The analysis thus provides a way of characterizing classical first order quantification by expressivist means.""
The logic of dominance arguments is analyzed using two different kinds of conditionals: indicativ... more The logic of dominance arguments is analyzed using two different kinds of conditionals: indicative (epistemic) and subjunctive (counter-factual). It is shown that on the indicative interpretation an assumption of independence is needed for a dominance argument to go through. It is also shown that on the subjunctive interpretation no assumption of independence is needed once the standard premises of the dominance argument are true, but that independence plays an important role in arguing for the truth of the premises of the dominance argument. A key feature of the analysis is the interpretation of the doubly conditional comparative BI will get a better outcome if A than if B[ which is taken to have the structure B(the outcome if A) is better than (the outcome if B)[.
I argue that indicative conditionals are best viewed as having partial truth conditions: "If A, B... more I argue that indicative conditionals are best viewed as having partial truth conditions: "If A, B" is true if A and B are both true, false if A is true and B is false, and lacks truth value if A is false. The truth conditions are shown to explain a variety of important phenomena regarding indicative conditionals, including Adams' Thesis about the assertability conditions of conditionals, and how indicative conditionals embed in more complex constructions. In particular, the truth conditions are shown to provide the semantic basis for characterising several distinct logics of indicative conditionals, of which the logic of assertion is the main focus of the paper.
Techné: Research in Philosophy and Technology, 2007
Safety factor rules are used for drawing putatively reasonable conclusions from incomplete datase... more Safety factor rules are used for drawing putatively reasonable conclusions from incomplete datasets. The paper attempts to provide answers to four questions: “How are safety factors used?”, “When are safety factors used?”, “Why are safety used?” and “How do safety factor rules relate to decision theory?”. The authors conclude that safety factor rules should be regarded as decision methods rather than as criteria of rightness and that they can be used in both practical and theoretical reasoning. Simplicity of application and inability or unwillingness to defer judgment appear to be important factors in explaining why the rules are used.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, a... more JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
Vann McGee has proposed a counterexample to the Ramsey Test. In the counterexample, a seemingly t... more Vann McGee has proposed a counterexample to the Ramsey Test. In the counterexample, a seemingly trustworthy source has testified that p and that if not-p, then q. If one subsequently learns notp (and so learns that the source is wrong about p), then one has reason to doubt the trustworthiness of the source (perhaps even the identity of the source) and so, the argument goes, one has reason to doubt the conditional asserted by the source. Since what one learns is that the antecedent of the conditional holds, these doubts are contrary to the Ramsey Test. We argue that the counterexample fails. It rests on a principle of testimonial dependence that is not applicable when a source hedges his or her claims.
This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities... more This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation-built on the principle that the antecedent of a conditional is probabilistically independent of the conditional-and a more transparent method of constructing such measures is provided. McGee's Dutch book argument is restructured to more clearly reveal that it introduces a novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee's analysis-generating a rather wide consensus that it yields 'unintuitive' or 'wrong' probabilities for compounds-fail to strike at their intended target; for to honour the intuitions of the counterexamples one must either give up the Ramsey Test or the standard laws of probability. It will be argued that we need to give up neither if we take the counterexamples as further evidence that the indicative conditional sometimes allows for a non-epistemic 'causal' interpretation alongside its usual epistemic interpretation.
This paper explores the possibility that causal decision theory can be formulated in terms of pro... more This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis (1974), p.337) 1 A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker (1980),p.87)
This paper calls for a re-appraisal of McGee’s analysis of the semantics, logic and probabilities... more This paper calls for a re-appraisal of McGee’s analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation—built on the principle that the antecedent of a conditional is probabilistically independent of the conditional—and a more transparent method of constructing such measures is provided. McGee’s Dutch book argument is restructured to more clearly reveal that it introduces a novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee’s analysis—generating a rather wide consensus that it yields ‘unintuitive’ or ‘wrong’ probabilities for compounds —fail to strike at the...
Annals of Mathematics and Artificial Intelligence, 2019
This paper is about the statics and dynamics of belief states that are represented by pairs consi... more This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent's credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing one's belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change.
It is argued that the "inner" negation ∼ familiar from 3-valued logic can be interpreted as a for... more It is argued that the "inner" negation ∼ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: ∼A is read 'A is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g.,"If Jim went to the party he had a good time"). It is shown that the logic induced by the semantics shares many familiar properties with classical negation, but is orthogonal to both intuitionistic and classical negation: it differs from both in validating the inference from A → ∼B to ∼(A → B).
A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presen... more A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of 'global' expres-sivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege-Geach problem). The expressivist framework is semantically characterised in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL ('Indicative Conditional Logic'). The expressivist framework extends the AGM framework for belief revision and so provides a categorical ('yes'-'no') epistemology for conditionals that complements McGee's probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives.
It is argued that truth value of a sentence containing free variables in a context of use (or the... more It is argued that truth value of a sentence containing free variables in a context of use (or the truth value of the proposition it expresses in a context of use), just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. On letting, say, x be such that x 2 ¼ 4, the sentence 'Either x ¼ 2 or x ¼ À2' is true but the sentence 'x ¼ 2' has an indeterminate truth value: it is determinate that the variable x refers to either 2 or À2, but it is indeterminate which of the two it refers to, as a result 'x ¼ 2' has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a 'radically' supervaluational (or plurivaluational) semantic framework closely analogous to the treatment of vagueness in
The connectives of classical propositional logic are given an analysis in terms of necessary and ... more The connectives of classical propositional logic are given an analysis in terms of necessary and sufficient conditions of acceptance and rejection, i.e.\ the connectives are analyzed within an expressivist bilateral meaning-is-use framework. It is explained how such a framework differs from standard (bilateral) inferentialist frameworks and it is argued that it is better suited to address the particular issues raised by the expressivist thesis that the meaning of a sentence is determined by the mental state that it is conventionally used to express. Furthermore, it is shown that the classical requirements governing the connectives completely characterize classical logic, are conservative (indeed make the connectives redundant) and separable, are in bilateral harmony, are structurally preservative with respect to the classical coordination requirements and resolve the categoricity problem. These results are taken to show that one can give an expressivist bilateral meaning-is-use analysis of the connectives that confer on them a determinate coherent classical interpretation.
Non-bivalent languages (languages containing sentences that can be true, false or neither) are gi... more Non-bivalent languages (languages containing sentences that can be true, false or neither) are given a probabilitistic interpretation in terms of betting quotients. Necessary and sufficient conditions for avoiding Dutch books-the laws of non-bivalent probability-in such a setting are provided.
It is argued that expressivists can solve their problems in accounting for the unity and autonomy... more It is argued that expressivists can solve their problems in accounting for the unity and autonomy of logic -- logic is topic independent and does not derive from a general `logic' of mental states -- by (1) adopting an analysis of the logical connectives that takes logically complex sentences to express complex combinations of simple attitudes like belief and disapproval and dispositions to form such simple attitudes upon performing suppositional acts, and (2) taking acceptance and rejection of sentences to be the common mental denominator in descriptive and evaluative discourse, and structural requirements governing these to be the basis for logic.
""Preprint. Published in Erkenntnis Volume 78, Issue 6 (2013), Page 1381-1403.
This paper provi... more ""Preprint. Published in Erkenntnis Volume 78, Issue 6 (2013), Page 1381-1403.
This paper provides finitary jointly necessary and sufficient acceptance and rejection conditions for the logical constants of a first order quantificational language. By introducing the notion of an \emph{assignment} as a distinct object level practice (as opposed to a meta-level semantic notion) and combining this with the practice of (hypothetical and categorical) acceptance and rejection and the practice of making suppositions one gains a structure that is sufficiently rich to fully characterize the class of classical first order theories. The analysis thus provides a way of characterizing classical first order quantification by expressivist means.""
The logic of dominance arguments is analyzed using two different kinds of conditionals: indicativ... more The logic of dominance arguments is analyzed using two different kinds of conditionals: indicative (epistemic) and subjunctive (counter-factual). It is shown that on the indicative interpretation an assumption of independence is needed for a dominance argument to go through. It is also shown that on the subjunctive interpretation no assumption of independence is needed once the standard premises of the dominance argument are true, but that independence plays an important role in arguing for the truth of the premises of the dominance argument. A key feature of the analysis is the interpretation of the doubly conditional comparative BI will get a better outcome if A than if B[ which is taken to have the structure B(the outcome if A) is better than (the outcome if B)[.
I argue that indicative conditionals are best viewed as having partial truth conditions: "If A, B... more I argue that indicative conditionals are best viewed as having partial truth conditions: "If A, B" is true if A and B are both true, false if A is true and B is false, and lacks truth value if A is false. The truth conditions are shown to explain a variety of important phenomena regarding indicative conditionals, including Adams' Thesis about the assertability conditions of conditionals, and how indicative conditionals embed in more complex constructions. In particular, the truth conditions are shown to provide the semantic basis for characterising several distinct logics of indicative conditionals, of which the logic of assertion is the main focus of the paper.
Techné: Research in Philosophy and Technology, 2007
Safety factor rules are used for drawing putatively reasonable conclusions from incomplete datase... more Safety factor rules are used for drawing putatively reasonable conclusions from incomplete datasets. The paper attempts to provide answers to four questions: “How are safety factors used?”, “When are safety factors used?”, “Why are safety used?” and “How do safety factor rules relate to decision theory?”. The authors conclude that safety factor rules should be regarded as decision methods rather than as criteria of rightness and that they can be used in both practical and theoretical reasoning. Simplicity of application and inability or unwillingness to defer judgment appear to be important factors in explaining why the rules are used.
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, a... more JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
Vann McGee has proposed a counterexample to the Ramsey Test. In the counterexample, a seemingly t... more Vann McGee has proposed a counterexample to the Ramsey Test. In the counterexample, a seemingly trustworthy source has testified that p and that if not-p, then q. If one subsequently learns notp (and so learns that the source is wrong about p), then one has reason to doubt the trustworthiness of the source (perhaps even the identity of the source) and so, the argument goes, one has reason to doubt the conditional asserted by the source. Since what one learns is that the antecedent of the conditional holds, these doubts are contrary to the Ramsey Test. We argue that the counterexample fails. It rests on a principle of testimonial dependence that is not applicable when a source hedges his or her claims.
This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities... more This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation-built on the principle that the antecedent of a conditional is probabilistically independent of the conditional-and a more transparent method of constructing such measures is provided. McGee's Dutch book argument is restructured to more clearly reveal that it introduces a novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee's analysis-generating a rather wide consensus that it yields 'unintuitive' or 'wrong' probabilities for compounds-fail to strike at their intended target; for to honour the intuitions of the counterexamples one must either give up the Ramsey Test or the standard laws of probability. It will be argued that we need to give up neither if we take the counterexamples as further evidence that the indicative conditional sometimes allows for a non-epistemic 'causal' interpretation alongside its usual epistemic interpretation.
This paper explores the possibility that causal decision theory can be formulated in terms of pro... more This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis (1974), p.337) 1 A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker (1980),p.87)
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This paper provides finitary jointly necessary and sufficient acceptance and rejection conditions for the logical constants of a first order quantificational language. By introducing the notion of an \emph{assignment} as a distinct object level practice (as opposed to a meta-level semantic notion) and combining this with the practice of (hypothetical and categorical) acceptance and rejection and the practice of making suppositions one gains a structure that is sufficiently rich to fully characterize the class of classical first order theories. The analysis thus provides a way of characterizing classical first order quantification by expressivist means.""
This paper provides finitary jointly necessary and sufficient acceptance and rejection conditions for the logical constants of a first order quantificational language. By introducing the notion of an \emph{assignment} as a distinct object level practice (as opposed to a meta-level semantic notion) and combining this with the practice of (hypothetical and categorical) acceptance and rejection and the practice of making suppositions one gains a structure that is sufficiently rich to fully characterize the class of classical first order theories. The analysis thus provides a way of characterizing classical first order quantification by expressivist means.""