{"title":"Compounds of conditionals, uncertainty, and indeterminacy","authors":"D. Edgington","doi":"10.4324/9781315111902-4","DOIUrl":"https://doi.org/10.4324/9781315111902-4","url":null,"abstract":"","PeriodicalId":355260,"journal":{"name":"Logic and Uncertainty in the Human Mind","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127536529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-10DOI: 10.4324/9781315111902-11
S. Rhodes, Niall Galbraith, K. Manktelow
{"title":"Delusional rationality","authors":"S. Rhodes, Niall Galbraith, K. Manktelow","doi":"10.4324/9781315111902-11","DOIUrl":"https://doi.org/10.4324/9781315111902-11","url":null,"abstract":"","PeriodicalId":355260,"journal":{"name":"Logic and Uncertainty in the Human Mind","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133739532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper argues that recent developments in inferentialism in the psychology of reasoning that challenge the suppositional approach advocated by David Over can be implemented in Causal Bayes Nets (CBNs). Inferentialism proposes that conditionals, if p then q, imply (either as a matter of their meaning or a conventional implicature) that there is an inferential dependency between p and q. These dependencies can be captured in the directional links of a CBN (p → q), which can, therefore, provide a theory of mental representation and inference that inferentialism currently lacks. This approach has already been demonstrated for causal conditionals. We conclude that this proposal, while losing some inferences valid in the suppositional view, gains others that we know people make while also retaining consistency with the general Bayesian framework for human reasoning.
{"title":"Integrating Causal Bayes Nets and inferentialism in conditional inference","authors":"M. Oaksford, N. Chater","doi":"10.4324/9781315111902-8","DOIUrl":"https://doi.org/10.4324/9781315111902-8","url":null,"abstract":"This paper argues that recent developments in inferentialism in the psychology of reasoning that challenge the suppositional approach advocated by David Over can be implemented in Causal Bayes Nets (CBNs). Inferentialism proposes that conditionals, if p then q, imply (either as a matter of their meaning or a conventional implicature) that there is an inferential dependency between p and q. These dependencies can be captured in the directional links of a CBN (p → q), which can, therefore, provide a theory of mental representation and inference that inferentialism currently lacks. This approach has already been demonstrated for causal conditionals. We conclude that this proposal, while losing some inferences valid in the suppositional view, gains others that we know people make while also retaining consistency with the general Bayesian framework for human reasoning.","PeriodicalId":355260,"journal":{"name":"Logic and Uncertainty in the Human Mind","volume":"259 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115010873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The contribution of David E. Over","authors":"K. Manktelow, Jonathan Evans","doi":"10.4324/9781315111902-1","DOIUrl":"https://doi.org/10.4324/9781315111902-1","url":null,"abstract":"","PeriodicalId":355260,"journal":{"name":"Logic and Uncertainty in the Human Mind","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132910171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Deduction from uncertain premises?","authors":"Nicole Cruz","doi":"10.4324/9781315111902-3","DOIUrl":"https://doi.org/10.4324/9781315111902-3","url":null,"abstract":"","PeriodicalId":355260,"journal":{"name":"Logic and Uncertainty in the Human Mind","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115643479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if $(B|K)|(A|H) = 1$. Then, we show that a p-consistent family $mathcal{F}={E_1|H_1,E_2|H_2}$ p-entails a conditional event $E_3|H_3$ if and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(mathcal{S})=1$ for some nonempty subset $mathcal{S}$ of $mathcal{F}$, where $QC(mathcal{S})$ is the quasi conjunction of the conditional events in $mathcal{S}$. Then, we examine the inference rules $And$, $Cut$, $Cautious $ $Monotonicity$, and $Or$ of System~P and other well known inference rules ($Modus$ $Ponens$, $Modus$ $Tollens$, $Bayes$). We also show that $QC(mathcal{F})|mathcal{C}(mathcal{F})=1$, where $mathcal{C}(mathcal{F})$ is the conjunction of the conditional events in $mathcal{F}$. We characterize p-entailment by showing that $mathcal{F}$ p-entails $E_3|H_3$ if and only if $(E_3|H_3)|mathcal{C}(mathcal{F})=1$. Finally, we examine emph{Denial of the antecedent} and emph{Affirmation of the consequent}, where the p-entailment of $(E_3|H_3)$ from $mathcal{F}$ does not hold, by showing that $(E_3|H_3)|mathcal{C}(mathcal{F})neq1.$
{"title":"Probabilistic entailment and iterated conditionals","authors":"A. Gilio, N. Pfeifer, G. Sanfilippo","doi":"10.4324/9781315111902-6","DOIUrl":"https://doi.org/10.4324/9781315111902-6","url":null,"abstract":"In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if $(B|K)|(A|H) = 1$. Then, we show that a p-consistent family $mathcal{F}={E_1|H_1,E_2|H_2}$ p-entails a conditional event $E_3|H_3$ if and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(mathcal{S})=1$ for some nonempty subset $mathcal{S}$ of $mathcal{F}$, where $QC(mathcal{S})$ is the quasi conjunction of the conditional events in $mathcal{S}$. Then, we examine the inference rules $And$, $Cut$, $Cautious $ $Monotonicity$, and $Or$ of System~P and other well known inference rules ($Modus$ $Ponens$, $Modus$ $Tollens$, $Bayes$). We also show that $QC(mathcal{F})|mathcal{C}(mathcal{F})=1$, where $mathcal{C}(mathcal{F})$ is the conjunction of the conditional events in $mathcal{F}$. We characterize p-entailment by showing that $mathcal{F}$ p-entails $E_3|H_3$ if and only if $(E_3|H_3)|mathcal{C}(mathcal{F})=1$. Finally, we examine emph{Denial of the antecedent} and emph{Affirmation of the consequent}, where the p-entailment of $(E_3|H_3)$ from $mathcal{F}$ does not hold, by showing that $(E_3|H_3)|mathcal{C}(mathcal{F})neq1.$","PeriodicalId":355260,"journal":{"name":"Logic and Uncertainty in the Human Mind","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115161537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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