Causation and the Probability of Causal Conditionals

2017 ◽  
Author(s):  
David E. Over
Keyword(s):  
Natural Language ◽  
Conditional Probability ◽  
Causal Reasoning ◽  
Probability Judgments ◽  
Counterfactual Conditionals ◽  
Bayesian Inferences ◽  
Conditional Inferences

Indicative and counterfactual conditionals are central to reasoning in general and causal reasoning in particular. Normative theorists and psychologists have held a range of views on how natural language indicative and counterfactual conditionals, and probability judgments about them, are related to causation. There is the question of whether “causal” conditionals, referring to possible causes and effects, can be used to explain causation, or whether causation can be used to explain the conditionals. There are questions about how causation, conditionals, Bayesian inferences, conditional probability, and imaging are related to each other. Psychological results are relevant to these questions, including findings on how people make conditional inferences and judgments about possibilities, conditionals, and conditional probability. Deeper understanding of the relation between causation and conditionals will come in further research on people’s reasoning from counterfactuals as premises, and to counterfactuals as conclusions.

Causality and Causal Reasoning in Natural Language

2017 ◽  
Author(s):  
Torgrim Solstad ◽  
Oliver Bott
Keyword(s):  
Natural Language ◽  
Cognitive Processing ◽  
Causal Reasoning ◽  
Causal Model ◽  
Discourse Markers ◽  
Causal Relations ◽  
Counterfactual Conditionals ◽  
Adequate Evaluation ◽  
Implicit Causality

This chapter provides a combined overview of theoretical and psycholinguistic approaches to causality in language. The chapter’s main phenomenological focus is on causal relations as expressed intra-clausally by verbs (e.g., break, open) and between sentences by discourse markers (e.g., because, therefore). Special attention is given to implicit causality verbs that are argued to trigger expectations of explanations to occur in subsequent discourse. The chapter also discusses linguistic expressions that do not encode causation as such, but that seem to be dependent on a causal model for their adequate evaluation, such as counterfactual conditionals. The discussion of the phenomena is complemented by an overview of important aspects of their cognitive processing as revealed by psycholinguistic experimentation.

Suppose and Tell

2020 ◽  
Author(s):  
Timothy Williamson
Keyword(s):  
Conditional Probability ◽  
Natural Deduction ◽  
Special Kind ◽  
Context Sensitivity ◽  
Modal Operator ◽  
Counterfactual Conditionals ◽  
Deduction Rules ◽  
Psychological Sense

The book argues that our use of conditionals is governed by imperfectly reliable heuristics, in the psychological sense of fast and frugal (or quick and dirty) ways of assessing them. The primary heuristic is this: to assess ‘If A, C’, suppose A and on that basis assess C; whatever attitude you take to C conditionally on A (such as acceptance, rejection, or something in between) take unconditionally to ‘If A, C’. This heuristic yields both the equation of the probability of ‘If A, C’ with the conditional probability of C on A and standard natural deduction rules for the conditional. However, these results can be shown to make the heuristic implicitly inconsistent, and so less than fully reliable. There is also a secondary heuristic: pass conditionals freely from one context to another under normal conditions for acceptance of sentences on the basis of memory and testimony. The effect of the secondary heuristic is to undermine interpretations on which ‘if’ introduces a special kind of context-sensitivity. On the interpretation which makes best sense of the two heuristics, ‘if’ is simply the truth-functional conditional. Apparent counterexamples to truth-functionality are artefacts of reliance on the primary heuristic in cases where it is unreliable. The second half of the book concerns counterfactual conditionals, as expressed with ‘if’ and ‘would’. It argues that ‘would’ is an independently meaningful modal operator for contextually restricted necessity: the meaning of counterfactuals is simply that derived compositionally from the meanings of their constituents, including ‘if’ and ‘would’, making them contextually restricted strict conditionals.

scholarly journals A Qualitative Approach to the Study of Causal Reasoning in Natural Language

2009 ◽  
Vol 19 (4) ◽  
pp. 475-500 ◽  
Author(s):  
Kieran C. O'Doherty ◽  
Daniel J. Navarro ◽  
Shona H. Crabb
Keyword(s):  
Natural Language ◽  
Causal Reasoning ◽  
Qualitative Approach

Facilitating Normative Judgments of Conditional Probability: Frequency or Nested Sets?

2003 ◽  
Vol 50 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Kimihiko Yamagishi
Keyword(s):  
Conditional Probability ◽  
Probabilistic Reasoning ◽  
Probability Judgment ◽  
Probability Judgments ◽  
Normative Reasoning ◽  
Roulette Wheel ◽  
Probability Task ◽  
Nested Sets ◽  
Probabilistic Structure ◽  
Inspection Machine

Abstract. Recent probability judgment research contrasts two opposing views. Some theorists have emphasized the role of frequency representations in facilitating probabilistic correctness; opponents have noted that visualizing the probabilistic structure of the task sufficiently facilitates normative reasoning. In the current experiment, the following conditional probability task, an isomorph of the “Problem of Three Prisoners” was tested. “A factory manufactures artificial gemstones. Each gemstone has a 1/3 chance of being blurred, a 1/3 chance of being cracked, and a 1/3 chance of being clear. An inspection machine removes all cracked gemstones, and retains all clear gemstones. However, the machine removes ½ of the blurred gemstones. What is the chance that a gemstone is blurred after the inspection?” A 2 × 2 design was administered. The first variable was the use of frequency instruction. The second manipulation was the use of a roulette-wheel diagram that illustrated a “nested-sets” relationship between the prior and the posterior probabilities. Results from two experiments showed that frequency alone had modest effects, while the nested-sets instruction achieved a superior facilitation of normative reasoning. The third experiment compared the roulette-wheel diagram to tree diagrams that also showed the nested-sets relationship. The roulette-wheel diagram outperformed the tree diagrams in facilitation of probabilistic reasoning. Implications for understanding the nature of intuitive probability judgments are discussed.

Towards a New Model for Causal Reasoning in Expert Systems

2017 ◽  
Vol 7 (1) ◽  
pp. 32-63 ◽  
Author(s):  
M. Keith Wright
Keyword(s):  
Expert Systems ◽  
Conditional Probability ◽  
Causal Reasoning ◽  
Causal Theory ◽  
Probability Judgment ◽  
Probability Assessment ◽  
Conditional Probabilities ◽  
Long Run ◽  
Causal Strength ◽  
As If

This paper presents ideas for improved conditional probability assessment and improved expert systems consultations. It cautions that knowledge engineers may sometimes be imprecise when capturing causal information from experts: their elicitation questions may not distinguish between causal and correlational expertise. This paper shows why and how such models cannot support normative inferencing over conditional probabilities as if they were all based on frequencies in the long run. In some cases, these probabilities are instead causal theory-based judgments, and therefore are not traditional conditional probabilities. This paper argues that these should be processed as if they were causal strength probabilities or causal propensity probabilities. This paper reviews the literature on causal and probability judgment, and then presents a probabilistic inferencing model that integrates theory-based causal probabilities with frequency-based conditional probabilities. The paper also proposes guidelines for elicitation questions that knowledge engineers may use to avoid conflating causal theory-based judgment with frequency based judgment.

Meaning, Modality, and Possible Worlds Semantics

2010 ◽  
Author(s):  
Scott Soames
Keyword(s):  
Natural Language ◽  
Classical Logic ◽  
Possible Worlds ◽  
David Lewis ◽  
Formal Languages ◽  
Possible Worlds Semantics ◽  
Natural Languages ◽  
Counterfactual Conditionals ◽  
Richard Montague ◽  
Close Parallel

This chapter begins with a discussion of Kripke-style possible worlds semantics. It considers one of the most important applications of possible worlds semantics, the account of counterfactual conditionals given in Robert Stalnaker and David Lewis. It then goes on to examine the work of Richard Montague. Montague specified syntactic rules that generate English, or English-like, structures directly, while pairing each such rule with a truth-theoretic rule interpreting it. This close parallel between syntax and semantics is what makes the languages of classical logic so transparently tractable, and what they were designed to embody. Montague's bold contention is that we do not have to replace natural language natural languages with formal substitutes to achieve such transparency. The same techniques employed to create formal languages can be used to describe natural languages in mathematically revealing ways.

scholarly journals MP10: ANALYTICAL STYLE PREDICTS RELIGIOUS AND TELEOLOGICAL BELIEF

2016 ◽  
Vol 64 (3) ◽  
pp. 808.2-809
Author(s):  
SM Steiner ◽  
JC Zemla ◽  
S Sloman
Keyword(s):  
Conditional Probability ◽  
Religious Belief ◽  
Causal Reasoning ◽  
Religious Beliefs ◽  
Amazon Mechanical Turk ◽  
Cognitive Reflection Test ◽  
Intuitive Thinking ◽  
Higher Power ◽  
General Preference ◽  
Causal Directionality

Purpose of StudyShenhav et al. (2011) found that individual analytical style (reflective vs. intuitive) predicts belief in God or a higher power. Although intuitive thinkers are more likely to have strengthened religious beliefs since childhood, there is no correlation between analytical style and familial religiosity during childhood. This study examines the hypothesis that the link between intuitive thinking and religious belief is part of a broader preference for teleological explanations. We also test a possible mechanism responsible for teleological endorsement: intuitive thinkers may endorse teleological explanations because they confuse causal directionality.Methods UsedA questionnaire comprised of a randomized series of stimuli was administered via Amazon Mechanical Turk. Stimuli included the Cognitive Reflection Test (CRT; Frederick, 2005) to determine analytical style, questions on conditional probability to judge causal reasoning (Kahneman & Tversky, 1977), and a series of true or false questions on various teleological statements (Kelemen et al., 2013). Participants were then asked to rank on a scale from 1–7 the extent to which they believe in the existence of God or a higher power, and the extent to which they believe such a higher power influences events in the world (agency). Statistical analysis was performed using Spearman correlation.Summary of ResultsAs expected, teleological endorsement levels positively predicted belief in agency of a higher power (R=0.28, p<.01) and CRT score negatively predicted teleological endorsement levels (R=−0.24, p<.01). However, no significant correlation was found between CRT performance and tendencies in responding to conditional probability stimuli (R=0.017, p=0.85). Individual belief in agency of a higher power predicts teleological tendencies to a greater extent than religious belief alone (p=0.075) for belief in higher power, compared with p=0.085 for belief in agency of higher power.ConclusionsOur results replicate previous findings that show a relationship between intuitive thinking and religious beliefs and suggest that this may reflect a general preference for teleological explanations. However, the reasons why intuitive thinkers endorse teleological explanations are still unclear.

Evidence for the Jeffrey Table

2019 ◽  
Vol 66 (3) ◽  
pp. 187-194
Author(s):  
Moyun Wang ◽  
Mingyi Zhu
Keyword(s):  
Conditional Probability ◽  
Fundamental Question ◽  
The Other ◽  
Adequate Account ◽  
Natural Languages ◽  
Probability Judgments ◽  
Low Level ◽  
De Finetti

Abstract. Conditionals statements are a common and necessary component in natural languages. The research reported in this paper is on a fundamental question about singular conditionals. Is there an adequate account of people’s truth, falsity, and credibility (probability) judgments about these conditionals when their antecedents are false? Two experiments examined people’s quantitative credibility ratings and qualitative truth and falsity judgments for singular conditionals, if p then q, given false antecedent, not-p, cases. The results demonstrate that, when relevant knowledge about the conditional probability of q given p, P( q|p), is available to participants in not-p cases, they tend to make credibility ratings based on P( q|p), and to make “true” (or “false”) judgments at a high (or low) level of these credibility ratings. These findings favor the Jeffrey table account of these conditionals over the other existing accounts, including that of the de Finetti table.

Ifs and Newcombs

1985 ◽  
Vol 15 (3) ◽  
pp. 449-481 ◽  
Author(s):  
Arthur E. Falk
Keyword(s):  
Conditional Probability ◽  
Possible Worlds ◽  
Deductive Inference ◽  
Strict Implication ◽  
Common Part ◽  
Counterfactual Conditionals ◽  
The Common

‘Ifs’ come washed or unwashed. The washed ifs are embedded in precise theories: the constantly strict implication of deductive inference, the variably strict implication of ‘nearness’ conditionals, and statements of conditional probability. By a nearness conditional I mean the common part of Stalnaker's and D. Lewis's theory of counterfactual conditionals, which depends on a notion that possible worlds are more or less near to each other, as a measure of their over-all similarity to each other.

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