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New Perspectives on Conditionals and Reasoning

September 5 - 6, 2018 



- John Cantwell (Stockholm)

- Vincenzo Crupi (Turin)

- Igor Douven (Paris)

- Paul Egré (Paris)

- Shira Elqayam (De Montfort)

Tim Kraft (Regensburg)

Karolina Krzyżanowska (Amsterdam)

- Katrin Schulz (Amsterdam)

Christoph Michel (Regensburg)

Niki Pfeifer (München)

Hans Rott ( Regensburg)

- Niels Skovgaard-Olsen (Göttingen)


                 New Frameworks of Rationality (SPP1516)


Vincenzo Crupi:

The logic of evidential conditionals

Once upon a time, some thought that indicative conditionals could be effectively analyzed by means of the material conditional. Nowadays, an alternative theoretical construct largely prevails and receives wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following earlier critical remarks made by others (most notably, Igor Douven), I advocate a revision of this consensus and suggest that incremental probabilistic support (rather than conditional probability alone) is key to the understanding of indicative conditionals and their role in human reasoning. There have been motivated concerns that a theory of such evidential conditionals (unlike their more traditional suppositional counterparts) can not generate a sufficiently interesting logical system. I will present results largely dispelling these worries. Happily, and perhaps surprisingly, appropriate technical variations of Ernst Adams's classical approach allow for the construction of a new logic of evidential conditionals which is nicely superclassical, fairly strong, and also (as it turns out) a kind of connexive logic.

Shira Elqayam, Igor Douven:

Inferential connections within conditionals: Ramsey still rules but not the Equation

Aim. Recently the reasoning field has undergone a paradigm shift, with probabilistic, decision-theoretic approaches increasingly on the ascent. The New Paradigm sees reasoning as a decision-theoretic behaviour, governed by the same parameters of probability and utility, with the Ramsey Test as a theoretical foundation of particular significance, often articulated in the form of the probability conditional, which conforms to the Equation. In this talk we present a novel approach, Hypothetical Inferential Theory (HIT), based on inferentialist semantics and dual process theories. According to HIT, people evaluate conditionals by testing if the consequent can be inferred from the antecdent. At the computational level of analysis, HIT still conforms to the Ramsey test, but not to the Equation.

Method and predictions. We developed several innovative experimental paradigms. For abstract conditionals, participants were presented with a soritical series of colour patches with hues that ran from blue to green. They were asked to evaluate conditionals such as ‘If patch 1 is green, so is patch 2’. We manipulated parameters that affect the strength of the inference from antecedent to consequent, such as the direction of the inference and the distance between the patches. We also measured directly the strength of the inference in a separate task. For content-rich conditionals, we pretested everyday conditionals such as ‘If oil prices continue to rise, then gasoline prices will rise’ (strong inference), and ‘If dictatorial regimes take control of the Western world, then refugees will colonise the moon’ (weak inference). We predicted and found a rich pattern of findings that connect between evaluations of conditional sentences and the strength of the inference from antecedent to consequent in a variety of ways.

Results. We report converging evidence from abstract and content-rich conditionals showing that:

(a)    When factors that determine inference strength are manipulated, test conditions in which inference from antecedent to consequent is stronger elicit a higher proportion of True responses.

(b)    When inference strength between antecedent to consequent is measured separately, it strongly predicts the proportion of True responses.

(c)     Interestingly, reasoners are also susceptible to the same biases that affect all inference. Specifically, we found a belief-bias analogue: the proportion of True responses was higher when participants believed that the consequent was true (analogous to belief in the conclusion in regular belief bias paradigms).

Conclusions. When people evaluate conditionals, they test if the consequent can be inferred from the antecedent. When this inference is valid or pragmatically strong, they tend to evaluate the conditional as True. When the inference is invalid or weak, they tend to evaluate the conditional as False or Indeterminate. This work is compatible with previous contributions to the New Paradigm in psychology of reasoning, in that it assumes the Ramsey Test as an underlying psychological process. Where this work starkly departs from previous contributions is by proposing that this evaluation rests on testing the strength of the inferential link between antecedent to consequent rather than on the Equation.

Paul Egré

Extracting conditionals from consequence relations

In this paper, based on joint work with Emmanuel Chemla and Benjamin Spector, we deal with the constraints that the definition of validity in a logic puts on the definition of a suitable conditional operator for that logic. In classical 2-valued logic, logical consequence is defined as the preservation of the value 1 from premises to conclusion, and the standard material conditional (>) is true provided the value of the antecedent is less than the value of the consequent. The object-level conditional well represents the meta-level operation of consequence, as captured by the full deduction theorem, that is (A > B) is valid whenever A entails B. In 3-valued logics and n-valued logics, on the other hand, several popular logics often fail the deduction theorem (this is the case for K3 or LP relative to the standard 3-valued conditional), without it being clear which operators would provide adequate substitutes or even whether they can be found. We study this problem for 3-valued and 4-valued logics which are "intersective mixed consequence relations", that is consequence relations that are obtainable as intersections of mixed relations (in which designated values can vary between premises and conclusions, see Cobreros et al. 2012, Chemla, Egré, Spector 2017, Chemla & Egré 2018). The space of such consequence relations is wider than the usual operations, but also better suited to think the way in which conditional operators represent consequence relations.

Niels Skovgaard-Olsen

Indicative Conditionals under the Microscope

Recently several experimental studies have reporting relevance effects on the cognitive assessments of conditionals, which pose an explanatory challenge to the suppositional theory of conditionals that currently finds a wide endorsement in the psychology of reasoning (Skovgaard-Olsen, Singmann, and Klauer, 2016a, 2016b; Skovgaard-Olsen, Kellen, Krahl, and Klauer, in review). Some of them concern the “Equation” (P(if A, then C) = P(C|A)), others the de Finetti truth table, and yet others the uncertain and-to-inference task. The purpose of this talk is to present a series of experiment that have a bearing on whether to count these effects as belonging to pragmatics or semantics. It is uncontroversial that some distinction between pragmatics and semantics must be drawn. Clearly linguistic expressions have some sort of content across contexts that we use to communicate, which can be modified by knowledge that only pertains to specific contexts. But in philosophy and linguistics it is highly controversial exactly how it should be drawn (Bach, 1997; Carston, 2002; Birner, 2013). This theoretical dispute has repercussions for the psychology of reasoning insofar as it remains an open question how to operationalize the semantic/pragmatic distinction.
To illustrate, in Skovgaard-Olsen et al. (2016a) it was found that "the Equation" (P(if A, then C) = P(C|A)) only holds under the condition of positive relevance (where P(C|A) – P(C|¬A) > 0). In the case of negative relevance (P(C|A) – P(C|¬A) < 0) or irrelevance (P(C|A) – P(C|¬A) = 0), the strong relationship between P(if A, then C) and P(C|A) is disrupted, because participants tend to view natural language indicative conditionals as defective under these conditions.
One possible reaction to this finding in Skovgaard-Olsen et al.(2016a) is that it may nevertheless be compatible with "the Equation", if one assumes that it is an effect of pragmatics rather than semantics that ΔP (P(C|A) – P(C|¬A)) modulates the relationship between P(if A, then C) and P(C|A). However, as long as we lack a good way of operationalizing the semantics/pragmatics distinction, we have no way of telling whether the results in Skovgaard-Olsen et al.(2016a) support a reason relation reading of the conditional known as inferentialism (Ryle, 1950; Rott, 1986; Brandom, 1994; Spohn, 2013; Douven, 2015; Krzyzanowska, 2015; Skovgaard-Olsen, 2016), or whether it can be accounted for as a pragmatic component within the suppositional theory of conditionals, favored by the new paradigm in psychology of reasoning (Evans and Over, 2004; Oaksford and Chater, 2007; Pfeifer, 2013). Until we have a principled way of experimentally distinguishing between the different roles that linguistic content can play, we are stuck with an interpretational ambiguity that impedes the testability of semantic theories in the psychology of reasoning. More specifically, as long as inconsistent evidence for a semantic theory can be attributed to the influence of pragmatic factors, without clarity about which detailed predictions follow from this attribution, it is difficult to devise a decisive test for a given semantic theory.
In this talk we seek to make progress on this topic by classifying relevance effects according to a series of diagnostic tests for distinguishing between conversational implicatures, presupposition failures, and conventional implicatures from the linguistic literature.

  1. Fakultät für Philosophie, Kunst-, Geschichts- und Gesellschaftswissenschaften
  2. Institut für Philosophie