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Abstract

According to the Principle of Conditional Non-Contradiction (CNC), condi-tionals of the form "If A, Bž" and "If A, not Bž" cannot both be true, unless A is inconsistent. This principle is widely regarded as an adequacy constraint on any semantics that attributes truth conditions to conditionals. Gibbard has presented an example of a pair of conditionals that, in the context he describes, appear to violate CNC. He concluded from this that conditionals lack truth conditions. We argue that this conclusion is rash by proposing a new diagnosis of what is going on in Gibbard's argument. We also provide empirical evidence in support of our proposal.
   
 
     
k.h.krzyzanowska@rug.nl
 
     
s.wenmackers@rug.nl
 
     
i.e.j.douven@rug.nl
Abstract
        
     𝑝 𝑞   𝑝  𝑞      𝑝  
            
         
             
          
           
          
  
1. Gibbards riverboat argument.       
         
        
,
 
           
          
           
      𝑝 𝑞   𝑝  𝑞    
𝑝             
             
            
  
                  
               
             
           
           
            
    
      
            
               
            
               
             
               
            
            

   
     

     
                
              
              
         
   
             
           
              
                
              
              
                 
        
              
       
         
            
             
   
               
       calls           
          folds         
   
               
                
                  
             
           
      
      
            
               
             
           
              
       

          
         
                
                 
                 
                
             fully    
  something              
               
                
                  
                 
          something    
     more           
               
                    
            
           
               
                
            
               
  and         
          
          
 mistaken              
         is         

     
2. Toward a new semantics for conditionals.       
                
              
           
              
           
              
           
         
  
           
             
             
           
    
              
            
          
             
          
              
          
         

           
           
            
             
           
            
        𝑞      𝑝 
    𝑞   𝑝      
  𝑞      𝑝      𝑞
      𝑝      
              
              
               
 has         
     inferential        
              
             
             
                
               
                  
             
        
           
           
              
     𝑞     𝑝        
 𝑞      𝑝     𝑝 𝑞   
            
               
           
            
           
      and        
            
             
       
            
             
           
          
              
              
            
 
   not        
            
           
            
            
                
        deductively  
             
          
       
Denition 1 A speaker 𝑆s utterance of “If 𝑝, 𝑞 is true iff (i) 𝑞is a consequence—be it de-
ductive, abductive, inductive, or mixed—of 𝑝in conjunction with 𝑆s background knowl-
edge, (ii) 𝑞 is not a consequence—whether deductive, abductive, inductive, or mixed—of
𝑆s background knowledge alone but not of 𝑝 on its own, and (iii) 𝑝 is deductively con-
sistent with 𝑆s background knowledge or 𝑞 is a consequence (in the broad sense) of 𝑝
alone.
      knowledge     beliefs
            
           
        
               
           
           
         
              
          
          
              

  not       
             
           
             
            
              
              
           
   
          
            

               
           
           
               
  nothing          
           
             
                
        
  2 + 2 = 5        
                
           

                
              
                
     
              

            
               
              
           
            
            
             
              
                
               
               
              
           
             
            
           
             𝑞
            𝑝  𝑝 𝑞
     𝑞            
 𝑝           
 𝑝  𝑞
           
             𝑝 𝑞  
  𝑝  𝑞          
              
 

  𝑞       
   𝑝  𝑞

          
   𝑝 𝑞        not  𝑞    𝑝 
  𝑝        𝑝
 𝑞             not
   𝑝 𝑞         not  𝑞   𝑝 
              
 𝑝 𝑞  𝑝  𝑞              
                    
                
𝑝  𝑞          
is              𝑝 𝑞 is

  

       
      𝑝  𝑞       
  𝑝  𝑞
         
    𝑝  𝑞 𝑟   𝑝   𝑞 𝑟    
  𝑝  𝑞 𝑟    𝑟        
    𝑝  𝑞  Δ         𝑟  
  𝑝  𝑞   𝑝     𝑟     𝑞 
  𝑝      𝑞      𝑝  𝑞 
   Δ   𝑟     𝑞    𝑞 𝑟 
   𝑝

     𝑝   𝑞 𝑟    
 𝑝   𝑞 𝑟     𝑝    𝑟     𝑞
    𝑝 𝑞     𝑝  𝑟    
𝑞      𝑞   𝑟    𝑟     𝑝  𝑞
        𝑝  𝑞 𝑟
            
              
           
         
            
          
             
             
              
  
             
           
       guaranteed       
                
               
              
          
                
            
             
              
                
               
              
               

                
𝑝 𝑞           𝑞  𝑝       
               
     
             
              
           
           
             
             
            
              
           
             
  at        
             
         
               
               
            
            
               
     
,
             
           
              
             
             
             
                
            
           
           𝑝 𝑞   𝑝 
𝑞               
          

           
                 
            
         

               
               
                 
               
               
               
                 
                     
    
            
            
             
             
            
          
           
              
           
                
             a   
    mixed     
              
               
               
               
                
    
            
                   
           
           
    
           
                  
           
           
             
         
           
            
            
         
  
3. Inferential conditionals and evidential markers.     
              
               
          
            
           

              

          
         
            
            
          
    raise       
             lower  
       
         
             
          
             
            
             
           
            
   that   
3.1. Method

          
     http://www.crowdflower.com  
      http://www.qualtrics.com   
            
           
           
          
            
              
       ±13      
            
    

            
              
           
             
           
            
          
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  
            
 𝑁 = 83          
            
  𝑁 = 100          
             
            
                
             
               
               
              
 
           
            
                
               
           
  
     
      
  
      
      
   
  
           
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            
                
               
             
            
  
  
     
      
  
      
      
   
  
             
              
            
            

               
           
               
           
           
      𝑁 = 87       
             
   𝑁 = 96              
             
              
          
            
             
            
            
            
             
         
           

                   
               

           
             
 𝑁 = 86     𝑁 = 97       
   𝑁 = 87     𝑁 = 96     
     𝑁 = 95     𝑁 = 88
3.2. Results
             
            
          
          
            
 𝜒
2
(3,𝑁 = 183) = 24.9 𝑝 < .0001   𝑝 < .0001 
                
           
               
            
         
              
             
              
            
     
            
               
            
            
     𝑝 = .053
          
 strong          
 𝜒
2
(3,𝑁 = 183) = 64.4 𝑝 < .0001   𝑝 < .0001 
              
            
            
               
             
             
 
            
          𝜒
2
(3,𝑁 = 183) =
60.2 𝑝 < .0001   𝑝 < .0001      
             

             
           
                
            
   
            
          𝜒
2
(3,𝑁 = 183) =
107.9 𝑝 < .0001   𝑝 < .0001      
             
             
           
             
             
   
           
          𝜒
2
(3,𝑁 = 183) =
54 𝑝 < .0001   𝑝 < .0001      
             
             
            
               
            
    
3.3. Discussion
            
             
             
              
             
             
              
          
               
  

        𝑝   
     𝑝       𝑝    

           
                

                 
               
              

              
               
             
          
             
            
         
            
             
              
            
         
              
             
              

4. Conclusion.       
             
            𝑝 𝑞  
    𝑝  𝑞             
             
               
            
          
         
              
           
            
            
               
           
             
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Appendix
              
    
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              
              
           
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DeRoses story, certain version           
             
                
                
                
                
                
               
               
   
Conditionals               
DeRoses story, uncertain version           
             
                
                
                
                
                
             
             
  
Conditionals               
Mr. Smith, certain version          
                
            
              
         
Conditionals                
               
              
Mr. Smith, uncertain version          
               
             
             
       
Conditionals               
               
              


Apple, certain version             
              
             
        
Conditionals                 
 
Apple, uncertain version          
                 
            
Conditionals                 
 
Linguistics exam, certain version          
               
                    
              
               
                
Conditionals               
                 
   
Linguistics exam, uncertain version          
               
                    
              
                
                
            
Conditionals                
                 
  
References
   e Logic of Conditionals  
   Assertion and Conditionals   

  A Philosophical Guide to Conditionals   
       Mind 
         Synthese


           Dialectica

         Cognition 
    Mind 
       If    
    e Reach of Abduction  
           
     Ifs    
          
   Psychological Review 
        Philo-
sophical and Formal Approaches to Linguistic Analysis   
 
         
  
      Uncertain Inference   
 
         
Philosophical Review 
         Mind

   Real Conditionals    
      Journal of Philosophy

           
 inking and Reasoning  
   If P, then Q  
    Philosophia 
   Possible Worlds Semantics for Indicative and Counterfactual
Conditionals?   
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... Mill possibly being an exception (Skorupski 1989, p. 73 f.), what the aforementioned authors meant by a consequent being inferrible from an antecedent is that the consequent follows deductively from the antecedent. But as Krzyżanowska, Wenmackers, and Douven (2014) point out, thus interpreted, the idea that a conditional means that its consequent is inferrible from its antecedent is difficult to maintain. Douven and colleagues (2018) give the example (4) If Betty misses her bus, she will be late for the movies, which, as these authors argue, could well be true in a situation in which there is still a remote possibility that, after she missed the bus, Betty is transported from where she is now to the cinema to still make it in time for the movies. ...
... That may be why the idea that conditionals embody inferential connections never gained much traction. However, as argued in Krzyżanowska, Wenmackers, and Douven (2014), there is no reason why someone attracted to the idea should want to commit to a reading of "inference" as meaning deductive inference. 4 In its place, these authors propose a broader understanding on which a consequent is inferrable from an antecedent if a compelling argument can be made for the consequent starting from the antecedent and whatever background assumptions are available in the context of evaluation. ...
... While this is again an area of vast disagreement, virtually all researchers agree that the conditional operator should validate Modus Ponens (MP): from A and "If A, B" we should be allowed to infer B. After all, this is a rule we rely on quite routinely in our reasoning. However, as Krzyżanowska, Wenmackers, and Douven (2014) acknowledged right away, their position does not validate MP, simply because we may deem an argument from a true premise A to a conclusion B compelling (making "If A, B" true, given our background knowledge), but, unbeknownst to us, B may be false. 13 As Krzyżanowska and co-authors also pointed out, however, the fact that inferentialism invalidates MP does not mean that, from an inferentialist perspective, there is anything wrong with our practice of relying on that rule of inference. ...
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Classical logic was long believed to provide the norms of reasoning. But more recently researchers interested in the norms of reasoning have shifted their attention toward probability theory and various concepts and rules that can be defined in probabilistic terms. In philosophy, this shift gave rise to formal epistemology, while in psychology, it led to the New Paradigm psychology of reasoning. Whereas there has traditionally been a clear division of labor between philosophers and psychologists working on reasoning, the past decade has seen an increasing collaboration between philosophers and psychologists, from which an experimental philosophy of logic and formal epistemology emerged. An area in which the fruits of this collaboration have been particularly in evidence is the research concerned with conditionals and conditional reasoning. This chapter showcases contributions to this area to underline the value of the said branch of experimental philosophy more generally.
... According to the account meant here-Inferentialism-the truth of a conditional requires the existence of a compelling, "strong enough" argument (in the sense of Simon, 1982) from the conditional's antecedent (plus background knowledge) to its consequent, where the antecedent is pivotal in the argument, meaning that, without the antecedent, the argument for the consequent is no longer compelling (Krzyżanowska, Wenmackers, & Douven, 2014;Krzyżanowska, 2015;Douven, 2016aDouven, , 2017Douven et al., 2018; see also Oaksford & Chater, 2010, 2013, 2014, 2017, 2020, Vidal & Baratgin, 2017, and van Rooij & Schulz, 2019, Krzyżanowska, Collins, & Hahn, 2021. Psychologically, this inference is driven by relevance and bounded by satisficing: that is, people represent by default the inferential connection as relevant, and they satisfice, rather than optimize (again in the sense of Simon) on the strength of the connection. ...
... As Krzyżanowska, Wenmackers, and Douven (2014) point out, however, this criticism presupposes that we are to interpret "inference" as meaning deductive inference, an interpretation to which the idea that the truth of a conditional requires the existence of an inferential connection is not wedded. It may instead refer to a broader notion of inference, one that encompasses other forms of inference besides deduction, most notably induction and abduction, and indeed also proximity-influenced inference, which is our main current topic. ...
... To forestall misunderstanding, we note that Inferentialism-as stated inKrzyżanowska, Wenmackers, and Douven (2014)-is limited to standard indicative conditionals, excluding so-called nonconditionals(Lycan, 2001) such as speech act conditionals ("If you're hungry, there are cookies on the table") and non-interference conditionals ("If hell freezes over, Alice will not marry Bob"), as well as subjunctive conditionals and concessives (i.e., "even if" conditionals, which are sometimes also expressed without "even"). As a result, criticisms that accuse Inferentialism of being unable to account for, for instance, concessives (e.g.,Mellor & Bradley, 2021) are misguided. ...
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Central to the conceptual spaces framework is the thought that concepts can be studied mathematically, by geometrical and topological means. Various applications of the framework have already been subjected to empirical testing, mostly with excellent results, demonstrating the framework's usefulness. So far untested is the suggestion that conceptual spaces may help explain certain inferences people are willing to make. The experiment reported in this paper focused on similarity-based arguments, testing the hypothesis that the strength of such arguments can be predicted from the structure of the conceptual space in which the items being reasoned about are represented. A secondary aim of the experiment concerned a recent inferentialist semantics for indicative conditionals, according to which the truth of a conditional requires the presence of a sufficiently strong inferen-tial connection between its antecedent and consequent. To the extent that the strength of similarity-based inferences can be predicted from the geometry and topology of the relevant conceptual space, such spaces should help predict truth ratings of conditionals embodying a similarity-based inferential link. The results supported both hypotheses.
... With the possible exception of Mill (Skorupski, 1989, p. 73 f ), the aforementioned authors meant the sense in which the consequent ought to follow from the antecedent to be deductive. However, as pointed out in Krzyżanowska, Wenmackers, and Douven (2014) and elsewhere, this insistence on a deductive-inferential link between antecedent and consequent makes the proposal open to immediate counterexamples. There are many conditionals we regard as true even though the truth of the antecedent does not guarantee the truth of the consequent. ...
... In particular, we do not want to suggest that some conditionals are intrinsically or objectively missing-link conditionals. Indeed, it was already emphasized in Krzyżanowska, Wenmackers, and Douven (2014) that whether a conditional embodies a deductive, abductive, inductive inferential connection, or no connection at all, is a question that can only be answered relative to a given body of background knowledge. What for one person is a deductive inferential conditional may be an abductive or inductive inferential conditional, or even a missing-link conditional, for another person, or for the same person at a different moment in time, when the person had or will have a different set of background beliefs. ...
... As explained in previous publications (e.g., Krzyżanowska, Wenmackers, & Douven, 2014), however, that inferentialism invalidates MP is not really a problem, given that it will be typically the case that if there is a compelling argument from A to B, and A is true, then B is true as well. Because in daily practice we tend to rely much more on compellingbut-inconclusive arguments than on deductively valid ones (Schurz & Hertwig, 2019), we would be in big trouble if the arguments we judge to be compelling were not highly truthconducive. ...
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In previous publications, we have proposed a new, inferentialist semantics for indicative conditionals. According to this semantics, the truth of a conditional requires the existence of a compelling argument from the conditional's antecedent together with contextually determined background premises to its consequent, where the antecedent is pivotal in the argument. In this paper, we recapitulate the position; report the progress we made over the past years, in particular highlighting the empirical support the position has garnered; and respond to criticisms that have been leveled at it.
... One view which sees the link requirement as a part of the semantic meaning of 'if-then' is 'inferentialism' (Douven et al., , 2019Krzyżanowska et al., 2014). It is the position which claims that a conditional is true if there is an inferential or reason-giving connection between the antecedent and the consequent, so to speak, the antecedent provides a strong enough argument for the consequent in light of some background knowledge. ...
... It is the position which claims that a conditional is true if there is an inferential or reason-giving connection between the antecedent and the consequent, so to speak, the antecedent provides a strong enough argument for the consequent in light of some background knowledge. This connection may be deductive, abductive, inductive, or mixed (see Krzyżanowska et al., 2014); at least, the truth of the antecedent does not have to guarantee the truth of the consequent. According to the most recent formulation of 'inferentialist' truth conditions (Douven et al., 2019, p. 16), a conditional is (i) true if there is a strong enough argument from the antecedent (plus background knowledge) to the consequent, (ii) false if either there is a very weak argument connecting the antecedent and consequent, or there is an argument from the antecedent to the negation of the consequent, (iii) neither true nor false if there is no argument from antecedent to the consequent at all. 5 Consequently, missinglink conditionals cannot be treated as 'true' according to inferentialism in any form (e.g., (4) is predicted to be truth-valueless by the presented version of inferentialism unless the fact about Poland's capital bears some relevance to the arithmetic truth). ...
... In light of this approach, missing-link conditionals are viewed as lacking a common topic.5 An important difference between the presented proposal and the earlier one byKrzyżanowska et al. (2014) is that the former incorporates the idea of semantic indeterminacy, i.e., predicts that conditionals may be neither true nor false in some cases.Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
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Based on the new experimental evidence, we argue that a link between a conditional antecedent and the consequent is semantically expressed rather than pragmatically conveyed. In our paper, we focus on particular kinds of links which conditionals may convey in a context. For instance, a conditional ‘If p , q ’ may convey a thought equivalent to ‘ p will cause q ’, ‘ p is the best explanation for q ’, ‘ q follows from p ’, etcetera. The traditional theoretical literature on conditionals seems to imply that these specific links are generated pragmatically and are akin to conversational implicatures. In order to test this hypothesis, we used a well-recognized linguistic test from ‘reinforceability’ (i.e., susceptibility to a non-redundant affirmation), which serves to distinguish between a semantic and pragmatic level of meaning, and we designed an experimental study based on that test. The outcome of our study is that specific links conveyed by conditionals exhibit features of semantic entailments rather than conversational implicatures. This result accords with some of the recent findings in empirical investigations on conditionals. In the final part of our paper, we discuss various accounts of conditionals which can accommodate the results of our study.
... Secondly, following van Fraassen (1976), Stalnaker (1988) or Krzyżanowska et al. (2014) one can claim that the meaning of conditionals depend on the beliefs of the speaker. In the case described by Gibbard, it is clear that both Zack and Jack based their conditionals on different beliefs based on different evidence. ...
... On the other hand, some authors regard CS to be unintuitive and developing semantic theories which do not validate it. An example of such theory is a promising inferential semantics defended in Krzyżanowska et al. (2014) or Douven et al. (2022). 6 The results of the empirical experiments concerning CS are somewhat mixed, but the majority of evidence seems to go against it. ...
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The Ramsey Test is considered to be the default test for the acceptability of indicative conditionals. I will argue that it is incompatible with some of the recent developments in conceptualizing conditionals, namely the growing empirical evidence for the Relevance Hypothesis. According to the hypothesis, one of the necessary conditions of acceptability for an indicative conditional is its antecedent being positively probabilistically relevant for the consequent. The source of the idea is Evidential Support Theory presented in Douven (2008). I will defend the hypothesis against alleged counterexamples, and show that it is supported by growing empirical evidence. Finally, I will present a version of the Ramsey test which incorporates the relevance condition and therefore is consistent with growing empirical evidence for the relevance hypothesis.
... To cite an example from Douven et al. (2018, p. 52), it is not hard to imagine circumstances under which we would regard "If Betty misses her bus, she will be late for the movies" as true, even if those circumstances do not completely rule out the possibility of some coincidence through which, in the event that she missed her bus, Betty might still make it to the cinema in time. Krzyżanowska et al. (2014) took this observation as a starting point for a new incarnation of the aforementioned approach, which they dubbed "inferentialism" (see also Douven, 2016a;Krzyżanowska, 2015;Krzyżanowska et al., 2021;Krzyżanowska, Wenmackers, & Douven, 2013;Mirabile & Douven, 2020;, 2014van Rooij & Schulz, 2019). In that proposal, for the conditional to be true, the consequent must still follow from the antecedent, but "follow" is no longer understood as entailment. ...
... Thus, reasoners only invest processing effort to a limited degree, and satisfice on arguments that are just compelling enough. In short, HIT postulates that the key to understanding indicative condi-4 It is worth mentioning that, as presented in Krzyżanowska et al. (2014), inferentialism was meant to apply to standard indicative conditionals, and explicitly not to what authors have called "nonconditionals" (e.g., Geis & Lycan, 1993)-such as speech act conditionals ("If you're hungry, there are cookies on the table") and non-interference conditionals ("If hell freezes over, Alice will not marry Bob")-nor to subjunctive conditionals and concessives ("even if" conditionals, which are sometimes expressed without "even"; see Douven & Verbrugge, 2012). Thus criticisms of the position that accuse inferentialism of being unable to account for such nonconditionals (e.g., Mellor & Bradley, in press; Over & Cruz, in press) are misguided. ...
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According to the philosophical theory of inferentialism and its psychological counterpart, Hypothetical Inferential Theory (HIT), the meaning of an indicative conditional centrally involves the strength of the inferential connection between its antecedent and its consequent. This paper states, for the first time, the implications of HIT for the probabilities of conditionals. We report two experiments comparing these implications with those of the suppositional account of conditionals, according to which the probability of a conditional equals the corresponding conditional probability. A total of 358 participants were presented with everyday conditionals across three different tasks: judging the probability of the conditionals; judging the corresponding conditional probabilities; and judging the strength of the inference from antecedent to consequent. In both experiments, we found inference strength to be a much stronger predictor of the probability of conditionals than conditional probability, thus supporting HIT.
... Gibbard draws from this example the conclusion that indicative conditionals do not have truth conditions. Krzyżanowska et al. (2014)-while rejecting the material conditional account-propose a truth-conditional semantics for indicative conditionals that renders both (*) and (**) true by relativizing the truth of a conditional to the speaker's background knowledge. ...
... The material conditionals P → W (which corresponds to sentence (*) above) and P → L (which corresponds to sentence (**) above) will be "objectively" true at world ω 4 as well as "subjectively true", that is, believed to be true-the former by Zack and the latter by Jack. 14 Like Krzyżanowska et al. (2014) we take the view that the interpretation of the conditionals (*) and (**) is relative to the speaker's background knowledge/beliefs, but unlike these authors we interpret the conditionals as material conditionals. ...
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There is an ongoing debate in the philosophical literature whether the conditionals that are central to deliberation are subjunctive or indicative conditionals and, if the latter, what semantics of the indicative conditional is compatible with the role that conditionals play in deliberation. We propose a possible-world semantics where conditionals of the form “if I take action a the outcome will be x” are interpreted as material conditionals. The proposed framework is illustrated with familiar examples and both qualitative and probabilistic beliefs are considered. Issues such as common-cause cases and ‘Egan-style’ cases are discussed.
... Beyond explaining the strangeness of unconnected conditionals, inferentialism is also able to match intuition about the or-to-if principle and provides a solution to Gibbard's Riverboat argument (Krzyżanowska et al., 2014). Furthermore, it is able to provide satisfying interpretations for complex cases that cannot be interpreted successfully by other conditional theories (Skovgaard-Olsen, 2016, pp. ...
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Abduction is considered the most powerful, but also the most controversially discussed type of inference. Based on an analysis of Peirce’s retroduction, Lipton’s Inference to the Best Explanation and other theories, a new theory of abduction is proposed. It considers abduction not as intrinsically explanatory but as intrinsically conditional: for a given fact, abduction allows one to infer a fact that implies it. There are three types of abduction: Selective abduction selects an already known conditional whose consequent is the given fact and infers that its antecedent is true. Conditional-creative abduction creates a new conditional in which the given fact is the consequent and a defined fact is the antecedent that implies the given fact. Propositional-conditional-creative abduction assumes that the given fact is implied by a hitherto undefined fact and thus creates a new conditional with a new proposition as antecedent. The execution of abductive inferences is specified by theory-specific patterns. Each pattern consists of a set of rules for both generating and justifying abductive conclusions and covers the complete inference process. Consequently, abductive inferences can be formalised iff the whole pattern can be formalised. The empirical consistency of the proposed theory is demonstrated by a case study of Semmelweis' research on puerperal fever.
... The Bayesian Network for the Modified Model A. 30 As a reviewer points out, this assumption might be incompatible with some versions of inferentialism, on which modus ponens is not valid (e.g. Krzyżanowska, Wenmackers, & Douven, 2014), though see, e.g., Skovgaard-Olsen et al. (2016a) for an alternative approach to inferentiailsm. See also Mirabile and Douven (in press) for an empirical investigation and a helpful discussion of inferential conditionals and modus ponens. ...
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Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much—perhaps most—of what we believe through the testimony of others, the simple matter of acquiring conditionals via others’ assertion of a conditional seems integral to any full understanding of the conditional and conditional reasoning. In this paper we detail a number of basic intuitions about how beliefs might change in response to a conditional being uttered, and show how these are backed by behavioral data. In the remainder of the paper, we then show how these deceptively simple phenomena pose a fundamental challenge to present theoretical accounts of the conditional and conditional reasoning – a challenge which no account presently fully meets.
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Indicative conditionals—that is, sentences typically, though not exclusively, of the form “If p, (then) q,”—belong to the most puzzling phenomena of language. One of the puzzles that has recently attracted attention of psychologists of reasoning stems from the fact that on the majority of accounts of indicative conditionals, “If p, (then) q” can be true, or at least highly acceptable, even when there is no meaningful connection between p and q. Conditionals without such a connection, dubbed missing-link conditionals, however, often seem very odd. A standard pragmatic account of their oddity rests on an observation that, whenever missing-link conditionals come out as true, these are situations in which speakers are justified in asserting stronger, more informative statements. Asserting a less informative statement is odd because it is a violation of the Maxim of Quantity. This paper reports four experiments that present a challenge to the Gricean explanation of why missing-link conditionals are odd. At the same time, we will argue that these findings can be reconciled with general principles of Gricean pragmatics, if the connection is treated as a part of a conventional, “core” meaning of a conditional.
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Many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to argue for an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on the evidential meaning of certain English and Dutch modal expressions.
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The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.
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The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals.
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Conditionals are of two basic kinds, often called 'indicative' and 'subjunctive'. This book expounds and evaluates the main literature about each kind. It eventually defends the view of Adams and Edgington that indicatives are devices for expressing subjective probabilities, and the view of Stalnaker and Lewis that subjunctives are statements about close possible worlds. But it also discusses other views, e.g. that indicatives are really material conditionals, and Goodman's approach to subjunctives.
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The truthful speaker wants not to assert falsehoods, wherefore he is willing to assert only what he takes to be very probably true. He deems it permissible to assert that A only if P(A) is sufficiently close to 1, where P is the probability function that represents his system of degrees of belief at the time. Assertability goes by subjective probability.
Book
Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. It is hence not surprising that conditional logics – logics specifically designed to account for natural language conditionals – are an active and interdisciplinary area. The present book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics. For that purpose a range of topics are discussed such as Bennett’s arguments against truth value based semantics for indicative conditionals. Matthias Unterhuber is currently post-doctoral research fellow at the Department of Philosophy at the Heinrich Heine University Düsseldorf, Germany. His research interests include Logic, Philosophy of Science, and Experimental Philosophy.