David Over Festschrift, London, September Iterated Conditionals Shira Elqayam* David E Over** Simon J Handley*Jonathan StBT Evans* Alison M Bacon* *University of Plymouth ** Durham University

David Over Festschrift, London, September things I have discovered about David in the last two years 1.What he most remembers from the UK naturalisation forms is a counterfactual 2.If God offered him the chance to know the meaning of life or the proper analysis of counterfactuals, he would choose the latter 3.He has the largest collection of anecdotes of famous logicians / philosophers

David Over Festschrift, London, September A psychological preamble Hypothetical thinking ( Evans, Over & Handley, 2003; Evans, in press ) is resource-limited Can bear only a limited amount of embedded iterations –Become intractable very quickly ( Elqayam, Handley, Evans 2005 ) So what happens when a conditional is iterated? 1.If it’s a vowel, then if it’s in the A-M range then it’s E 2.If it’s a vowel and in the A-M range then it’s E

David Over Festschrift, London, September McGee’s (1985) counterexample to MP 1980 US presidential election Republican Ronald Reagan leading, Democrat Jimmy Carter second Other Republican John Anderson distant third Good reason to believe: If a Republican wins the election, then if it’s not Reagan who wins it will be Anderson A Republican will win the election. No reason to believe If it’s not Reagan who wins, it will be Anderson.

David Over Festschrift, London, September McGee’s (1989) counterexample to MP 1980 US presidential election Republican Ronald Reagan leading, Democrat Jimmy Carter second Other Republican John Anderson distant third Good reason to believe: If p, then if q then r p No reason to believe If q then r

David Over Festschrift, London, September How do theories of conditionals fare with iterated conditionals? – T1 Edgington’s T1 – material conditional True whenever the antecedent is false or the consequent is true Under the material conditional the McGee form is logically valid

David Over Festschrift, London, September How do theories of conditionals fare with iterated conditionals? – MMT Mental model theory ( Johnson-Laird & Byrne 2002 ) overlaps to some extent with T1 Johnson-Laird & Byrne 2002: ‘From a formal standpoint, the [McGee 1985] inference is valid’ (p. 665). However, pragmatic modulation renders it invalid. ‘Lycan (1991) drew the following moral: In certain contexts and with certain interpretations, modus ponens is valid. He denied only that such inferences are valid in virtue of their form. We agree. Problems arise only if one envisages a formal rule of modus ponens that is automatically triggered by any sentences that match its syntactic form, regardless of their content or context.’ (JLB p. 666)

David Over Festschrift, London, September How do theories of conditionals fare with iterated conditionals? – MMT Not clear how this is consistent with MMT definition of validity, in which –‘[A conclusion is] necessarily true given the truth of the premises, because it holds in all the models […] consistent with the premises. (p. 654) Ignore the validity problem and treat model theory as a purely psychological theory –The McGee form should be endorsed with abstract materials but may be rejected with realistic materials due to pragmatic modulation

David Over Festschrift, London, September MP with iterated conditionals should be endorsed whether abstract or realistic (MC) –Realistic = Abstract > 0 But may be rejected due to pragmatic modulation (MMT) –Realistic < Abstract How do theories of conditionals fare with iterated conditionals? – T1 / MMT

David Over Festschrift, London, September How do theories of conditionals fare with iterated conditionals? – Supp The suppositional conditional (Edgington, 2006; Evans & Over, 2004) – mentally simulate antecedent, evaluate consequent in that context (Ramsey test) Iteration breeds intractability  Iterated conditionals more difficult to process then conditionals with conjunctive antecedent –‘Compounds of conditionals are a hard problem for everyone’ (Edgington 2006) Evans & Over undecided with respect to T2 / T3

David Over Festschrift, London, September How do theories of conditionals fare with iterated conditionals? – T3 T3 – the Adams conditional True for TT, false for TF, and indeterminate otherwise –But has probability that is equal to the CP Iterated conditionals have no plausible semantic interpretation – whether ordinary or abstract Unless pragmatically imported –i.e., interpreted as ‘if p and q then r’ –in which case the McGee form is simply invalid ( Edgington, 2006 ) Either way, should be rejected –Realistic = Abstract = 0

David Over Festschrift, London, September How do theories of conditionals fare with iterated conditionals? – T2 T2 – the Stalnaker conditional True for TT, false for TF FT / FF truth value depends on truth conditions in nearest possible world

David Over Festschrift, London, September Iterated conditionals have truth value that depends on nearest possible world Decision procedure applies to abstract materials as well as realistic ones Possible worlds analysis easier to work out for realistic conditionals, especially when there is a causal chain –Realistic > Abstract How do theories of conditionals fare with iterated conditionals? – T2

David Over Festschrift, London, September Experiment 1 Deductive reasoning instructions Abstract / realistic Iterated / conjunctive major premise Categorical / non-categorical conclusion

David Over Festschrift, London, September Sample item, abstract Suppose the following rule is true for a card drawn at random from a pack of ordinary playing cards: If it’s a ten, then if it’s red then it’s a diamond. It is also true that: It’s a ten Does it then necessarily follow that: If it’s red then it’s a diamondYES / NO / CAN’T TELL

David Over Festschrift, London, September Sample item, realistic You are a doctor in a medical ward. Suppose you know that the following rule is true for a particular patient: If Bill has typhoid, then if he is given the new medicine, then he will make a good recovery. It is also true that: Bill has typhoid. Does it then necessarily follow that: If he is given the new medicine then he will make a good recovery. YES / NO / CAN’T TELL

David Over Festschrift, London, September Experiment 1 – endorsement rates IteratedConjunctive

David Over Festschrift, London, September Expt. 1 Conclusions and questions Ps seem to be able to make at least some sense of the McGee form (at least in realistic conditionals) Endorsement rate drops for abstract iterated conditionals but not for realistic ones – this looks better for T2 than T3 or T1 / MMT The invalid form ‘If p and q then r; p; therefore if q then r’ has the lowest endorsement rates

David Over Festschrift, London, September Expt. 1 Conclusions and questions No difference between abstract / realistic materials for ‘if p then if q then r; p and q; therefore r’ –The conjunctive minor premise may have encouraged importation of the major premise as ‘if p and q then r’ –Or there may be bias against conditional conclusions Our iterated conditionals had conditional consequent – what about conditional antecedent? Embedding of mental simulation Should be more difficult under the suppositional conditional

David Over Festschrift, London, September Experiment 2 If p then if q then r;p;  if q then r If q if p then r;q if p;  r *if p and q then r; p  if q then r If p and q then r;p and q;  r If p then either q or r;p;  either q or r If either p or q then r;either p or q;  r

David Over Festschrift, London, September Experiment 2 Deductive reasoning instructions Abstract / realistic Iterated / conjunctive / disjunctive major premise –2 types of iterated conditionals – iterated antecedent / consequent Categorical / non-categorical conclusion Note: yr olds

David Over Festschrift, London, September Experiment 2 IteratedConjunctiveDisjunctive

David Over Festschrift, London, September Expt. 2 Conclusions and questions In contrast to Expt. 1, endorsement rates drop both for abstract iterated conditionals and for realistic ones – looks better for T3 –Younger Ps? The drop is more dramatic for conditionals with iterated antecedents – works well for the suppositional account and HTT The invalid inference ‘if p and q then r; p; therefore r’ is still quite low No bias for categorical conclusions or against conditional conclusions

David Over Festschrift, London, September Individual differences T3 default & for less sophisticated reasoners T2 for specific difficulties & more able reasoners –And only when supported by realistic materials Expt. 1 endorsement rates correlations with WM –All endorsement rates correlate –Indeterminate response bias of low WM Ps Determinate responses (yes / no) index –‘If p then q then r; p; therefore if q then r’ –Abstract n.s.; realistic (p=.075);

David Over Festschrift, London, September Take home message Iterated conditionals are difficult to process, especially when the iterated term is the antecedent This demonstrates yet again the difficulty of embedding hypothetical processes The evidence for T2 vs T3 seems equivocal –T3 may be the default with T2 for specific problems –T2 seems to work better when it can be pragmatically supported –And is perhaps employed more by older / more able reasoners ‘No theory has an intuitively adequate account of compounds of conditionals’ ( Edgington, 2006 ) is still the case

David Over Festschrift, London, September Thank you!