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How much of the meaning of 'if' does the material conditional (i.e…

- - - - This means that the logical connectives should make the same contributions to truth functions as their English equivalents
      - Looking at whether the arrow matches 'if..then...' (skipping the sections about the other connectives)
        
        Problem 1- lack of causal connection between the antecedent and consequent in the arrow, which should be present in English
        
        Example- of a body of water which will not be heated to 90 degrees this year, "if this body of water is heated to 90 degrees this year, then it will turn to ice" which is false in the English, but true in the logical language (because conditionals with a false antecedent are always true)
        
        Sainsbury says that this problem concerns indicative rather than subjunctive conditionals (explaining the distinction by use of the Kennedy examples- "if Oswald didn't shoot Kennedy someone else did" vs. "if Oswald hadn't shot Kennedy someone else would have"- the first can be true while the second is false
        
        Other cases in which the material conditional does not match 'if'= use of the word 'if' in non-indicative'-conditional ways in English
        
        If someone is in debt, he should curb his expenditure
        
        'he should curb his expenditure' - the 'he' does not refer to any specific person and so cannot be formalised, on its own
        
        Cases in which a grammatically indicative constional may be better classed as a subjunctive conditional 'if John dies before Joan, she will inherit the lot' seems to say the same thing as 'if John should die before Joan, she would inherit the lot'
        
        Cases where if does not express a conditional at all, but is synonymous wit 'whether' e.g. 'John wonders if his life is meaningful' is not 'if John's life is meaningful, then John wonders' but rather 'John wonders whether his life is meaningful'
        
        The sentences involved in subjunctive conditionals don't have truth values in the way required for formalisation (what is the truth value of 'someone else would have shot Kennedy', on its own?)
        
        Attacking the view that material conditional= indicative conditional
- - - - why should we regard this as undesirable? well, beyond our intuions, it does not fit wit how we might use a conditional in reasoning. Take the example of someone who does not think that the Republicans will win he election, but hinks that, if they do, they won't riase income tax
        
        This person thinks not R, and if R not D. However, if we take a truth functional analysis, these two are inconsistent- the only way in which one could say that if R then D is false, is to assert that R is true and D false
        
        (a possible resposne- mine, not in the reading- could we say that this is not an indicative conditional at all, but rather a subjunctive one, despite being grammaticaly indicative? would this help, if we accept that material conditionals don't correctly formalise subjective conditionals?)
        
        On this analysis, believable and unbelievable conditionals with a false antecedent both come out as equally true- but this does not fit our patterns of reasoning
    - - The other paradox of material implication is that according to Hook all conditionals with true consequents are true: from B it follows that A ⊃ B. This is perhaps less obviously unacceptable: if I'm sure that B, and treat A as an epistemic possibility, I must be sure that if A, B. Again the problem becomes vivid when we consider the case when I'm only nearly sure, but not quite sure, that B. I think B may be false, and will be false if certain, in my view unlikely, circumstances obtain. For example, I think Sue is giving a lecture right now. I don't think that if she was seriously injured on her way to work, she is giving a lecture right now. I reject that conditional. But on Hook's account, the conditional is false only if the consequent is false. I think the consequent is true: I think a sufficient condition for the truth of the conditional obtains.
- - - - "This conclusion has the virtue of validating the two most obviously valid inferences governing conditionals – modus ponens: ‘A, if A then C, therefore, C‘, and modus tollens: ‘Not-C, if A then C, therefore, not-A‘."
    - - "This is implausible. ‘If I live in London then I live in Scotland’ strikes us as false (it is rather ‘If I live in London then I do not live in Scotland’ which is true), but because I do not live in London, it is true on the equivalence thesis. Also, it entails that any conditional with a true consequent is true: the account validates ‘C, therefore, if A then C‘. But ‘If I live in London, then I live in Australia’ strikes us as false even after we learn that I do in fact live in Australia. "
  - - - This could mean introducing another necessary conditonal- that the antecedent and consequent be appropriately connected
        
        "However, we sometimes use conditionals precisely to deny that there is a connection between antecedent and consequent. A doctor who says that if you go to bed and take an aspirin you will get better in a week, whereas if you go to work it will take seven days, is saying that there is no connection between going to bed and getting better".
      - Or, a different additional necessary condition to add could be to say that if A then B is true iff A arrow B is true in our world and also in the closest possible worlds in which A is true
        
        This seems to work well for subjunctive conditionals, wehre we consider statements about how things might have been but are not, but less well for indicative conditionals
        
        "It construes indicative conditionals as being in part about the way things might have been but are not in fact."
        
        Or consider the difference between ‘If Oswald had not shot Kennedy, Kennedy would have won a second term’ and ‘If Oswald did not shoot Kennedy, Kennedy won a second term’. The reason we reject the second, despite accepting the first, is that we know that the way things actually are Kennedy did not live to win a second term. Subjunctive conditionals typically concern non-actual worlds, whereas indicative conditionals concern the actual world under various hypotheses about what it is like. Thus we say that if Oswald did not shoot Kennedy, someone else did, because that is the only thing to think about the actual world (in which we know that Kennedy was shot) given that Oswald was not responsible.
  - - - A strength of this approach- it explains our reluctance to asser both if A then C and if A then not C, as if we assume that a is cnstanc tthen the probability of C given A is = to 1-the probability of not C. So not C is ust as likely as C is unlilkey, and we couldn't assert both together
    - - Many respond to this proof by holding that indicative conditionals do not have truth-conditions at all;they only have assertion or acceptance conditions. This theory undoubtedly has its attractions but faces two problems. What should be said about the powerful intuition that a conditional with a true antecedent and a false consequent is false? And how should the relevant notion of assertibility be elucidated? Not in terms of likelihood of truth, obviously.
    - - Grice implicatures
        
        Likewise, runs the suggestion, ‘If A then C’ has the same truth-conditions as ‘A ⊃C’ but its use carries the implicature that my reasons for ‘A ⊃C’ are such that it would be right, on learning A, to infer C (that is, to use modus ponens).
        
        What do supplemented equivalence theorists say about our earlier example ‘If I live in London, then I live in Scotland’, which comes out true on the equivalence theory and so on the supplemented equivalence theory? They say that it seems false not because it is false but because it has very low assertibility – Pr(I live in Scotland/I live in London) = 0 – and in general that our intuitions about truth and validity of inferences involving indicative conditionals are governed by responses to assertibility rather than truth. #