Language: Conditionals, Part 4

welcome to the fourth and final part in our series on conditionals I'm Justin ku to briefly recap what we've covered so far recall that we began with the question of what conditional sentences like 1 mean if the safety net needs repair I will fix it so far we tackled this question by thinking about the conditions under which one would be true or false thus we treated one as similar in this respect to two the cat is on the mat 2 makes a categorical claim about the cat saying that it is on the mat it describes the world as such that the cat is on the mat so it is true just if the cat is on the mat similarly according to the material and strict conditional theories one also categorically describes the world as being some way according to the material conditional theory one is true just if either its antecedent is false or its consequent is true according to the strict conditional theory one is true just if it is impossible for its antecedent to be true and it's consequent false both theories face the problem of making it too easy for conditionals to be true especially in cases in which their antecedents are false either actually or necessarily however notice that our assumption that one is just like 2 in expressing a categorical claim about the way the world is might be rejected to see why consider what happens when we make bets on conditionals suppose that I bet you five dollars that if it rains tomorrow the baseball game will be canceled and suppose that you accept let's now consider under what conditions we would each other money we can use the following betting outcome table which is analogous to a truth table from before notice that on line one which represents the outcome of rain and a canceled match you owe me five dollars on line two which represents the outcome of rain and cancelled match I owe you $5.00 this much should be unsurprising however notice that on lines 3 & 4 which represent the outcome of no rain tomorrow neither of us owes the other anything one way to think of it is that in that case the bet is called off another way to think of it is that our bet only binds us on the condition of rain the question of who wins or loses doesn't arise if it doesn't rain let's summarize our observation here by noting that to bet on this conditional is to make a conditional bet that the game will be canceled on the condition of it raining tomorrow notice that making a conditional bet is not the same as making a categorical bet a categorical bet is automatically binding if accepted it ensures that someone will win and someone will lose suppose I bet you five dollars that the cat is entirely let's say on the mat and you accept then you owe me five dollars if the cat is in fact entirely on the mat and I owe you five dollars if the cat isn't entirely on the mat this categorical bet ensures a winner and loser but conditional bets are not like that they are conditional on their antecedents and if their antecedents are false there are no winners or losers our final theory says that uttering a conditional is like making a conditional bet rather than a categorical bet we call this the conditional assertion theory of conditionals since according to it when I utter a conditional I do not make a categorical assertion but rather a conditional assertion to spell out what this means we need to say more about the difference between categorical and conditional assertion in what follows when I say assertion understand me as meaning categorical assertion when I assert to you that the cat is on the mat I expressed that I believe that the cat is on the mat and I try to get you to share that belief another way to think of it is that in asserting this I commit myself to it being true that the cat is on the mat we could put it this way to assert something is to try to get other is to believe it by committing yourself to its being true to understand what a conditional assertion is it's helpful to keep in mind the difference between categorical and conditional bets here an assertion is like a bet in many ways to assert that the cat is on the mat is to commit yourself to its being true that the cat is on the mat just as to bet that the cat is on the mat is to place a wager that the cat is on the mat a conditional assertion is like a conditional bet to conditionally assert that the match will be canceled on the condition of rain is to commit yourself to it being true that the match is canceled but only on the condition of rain and make no commitments otherwise notice that this is just like making a conditional bet to bet that the match will be canceled on the occasion of rain is to wager that the match will be canceled but only on the condition of rain and make no wager otherwise a crucial and important difference between the conditional assertion theory and the other two theories we've considered is that on the conditional assertion theory we think of the meaning of the conditional sentence in terms of what we do when we utter it namely make a conditional assertion this is just the opposite from the material in strict conditional theories according to them we think of the meaning of the conditional sentence in terms of the meanings of its smaller parts its antecedent and consequent we can helpfully compare the two kinds of theories by seeing what the truth table would look like according to the conditional assertion theory the most natural way to do so is to translate our betting outcome table back into a truth table as follows notice that we get to the truth values of the sentence 3 by considering what someone uttering 3 is thereby asserting or committing herself to according to the theory someone uttering 3 is asserting that the match will be canceled but only on the condition of rain and not asserting anything otherwise that is why the sentence is true on the first line false on the second but what about the third and fourth lines which represent the case in which it doesn't rain well in a sense the question doesn't arise on the conditional assertion theory since someone uttering 3 doesn't commit themselves one way or the other on the condition that it doesn't rain tomorrow it doesn't seem that either true or false would be correct on Alliance at best maybe we should think that the conditional isn't neither true nor false in that case that's an interesting difference between the conditional assertion theory and the material and strict conditional theories let's turn now to the question of how the conditional assertion theory fares with respect to the problems facing the previous theories consider for again if the earth is flat I will win the lottery tomorrow according to the theory someone who utters four asserts that they will in the lottery but only on the condition that the earth is flat so since the earth isn't flat they in fact assert nothing in other words they don't commit themselves either way on whether they will win the lottery tomorrow similar remarks apply it to the Goldbach conjecture problem facing the strict conditional theory on the one hand this is a significant advance over the previous two theories however no philosophical theory is uncontroversial and I want to leave you with one potential problem facing the conditional assertion theory recall our proof of the existence of god from before it's false that if God exists then God doesn't exist therefore God exists this was a problem for the material conditional theory because it predicts this argument is valid but intuitively it's not my challenge to the conditional assertion theory is that it seems to also predict that this argument is valid here's what look back at the truth table we got from the conditional assertion theory notice that there's an F only on one line line to where the conditionals antecedent is true and its consequent is false this means that according to the theory the only way for the conditional to be false is if it's antecedent is true and consequent false and so the theory should also predict that this proof is valid for the same reason that the material conditional theory does hence the conditional assertion theory seems to be in the same boat as the material conditional theory incorrectly predicting that this argument for the existence of God is valid what do you think I hope you've enjoyed learning about conditionals and as I'm sure you can now imagine there's plenty more to think about if you're interested learning more about conditionals I recommend Dorothy edgington's Stanford encyclopedia