The horseshoe analysis identifies indicatives as having the same semantic content with material conditionals. But is that right? Look at the following conditional:
C: "If I ate one and only one egg this morning, I ate two eggs this morning."
C is obviously false, actually necessarily false. But suppose I did not eat any egg this morning. Then, given the horseshoe analysis, C is true because it has a false antecedent and false consequent. So the horseshoe analysis is committed to treating something necessarily false as true. This I take to be evidence against the horseshoe analysis.
Of course, a horseshoe analysis may retort to my example this way. Since I know that I didn't eat any egg this morning and indicative conditionals do not tolerate known-to-be false antecedents, C is inappropriate. But this reply may commit the horseshoe analysts to much bigger problems, I reckon.
Tuesday, January 19, 2010
Thursday, January 7, 2010
Tricky conditionals
First, to get started, do you think the following two conditionals are contrapositives to each other?
(1) If he made a mistake, then it was not a big one.
(2) If he made a big mistake, then he did not make any mistake.
These two have been used by some as evidence that indicative conditionals in real life do not abide by the inference of contraposition. What do you think?
There is a huge number of tricky conditionals, couples or singles. Here is a really interesting and really tricky one:
(R): If Reagen was a KGB, no one would ever know it.
You can opt to replace the "know' in the consequent with anything you like, "believe", "find out", "think of", etc. (I actually can't think of more that makes sense.)
This conditional is intended by some as evidence against the Ramsey test. But, alas, as I see people do such things, I am wondering inside of me whether they are sincerely naive or they are sophisticated animals intending to make the water ever blurrier. The operator of the consequent--"no one would ever know"--is a modal operator! It's as much a modal operator as devices like "Shakespeare believed", "Necessarily it is the case that", "It is morally obligatory that", etc. (Don't get me wrong. This time I do have a lot of backups reserved in my mind. Sorry, a bit overly alert to etcs.) Should we not separate out modal operators when we are analyzing truth conditions of a logical connective like "if"? We did so when we defined truth-functional connectives like "or", "only if", "and", etc. (I am silent this time.)
(1) If he made a mistake, then it was not a big one.
(2) If he made a big mistake, then he did not make any mistake.
These two have been used by some as evidence that indicative conditionals in real life do not abide by the inference of contraposition. What do you think?
There is a huge number of tricky conditionals, couples or singles. Here is a really interesting and really tricky one:
(R): If Reagen was a KGB, no one would ever know it.
You can opt to replace the "know' in the consequent with anything you like, "believe", "find out", "think of", etc. (I actually can't think of more that makes sense.)
This conditional is intended by some as evidence against the Ramsey test. But, alas, as I see people do such things, I am wondering inside of me whether they are sincerely naive or they are sophisticated animals intending to make the water ever blurrier. The operator of the consequent--"no one would ever know"--is a modal operator! It's as much a modal operator as devices like "Shakespeare believed", "Necessarily it is the case that", "It is morally obligatory that", etc. (Don't get me wrong. This time I do have a lot of backups reserved in my mind. Sorry, a bit overly alert to etcs.) Should we not separate out modal operators when we are analyzing truth conditions of a logical connective like "if"? We did so when we defined truth-functional connectives like "or", "only if", "and", etc. (I am silent this time.)
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