## Wednesday, October 22, 2008

### Quiz on "If... then..."

I am holding out to you my two closed fists. Let us suppose that I know that you know that I know which, if any, of my fists are empty and which are full (for simplicity, I take "full" to be the denial of "empty"). You don't know which, if any, of my fists are empty and which are full. In which of the following cases would I be telling you a lie if I said: "If my left hand is full, then my right hand is full" while competently using English? (Choose "depends" if you think the answer depends on factors that I didn't include in the description of the case.)

1. In fact my left hand is full and my right hand is full: lie not a lie depends don't know
2. In fact my left hand is empty and my right hand is full: lie not a lie depends don't know
3. In fact my left hand is full and my right hand is empty: lie not a lie depends don't know
4. In fact my left hand is empty and my right hand is empty: lie not a lie depends don't know

#### 1 comment:

Alexander R Pruss said...

As of November 4, 2008, the statistics I have are:

Saying 'If my left hand is full, then my right hand is full' is or is not a lie when:

1. left is full, right is full? 0.7% lie, 98.2% not a lie, 0.8% depends, 0.3% don't know (728 respondents)
2. left is empty, right is full? 2.2% lie, 94.8% not a lie, 2.2% depends, 0.8% don't know (729 respondents)
3. left is full, right is empty? 98.9% lie, 0.4% not a lie, 0.5% depends, 0.1% don't know (730 respondents)
4. left is empty, right is empty? 1% lie, 96.6% not a lie, 1.9% depends, 0.5% don't know (729 respondents)

You can click on "Submit" with all the circles unchecked to see the current statistics.

So for this kind of case, the vast majority of my readers agree with the material conditional's truth conditions.