T2.3: 3 of 6
We need to be careful with this last example. You've just seen that in
3. If Frank were to attend graduate school, then it would be the case that he needs to take out a loan.
"if ... then..." is not used truth functionally. But why not? We need to see that this sentence's truth value depends on more that the truth value of its component parts. To do this, again think about constructing a truth table – we need to see that this construction attempt will fail. (We will see that there is no truth table possible for conditionals involving "were" and "would" as in 3. This is our indication that such "were-would" conditionals are NOT truth functional.)
Think about this table:
| P | Q | If P then it would be that Q | |
| row one: | T | T | ??? |
| row two: | T | F | ??? |
| row three: | F | T | ??? |
| row four: | F | F | ??? |
Let's just think about the last, highlighted row. If both components P and Q are false, what truth value will the whole have? It's hard to say, isn't it? OK, so think about 3 displayed above.
Suppose we know that in fact Frank will not attend graduate school (so the antecedent is false) and we know that in fact he does not need a loan (so the consequent is also false and row four applies). But this, of course, tells us nothing about what would be the case were the situation different and Frank decided to attend grad school.
The bottom line is this. What would happen to Frank depends on more than the actual truth values of antecedent and consequent. (It depends on what would happen in an alternative situation.) So, were-would conditionals are not truth functional. (Thus, were-would conditionals are different from more ordinary conditionals we treated in the last tutorial and symbolized with a horseshoe. More on symbolization later.)
Now one of the following is not truth functional but for a different reason. Click on that connective.