In the essay Validity and necessary truths I used truth tables with necessary truths and impossibilities in it. I did it like this:
| P | □Q | P→□Q |
| T | T | T |
| F | T | T |
Note that the modal operator is placed in the truth table also. It could also be done like this:
| P | Q | P→Q |
| T | T | T |
| F | T | T |
Note that Q is true on all rows. When thinking about a necessary truth or an impossibility we can simply choose only to look at the rows where the proposition is true. The truth table above is a part of this larger truth table:
| P | Q | P→Q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
We simply only looked at rows 1 and 3.
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