Alright, I have just realized constructing a valid argument is impossible with the given conclusions. Sorry for the waste of time.
That's not really the point, but the point is somewhat technically interesting (at least to some people).
The only things that it even makes sense to talk of constructing truth tables for are words and symbols that can be applied to, or join together, true or false sentences.
However, in order for these words to have actually have a truth table, they need to be truth functional. This means when we apply these words to true or false sentences, the truth or falsehood of the resulting complex sentences is entirely dependent on the truth values of their component sentences.
For example, 'and' is an example of a truth functional operator. The truth value of the sentence, P and Q
, is determined by its constituent sentences; if P is false, or Q is false (or both), then P and Q
is not true.
'I know', however, is not truth functional. Look what happens when we attempt to come up with a truth table for it. Take 'I know P', for example. I cannot know something that is false, so it follows that if P is false, then 'I know P' is false:
P| I know P
However, just because something is true, it doesn't follow that I know it (if only!); there are many true propositions that I do know know, so all we can say is:
P| I know P
Immortality is not something that can be applied to true or false sentences, and even if you tried to, it would probably mean something similar to 'It is necessary that ...', which isn't truth functional.