This reminds me of a proof I was working on the other day. I was trying to show that a proposition (c) is true, so I used the following argument.
If (1) is true, then either (a) is true or (c) is true.
If (2) is true, then either (b) is true or (c) is true.
(a) and (b) cannot both be true.
(1) and (2) are true, so therefore (c) must be true.
This seems to follow Descartes' model of consideration and then acceptance of the proposition (c). However, I could have saved myself about half a page of space if I had simply started out by rejecting (c) and then waiting for a... (read more)
This reminds me of a proof I was working on the other day. I was trying to show that a proposition (c) is true, so I used the following argument.
If (1) is true, then either (a) is true or (c) is true. If (2) is true, then either (b) is true or (c) is true. (a) and (b) cannot both be true. (1) and (2) are true, so therefore (c) must be true.
This seems to follow Descartes' model of consideration and then acceptance of the proposition (c). However, I could have saved myself about half a page of space if I had simply started out by rejecting (c) and then waiting for a... (read more)