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 contradiction to “appear.”
Of course this is quite the opposite of the Spinoza model, but like Constant said, it makes sense that you can save time and brain power by actively modeling a belief and then seeing what follows. As for why acceptance is the default, I’m not exactly sure. Perhaps it is simply quicker to accept a proposition rather than to waste time looking for its opposite.
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 contradiction to “appear.”
Of course this is quite the opposite of the Spinoza model, but like Constant said, it makes sense that you can save time and brain power by actively modeling a belief and then seeing what follows. As for why acceptance is the default, I’m not exactly sure. Perhaps it is simply quicker to accept a proposition rather than to waste time looking for its opposite.