Okay, so it’s pretty long. I am trying to write an explanation from the ground up as to how logic actually works and why a good grasp of this will show that we shouldn’t be thinking the effectiveness of logic somehow clues us in on something cosmic or divine. I know logicians themselves have sometimes even affirmed some logic/god connection, so in that sense maybe I’m on shaky ground here, but anyway, here I’m trying to express my own view clearly and accessibly.
My original audience was this guy who thinks that the fact that non-contradiction is always true is very good evidence for God’s existence. However, after writing a fwe pages I stopped really writing directly to or for him, and started trying to craft something more widely applicable.
Well, please do read it, if you’re interested, and tell me what you think as regards clarity, accuracy and so on.
I feel like the basic introductory stuff (the Boxes and Buckets and the stuff about arithmetic) is pretty clear, and gives a good intuitive picture of where things are heading. But then I feel like once I get around to actually discussing non-contradiction directly, I am maybe less clear.
What do you think about all this, though?
Also, let me know what font it shows up in for you? (Apologies if font problems end up screwing up the formatting. I am presently unable to save documents to my computer so I had to do all this in Word Online, so couldn’t save as PDF.)
I’ve just done a brief reading of your essay. One major thing that jumped out at me was that
Apply this rule to two boxes by creating a new box and coloring it blue if at
least one of the two boxes is blue and leaving it bald if both of the two boxes
are bald.
should really be written as:
Apply this rule to two boxes by creating a new box and coloring it blue if and only if (iff) at least one of the two boxes is blue.
That would be more in keeping with the tone I think you’re trying to set.
In general I think that the ideas are sound, but perhaps it takes too long to arrive at them - the paper could be much more succinct. Also, I accepted that the box system was a model for the bucket system only for the sake of argument. It was clear that it could not actually be a model, because the box system tends towards blueness, and the bucket system tends towards fullness, meaning that ever bigger buckets will be necessary to hold the water.
You pose an interesting question about the boxer coming to terms with our (non boxing) world. But can you be sure that s/he would not come to the conclusion that the boxing model is not true for this world? I think that would be a more likely conclusion than disregarding everything s/he experiences. For example, if I were to go to a new world where I could fly, I would not play semantic games and think to myself that I cannot be flying as humans cannot fly and therefore must be walking with rather large steps. I would instead wonder what other things may be different in this new world.
What is the intended audience? I know you addressed it some, but are you thinking of something specific - a class, for example?