Hi Eugen, > Yeah. I'm saying that, say, > 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20 d9 > f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259 > didn't exist in this universe (with a very high probability, it being a > 512 > bit number, generated from physical system noise) before I've generated > it. > Now it exists (currently, as a hex string (not necessarily ASCII) on many > systems > around the world, rendered in diverse fonts), as soon as I remove all > its encodings it's gone again. P00f!
I can't identity with your conception of numbers but I guess you're entitled to it! You admit a base 16 notation for numbers - which means you allow numbers to be written down that aren't "physically realized" by the corresponding number of pebbles etc. So much for talking about pebbles in your previous emails! In statements of the form "There exists integer x such that p(x)" do you say this is vacuous because x hasn't been specified yet, or is it sufficient to merely name an unspecified integer to allow it to exist? Many proofs make these sorts of statements, and no where is the named integer given a specific value (even though its purported existence is crucial to the proof). Do you say these proofs are vacuous? If I write the statement "for all integer x, x+1 > x", does this make all the integers come into existence? Or is this another vacuous statement? - David
