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Archive April 2007
Sunday 29 April 2007
Why is it that "this sentence is true" hardly ever gets any attention, but logical paradox people love "this sentence is false"? Is it that hard to recognise that they are equally broken?

In fact, "this sentence is true" has an advantage over "this sentence is false", in that one of the more elegant solutions resolves the latter but not the former; the solution suggests that all statements are contractions of "it is true that (statement)", which is itself a contraction of "this statement is true: (statement)". Inserting our much-loved paradox, we get "this statement is true: this statement is false", which is logically equivalent to "A and not A", which always resolves to false.

But try that with "this sentence is true" and it resolves only to "A and A", whose truth value remains dependent on whether A was true to begin with.

This topic came up in conversation the other night, and most of the usual arguments were made, including splitting the sentence into two and constructing similar self-referencing-but-non-paradox sentences to show why it's difficult to produce a cohesive rule for what sentences you can designate "indeterminate" and move on. Two things didn't come up - one was what I've just said, that "this sentence is true" is not an example of a similar self-referential sentence that is okay (in fact, it was proposed as a logically acceptable sentence, and I didn't catch it), and the other was the clarification I woke up thinking this morning.

The trick is that it's not the sentence that can't be self-referential; "this sentence contains more than two words" is fine, for example. It's the truth value of the sentence that can't be self-referenced. I don't think you can construct a logical paradox that doesn't reference an 'output' truth value within the paradox. It is possible to construct a non-paradox that does reference a truth value within itself, but only if you allow a logical 'indeterminate' to exist during the resolution, eg. "this sentence is false, and one equals zero." {Indeterminate AND false} equals false, so the sentence is false, so it's {true AND false}, which still equals false (I don't think you can produce a paradox flip-flop with indeterminates, only indeterminates that may later resolve in one direction).

My tentative conclusion; all logical paradoxes can be resolved by the addition of an 'indeterminate' state, which is the result whenever an unassigned truth value within the paradox is referenced. {Indeterminate OR true} is true, {Indeterminate AND false} is false, and all other logical operators with an indeterminate parameter are indeterminate. Can you construct me a paradox that doesn't match these rules, or a non-paradox that resolves to indeterminate by these rules? [15:18] [12 comments]

Friday 13 April 2007
Last night there was a sound like our front door being operated. Nothing seemed amiss when checked downstairs, but then half an hour later or so, there was a muffled shout through the letterbox. Later, another. While some food was being prepared, I lurked near the front door, and there was one more tap, something thrown at the door or window this time. I quickly stepped outside, too late to see anyone there, but quick enough to hear the running footsteps, which I followed to the corner, to find three kids. And that's where their stupid game went awry.

As I rounded the corner, to find them facing away and giggling to themselves, I shouted "oi", which was met with mixed reactions - one panicked turning to look while simultaneously running away, causing comical horror-movie-style stumbling, one denial of having done it (whatever 'it' was), and one unconvincing "what?"

They got their game together a bit when told not to throw stuff at my house, with what might have been a mildly convincing denial ("we didn't even come from that way, we just came down here") if it hadn't been for that first reaction. And the thing of facing the wrong way. So I told them, "no, you're lying, don't throw stuff at my house," and returned home. Except on the way home there were a couple of older people now, who asked what happened - I told them, and they went round the corner to give their son and his friends a telling off.

When I got home, I noticed what I'd missed before, some graffiti on the door, "SBK". So I went out again, and asked the parents if they knew the names of the kids, and whether one had the initials SBK. Apparently not, but the parents were quick to grasp the implications (perhaps having seen the letters before), and demanded to know what SBK is. Twice it was "I don't know" and a denial of having a pen, then it was a sheepish "south bank killers" (or possibly "souf banq killaz" or something). Which really made it for me - the idea of a skinny barefoot unarmed guy chasing and scaring a gang of three 'killers' makes me smile, as does only being willing to name your gang under duress and sheepishly.

The one kid with the parents was ordered into their car. Later, while we were washing the writing off the door (it mostly came off), the other two were returning to their home, which involved passing our house - seeing four of us standing in the doorway (we had guests), one of them almost scarpered again, but then they rallied and just walked past with their heads down. In case of repetition, I followed just out of sight to see which house was theirs, so if it happens again I now know where to go. But hopefully my being a scary barefoot skinny guy will be the end of it. [22:15] [7 comments]

Saturday 31 March 2007
The movie 300 is made ten times more entertaining by mentally interjecting "lol gay" after approximately every second line. The titular 300 apparently doesn't refer to anything in the movie, but rather to the percentage by which the movie is made longer by slow-motion, including two shots of slow-motion water and some slow-motion seabirds. [22:57] [8 comments]