[r-t] Anything Goes vs Peals Mean Something

[Mark Davies]

RAS writes,

> Is that what we're discussing?  Oh!  In that case I agree with you: such a
> performence is definitely false. Unquestionably.  Without a doubt.

Yes! I thought you might have lost track somewhere. ;-)

I think Iain's recursive definition of truth and Don's "sets" definition
both suffer from this problem: they work at the level of individual changes,
and individual changes don't have a stage. Hence by pretending to ring 
multi-stage peals you can ring any false stuff you like.

> (By the way, can your mail client really not manage to preserve message
> threading?

Yes it probably can, but as usual I do all my reading and replying from the
web archive, so no thread ids. Sorry.

>>it might be acceptable to spread an extent of Minor through a peal of
>>Triples by leads or courses, but not by individual changes.
> But are you actually enforcing that requirement in any way?

Trying to! I'm only allowing "methods" to be considered at different stages.
In practice I'm not yet sure whether that means every time you ring a given
method, or just whole leads.

To recap, my definition of truth is as follows. A peal is true if:

1. It is rung on one stage, and each change in the extent at  this stage is
rung either N or N+1 times in the peal, and no more, for N>=0.

2. It is rung on two stages, A and B, where |B-A|=1, and each change in the
extent on A is rung M times in the peal, and no more, and each change in the
extent on B is rung N or N+1 times, and no more, for M>0 and N>0.

3. For the purposes of proof in (1) and (2) above, methods at any lower
stage may be considered rung at a higher stage by: (a) including leading or 
covering bells; (b) ringing two or more methods at a lower stage in 
parallel; or (c) both of the above.

> The point I'm making is that either you take an algorithmic approach to
> truth -- such as IJA does explicity, or as DFM does implicitly.  Or you
> have admit that truth is both subtle and subjective, and give up
> attempting to codify it.

I think that's both too perfectionist and not perfectionist enough. Too
perfectionist because we can't expect any rules we right down to be
perfectly applicable to every case - but that shouldn't stop us having a
good go, and anyway, individual cases should always be open to independent
evaluation at the time they are rung. If it breaks the rules but in a good 
way, accept the peal.

But you're not perfectionist enough because you're not doing anything to
prevent blatantly false peals being rung - such as the Singles and Triples,
or the Minor changes spread throughout the Triples peal. These really are a 
bit crap. Any definition of proof which includes them is shoddy in my book.

> In particular, your definition of 'truth' brings in too much baggage in
> terms of leads and methods and so on. I simply don't like it.

All peals are made up of methods. OK, we might want a damned broad
definition of method. And anyway, even if you don't like my definition, it 
has the practical benefit of working - at least 99.999% of the time!

MBD