[r-t] Anything Goes vs Peals Mean Something

[Richard Smith]

Mark Davies wrote:

> 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.

No, not "any false stuff you like".  Not even remotely. 
Iain requires that the rows on all but the highest stage 
form a complete extent.  Don, as modified my me, requires 
that the rows on all but one stage form a complete extent. 
I don't think anyone (Don included) is championing Don's 
original version that allowed incomplete extents on all 
stages: that was a minor oversight which was quickly 
corrected.

So yes, you can ring a whole extent on the higher stage 
(say, triples) plus a few scattered rows on the lower stage 
(minor, perhaps).  But this is just a special case of 
one-plus-a-bit extents of triples.

Or you can ring a partial extent of triples plus a whole 
extent on the lower stage.  But if you do that, then all of 
the repeated rows must have the same non-changing bells. 
This is what your contrived touch of triples and singles 
does.  But in practice, with real-world 'accidentally'-false 
touches, the repeated rows just don't form one or more 
extents on lower numbers.  Don has already pointed out that 
his definitions require the stage to be greater than one, so 
we can't have n extents on one bell, one per repeated row. 
I wouldn't object to increasing this to require the stage to 
be greater than two, if it'll make you feel more 
confortable.

Consider a false touch of Plain Bob Triples with a repeated 
lead.  You can't mould these 14 rows into a set of extents 
on any number -- you just don't have enough rows with fixed 
bells.  Perhaps there's a whole repeated course?  The 
rows with the treble in 1-2 form 12 extents on two with 
five covers.  But I can't do anything useful with the 
other 60 rows.

Show me a false touch that isn't clearly contrived and that 
can be described as true under the mixed stages rule.  Then 
I might take this objection a bit more seriously.

RAS