The Shakespeare Conference: SHK 15.0974  Wednesday, 28 April 2004

From:           Gabriel Egan <This email address is being protected from spambots. You need JavaScript enabled to view it.>
Date:           Wednesday, 28 Apr 2004 11:25:32 +0100
Subject: 15.0964 Stylometrics
Comment:        Re: SHK 15.0964 Stylometrics

I thank Marcus Dahl for elucidating his understanding of Godel:

 >According to my non-mathematician's understanding
 >of Godel he demonstrated that there is no fundamental
 >axiom for all mathematics thus putting pay to about
 >30 years of work by Russell and Whitehead et al who
 >were trying to show just the opposite in (I think) their
 >'Principia Mathematica' (or some such pseudo Newtonic title).

If 'no fundamental axiom for all mathematics' is a shorthand way of
saying that no single, consistent set of axioms can prove all the truths
of arithmetic-for each set there are always truths of arithmetic it
can't prove-then this non-mathematician agrees. But the next bit of
Dahl's post is a leap I can't follow:

 >My comment was then intended to refer to certain negative
 >outcomes of Stylometry and one conclusion:
 >(1) Rather than making a positive demonstration of authorship it may be
 >possible to 'prove' instead that we cannot know who wrote certain texts
 >attributed to certain authors. i.e. there may be a limit to either the
 >theoretical or empirical evidence avilable to 'prove' positive authorship.

Or, put another way, Godel found a limit to what a single, consistent
set of axioms can prove about arithmetic, so it's not surprising that
other attempts to prove things have limits too.

The unspoken link here is Artificial Intelligence and the popular (but
false) idea that Godel had shown that no Turing Machine could do the
intelligent things that we humans can do. The special thing we can do is
spot when a candidate for arithmetic truth really is true, which Godel
showed is something that no machine (because no algorithm) can do in
every case.  In fact, Godel's theorem doesn't apply even here, since in
fact no human can spot arithmetic truths unfallibly either: we
undoubtedly use algorithms just as a machine would. Godel dealt in
philosophical absolutes, while our minds only have to be clever enough
to get ourselves reproduced in order to fulfil the role they're made for.

Having made the leap, Dahl has doubts about it:

 >(2) That such negative apriori or apostiori proofs may be non-the-less
 >formally acceptable as 'proof'. Thus it may be possible to make some
 >priori requirements for evidence and statements about that evidence
 >before surveying that evidence which would formally curtail our ability
 >to demonstrate positive proof.
 >(3) That this situation could be beneficial to Attribution Studies
 >Now: I am to some extent conflating two things here (but I know I am) -
 >the possibility of mathematical proofs (i.e. in a closed language
 >system) and the possibility (imagined or real) of empirical proofs (or
 >sets of statements etc for which falsifiable and repeatable evidence
 >exists or might exist).

Precisely. I wasn't trying to be mean in refusing to make the leap; the
reasons against it are strong. I agree that 'good enough' proofs will
often do in life, even though that's clearly an oxymoron.

 >My essential point remains the same - it is sometimes better
 >to show that 'you don't know' by some form of universally
 >acceptable proof or evidence than it is to show that 'you
 >might know' by a set of non-universally accepted proofs
 >or evidence.

Again, I can't see how Godel helps here, since his work is on what can
or cannot in principle be proven. The acceptability of stylometic
methods is quite a distinct matter.  The major barrier to the acceptance
of stylometric 'proofs' is ignorance of how they're arrived at. If lots
more people knew what the jargon and the statistics meant, the debates
would become considerably more productive.

Ward E. Y. Elliott and Robert J. Valenza, unlike others, are rather good
at explaining what they do. Their "Glass slippers and seven-league
boots: C-prompted doubts about ascribing _A Funeral Elegy_ and _A
Lover's Complaint_ to Shakespeare" Shakespeare Quarterly 48 (1997) pp.
177-207 is an excellent introduction to the subject.

Gabriel Egan

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