Walls, Reasonable and Unreasonable

 

(Those of my readers who are interested in the specific research findings about the Isthmian Cyclopean wall are referred to my previous post which is here.  This current post is about a specific logical approach to argumentation about that wall.)

Archaeologists form hypotheses about what they find.  They then proceed by attempting to show that some favored hypothesis is more probable than any other.  This is ordinarily accomplished by piling up data that support it and ignoring, downplaying, or attempting to refute the data that do not.  The typical archaeologist supposes that if he or she can make the pile of supporting facts large enough then eventually someone will stumble over them and land on the preferred conclusion.

And yet few hypotheses in this field can be directly demonstrated.   Why is this?  Simply because the nature of the field necessitates that archaeologists are (through no fault of their own) almost always reasoning from a scanty and incomplete evidence base in which the testimonia are ambiguously dated.

A case in point is the fight that erupted over the nature of the wall fragments discovered on the Isthmus of Corinth.  As I attempted to show in previous blog posts the hypotheses regarding the wall were chaotically distorted by irrelevant add-ons such as the appeal to the Dorian invasion. 

Is there a way to support a hypothesis that is based on fragmentary data without introducing fugitive and irrelevant ideas?   Sure there is.  We call it the scientific method. 

To approach the question in this way requires that we form the negation of the hypothesis and then attempt to prove the negation.  If we cannot demonstrate or support the negation (that is, if we reject the negation) then we will have supported the original hypothesis.  We can never directly prove the original hypothesis but we can show that it is supportable and more probable than its negation.

Proceeding in this way helps to avoid the tendency to observer bias - particularly important in this case because most arguments in this field are tainted with such bias to a greater or lesser degree.

What steps should we adopt here?

a. form the hypothesis

What is the original hypothesis?  Simply this: The identified fragments are parts of a single wall that was built to stretch across the Isthmus.

In logical form our hypothesis (H0) is A ∧ B; where A is ‘the fragments form a single wall’ and B asserts that ‘this wall was trans-Isthmian.’ [1]   So:

H0 : A ∧ B

b. Now we form the negative of the original hypothesis

In order to negate this hypothesis we can first recast H0 as ~ (~A ∨ ~B).  This is a standard transformation (it is the same as H0 and does not negate it) which could be rendered into English as 'It is not the case that (the fragments do not form a single wall or the wall was not trans-Isthmian)

We can convert this into the negation of H0 (that is into H1) by simply removing the outer negation from H0.  Doing this produces:

H1:  ~A ∨  ~B;  in English as 'The fragments did NOT form a single wall OR the wall was not trans-Isthmian’.

c. Now we are to support H1 as best we can.  Notice here that the form of H1 is a disjunction, an ‘OR’ statement.  If we can support either part then H1 is supported and not rejected.  What are these parts?

H1:A is ‘The fragments did NOT support a single wall’

H1:B is ‘The wall was not a trans-Isthmian wall’

We can support H1:A by showing that

i)             the several segments are not of identical work

ii)            the fragments were made at different times.

We can support H1:B by asserting:

i)             no evidence of the wall has ever been found W of the Temple of Poseidon

ii)            there are potentially local purposes that the fragments served.

iii)           long walls of whatever kind are unknown in the Mycenaean world.  (The example of the Copais basin shows that this is untrue.  The Mycenaean people were capable of large feats of terra-forming and, had they chosen to, were perfectly capable of building some sort of trans-Isthmian wall.)

iv)           there were better defense alternatives for protecting the Peloponnese.

v)            the route, insofar as we can reconstruct it, was poorly chosen for the stated purpose of protecting the Isthmus.

vi)           the absence of specific wall features that are characteristic of defense walls, the existence of towers, being freestanding at the top of slopes, etc.

If we can show that these things are improbable or false outright then we can reject H1 and end up supporting H0.  In this case, however the factors I've named, with the exception of H1:B:iii, are known by researchers to be true.  As a result we have supported H1 and not rejected it.   We conclude that we cannot support H0. 

One of the benefits of this approach (besides eliminating observer bias) is that the mythological justification for H0, the Dorian invasion, floats away as chimeras are wont to do.  It is an obvious irrelevance whose only purpose has been to support the argument through a specious suggestion of causality.   If we had been able to support H0 then, in a second phase, we might go on consider what may have been true with respect to potential invasions to which the response might have been the creation of a defensive wall.  However, we cannot support H0 and so speculation on invasions that might have given rise to these particular fragments is a logical irrelevance.  Up until now the reasoning on the part of those who have supported the idea of a trans-Isthmian wall has been circular.   It worked like this:

“There was a Dorian invasion and so there must have been a defensive wall to oppose it.  Because these fragments form part of a trans-Isthmian defensive wall it must have been the Dorian invasion that gave rise to it.”  Each assumption brings the other into existence by logical  parthenogenesis.

To conclude.  Few hypotheses in archaeology can be directly demonstrated.  The coin of the realm here is the inductive argument – reasoning from probabilities.  Inductive arguments work best by using long-established logical procedures such as those I have demonstrated in this case.

Footnotes

[1] Logical symbols:  ~  Not;    ∨: inclusive OR;    ∧: AND.