Dr. Kelder and the Null Hypothesis

There's an old joke about historians which says historians start out by looking backwards and they end up by thinking backwards.  

And yet I've never found this to be true.  Most historians carefully lay out the evidence and give a detailed demonstration showing how the data supports some hypothesis. It's true that almost every historical argument is probabilistic in nature (an induction) and, as a result, arguments may be well or poorly supported. Nevertheless, almost all historical reasoning proceeds methodically from data to conclusion.

A case in point is Dr. Jorrit Kelder of Oxford who maintains the position that the people of Mycenaean Greece lived in a single state. I have called this the Unified Mycenaean State (UMS) hypothesis.[1]

Dr. Kelder’s hypothesis has three parts:

A. The Mycenaean civilization was a single and united political unit

B. This political unit was a monarchy

C. The central place in this political unit was Mycenae.

And that’s it.  Three parts, a united monarchy centered in Mycenae.[1]

To support this thesis Kelder has piled up a series of barely related observations hoping, I suppose, that if the pile of facts can be made high enough scholars will ultimately be compelled to accept his conclusion.  But, logically, this method can never succeed.  This argument can never be made more than a probabilistic one (i.e. cannot be made deductive) and the facts as they stand are very far from supporting his conclusion.  Speaking in general, the risk of proceeding in such a way is to expose the advocate to confirmation bias.[2]  In order to avoid this it is necessary to proceed in a very different way. That way, in a nutshell, is to form the logical opposite of the desired hypothesis and do one's best to support this null hypothesis. If the null hypothesis can be shown to be probable then, fine, we can reject the original hypothesis and be on our way. If the null hypothesis cannot be supported and is shown to be less probable or even improbable then that supports the original hypothesis (note: it does not prove the original hypothesis). What happens when we try this with Kelder's thesis? Let's find out.

We have stated Kelder's actual thesis above; how do we form its opposite? Let's start by expressing the three parts (A, B, and C) of his thesis (H0) in logical notation:

H0: A ∧ B ∧ C;             where '∧' indicates logical 'AND'.

It’s easier to negate if we change the AND operators to ORs.  This kind of transformation is done all the time in formal logic, circuit design, etc.  We do it like this:

H0:      ~(~A ∨ ~B ∨ ~C);     where '∨' indicates logical 'OR'.

This is the exact logical equivalent of H0.  Its negation is straight-forward; we simply remove the outer negation sign with its parens.  The result looks like this:

~H0:      ~A ∨ ~B ∨ ~C

... or stating it in words:

~H0:       “The Mycenaean civilization was NOT a single and united political unit OR it was NOT a monarchy OR it was NOT centered at Mycenae”

This is the negation of the original thesis.  If we can make ~H0 fail then that lends support to H0.  But if we cannot reject ~H0 then H0 is not supported and, perhaps, even rendered less tenable. 

Of course, if we look at what we’ve done we notice that some of these clauses are of less worth than the others.  The original hypothesis is really overdetermined.  

The idea that Mycenae was a significant political center of some sort is, actually, overwhelmingly probable given what we know about it.  And we know that the monarchical form was common enough in the BA so that positing a king for our hypothetical state is not improbable.  So that this hypothesis wants to join two ideas which are highly probable to a third idea (that the Mycenaeans lived in one united state) which is highly controversial.  No doubt this is to give the UMS hypothesis logical cover.

It would be a good idea to examine the UMS hypothesis on its own and separate from the other two.  For example, if Mycenaean civilization did NOT form a united state then it hardly matters what the governance of this non-existent state was or where it was headquartered.   If the Mycenaean polities were truly independent of each other then it wouldn’t matter whether they were governed by a Sun King or the United Agricultural Worker’s Council of the Argolid, local 38.    Nor would it matter if this non-existent state was headquartered at Mycenae or in a rowboat in the Saronic.  The gravamen of Kelder’s thesis is that the Mycenaean people were united in a single polity of whatever form and wherever headquartered.

I propose, then, that we can restate Kelder’s thesis as simply:  The Mycenaean people were united in a single state.  H0 now becomes H0’.  And this is just

H0’:      A             ; the Mycenaean  people were united in one state

And the negation is:

~H0’:      ~A            ; the Mycenaean people were NOT united in one state.

Now our approach is to support ~H0’.   If we can do this then H0 is weakened or even rejected.  But if we must reject ~H0' then H0' will be supported and we can go on to discuss style of leadership and location of its headquarters which are really separate questions and for which different types of arguments will be appropriate.

What would it take to support ~H0’?

1. Well, we could suggest that, among the many Mycenaean projects that we can identify, there is no sign that they were dictated by the concerns of the political center.  In other words we could say that, while there are some similarities (due primarily to karstic geography), there is no unifying vision.
2. We could point to the natural behavior and tendency of equipotent (or nearly equipotent) states to refuse voluntary unification.
3. We might point to the likely infeasability of such a project of unification of governance by showing that the landscape involved posed severe geographic obstacles to a program of political/military unification.
4. We might show that the different divisions of the Mycenaean world were often at war and that great schemes of defence are everywhere visible.
5. We might demonstrate the difficulty of picking any specific Mycenaean statelet as having a clear resource advantage over the others.  We would be trying to show that the various statelets were equipotent, or nearly so.
6. We could point out that none of the Mycenaean statelets had any clear technological advantage over the others.
7. We could say that the historical record suggests that nearly matched states who go to war over unification typically wage those wars over long periods of time, even centuries.  It took Rome more than a century to unite itself to the Samnites.

If we could show that these things were true then we would have taken a big step towards supporting ~H0’ and thus weakening support for Kelder’s original thesis (H0').  If these things were false then we could reject ~H0' and, consequently, support H0'.

Unfortunately, we do not end up supporting H0'.

That is because every last one of these proposed criteria are either true or exceedingly probable.  In other words, under these criteria, we cannot reject ~H0'.

Footnotes

[1] For my extended critique of Kelder's position see this, this, and this.   I do not accept Dr. Kelder's thesis but just to be clear: Kelder is an historian for whom I have a profound respect.  He has done a great service to BA studies by maintaining this position on the dominance of Mycenae and he has argued for it as well as anyone could.  I may have given the impression in my other writings that Kelder originated this position.  That is not the case.  In its modern form this hypothesis is at least a century old and has been argued for by Desborough among others.

[2] I'm sure that Kelder has not done this.  

Confirmation bias is not the tendency to 'cherry-pick' the facts.  It is the psychological tendency to notice those facts which support some conclusion and not to notice facts that do not.  It is a subtle problem because it is almost indistinguishable from ordinary scholarly argumentation.  After all, noticing relevant facts is what we do.