An objection to the middle term being the reason why

The Aristotelian tradition discovered that the middle term of a syllogism in a scientific argument as not just a part of a valid structure but the proper reason why the conclusion is true. For example, the schoolbook syllogism

All men are mortal

All Greeks are men

All Greeks are mortal

is not a scientific argument, since the reason why Greeks are mortal is not because they are men – if it were, then elephants would not be mortal. For the argument to be scientific, the middle term has to be the definition of mortal, which means that it not only is convertible with mortal (i.e. All mortal things are X and all X are mortal things) but also that it be what is mortal first (i.e. it can’t be something essential, which, though convertible, follows from something more causal or fundamental. For example, it’s true that the Enola Gay dropped a bomb on Hiroshima and The thing that dropped the bomb on Hiroshima was the Enola Gay, but it was Truman who dropped the bomb first of all – everything after him was functioning secondarily and as a sort of instrumental extension).  This aim of identifying what is first (what we today call “root” causes) has always defined what is scientific, whether we are speaking of Aristotle defining the first cause of the eclipse or modern researchers defining ATP/P2X7R as the first cause of diabetes.

Here’s an objection to the idea of identifying root causes: the more we understand thing, the more we must reduce them to multiple fundamental accounts for which we cannot find a unifying reality. But the root cause is the fundamental, unifying reality of all accounts of a thing. Therefore, we cannot find first/ root causes.

The major premise was suggested by the puzzle over how to define things in mathematics. Take, for example, “phi”. What is it first? For Euclid, it was first of all a sort of divided line, such that the ratio of the whole to the larger part equalled the ratio of the larger to the smaller. In Algebra, this is defined more broadly in terms of relations of any quantities, such that phi is when the sum of any two quantities divided by the first equals their quotient. or

 \frac{a+b}{a} = \frac{a}{b} = \varphi.

A third account – which is one of the most popular ones – sees phi as the limit of the quotients in a Fibonacci series.

And so we have at least three different accounts of what phi is first: a divided line, a relation between quantities, or the limit of a numerical sequence. But the problem is more fundamental than this since the Euclidean definition also includes the means by which the line is constructed, which puts us in the position of having to decide which construction is fundamental. To take a similar problem: which among these 99 proofs of the pythagorean theorem is the first one? Which construction gives the root cause of the truth of the theorem?

The upshot of the objection is that the root causes of things remain hidden from us. We cannot, moreover, be said to approach them, since the increase in knowledge does not lead to a tighter unification but to a greater and greater plurality of fundamental accounts. If this is right, we should expect our increasing knowledge of the physical world to lead to more and more radically diverse, and perhaps even incompatible accounts. On this way of looking at things, the spit between QM and relativity is either fundamental, or the first of an even greater number of fundamental divisions.

 

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