What is wrong with teleoanalysis (if anything)? I came across the term 'teleoanalysis' in relation to medical trials. There is no Wikipedia article on it yet, but Google search has a few links to scientific papers and their critiques.
As far as I understand, one of the main concepts of teleoanalysis is: if A causes B, and B causes C, then we can conclude that A causes C. Here is a quote from the teleoanalysis founding paper:

‘It may also be necessary to quantify the individual effects that relate to
  separate steps in a causal pathway–that is, the effect of factor A on disease C
  is determined from the estimate of the effect of A on an intermediate factor B
  and the estimate of the effect of B on C, rather than by directly measuring the
  effect of A on C. The exercise is like putting together the pieces in a jigsaw
  puzzle.’

One of the criticism mentions that this A->B->C logic is deployed when randomised trials either failed to prove relationship between A and C or are impossible to conduct, but there is some evidence of relationship between A and B  as well as B and C. The objection is that this logic is unscientific.
I was wondering if there is anything wrong with A->B->C reasoning from experiment design and general statistical science point of view?
 A: I've just encountered this concept, "teleoanalysis" today, also in the context of medical trials. I consider it fallacious.
In logic, a conditional argument is one of the form:
If A, then B.
There are four "modes" of argumentation in a conditional argument:
1: Affirming the antecedent,i.e.
A
=> B
2: Denying the consequent, 
not B
=> not A
3: Denying the antecedent:
not A
=> not B
4: Affirming the consequent:
B
=> A
Modes 1 and 2 are logically valid, while modes 3 and 4 are not. This is because there may be other causes of B, e.g. D. For example, in mode 3 above, the following situation may occur.
If D, then B
not A,
D
=> B
In your example causal chain above, consider the additions of causes D and E, added as follows:
If D, then A
If E, then B
If F, then C
D   E   F
 \   \   \
  A-->B-->C

As we can see, arguing that A leads to C is fallacious, as the causes D, E and F may be involved, which are all independent of A.
There may also be a cause G, such that:
  G
 / \
A-->B-->C

and so on.
As experiment and statistical inference are predicated on sound logic, there is no possible way for them to lend strong support for teleoanalysis.
Its proponents may argue that by controlling for the "lurking variables" D, E and F, the causal chain A-->B-->C can be verified. However, "lurking variables" may occur at any stage of the experiment, even as a consequence of randomisation etc. and therefore are possibly unavoidable, both theoretically and practically. 
