VERY CURSORY Notes on R.J Hankinson, chapter 4 of the Cambridge Companion to Aristotle

Aristotle has a strong idea of what constitutes scientific knowledge: it must be able to take the form of explanatory syllogisms, preferably Barbara's (AaB, BaC, therefore AaC). What is more, Aristotle held that for such a syllogism to express scientific knowledge, the premisses must be necessary.

To have scientific knowledge of X, you must not merely hold that X is true. You must also be able to explain why it is the case. Thus thinking that humans are mortal is not scientific knowledge unless you also can explain why: because they are animals, and all animals are mortal. But even that is not quite enough: you might say that humans are mortal, because they are mammals, and all mammals are mortal. That would be valid and sound, but not scientific, because 'mammal' is not the highest level in the genus-species hierarchy of which "mortal" is a property. You must use the highest level in the hierarchy to which the property applies.

What is more, you must be aware of the causal direction. Both of the following syllogisms are valid and sound (according to Aristotle):

1. 
   
1. All broad-leaved trees are deciduous;
2. Vines are broad-leaved;
3. Thus vines are deciduous.
2. 
   
1. All deciduous trees are broad-leaved;
2. Vines are deciduous;
3. Thus vines are broad-leaved.

Only one of the above is explanatory according to Aristotle, namely A (being broad-leaved causes being deciduous, but not vice versa). But it is not yet fully scientific, because :

3. 
   
1. All sap-coagulators are deciduous (that is the definition of deciduous);
2. All broad-leaved trees are sap-coagulators;
3. Thus all broad-leaved trees are deciduous.

C justifies A1, and so C is more fully explanatory.

So, from Posterior Analytics, it looks as if Aristotle wants scientific inquiry to consist of the construction of explanatory syllogisms within certain constraints. But the scientific treatises we have by Aristotle rarely, if ever, exhibit that form. It is unclear what that means.
Perhaps in the Posterior Analytics he is sketching an ideal structure that he simply did not use in the down and in the dirt investigations that he undertook.

A further problem is that Aristotle held that in the sublunary world (i.e. on Earth itself, not orbiting Earth or further out in space), generalities about substances tend to hold only for the most part. While certain logical syllogism do work with "for the most part" premisses, others do not: "Most Catholics are encouraged to marry; all Carmelites are Catholics; so ...  (nothing true results)". Perhaps Aristotle held that once science advances far enough, for-the-most-part premisses will be eliminated and replaced with more fine-grained universal premises (e.g., "All Catholics who have not taken celibacy vows are encouraged to marry"), but he nowhere explicitly pursues that possibility. What is more, that possibility is probably a dead end for him: he held that the reason why things occur only for the most part is because they involve matter. Matter somehow resists form, and so there will always be times when the form-matter composite will fail. In such cases, there will be no general explanation: rather, each particular case will have a particular reason. Hence for-the-most-part premisses are not eliminable.

Aristotle is not concerned with particular accounts of what causes some event (e.g. So-and-so died by violence because he went out. He went out because he was thirsty. He was thirsty because he ate spicy food. He ate spicy food because ... etc.). That, for him, is not a scientific explanation: he wants general explanation. It is simply not the case that generally people who go out die by violence, nor that people who are thirsty go out. It might be a general explanation of thirst to say that eating spicy food causes thirst. But the point is that Aristotle is simply not concerned with particular explanation of particular happenings: he wants general explanations. For something to be 'science,' he wants to know about things that generally run through the structure of the world and its changes.

What he needs, but does not have, is statistics and big data!

Aristotle addresses the following situations: I happen to be at the well when the robbers are there, and so something happens, but it was chance that I was there when the robbers were. No general explanation is possible. A. says that chance caused the thing to happen, and there is no further causal history to chance. One aspect of this is that A. says that chance events have no final causes, although they can have one in a sense (if craft could have led to the result, Aristotle calls it chance that is a sort of final cause: if craft could not have, then he calls it chance). An example: if I happen on treasure while ploughing my garden, then "digging for treasure" is the accidental final cause of my finding it.