Scientific reasoning

At the end of Posterior Analytics, book I, Aristotle gives some examples of scientific reasoning.

Quick wit is a faculty of hitting upon the middle term instantaneously. It would
be exemplified by a man who saw that the moon has her bright side always turned
towards the sun, and quickly grasped the cause of this, namely that she borrows
her light from him; or observed somebody in conversation with a man of wealth
and divined that he was borrowing money, or that the friendship of these people
sprang from a common enmity. In all these instances he has seen the major and
minor terms and then grasped the causes, the middle terms. Let A represent
‘bright side turned sunward’, B ‘lighted from the sun’, C the moon. Then B,
‘lighted from the sun’ is predicable of C, the moon, and A, ‘having her bright
side towards the source of her light’, is predicable of B. So A is predicable of
C through B. (Posterior Analytics I.34 89b 10)

The syllogism that Aristotle gives right at the end is demonstration propter quid, reasoning from cause to effect.

The moon is lit by the sun
Things lit by the sun have their bright side turned towards the sun
The moon has her bright side turned towards the sun

But the reasoning process he describes is demonstration 'quia', reasoning from effect to cause. The man sees that the the moon has her bright side always turned towards the sun, and reasons from this effect to the cause of it, namely sunlight.

The moon has her bright side turned towards the sun
Things that have their bright side turned towards the sun are lit by the sun
The moon is lit by the sun

Are either of these illustrative of scientific reasoning itself? Surely not. Whoever has grasped the truth of the minor premiss or 'middle' has already grasped why the effect follows from the cause. The 'reasoning' described by Aristotle does not describe the thought-process that solves the scientific puzzle. What is the thought process that leads to the discovery of the middle? Aristotle merely says it is 'quick wit'.

There are some examples of scientific reasoning here. Unfortunately these do not describe how individuals such as Archimedes or Galileo or Newton actually hit upon the ideas that led to their discoveries. In this paper the nineteenth century epidemiologist John Snow argues, using the case of a water pump Broad Street, Soho in 1854, that cholera must be transmitted by drinking water. He reasons that there was no particular outbreak or increase of cholera except among the people who were in the habit of drinking the water from the pump. Nearly all the deaths were within a close distance of the pump. People who lived close to the pump but did not use it (such as the employees of a local brewery who only drank ale). But the paper is a reasoning process intended to convince others - it does not necessarily represent the thought process that Snow went through in arriving at his discovery. There is an important distinction between proving something to yourself, and proving it to others.

Is there any common thought process that underlies scientific reasoning and scientific discovery?