Aquinas on Aristotle's Posterior Analytics

Just out in the Logic Museum. Thomas's very accessible and highly recommended commentary on Aristotle's Posterior Analytics.

Why light passes through glass

The Longeway book arrived very quickly (2 days) and is a credit to Amazon . Compare this with Waterstone's, who had no copy in any of their London shops, and who said that ordering may take weeks or months, or with the university libraries in London (only UCL library had a copy, but this horribly-designed and uncomfortable building is to be visited only as a last resort).

There is much to say about the book. The introduction is long and as interesting as the reviews suggest. One example, illustrating Longeway's attention to detail, is the way he notices the interesting passage by Aristotle at 88a11. This is in some ways more interesting than the later and better known passage about the lunar eclipse beginning at 89b26. In the case of the eclipse it is theoretically possible for us directly to observe to cause of the eclipse (namely, as he says at 90a24, if we were living on the moon). In the case the transparency of glass, by contrast, it is theoretically impossible for us to observe directly the passage of light through the 'pores' in glass. The passage is also interesting for the insight that some ancient Greek scientists thought that the transparency of glass could be explained through some atomic or molecular theory.

On why glass actually is transparent, see this elementary explanation. It is intended for children, although I didn't follow it that well. It says the reason is that the molecules in liquids are disorganised and random, and so light can pass through them. It cannot pass through solids, because the arrangement of molecules is ordered (I didn't follow this reasoning). Light passes through all liquids, glass is a liquid, therefore light can pass through glass (I did follow this, however).

Note we can express the second reasoning in both Aristotelian propter quid and quia forms, as follows.

Propter quid
Light passes through liquids
Glass is a liquid
Therefore, light passes through glass

Quia
Light only passes through liquids
Light passes through glass
Therefore glass is a liquid

My earlier observations apply here as well. Both syllogisms are essentially trivial and hardly count as 'reasoning' at all. The real reasoning involves how we arrive at the (superficially implausible) premiss that glass is a liquid.

A priori and propter quid

In chapter 17 of Book III part 2 of Summa Logicae, Ockham gives a neat explanation of the terms propter quid and quia that shows how they are close, or even equivalent to the terms a priori and a posteriori respectively. I discussed this earlier. The translation is mine. (Sadly, I failed to get John Longeway's translation from our local Waterstone's, or indeed any Waterstones in the country, and had to resort to Amazon).

Separately, I am working on a translation of Buridans Questions on the Posterior Analytics. The translation of 'scire' is tricky, as both Ockham and Buridan use it with 'notare'. Both mean a sort of knowing. As they use it (and define it) 'scire' means a sort of reasoned knowing, the thing you get from understanding a demonstration, or 'syllogism that produces knowing'. Thus scientia, from which we get the English word 'science'. The modern and the medieval Latin meaning are closely connected. Understanding how they are different is a difficult matter that needs teasing out.

Latin	English
Propter quod oportet scire quod quaedam est demonstratio cuius praemissae sunt simpliciter priores conclusione, et illa vocatur demonstratio a priori sive propter quid.	On account of this we must know [scire] that one sort of demonstration whose premisses are absolutely prior to the conclusion, and this is called demonstration a priori or propter quid.
Quaedam est demonstratio cuius praemissae non sunt simpliciter priores conclusione, sunt tamen notiores sic syllogizanti, per quas devenit sic syllogizans in notitiam conclusionis, et talis demonstratio vocatur demonstratio quia sive a posteriori.	Another sort is demonstration whose premisses are not absolutely prior to the conclusion, and which are nevertheless better known to the syllogiser in this way, through which the syllogiser thus arrives at knowledge of the conclusion. And such demonstration is called demonstration quia or a posteriori.

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?

Longeway on Ockham on science

There's a neat review here of John Longeway's translation of book III-II of Ockham's Summa Logicae*. I can't vouch for it, as I haven't got hold of the book itself (it is on the reading list), but it seems coherent and well-written (my first line of defence against nonsense on the Internet).

The book is an English translation of Ockham's commentary on Aristotle's Posterior Analytics, and includes an extensive commentary and a history of the intellectual background to Ockham's work. Longeway argues for Ockham's importance as the founder of empiricism in the West. According to the review:

... he avoided that error of Early Modern empiricism that now seems most
objectionable: the attempt to construct our public world from purely subjective
experience. Ockham is a direct realist, relying on the causal relation between
concept and object to establish the concept's reference. In his view, what makes
belief cognition is the right causal relation between the knower and what is
known, not the possession of a sufficient justification for one's belief.

Definitely worth acquiring. Unfortunately (and surprisingly) not yet in the Warburg Library, so we shall see if Waterstones can deliver.

* Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio.