New Aristotelians according to Connolley

A piece here by William Connolley gives me a chance to write about something today.  He says that 'with the success of science' the idea of 'abstracting problems', i.e. abstraction, isn't difficult. He considers the example of a ball moving on a surface, which requires the idea of a perfect sphere on a perfectly flat surface, 'ignoring friction'. This takes us straight away to Newton's laws of motion, such as the law that the ball moves in a straight line unless deflected or stopped by some force, and so on.

He claims that the ancients, such as Aristotle, were unable to make that abstraction. "They were still trying to understand the whole world as it was".

...It was "obvious" to them that the first and most obvious property of moving objects was that they stopped moving once you stopped pushing them. An ox-cart rumbling down some rutted muddy path stopped when the oxen stopped pulling it; that was obvious, and the study of such was so mired in the nitty-gritty reality of the world that precious little progress was made until Galileo abstracted (I know, I know, I simplify: Oresme etc worked on the problem too and got some of the way there; but again, only by picking on simpler examples).

Sorry, but that's quite horrible.  The ancients such as Aristotle were well used to abstraction.  Aristotle, as is well known, was profoundly influenced by Euclid and the abstract world of geometry, you know, perfect circles, spheres, lines, planes and so on.  As was Plato before him, of course, who was so impressed with abstraction that he constructed a quasi-religious theory about it.

To get Newton's laws abstraction may be necessary, but not sufficient. The crucial part of Connolley's example is the 'friction' bit. We have to 'ignore friction'. Yes, but what is friction?  Well, as we observe it with our own eyes in the natural world, it simply is the tendency of bodies in the sublunary world to slow down and stop.  An ancient philosopher could easily have abstracted away friction, after all, that's exactly what Euclid did.  There is no friction in Euclid's geometry, nor is there gravitation.  But there's nothing in that abstraction that tells you what friction really is.  The ancients thought that bodies slow down because that's what they naturally do, just as we think that bodies are naturally attracted to each other by gravitational force (which we still don't understand, except as some Aristotelian essential characteristic of matter).

The capacity to abstract is nothing to do with ancient science.  In fact, the problem was too much abstraction. By contrast, a little more observation and attention to the actual world would have done the trick. As I observed here and elsewhere, it was Buridan's observation of milwheels and ships, plus a spell in an armchair, that led him to reject Aristotle's theory of impetus.  Forget abstraction.

Buridan on impetus

Belette's comment the other day, and my follow-up yesterday led me to a further search, and further frustration. Is the 1509 edition the only available edition of a historically important work by Buridan, where he introduces the modern conception of impetus? Yes and no. It turns out there is no newer edition than the one published in 1509 by Johannes Dullaert. It was reprinted by Minerva G.M.B.H. in Frankfurt in 1964 but that is merely a copy, and a quick search reveals that it is now unavailable. The Warburg (my usual flight to safety) does not stock it.

I did find a digitised version of the original edition on Gallica, and here is the very page – question 12 of book VIII on Aristotle's Physics - but that got me very irritated, as it is completely unreadable. If you try magnifying it, you see that the resolution is low, and also the greyscale is wrongly set and inconsistent. Some pages are nearly black, some are nearly white, nearly all are unreadable. A further irritation is the gimmick application that organises page-turning views making it look as though it were a real book. I used to work with the Digital Medievalist IT specialists, who would come up with stuff like magnifying glasses when you want to zoom the text, fancy banners and borders and so on, when the real need is for better photography, better access to collections, and better organisation of archives and so on.

I also found an old translation by J.J. Walsh, of part of question 12, and was awestruck by Buridan's insight and clear thinking. He notes, as I mentioned in the previous post, that a millwheel keeps rotating once in movement, even though there is no external force acting on it, and no air displaced. He also argues that if we sharpened a spear at both ends, instead of just the front end, it could still be hurled in the same way through the air. Yet how could the air maintain pressure at the sharpened back, when we all know that sharpness easily displaces air? And all this from the comfort of an armchair. He further notes that once a ship is in motion, it keeps moving for a while even when the current is against it, and even though the movement of the air is not from behind, but from the front*. All this is clear evidence that it is not the air that maintains the impetus of a moving object.

He even suggests a theory to explain all this. Noting that a thrown feather does not travel as far as a heavy metal ball, he suggests that the impetus of a body is in proportion to its weight (I don't know the Latin word translated by 'weight'). Thus the motion of a feather is soon halted by the resistance of the air, whereas the motion of a heavy ball is not. And he suggests that because there is no resistance in the heavenly space, God only needed to set the whole thing in motion once, when the universe was created, from which point it kept going by means of impetus. Which is absolutely bang on, no? (Except, possibly, for the part about God).

*I concede he may have had to leave the comfort of his chair to ascertain this.

Armchair science

Stephen Law has an excellent post here about why science is better done in armchairs, which has a connection with Belette's question about the philosophy of Jean Buridan

Imagine two balls, one heavier than the other, connected by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter ball drags on and slows the fall of the heavier ball. But the system considered as a whole is heavier than the heavy ball alone, and therefore should fall faster than the heavy ball on its own. So Aristotle’s theory, just like the claim that there exists a four-sided triangle, generates a contradiction. Galileo could establish that it is false from the comfort of his armchair.

Quite. Philosophers have always preferred the comfort of armchairs and a good book, perhaps scientists should try this too. And following up Belette's question about Buridan's theory of impetus, I looked this up too. Buridan (in the twelfth question of Subtilissimae Quaestiones super octo Physicorum libros Aristotelis) challenges Aristotle's theory of why, when we throw an object through the air, it does not come to an abrupt halt and does not come crashing to the ground, as Aristotle's theory says it should. Aristotle's daft explanation is that the air projected by the thrower somehow propels the object forward. Buridan puts forward a number of armchair objections to this, of which the nicest involves the motion of a millwheel. This keeps turning in a circle once put in motion, yet circular motion does not displace any air. And this was even before the invention of armchairs (although admittedly you would have had to have seen a millwheel in operation to make this argument, and thus armchairs while necessary are not sufficient).

I would love this to be in the Logic Museum but the only edition I can find is from 1509, and early printed books are generally resistant to scanning. Something for the summer break, perhaps.

Anachronism and infinity

William Connolley (aka our commenter 'Belette') is discussing the problems of characterising early scientific thinking - in this case, Galileo's thinking about infinity. Everyone who has tried this is familiar with the problem of anachronism: mistakenly characterising the thoughts and ideas of early thinkers in a way that they would not have recognised or understood. This is particularly difficult when, as usually happens you are translating their work from another language. Clearly you cannot use exactly the terms  they would have used, since they were writing a different language. So you have to use terms with the same meaning, while avoiding meanings they may not have understood. For example 'one to one correspondence' or 'set'.

A further wrinkle is terms in modern mathematical and scientific and philosophical language that are directly inherited from early writers. Most scientific language before the twentieth century was imported from Latin or Greek. Thus, we have the word 'continuum'. In Latin this just means 'the continuous'. Do you translate it as 'continuum' - running the risk of connoting ideas probably alien to medieval and early modern writers on mathematics? Or 'the continuous', which may wrongly imply that the Latin word had no technical meaning. Similarly 'vacuum', which would be wrongly translated as the modern 'vacuum', i.e. airless, when the Latin writers didn't just mean without air, but without anything at all, 'the void'. On other hand, it is clearly correct to ascribe concepts like 'concentric', which simply means 'having the same centre', and is derived from 'concentricus' which entered the Latin language in about 1260.

Concerning Galileo's problem, of explaining how the points of a circle can be put into 'one to one correspondence' with a smaller concentric circle, here is a chapter from Ockham I am working on, which addresses a similar issue.  He writes (my translation)

Likewise, it is of the thinking of Aristotle (as is clear in Physics IV) that air can be condensed without all or some of its qualities, changing. Hence, when air is condensed, it does not have to lose any quality, or at least it does not have to lose every quality which it had before. From which I argue that when air is condensed, either the whole preceding quantity remains, and precisely that which [was there] before, or not. If so, then the same quantity is now less than before only because the parts of quantity lie closer now than before. Therefore since the parts of the substance are in the same way lying closer now than before, and quantity is not supposed to exist for any other reason, it seems quantity is superfluous. But if the whole quantity which was there before does not remain, therefore some part is lost, and since from the corruption of the immediate subject there some accident of it is corrupted, it follows that not every quality remains, which is against Aristotle.

This clearly has an affinity with Galileo's problem of "a small ball of gold expanded into a very large space without the introduction of a finite number of empty spaces, always provided the gold is made up of an infinite number of indivisible parts".

Isaac Watts on the size of the universe

I read through chapter X of Isaac Watts’ Philosophical Essays, where he talks about light from stars. My memory was bad: it is nothing to do with Olbers' paradox. The first section discusses whether space can be empty or not, and Watts argues it cannot. For light particles are passing through all parts of space in all directions. He gives a neat Fermi-like example. Imagine an auditorium containing a thousand plates, surrounded by an audience of a thousand people. Each person can see each plate. Thus, we can draw a line from any plate to every person. And similarly from any person to every plate. And (assuming light is particles) there is a constant emission of particles filling the air. The same must be true of space and the light emitted from stars. Thus, space must be full up of light particles. He wonders why the planets are not slowed down by all of this (an interesting question that I will leave to the experts).

The second section is on whether the universe is infininitely large or not. Watts argues not. For although the Earth was created by God 6,000 years ago (remember the time he was writing, in 1742), it is probable that the other solar systems were created long before that. In which case, if the light particles were being constantly emitted from the stars, the universe would be all used up and dark and dead, which it isn’t.

He mentions with apparent approval the opinion that when light particles are emitted from a star, gravity eventually draws them back to their source. Thus the universe will not be depleted by the constant emission of light, and it will have a finite size.

I was surprised to find he knows the speed of light (“one hundred and four score miles per second of the Minute”). I always imagined this was a nineteenth century discovery.

Olbers' paradox

Hunting through the internet to find something about Hubble's constant I found something on Olbers' paradox.  The Wikipedia article is not bad (but I have never disputed Wikipedia's generally good coverage of non-soft subjects).  The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark.  For if there were an infinite number of stars, evenly dispersed, the then for any angle of vision, the number of stars would be proportional, but the intensity of light inversely proportional to the square of distance. The two effects would cancel out thus, with an infinite number of stars, the sky would be uniformly bright, which it isn't.

The article says that Olbers was not the first to describe the paradox, without mentioning any earlier description. I remember reading a similar paradox by the English logician (and hymn writer) Isaac Watts (1674–1748), I shall look for his book tonight, and report back.

Meanwhile - and this is really a philosophical question - why is Hubble's constant a constant? 

Aristotle's Physics (Logic Museum)

Just out. A version of Aristotle' Physics in the Logic Museum. Fully indexed with Bekker numbers and other references so that (unlike other versions on the web) you can take a reference from some other source and locate it exactly. Accompanying it is Thomas Aquinas' commentary, fully linked to Aristotle's text.

The Physics includes many of Aristotle's most famous claims, some of them now discredited, such as that

• the void (Latin: vacuum) does not exist.
• motion in a void is impossible.
• there are four types of cause.
• nature has a purpose.
• there is no actual infinite.
• the world has existed from eternity.
• the continued motion of projectiles is caused by the surrounding medium.
• a body in moving in a void would continue moving if externally unimpeded.
• bodies of different weights fall at different speeds.

Reply to Freeman

Charles Freeman has commented on my last post in a way that misunderstands my point so fundamentally that it probably needs stating again, more clearly. It was as follows.

1. Many of Aristotle's scientific explanations are obviously wrong.

2. On the assumption that Greek science ended in the 4th century, Greek science had about 700 years to correct these obvious errors. But it didn't (in the sense that it did not arrive at a consensus of where Aristotle was wrong).

The first point is not simply that Aristotle was wrong. It was that he was obviously wrong. For example, he states in De Caelo (tr. Guthrie, Cambridge 1960 pp. 49-51) that if a weight falls a certain distance in a given time, a greater weight will move faster, with a speed proportional to its weight. This is obviously wrong: obvious in a way that his statement about why glass is transparent is not obviously wrong. To refute his theory about glass requires instrumentation and a complex atomic theory, neither of which was available to Aristotle. So while his transparency theory is wrong, it was not obviously wrong. But to refute his theory about falling bodies requires only a few simple experiments. In the 6th century A.D., loannes Philoponus challenged this as follows.

But this [i.e. Aristotle's theory] is completely erroneous, and our view may be
corroborated by actual observation more effectively than by any sort of verbal
argument. For if you let fall from the same height two weights of which one is
many times as heavy as the other, you will see that the ratio of the times
required for the motion does not depend on the ratio of the weights, but that
the difference in time is a very small one." [M. R. Cohen and I. E. Drabkin, "A
Source Book in Greek Science" (McGraw Hill. N.Y.) 220 (1948) - my emphasis].

So my first point stands: some of Aristotle's scientific observations are obviously wrong, in a way that the technology and understanding of the time could easily have shown. On my second point, that Greek science did not correct these obvious mistakes, the history shows that clearly enough. You may object that Philoponus was Greek, and that he spotted at least one obvious error. I reply: Philoponus' observation does not amount to a scientific consensus. We make progress in science when we arrive at a view that is not necessarily correct, but which is accepted by a majority, or a significant majority, of the scientific community. This was not properly achieved until Galileo. And note also that Philoponus was writing somewhat later than Freeman's 'cutoff point' of 381 AD. Moreover, he was a Christian thinker.

The problem of Aristotle

I have just noticed The Closing of the Western Mind by Charles Freeman. The thesis is that after Constantine declared Christianity the state religion in 312, the church successfully quashed any challenges to its religious and political authority, in particular any challenges arising from the tradition of Greek rationalism and (in effect) held up human development for a thousand years until the Renaissance.

The difficulty with any such view is that it must face up to the 'problem of Aristotle'. If there really was a 'spirit of Greek rationalism', why did Greek science and philosophy apparently not advance much beyond Aristotle, writing in the fourth century BC, and Constantine in 312 (that's about 700 years)? And if Christian dogma was really that stifling, how was it that Western science developed from the rediscovery of Aristotle's work at the end of the 12th century to the scientific revolution in the 17th century (that's about 500 years)?

It is particularly difficult to explain given that (as I noted here, and as everyone knows) Aristotelian science is so spectularly wrong. Nearly all his scientific views are false, indeed spectacularly and obviously false, and in a way that the simplest experiment would confirm. How did the Greeks did not notice this? As Hannam notes (God's Philosophers chapter 11), simple observation of the trajectory of an arrow or of a ball thrown through the air, noted by Albert of Saxony as early as the 14th century, would have refuted a considerable part of Aristotle's physics.

Why and how was it that the medieval West eventually progressed well beyond Aristotle's science, when Greek culture did not? Constantine's state religion seems completely irrelevant.

Hasty generalisation?

After a demanding and sometimes painful week with Longeway I am taking it relatively easy with James Hannam's Gods of the Philosophers. "With an engaging fervour, James Hannam has set about rescuing the reputation of a bunch of half-forgotten thinkers, and he shows how they paved the way for modern science" says Boris Johnson, no less.

It is an engaging and entertainingly written book, whose purpose is to show the extent of scientific progress in the Middle Ages, and to dispel some prevalent and persistent myths about the period. I can't find serious fault so far (I have reached the 'condemnations' of 1277). While it has no news for students of the period, being mostly taken from (generally reliable and authoritative) secondary sources, the subject desperately needs a popular audience, and Hannam has succeeded brilliantly

Yet it has attracted fierce criticism. Charles Freeman, author of The Closing of the Western Mind, attacked the book in an essay in New Humanist, arguing that it presents a distorted view of the medieval period.

God’s Philosophers is ... poorly structured, without a
coherent argument and often misleading, either through making assertions for
which there is no, or contrary, evidence or by omitting evidence that would
weaken its case. The review that called it “a spirited jaunt” was spot on. It
catches the mood of serendipitous ramblings, anecdotes and asides that make it
an easy read but hardly a serious contribution to our understanding of medieval
and sixteenth century science. Its success is mystifying.

Hannam replied, and Freeman followed with a further critique.

I won't attempt any serious analysis of these, except to note Freeman's frequent accusation of Hannam's 'sweeping assertions'. Generalisation is difficult to avoid when you are attempting to cover nearly a thousand years of intellectual history in 300 pages. So far, Hannam has avoided it very well. His main arguments is are from example. He gives many stories and accounts, all sourced, showing the extent of medieval innovation. Many of them are simply intended to debunk myth and prejudice (I was particularly struck by the revelation that the synthesis of hydrochloric, sulphuric and nitric acid first occurred in the West in the thirteenth century, and not earlier in the Middle East). The only hint of generalisation I have found so far is on page 105. Hannam writes:

The condemnations [of 1277 when 219 propositions were banned in Paris] and
Thomas's Summa Theologiae had created a framework within which natural
philosophers could safely pursue their studies. The framework first defined
clear boundaries between natural philosophy and theology. This allowed the
philosophers to get on with the study of nature without being tempted to indulge
in illicit metaphysical speculation. Then the framework laid down the principle
that God had decreed the laws of nature but was not bound by them. Finally, it
stated that Aristotle was sometimes wrong [...] and if Aristotle could be wrong
about something that he regarded as completely certain, that threw his whole
philosophy into question. The way was clear for the natural philosophers of the
Middle Ages to move decisively beyond the achievements of the Greeks (God's
Philosophers p. 105).

The passage is not sourced, and Hannam does not explain clearly the logic for his assertion. It is one of at least three views which Hyman and Walsh summarise it as follows.

Most scholars agree that these condemnations had a profound effect on the
history of medieval thought, but they disagree as to the nature and significance
of that effect. The condemnations have been called [1] a brutal victory
Augustinianism over Aristotelianism, but Aristotle flourished in the schools
after as well as before. It has been said [2] that by freeing the later Middle Ages
from the domination of a rigid Averroistic Aristotelianism, the way was opened
for the development of natural science as the inquiry into nature rather than
the dogmatic reiteration of the Aristotelian corpus. But surely this exaggerates
the monolithic character of the acceptance of Aristotle even by masters such as
Siger of Brabant, and underestimates the continued influence of Aristotle and
Averroes on the development of natural science. A more general and widely
accepted view [3] is that with the Condemnation of 1277, the scholastic effeort to
inforporate and renovate philosophy came to an end. But this surely
underestimates the philosophical advances, especially the methodological ones,
of the later period.

But it is a recognised view for all that. So far there is very little of distortion or falsification. I recommend the book.