Aristotle’s errors

How many teeth did Bertrand Russell have? Did Galileo float in water?

Ἔχουσι δὲ πλείους οἱ ἄρρενες τῶν θηλειῶν ὀδόντας καὶ ἐν ἀνθρώποις καὶ ἐπὶ προβάτων καὶ αἰγῶν καὶ ὑῶν· ἐπὶ δὲ τῶν ἄλλων οὐ τεθεώρηταί πω.

Males have more teeth than females, in the cases of humans, sheep, goats, and pigs. In other species an observation has not yet been made.

-- Aristotle, History of animals 501b (2.3.13)

Aristotle sometimes gets a rep nowadays as a pretentious idiot: The Scientist Who Got Everything Wrong. Sometimes even Aristotle’s fans think this --

[Bertrand] Russell provides a concise summary of the thoughts of both [Plato and Aristotle], as well as painting a picture as to why they are so important, despite being wrong about almost everything.

-- David James, ‘Tigerpapers’ blog, 8 March 2012

This from a fan of Aristotle! And Bertrand Russell loathed Aristotle:

Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives’ mouths. He said also that children will be healthier if conceived when the wind is in the north. One gathers that the two Mrs Aristotles both had to run out and look at the weathercock every evening before going to bed. He states that a man bitten by a mad dog will not go mad, but any other animal will (Hist. An., 704a); that the bite of the shrewmouse is dangerous to horses, especially if the mouse is pregnant (ibid., 604b); that elephants suffering from insomnia can be cured by rubbing their shoulders with salt, olive-oil, and warm water (ibid., 605a); and so on and so on. Nevertheless, classical dons, who have never observed any animal except the cat and the dog, continue to praise Aristotle for his fidelity to observation.

-- Bertrand Russell, The Impact of Science on Society (2016) pp. 6-7 (orig. publ. 1952)

The trouble with attacking the entire oeuvre of a scholar and scientist in this way is that the examples are very, very cherry-picked. These five blunders are taken from a span of over 400 pages of tiny print full of literally thousands of observations about the animal world. Do we take Russell on faith that they’re representative?

No, we don’t. And I’m not going to let that ‘and so on and so on’ pass. If you want to show that Aristotle was wrong about almost everything, show that he was wrong about almost everything. ‘And so on’ is lazy if you can’t back it up. Russell couldn’t.

Russell’s first criticism, about women’s teeth, is the one that gets the most traction. That must be because it’s the easiest one to correct. Testing the claim about conception during a north wind would require an enormous amount of coordination and many years of research; no one is going to try out the effects of rabies on humans; I defy anyone to get a shrew to bite a horse on command; and elephants were not exactly an everyday sight in ancient Greece.

In fact some of them don’t even necessarily look like blunders, if you approach them in the right way. Seasonal winds are a thing: in Greece, a north wind at conception will often correspond to a birthday between mid-February and the summer solstice. And the time of year of a birthday can correlate very strongly with a child’s success under some circumstances. Aristotle didn’t know why that was, but he did know something about astrology, a field which was not considered ridiculous in his day, and which made similar kinds of predictions. And the behavioural effects of rabies are unquestionably different in animals that can talk and communicate their distress (humans) and those that cannot (every other species). I won’t venture to defend Aristotle on shrew bites and elephant massages.

And then there’s the teeth thing. Aristotle doesn’t use it as a way of showing that women are inferior to men, contrary to what is often claimed -- but it does look ridiculous.

Aristotle on teeth

Did Bertrand Russell count the teeth of any of his wives?

Robin Herbert poses this question in an eloquent defence of Aristotle written in 2014. I certainly haven’t ever counted anyone else’s teeth. I only even counted my own when I was about 10 and was wondering how my adult teeth were coming on. Aristotle, Russell, Herbert, and myself -- we all rely on other people to do that for us.

It may still be fairly argued that women’s teeth is one observation that Aristotle really should have done for himself. I think that’s fair. But only on one condition: you’re only allowed to make that argument if you first go and count the teeth of someone of the opposite sex. After all, you’re the one claiming it’s easy to check ...

Herbert’s defence of Aristotle focuses on rejecting the false idea that Aristotle put his own preconceptions ahead of any observations.

Of course Aristotle is wrong, but he is wrong because he was misinformed about the observation, not — as Russell and de Bono suggest, because he did not believe that observations were important.

With that in mind, let’s do a fact-check of all of Aristotle’s claims about teeth in History of Animals book 2 chapter 3. We don’t want to cherry-pick, do we?

1. All mammals have teeth -- TRUE
2. Camels have no teeth in the upper jaw -- FALSE
3. Some species have tusks, e.g. boars -- TRUE
4. Some species have pointed teeth, e.g. lions, panthers, and dogs; in such cases, the teeth on either jaw fit into each other -- TRUE
5. No animal has both tusks and horns -- TRUE as far as I can find out
6. In general front teeth are cutting teeth, hind teeth are molars -- TRUE
7. There are exceptions: seals have only cutting teeth -- TRUE
8. No mammals have a double row of teeth -- TRUE as far as I can find out (apart from anomalous situations, e.g. when a child’s milk teeth don’t fall out until after the permanent teeth have come through)
9. Doubt cast on Ctesias’ claim of a species called ‘martichora’ that has three rows of teeth -- TRUE that Ctesias’ claim is nonsense
10. Some species shed their teeth, including humans, horses, mules, and asses -- TRUE
11. But no species sheds molars -- FALSE
12. Doubt expressed over reports that some species shed only canines -- TRUE that caution warranted, because the report is inaccurate
13. Older dogs have blunter teeth -- TRUE
14. Most animals’ teeth darken as they age; horses are an exception, as their teeth whiten with age -- TRUE observation, but FALSE interpretation in the case of horses: horses’ permanent teeth gradually emerge from the gums and wear down at the tips, over a period of many years, meaning that there will be less discolouration
15. Canines, between the cutting teeth and molars, are wide at the base but sharp at the tip -- TRUE
16. Males have more teeth than females in humans, sheep, goats, and pigs -- FALSE
17. Humans with more teeth tend to be longer-lived; humans with gaps between teeth tend to be shorter-lived -- probably TRUE (edit: because of the economic implications of having good/bad teeth, if nothing else)
18. Wisdom teeth appear around the age of 20; but sometimes at an advanced age, in which case they are very painful -- TRUE (I haven’t been able to confirm/reject Aristotle’s claim about wisdom teeth erupting as late as age 80, but it is true that problems with wisdom teeth increase significantly with age)
19. Elephants have four molars on each side -- TRUE
20. Elephants have two tusks: large and turned upwards in the case of males, small and bent downwards in the case of females -- mostly TRUE: female elephants’ tusks do curve upwards, like males’, but often will be too short to have a significant curve
21. Elephants have teeth at birth -- TRUE

I’ll score TRUEs as 1. Number 14 gets 0.75: the observations are all accurate, but the interpretation is only half accurate. Number 20 gets 0.75 as well, since female elephants’ tusks curve upwards.

So Aristotle on teeth gets a score of 17.5 out of 21, or 83.3% correct. In my university’s marking schedule, that would get him a grade of A-. Certainly not perfect. But it could be much much worse.

The usual accusation cast at Aristotle is that he put theory, logic, and his own preconceptions ahead of any empirical evidence. Do you seen any sign of that in the list of his claims about teeth? I sure don’t. I see a whole bunch of second-hand reports of empirical observation: most accurate, some inaccurate. I don’t see any trace of a priore assumptions.

Aristotle on gravity

Robin Herbert’s essay brings up another common accusation against Aristotle: that, according to Aristotle, heavier things fall faster than light things. Many modern scientists will put it even less generously: the historian Herbert Butterfield claimed that

Aristotle’s argument [was] that the falling body moved more jubilantly every moment because it found itself nearer home.

-- H. Butterfield, The Origins of Modern Science: 1300-1800 (1959) p. 6

-- and many eminent scientists, like B. F. Skinner and Stephen Hawking, have taken this claim on faith even though it is the most bald-faced lie.

Now, it is true that Aristotle probably believed that heavier bodies fall faster than light bodies. And it is certainly true that he was interpreted that way throughout the Mediaeval period and Renaissance, until Galileo’s famous experiments. But once again, Aristotle’s problem isn’t a result of letting a priore assumptions take precedence over empirical evidence: the problem is one of confusion.

The confusion is between gravity and buoyancy. Because in buoyancy, things absolutely do accelerate differently depending on their density.

The context of Aristotle’s claims about heavy and light bodies accelerating differently, in On the sky 308a-b (4.1-2), makes it crystal clear that he is really talking about buoyancy, without realising it.

Language recognizes (a) an absolute, (b) a relative heavy and light. ... Our predecessors have not dealt at all with the absolute use of the terms, but only with the relative. I mean, they do not explain what the heavy is or what the light is, but only the relative heaviness and lightness of things possessing weight. ... By absolutely light, then, we mean that which moves upward or to the extremity, and by absolutely heavy that which moves downward or to the centre. By light or relatively light we mean that one, of two bodies endowed with weight and equal in bulk, which is exceeded by the other in the speed of its downward movement. Those of our predecessors who have entered upon this inquiry have for the most part spoken of light and heavy things only in the sense in which one of two things both endowed with weight is said to be the lighter.

-- Aristotle, On the sky 308a7-308b2, trans. J. L. Stocks

(My underlinings.) You see how the confusion arises? He believes some things like flames are ‘absolutely light’ because apparently they always go up; and he’s wrong about that, because fire is buoyant in air, not because it’s ‘absolutely light’. He hasn’t understood that light : heavy is something different from buoyant : unbuoyant. His definition of heaviness relates to buoyancy, not weight: ‘that one, of two bodies endowed with weight and equal in bulk, which is exceeded by the other in the speed of its downward movement’. This is an exact description of a relatively dense body, that is to say, an unbuoyant body.

So, once again, his problem isn’t that he hates empirical evidence. On the contrary: he has a good grasp of how buoyancy works in practice. It’s that he doesn’t realise that there are situations where even a maximally buoyant object, like a flame, won’t move upwards -- namely, in a vacuum.

If he had lived a century later, and had a chat with Archimedes (whose discovery of the Archimedes principle was more explicitly about buoyancy), Aristotle might well have worked it out. Unfortunately, he didn’t. Archimedes didn’t connect the dots, though he could have. Nor did any of Aristotle’s mediaeval followers. Instead, we had to wait for Galileo, who wasn’t interested in the context of Aristotle’s original claim. Because in context, the underlying idea was dead right: Aristotle’s mistake was in generalising from it.

In fact, it’s hard to believe Galileo even read the Aristotle passage I quoted above.

Salv. ... I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits.

Simp. His language would seem to indicate that he had tried the experiment, because he says: We see the heavier; now the word see shows that he had made the experiment.

Sagr. But I, Simplicio, who have made the test can assure you that a cannon ball weighing one or two hundred pounds, or even more, will not reach the ground by as much as a span ahead of a musket ball weighing only half a pound, provided both are dropped from a height of 200 cubits.

Salv. But even without further experiment, it is possible to prove clearly, by means of a short and conclusive argument, that a heavier body does not move more rapidly than a lighter one provided both bodies are of the same material and in short such as those mentioned by Aristotle.

-- Galileo, The Two Sciences (1638) p. 63; p. 62 in the 1914 Crew-De Salvio translation

First, Aristotle does not say ‘We see the heavier’ at any point; where he does describe his observations of buoyancy, they are strictly accurate. And second, ‘a heavier body ... [and] a lighter one provided both bodies are of the same material’ is exactly not ‘such as those mentioned by Aristotle’. What Aristotle actually says is: ‘two bodies endowed with weight and equal in bulk’ (δυοῖν ἐχόντων βάρος καὶ τὸν ὄγκον ἴσον).

Galileo, who was not a well-mannered man at the best of times, is arguing against what he imagines Aristotle said. Recent figures like Russell, Butterfield, Skinner, and Hawking are following all too closely in Galileo’s footsteps: in misrepresenting an exceptionally clear-headed researcher who was an empiricist, albeit one who made mistakes; someone whose chief flaw was that he sometimes trusted reports of observations which, in hindsight, he should not have trusted.

Put another way: taking other people’s reports on faith is a flaw shared by Aristotle, Skinner, and Hawking. If that makes Aristotle the scientist who got everything wrong, doesn’t it do the same for Stephen Hawking?