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Seán Moran investigates indoor ornithology.
It’s not a typo: I’m talking about the biological genus Corvid, rather than the COVID we’ve been enduring. At times like these, the consolations of philosophy can help to restore our peace of mind. And the corvids – the crow family – have some surprising philosophical relevance.
Photo © Seán Moran
My photograph, taken in Mumbai, shows a heart-warming daily ritual for feral dogs. This retired sailor spends most of his small pension from the Indian Navy feeding streetwise canines. They gather at the same spot every day, anticipating his arrival with chicken and fish scraps for them. But the pariah dogs (from the Hindi for ‘outcast’) are not the only beneficiaries of his kindness. Behind him, a cheeky crow is helping himself to a free lunch.
The dogs give structure and purpose to the man’s day, which begins with an early morning trip to the Mumbai docks for cheap offcuts; back home for breakfast; then off on foot to his lunchtime distribution spot. In return, the dogs receive nourishment. Being a devout Hindu, he is keen to polish up his karmic profile in his final years. He hinted to me at some unspecified naughtiness in his naval days, and his service to these outcast canines is an atonement for that. But the bird is a free rider in the transaction. Brother crow is just an opportunist.
Corvids are smart creatures. Although they have nut-sized brains, they seem to be cleverer than dogs, and second only to primates. Barbara Clump et al’s research with crows on the Pacific island of New Caledonia reports them demonstrating remarkable levels of intelligent craftsmanship (Biology Letters, 2019). And crows can recognise and remember individual human beings; so it’s probably no coincidence that our crafty corvid was ready and waiting on an Indian street. We humans, on the other hand, sometimes struggle to tell species of birds apart, let alone individual birds – which brings me to a bizarre philosophical paradox.
Whilst sitting in our homes during the lockdown, we might have amused ourselves by producing evidence for the statement ‘All crows are black’. Unexpectedly, we could do this without binoculars; without even looking out of the window. How can this be? Here’s how: observing a grey pork-pie hat, white piano keys, and a red tablecloth in my room provides real evidence that all crows are black. American philosopher Nelson Goodman called this strange practice ‘indoor ornithology’, and said that “the prospect of being able to investigate ornithological theories without going out in the rain is so attractive that we know there must be a catch in it.”
Let’s look at how the bizarre paradox arises. We can write the proposition ‘All crows are black’ as ‘If x is a crow, then x is black’. This becomes an interesting proposition when we apply the rules of logic to it – in particular, when we translate it into its logical equivalents.
We can start by simply reversing the statement to see if that means the same thing. It doesn’t. The sentence becomes: ‘If x is black, then x is a crow’. This isn’t right, since many things are black that are not crows; not even all black birds are crows.
In fact, this is an example of the well-established fallacy called ‘affirming the consequent’. In other words, universal statements such as this don’t work backwards. It is a logical fallacy to go from ‘All members of London’s Garrick Club are men’ (true, at the moment) to ‘All men are members of London’s Garrick Club’ (definitely false).
However, what about this statement: ‘If x is not black, x is not a crow’? Is that saying the same thing as ‘If x is a crow, then x is black’?
It seems to work. It captures the proposition that ‘No non-black things are crows’, and it is logically interchangeable with ‘All crows are black’. This all seems pretty innocuous – until we start gathering evidence to support the claim that all crows are black. We can either check out lots of crows to see if they really are black; or, in light of the new formulation, we can investigate a multitude of non-black things to check that they’re not crows. The two statements ‘All crows are black’ and ‘No non-black things are crows’ are logically equivalent, after all. So, as I mentioned, a white piano key, a grey hat, and a red tablecloth are all solid evidence that ‘All crows are black’ (they’re also equally good evidence that ‘All crows are pink’, but we’ll let that pass).
Convinced? Me neither. The German-American philosopher Carl Hempel first identified this puzzling outcome; hence its name: ‘Hempel’s paradox’. It’s also called ‘the raven paradox’ or ‘the paradox of confirmation’.
The Eighteenth Century Irish philosopher George Berkeley famously said that philosophers raise dust then complain that we cannot see. Hempel’s paradox has certainly generated a great deal of philosophical dust. All sorts of solutions have been proposed, including complicated Bayesian equations that some people find interesting. But perhaps it merely shows that the method of confirmation of such statements by observation is itself flawed. Counting a million black crows, then observing a white piano key, a grey hat, and a red tablecloth confirms that ‘All crows are black’; but it does not prove it. By contrast, finding a single white crow disconfirms the hypothesis. What’s more, there is no paradox of disconfirmation paralleling the paradox of confirmation. So we are on much safer ground when attempting to refute hypotheses rather than trying to confirm them. Indeed, the Austrian philosopher Karl Popper strongly advocated falsifiability as a more solid criterion for science than confirmability.
In their article ‘Black Ravens, White Shoes and Scientific Evidence’ (University of Ghent website, 2020), Erik Weber et al use the concept of falsification to solve Hempel’s paradox. Here they point out an asymmetry between confirming and refuting a hypothesis. To refute the statement about crows, we need only produce one white crow (and it doesn’t matter how we located it). But to confirm that ‘All crows are black’, we’d need to check every crow, or at least to inspect a properly random large sample of crows. This second confirmation approach is just about feasible. It doesn’t work with the logically equivalent statement ‘No non-black things are crows’, though. What on earth would we include in a random sample of non-black things to confirm that statement plausibly? So white shoes do not support the proposition ‘All crows are black’, unless they are part of an (unattainable) sufficiently large properly random sample of non-black things.
Furthermore, even with careful methods, including random sampling, we can never be sure that any universalised piece of empirical information (a.k.a. a scientific fact) is fully confirmed. So, a modest hedging of bets can be a pleasing quality of scientific statements; for example, ‘Crows appear to be black, but more research is needed to rule out the existence of non-black crows’. This is not like a politician’s hedging (which they sometimes do to avoid being tied down), but is rather a humble acknowledgement that universal scientific ‘facts’ are provisional and remain open to future refutation.
Everyday Empirical Errors
We ought to be careful about confirming our views in everyday life, too. Confirmation is a flawed strategy, as we have seen; but the all-too-human phenomenon of ‘confirmation bias’ makes it worse.
Confirmation bias is the idea that we tend to pay attention only to evidence that supports our prejudices. When the propositions in question are not about crows, hats, or shoes, but about fellow human beings this becomes a particular problem. If someone really believes that ‘All x are y’, where x is an ethnic group, or class, or gender, and y is a negative attribute, they will probably relatively easily find examples that confirm that prejudice. (What’s even sadder is that if a stereotype has been pervasively confirmed in a culture, the xs themselves might start to behave in the ways people have come to expect, further entrenching the pernicious generalisation.) And if any inconvenient counterexamples turn up, the prejudiced person will ignore them. What they should be doing is looking for evidence that refutes their preconceptions. But that doesn’t seem to be human nature. I would say that ‘All humans suffer from confirmation bias’, were it not for the inconvenient fact that this too is a statement of the form ‘All x are y’.
One cure for this tendency is to cultivate ‘sonder’. This new noun expresses the realisation that any random person has an internal life every bit as rich as our own. It is the converse of solipsism, the idea that one alone has a mind. Cultivating sonder helps us attune to the lives of those around us. At first we hardly notice an elderly man in a bustling Mumbai street; but a closer look reveals that he’s feeding stray dogs. Over time, we see that this is a daily event. Then we talk to him and hear his story. His evident individuality dispels any temptation to make statements such as ‘All Indians are x’. Sonder and a benign curiosity has made us disaggregate our casual generalisations about people.
Perhaps this attitude can be extended to other living things. I described the crow in my photograph as ‘cheeky’. Maybe his sister is more diffident, and he has a mad uncle who will do anything to entertain his nephews. Not all crows are the same, and I’d like to know more. While strolling the streets of an Irish town, I once tried to engage passing crows in small-talk, using an Acme™ crow call. Some crows became curious and deviated from their flight-paths, but none took up my conversational gambit. My partner, however, practised social distancing – long before it became a thing.
Just around the corner from where I took this photograph, I saw a rat carrying a coffee cup, complete with lid. From the foam around her nose, I would say it was either a latte or a cappuccino. This behaviour is probably a quirky trait of that individual rat. Not all rats are the same. My stories about crafty corvids and coffee-swilling rats might however attract accusations of ‘anthropomorphism’ – wrongly imputing human motivations to non-human animals. But we share so much DNA with fellow creatures that some similarities are plausible.
And of course, if anyone brings up Hempel’s paradox, we can casually point out that white (albino) crows do exist. And if they call that a red herring, we can reply that red herrings were once thought to confirm the discredited theory that all crows are black.
© Dr Seán Moran 2020
Seán Moran teaches postgraduate students in Ireland, and is professor of philosophy at a university in the Punjab.