an autodidact meets a dilettante…

‘Rise above yourself and grasp the world’ Archimedes – attribution

Posts Tagged ‘reason

What is inference?

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Don’t believe everything you read

What are you inferring?

So am I to infer from this you’re not interested?

What does inferring actually mean? What is it to ‘infer’? Does it require language? Can the birds and the bees do it? We traditionally associate inference with philosophy, which talks of deductive inference. For example, here’s a quote from Blackwell’s dictionary of cognitive science:

Inferences are made when a person (or machine) goes beyond available evidence to form a conclusion. With a deductive inference, this conclusion always follows the stated premises. In other words, if the premises are true, then the conclusion is valid. Studies of human efficiency in deductive inference involves conditional reasoning problems which follow the “if A, then B” format.

So according to this definition, only people, and machines constructed by people, can do it, deductively or otherwise. However, psychologists have pretty thoroughly demolished this view in recent years. In ‘Understanding Inference’, section 2 of their book The enigma of reason, cognitive psychologists Hugo Mercier and Dan Sperber explore our developing view of the concept.

Inference is largely based on experience. Think of Pavlov and his dogs. In his famous experiment he created an inferential association in the dogs’ minds between a bell and dinner. Hearing the bell thus set off salivation in expectation of food. The bell didn’t cause the salivation (or it wasn’t the ultimate cause), the connection was in the mind of the dog. The hearing of the bell set off a basic thought process which brought on the salivation. The dog inferred from experience, manipulated by the experimenter, that food was coming.

Mercier and Sperber approvingly quote David Hume’s common sense ideas about inference and its widespread application. Inference, he recognised, was a much more basic and universal tool than reason, and it was a necessary part of the toolkit of any sentient being. ‘Animals’, he wrote, ‘are not guided in these inferences by reasoning: Neither are children: Neither are the generality of mankind, in their ordinary actions and conclusions. Neither are philosophers themselves, who, in all the active parts of life, are, in the main, the same with the vulgar…. Nature must have provided some other principle, of more ready, and more general use and application; nor can an operation of such immense consequence in life, as that of inferring effects from causes, be trusted to the uncertain process of reasoning and argumentation’.

This is a lovely example of Humean skepticism, which flies in the face of arid logicalism, and recognises that the largely unconscious process of inference, which we would now recognise as a product of evolution, a basic survival mechanism, is more reliable in everyday life than the most brilliantly constructed logical systems.

The point is that we make inferences more or less constantly, and mostly unconsciously. The split-second decisions made in sport, for example, are all made, if not unconsciously, then with an automaticity not attributable to reason. And most of our life is lived with a similar lack of deep reflection, from inference to inference, like every other animal. Inference, then, to quote Mercier and Sperber’s gloss on Hume, is simply ‘the extraction of new information from information already available, whatever the process’. It’s what helps us slip the defender and score a goal in soccer, or prompts us to check the batteries when the remote stops working, or moves us to look forward to break-time when we smell coffee. It’s also what wags your dog’s tail when she hears familiar footsteps approaching the house.

There’s a lot more to be said, of course…

Written by stewart henderson

December 3, 2019 at 9:53 pm

nothing so simple? the gambler’s fallacy

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Humans are capable of reasoning, but not always or often very well. Daniel Kahneman’s famous book Thinking, fast and slow provides us with many examples, and not being much of a clear thinker myself, where probability and all that Bayesian stuff is concerned, I’ll start with something really simple before ascending, one day, to the simply simple. And not being much of a gambler, I’d never heard of the gambler’s fallacy before. It appears to be a simple and obvious fallacy, but I’m sure I can succeed in making it more confusing than it should be.

The fallacy involves believing that what has occurred before might dictate what happens in the future, in a particular context. It’s best explained by the tossing of a coin. With a fair coin, the probability of it landing tails up, on any toss, is .5, given that, in probability language, absolute certainty is given a value of 1, and no possibility at all is given 0. The key here is what I’ve italicised – the fallacy lies in believing that the coin, as if it’s a thinking being, has an interest in maintaining a result, over many tosses, of 50% tails – so that if results skew towards zero, say after 6 heads results in a row, the probability of the next toss being tails will rise above .5. 

Put another way: assuming a fair coin, the probability of it landing heads on one toss is .5. That should mean that over time, with x number of tosses, assuming x to be a very large number, the result for a heads should approach 50%. So it would seem quite reasonable, if you were keeping count, to bet on a result that brings the average closer to 50%. That’s without imagining that the coin wants to get to 50%. It just should, shouldn’t it?

The clear answer is no. There can be no influence from the past on any new coin toss. How can there be? That would be truly weird if you think about it. The overall results may approach 50%, according to the law of large numbers, but that’s independent of particular tosses. If you look at it this way, creating a dependency, you decide to bet on a pair of tosses. It could be HH, TT, HT or TH. Those are the only four options and the probability of each of them is .25 (i.e .5 x .5). So you might think that, after two heads in a row, it would be wise to bet on tails. But this bet would still have a .5 probability of succeeding, and the result HHT, taken together, would be .5 x .5 x .5, which is .125 or one eighth, the same as all the other seven results of three coin tosses. The probability doesn’t change before each toss, no matter the result of the previous toss. 

So far, so clear, but it would be hard not to be influenced into betting against a run continuing. That’s not irrational, is it? But nor is it rational, considering there’s alway a 50/50 chance with each toss. It’s just a bet. And yet… I’m reminded of Swann in a A la recherche du temps perdu, as my mind clouds over…

Written by stewart henderson

November 17, 2019 at 2:19 pm

Posted in gambling, probability

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