Friday, 26 July 2019

The Gettier Problem, Relativism, and Bayesianism

A naive definition of knowledge is "justified true belief". To have knowledge, you must believe something. That belief must be true otherwise it is not knowledge. And it must be justified. If your beliefs are true by accident, it is not knowledge.

Edmund Gettier came up with a thought-experiment to criticise this definition. You look through a window and you see your friend Bob sitting with his back to you in an arm-chair. You believe "Bob is in the room". But in fact the figure in the armchair is an effigy, not Bob. However, Bob is in the room, hiding behind a curtain. Your belief is justified and true, but it does not appear to be knowledge. It is true by luck. The justification and the truth are not connected.

The probabilistic view sidesteps the Gettier problem. Beliefs are probabilistic. You see the effigy and you increase your subjective probability that Bob is in the room. But you know you could be wrong. You also believe that the figure in the chair is Bob. You could make bets about it. As it happens, you win the former bet but lose the latter bet. Tant pis.

Relativism is the bizarre view that truths are relative to people, that there is no objective reality regarding certain issues. For example, the belief that a Bob is in the room is true for one person but not for another. This view is rarely thought through by the few who hold it, but probabilism sidesteps it, by clarifying that two people can hold different beliefs based on the evidence they have seen and their priors, but beliefs must be testable by objective reality to qualify as beliefs. Under probabilism, it is meaningless to have a belief you cannot bet on - you need some way of deciding the bet!

Sunday, 16 June 2019

Laplace's rule of thumb

Laplace's rule of succession is only a rule of thumb. The idea is that since probabilities cannot be zero or one, if one has seen a hundred white swans and no black swans, one should not assign a probability of 100/100=100%. Instead, one assigns 100/101 = 99.01%. n/n+1, not n/n.

This is more sensible than assigning 100% because it is open to the possibility of error, and makes it possible to change your mind. If your prior probability is zero or one, no amount of evidence can change your mind according to Bayes' theorem.

However, in the real world, events are rarely exclusive. There are many alternatives to a hypothesis. We should not assign equal probability to the alternatives. For example, if you had only seen five white swans, there might exist red, green, blue, orange or black swans. According to a naive version of Laplace's rule, we would expect a random swan to be white with only 50% probability, assigning 10% each to red, green, blue, orange and black.

Clearly, a more sensible prediction for the colour of a random adult swan in Europe is more like 99% white, 1% black and close to zero for red, green, blue and orange, even if you have only seen fifty swans in your lifetime.

Popper versus Bayes

Popper thought he could turn inductive science into a deductive process. We only see white swans, so we form a theory that all swans are white, but we might turn out to be wrong. The theory can never be proved. Aha, says Popper, but it can be disproved. If we see a single black swan, that disproves the theory.

The problem is that one can never be sure of evidence. Perhaps the evidence is wrong and the theory is correct. One man's modus ponens is another man's modus tollens. If I receive reports of black swans from Australia, maybe the reports are wrong, for a variety of reasons. Maybe all swans I have ever seen are in disguise. Maybe I am in the Matrix.

Another criticism of Popper's method is that his deductive claims are not very useful. If it is true that "not all swans are white", this does not help me make predictions. Such a statement says nothing about the probability that a given swan is black of white.

David Stove showed that criticisms of inductivism, that it doesn't live up to deductive standards, are misguided. They beg the question by assuming "deductivism", that only deductive arguments are valid. In fact, inductive arguments can be useful, with evidence supporting a conclusion despite not logically entailing it. Perhaps inductivism should be renamed "probabilism", or "Bayesianism".

The correct epistemology is Bayesian: knowledge is probabilistic. A correct epistemology covers everything: science is a subset of it. You don't have different epistemologies for different things. Therefore the practice of science should be probabilistic. What makes science special, then? It involves techniques of "epistemic hygiene" to increase our confidence in our beliefs. By carefully designing experiments, and using good statistics, we can increase the probability of a hypothesis by reducing the probability of alternative hypotheses.

Bayesianism makes one hyper-aware of the infinite number of hypotheses.

Tuesday, 28 May 2019

Group selection

I have written about group selection before.

The orthodox Darwinian position on group selection is that it does not happen. If an individual makes sacrifices for his group (a collection of people who are not sufficiently closely related), his altruistic genes will suffer and the non-altruistic genes of the group will flourish.

However, researchers like Michael Woodley, Ed Dutton, Bruce Charlton have written about the consequences of group selection and their benefits. For example, Charlton and Dutton in "The Genius Famine" argue that the genius is an example of group selection. Geniuses are anti-social figures whose inventions benefit the group, but not themselves. Geniuses typically do not reproduce. 

This is Bayesian evidence for the existence of group selection. Perhaps the logical argument against group selection is flawed.

Tuesday, 12 March 2019


  • Minimal marginal cost
  • Minimal financial risk - you can't print too many
  • Lightweight. You can carry a thousand books in your pocket for less weight than a paperback
  • Harder for people to peruse your bookshelf, or see what you are reading. Less chance for serendipitous discoveries
  • Can't lend them to other people, no second-hand market (bad for readers, good for booksellers)
  • Piracy much easier (good for readers, bad for booksellers)
  • Authors don't need a publisher, can easily self-publish through Amazon. Good for authors, bad for publishers, risk of Amazon establishing a monopoly (bad for authors)

Saturday, 9 March 2019

How is the left responding to new genetic discoveries?

We have long had circumstantial evidence that racial differences in intelligence are partly genetic. We know that the races differ in average intelligence, and we know that intra-race differences in intelligence are partly genetic, partly non-shared environment (random effects, measurement error), therefore it is likely that the same applies to inter-race differences.

No one denies that Tibetan adaptations to high altitude are entirely genetic, not cultural, and there are many other race-specific traits which are uncontroversially attributed solely to genetics. But when it comes to intelligence, the obvious inference is not drawn.

Genome-wide association studies are finally identifying specific genes for traits. We can now make accurate predictions about someone's traits from their genome. As individual genes are identified, and these genes are shown to have different frequencies across the races, how will the left react? How is the left reacting?

Denial will continue for a long time. We've had evidence for a long time; why should one more piece of evidence make a difference?

To some extent it doesn't matter. Philosophical obfuscation about the concept of race won't work any more. Ordinary people will be able to see the validity of the science with their own eyes. The leftist obfuscation will be ignored. Ordinary people already want to choose high-IQ, tall, good-looking sperm and egg donors; they understand the truth on an implicit level at least.

Eventually the left will have to adapt its theories to the reality of human genetics. I expect people will realise that "meritocracy" means "genetic advantages", and egalitarianism will attempt to equalise these, either with monetary redistribution, or genetic engineering (state-subsidised embryo selection for the poor, banning embryo selection for the rich, etc).

The Multiplier Effect: wrong in so many ways

The "Multiplier Effect" story goes like this: The state increases spending by £100. The person they pay this to saves 10% and spends the remaining £90. The next person saves 10% of that and spends the rest, and so on. An initial increase in state spending of £100 leads to an increase in GDP of £1000.

This is nonsense.

If it were true, all money would end up "saved" in vaults, and there would be no money circulating. In reality, money continues circulating indefinitely. Money that is saved bids up the price of money, causing other savers to withdraw their savings and spend. For every young person saving, there is an old person spending. There will be an equilibrium where a certain proportion of money is saved at any given time.

An alternative to saving is investment. Money that is spent on investment continues circulating.

The multiplier effect argument applies to all spending, not just government spending. Increases in state spending have to come from somewhere, whether it is taxation, borrowing or money creation. All three decrease purchasing power (i.e. spending) elsewhere.

A clearer way to look at things is to ignore money. An increase in government spending reallocates resources to the government. It does not increase the amount of resources available. It does not actually increase GDP.

So the above "multiplier effect" story is nonsense.

The real multiplier effect concerns productive, profitable investment. If an investment is profitable, it takes resources as input, and outputs a larger amount of resources. The multiplier factor is a measure of how profitable it is. Government spending, like private spending, only has a multiplier effect on GDP if goes into a successful, productive, profitable investment. If it goes into a foolish, loss-making investment project, or into consumption and spending, it has a demultiplier effect.