More thoughts on problem solving

Elliot Temple asked some questions about my postmodernism blog post:

 “You keep doing this until you find some guesses with no known problems.”

what if that takes 500 years?

Under some circumstances you might be willing to wait 500 years to solve a problem. For example, if there is a star 250 light years away and you want to send a probe there to gather some data and send it back to you, then you would have to wait 500 years to get the results.

That sort of problem doesn’t come up in the lives of most people at present for various reasons. If you’ve been working on a problem for a longer time than you expected without solving it, then you may be doing something wrong in your strategy for solving it. The way to deal with this is to ask for criticism of what you’re doing and why. Sometimes another person will see a problem with what you’re doing that you don’t see. You could also ask for criticism before starting so you don’t waste time on something when somebody else knows it won’t work.

what if there’s a disagreement (in your own mind or with another person, doesn’t matter) about whether an answer to a criticism works?

If somebody disagrees with the answer, that’s a criticism of the answer. The critic has some objection you haven’t addressed. You should come up with a new variant of the idea that meets any objection the critic explains, or find a better idea that isn’t a close variant. If the critic doesn’t explain his objection in a way you understand that is a criticism of the objection. You can have an open invitation for the critic to continue trying to explain his objection as long as he is interested in doing so, but you needn’t change your position.

Postmodernism debate

Stefan Molyneux and Thaddeus Russell had a debate about postmodernism. The meat of the debate starts at about 25 minutes. Molyneux and Russell have a false idea in common that results in them making bad arguments. I’ll explain enough of their positions to explain their mistakes and point out an alternative that doesn’t have any known problems.

Molyneux is trying to defend the idea that reality is objective and we can know stuff about it. He ends up talking about whether we know for certain that stuff falls down instead of up. He calls this sort of statement “base reality”. He distinguishes this base reality sharply from theories about what is causing the base reality. Molyneux also sez scientists don’t completely repudiate previous scientific theories.

Russell’s position is that any idea can be reinterpreted. So the idea that things fall down depends on your interpretation of the word “down”. For example, if you’re in Australia, “down” is a different direction from “down” in the UK. His least bad argument is that knowledge changes over time, including scientific knowledge. For example, astronomical observations of distant galaxies are not compatible with previous cosmological theories, so cosmologists have been scrambling for about 20 years to come up with better ideas.

Russell also states that people interpret ideas using their values. In particular, scientists use the scientific method to bolster their values. The scientists do observations and draw conclusions from them to label some people as mentally ill. Molyneux’s reply to this sort of point is that scientists are not using the scientific method to do this. Neither of them bother to explain how they imagine science works.

At one point at about 68 minutes Russell states that the world looks flat and Molyneux sez that’s just an interpretation. They’re beginning to sound kinda similar at this point. What’s going on?

Justificationism

Russell and Molyneux share an idea: they both think that the standard by which ideas should be judged is whether they can be shown to be true or probably true or good. This is a common idea in philosophy. The process that allegedly shows an idea is true or probably true or good or whatever is called justification. The position that justification is desirable or necessary in epistemology is called justificationism.

Justificationism sounds superficially reasonable, but it leads to unsolvable problems. Any argument uses assumptions and rules that supposedly lead from those assumptions to conclusions. If the assumptions are true, and the rules are correct, then the conclusion is true. People then assume that we can proceed by showing that the assumptions and rules are correct, so our ideas are correct.

But if the standard is that ideas have to be justified, then we have to show the assumptions are true and the rules of inference are correct. You might imagine that you could do this with another argument. But that argument uses assumptions and rules, so what do you do next? Do you make another argument: argument 3? What about the assumptions and rules of argument 3? If you want to use arguments for justification, you have to make an infinite series of arguments, which is impossible.

Another way of trying to do justification is to say that some ideas are obviously true, e.g. – Molyneux’s ideas about base reality. You then justify your ideas starting with the obviously true ideas. This means that as far as those ideas are concerned you have given up on argument. This means those ideas can’t be discussed or explained in any way. But ideas you can’t discuss or explain are useless. To use an idea you need an explanation of how it’s connected to other ideas. For example, to understand what you see you need to understand how your eyes work, which involves the laws of optics. And if there is an explanation, it is not justified. So the basic sense experience or whatever you want to call it is either fallible or useless.

These problems lead many people to reject that objective knowledge is possible. Since no knowledge measures up to justificationist standards, none of our knowledge is objective. And if we can’t have objective knowledge of reality, then why should we even think that reality is objective?

Critical rationalism

The only known way to deal with this problem is to reject the idea that justification is required for knowledge. We should replace justification with a different standard: you can separate ideas that should be rejected by criticism. This was explained by Karl Popper who called this idea critical rationalism (CR), see e.g. – “On the sources of knowledge and of ignorance” in Conjectures and Refutations and Chapter I of Realism and the Aim of Science. Other people have improved on Popper’s ideas, such as David Deutsch in his books The Fabric of Reality (Chapters 1,3,7) and The Beginning of Infinity  (Chapters 1,2,10,12) and Elliot Temple: Fallible Ideas and Yes No Philosophy.

Let’s go back to looking at arguments and consider what we can do with them, other than justification. Suppose that you make an argument that if some premise A is true and some set of rules B is correct, then the conclusion C is true. Then you make another argument with premise C, rules D and conclusion E. And suppose that you make another argument that E and C can’t both be true. And suppose you think that all of these arguments are correct. They can’t all be correct, so you should discard one of your arguments. Note that you didn’t have to justify anything to do this. All you have to do is say that they are all true and you have a problem. You don’t have to show that they’re true. You can just guess.

What can you do about a problem? You can guess solutions and then look for problems with the guesses. You keep doing this until you find some guesses with no known problems. This process just requires guesses and criticisms, not justification.

CR requires that you should treat ideas by the objective standard that they should answer criticisms. Ideas that answer criticisms are knowledge. Ideas that fail to do this are not knowledge.

The parts of knowledge that are commonly called science use experimental and observational testing as one of the kinds of criticism used to eliminate bad ideas. People who claim to justify their positions using science have fundamentally misunderstood science and the theory of knowledge more generally.

Russell and Molyneux don’t resolve the issue of the role of values in science and knowledge more generally. Values can play a role in the selection of problems. For example, people do a lot of work on aerodynamics partly to make air travel safer (they value people not being hurt or killed) and more efficient (they value fuel and want to save it). But values aren’t exempt from criticism, so they are not the source of scientific knowledge or any other kind of knowledge.

If you’d like to know more about this, you can read some of the material linked above and discuss it as you go along at the Fallible Ideas group.

Yudkowsky on Popper

In Rationality From AI to Zombies Eliezer Yudkowsky writes some stuff about Popper. He does a bad job of discussing Popper’s ideas. On pp. 820-821 he writes:

Previously, the most popular philosophy of science was probably Karl Popper’s falsificationism—this is the old philosophy that the Bayesian revolution is currently dethroning. Karl Popper’s idea that theories can be definitely falsified, but never definitely confirmed, is yet another special case of the Bayesian rules; if P(X|A) ≈ 1—if the theory makes a definite prediction—then observing ¬X very strongly falsifies A. On the other hand, if P(X|A) ≈ 1, and we observe X, this doesn’t definitely confirm the theory; there might be some other condition B such that P (X|B) ≈ 1, in which case observing X doesn’t favor A over B. For observing X to definitely confirm A, we would have to know, not that P(X|A) ≈ 1, but that P(X|¬A) ≈ 0, which is something that we can’t know because we can’t range over all possible alternative explanations. For example, when Einstein’s theory of General Relativity toppled Newton’s incredibly well-confirmed theory of gravity, it turned out that all of Newton’s predictions were just a special case of Einstein’s predictions.

Popper didn’t call his position falsificationism. He explicitly rejected that label, see the introduction to ‘Realism and the aim of science’.

Popper called his position critical rationalism. Popper said that all knowledge creation proceeds by guessing and criticism. First, you spot a problem with your current ideas, then you guess solutions to the problem, then you criticise the guesses.

Falsifying an idea by experimental testing is just one of the possible ways of criticising an idea: it’s not central to Popper’s ideas.

You can even formalize Popper’s philosophy mathematically. The likelihood ratio for X, the quantity P(X|A)/P(X|¬A), determines how much observing X slides the probability for A; the likelihood ratio is what says how strong X is as evidence. Well, in your theory A, you can predict X with probability 1, if you like; but you can’t control the denominator of the likelihood ratio, P(X|¬A)—there will always be some alternative theories that also predict X, and while we go with the simplest theory that fits the current evidence, you may someday encounter some evidence that an alternative theory predicts but your theory does not.

It is possible to formalise reasoning, but not using the rules of probability. Reasoning is a form of information processing: you use information and the knowledge you already have to find new and better ideas. Any physically possible information processing can be simulated by a computer. This simulation can simulate both the results and the process by which they were created. So reasoning can be formalised. Nobody knows how to do this, but it is possible.

Back to Yudowsky:

That’s the hidden gotcha that toppled Newton’s theory of gravity. So there’s a limit on how much mileage you can get from successful predictions; there’s a limit on how high the likelihood ratio goes for confirmatory evidence.

The idea that Newton’s theory was replaced cuz it was incompatible with evidence is misleading. Newton’s theory of gravity got into trouble because it is incompatible with the special theory of relativity.

One problem is that Newton’s theory implies that changes in the mass distribution instantly change gravitational forces everywhere. Special relativity sez that the maximum speed at which one system can influence another is the speed of light.

Another problem is that special relativity sez that mass and energy are tied together as parts of a single conserved quantity. So what should take the place of mass in a relativistic theory of gravitation?

Einstein thought about how to solve those problems and others and came up with the general theory of relativity. Newton’s theory of gravity was replaced because it was a bad explanation. The experimental evidence that Newton’s theory was wrong was mostly found after general relativity was invented. Until then, nobody knew where to look for experimental evidence against Newton’s theory.

There’s a lot of historical discussion of the origin of general relativity, e.g. – ‘The genesis of general relativity’ vols 1-4 edited by Jurgen Renn (I’d link to it on Amazon but it’s super expensive). If Yudkowsky is going to use historical examples, he should look them up.

On the other hand, if you encounter some piece of evidence Y that is definitely not predicted by your theory, this is enormously strong evidence against your theory. If P (Y |A) is infinitesimal, then the likelihood ratio will also be infinitesimal. For example, if P (Y |A) is 0.0001%, and P (Y |¬A) is 1%, then the likelihood ratio P (Y |A)/P (Y |¬A) will be 1:10,000. at’s −40 decibels of evidence! Or, flipping the likelihood ratio, if P (Y |A) is very small, then P (Y |¬A)/P (Y |A) will be very large, meaning that observing Y greatly favors ¬A over A. Falsification is much stronger than confirmation. It is is a consequence of the earlier point that very strong evidence is not the product of a very high probability that A leads to X, but the product of a very low probability that not-A could have led to X. This is the precise Bayesian rule that underlies the heuristic value of Popper’s falsificationism.

Similarly, Popper’s dictum that an idea must be falsifiable can be interpreted as a manifestation of the Bayesian conservation-of-probability rule; if a result X is positive evidence for the theory, then the result ¬X would have disconfirmed the theory to some extent. If you try to interpret both X and ¬X as “confirming” the theory, the Bayesian rules say this is impossible! To increase the probability of a theory you must expose it to tests that can potentially decrease its probability; this is not just a rule for detecting would-be cheaters in the social process of science, but a consequence of Bayesian probability theory. On the other hand, Popper’s idea that there is only falsification and no such thing as confirmation turns out to be incorrect. Bayes’s theorem shows that falsification is very strong evidence compared to confirmation, but falsification is still probabilistic in nature; it is not governed by fundamentally different rules from confirmation, as Popper argued.

 

Popper made many arguments against the idea of inductive probability, see Realism and the aim of science, part II, chapter II. For example, in Section 13 of that chapter Popper points out that we must have an explanation of what counts as repeating the same experiment to do induction, but induction provides us with no means to get that explanation. Yudkowksy shows no sign of being aware of any of these arguments.

The only Popper book Yudkowsky cites is LScD and he doesn’t seem to have understood it.

The repugnant conclusion is garbage

I recently watched a YouTube video on the repugnant conclusion (TRC). The creator of the video explains TRC, sez he thinks it’s wrong but doesn’t explain why. Explaining a bad idea, but not the criticisms of that bad idea, is dumb. It gives the impression that there are no actual arguments against the bad idea. Even explaining a good idea, but not attempted criticisms, is often misleading. A person will think the good idea is not so good cuz you don’t address common criticisms of it. So I’m going to explain TRC and why it’s wrong.

TRC sez that there is a quantity called utility that measures how happy you are. You can add up utility from a group of people and find the total utility of those people. Higher total utility is better than lower total utility. Suppose group A consists of a lot of people with low but positive utility, then their total utility might be 500 say. Group B consists of a smaller number of people who are super happy and their utility only adds up to 450. So if you can choose between a policy that makes society into group A instead of group B you should choose the group A policy.

TRC is a thing that academic moral philosophers write about and take seriously. Every step and assumption in the TRC argument is wrong.

There is no numerical quantity called utility that measures how happy you are. Nor can you take the utility of different people and add it up. There is a set of sensations and ideas that people commonly call happiness. A person might prefer one state of happiness to another state of happiness. For example, a person might prefer the happiness he experiences when he has sex to the happiness he experiences when he eats pizza. Given a chance to have sex or to eat pizza he might choose the sex instead of the pizza. But there is no single number such that having sex has a larger number than eating pizza, and the number captures all of the differences relevant to that decision. Having sex and eating pizza solve different problems in that person’s life. So how can you add them up even for a single person? And for Pete having sex might solve a different problem than it solves for Jim. For example, Pete might value sex cuz he likes the sexual attention of one particular person. But Jim might just want his genitals stimulated without caring much who does it because he values the resulting orgasm. How are we supposed to add up or subtract Jim’s problem and Pete’s problem. They are qualitatively different.

You can add up quantities of goods like money or oranges or whatever. You can prefer 7 oranges to 3 apples in the sense that you would give up 3 apples to get 7 oranges. Perhaps you would give up 3 apples for 5 oranges but you wouldn’t give up 3 apples for 4 oranges. But that doesn’t mean there is some quantity called utility such that oranges have less than 3/4 times as much utility as apples. There is a well-developed theory about how to understand the quantities of stuff that people will exchange: it’s called the subjective theory of value.

Since there is no quantity called utility that could be added up to compare different populations, the thought experiment imagined in TRC is impossible.

There is another problem with TRC. It presupposes, wrongly, that you can and should make decisions about how many people there are and how happy they are. There is a word for this kind of behaviour: tyranny. You can’t decide how many people there are and what they think and feel. A tyrant can try to approximate such control through threats of physical violence, e.g. – Nazi Germany and the Soviet Union. A tyrant can threaten to use murder, torture, theft etc. against people who don’t follow the ideas you lay down about what they should say, and write and who they should fuck. To the extent that the tyrant is successful at doing this, everyone is stuck on with the same stupid ideas as the tyrant. This is grossly immoral and irrational since it prevents bad ideas from being criticised and replaced by better ideas.

Academic moral philosophers haven’t reacted to TRC by explaining why it is evil and stupid. They don’t know about economics, and they don’t think seriously about morality. They just like to say stuff that annoys and disturbs other people. They are worthless except as a negative example.

Popper vs Conventionalism

Somebody called Noah Smith posted a tweet claiming that falsification is impossible cuz you can change your theory to get around a falsification. He cites a blog post, which never quotes Popper and gives no account of his ideas. Not surprisingly, both the post and the tweet quoting it are wrong on this issue.

Popper addressed this criticism in his first book The Logic of Scientific Discovery: some quotes are given below.

Chapter 1 Section 6

A third objection may seem more serious. It might be said that even if the asymmetry is admitted, it is still impossible, for various reasons, that any theoretical system should ever be conclusively falsified. For it is always possible to find some way of evading falsification, for example by introducing ad hoc an auxiliary hypothesis, or by changing ad hoc a definition. It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsifying experience whatsoever. Admittedly, scientists do not usually proceed in this way, but logically such procedure is possible; and this fact, it might be claimed, makes the logical value of my proposed criterion of demarcation dubious, to say the least.
I must admit the justice of this criticism; but I need not therefore withdraw my proposal to adopt falsifiability as a criterion of demarcation. For I am going to propose (in sections 20 f.) that the empirical method shall be characterized as a method that excludes precisely those ways of evading falsification which, as my imaginary critic rightly insists, are logically possible. According to my proposal, what characterizes the empirical method is its manner of exposing to falsification, in every conceivable way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival.

Chapter 4 Section 19

Thus my conflict with the conventionalists is not one that can be ultimately settled merely by a detached theoretical discussion. And yet it is possible I think to extract from the conventionalist mode of thought certain interesting arguments against my criterion of demarcation; for instance the following. I admit, a conventionalist might say, that the theoretical systems of the natural sciences are not verifiable, but I assert that they are not falsifiable either. For there is always the possibility of ‘. . . attaining, for any chosen axiomatic system, what is called its “correspondence with reality”’;3 and this can be done in a number of ways (some of which have been suggested above). Thus we may introduce ad hoc hypotheses. Or we may modify the so-called ‘ostensive definitions’ (or the ‘explicit definitions’ which may replace them as shown in section 17). Or we may adopt a sceptical attitude as to the reliability of the experimenter whose observations, which threaten our system, we may exclude from science on the ground that they are insufficiently supported, unscientific, or not objective, or even on the ground that the experimenter was a liar. (This is the sort of attitude which the physicist may sometimes quite rightly adopt towards alleged occult phenomena.) In the last resort we can always cast doubt on the acumen of the theoretician (for example if he does not believe, as does Dingler, that the theory of electricity will one day be derived from Newton’s theory of gravitation).

Thus, according to the conventionalist view, it is not possible to divide systems of theories into falsifiable and non-falsifiable ones; or rather, such a distinction will be ambiguous. As a consequence, our criterion of falsifiability must turn out to be useless as a criterion of demarcation.

Chapter 4, Section 20:

These objections of an imaginary conventionalist seem to me incontestable, just like the conventionalist philosophy itself. I admit that my criterion of falsifiability does not lead to an unambiguous classification. Indeed, it is impossible to decide, by analysing its logical form, whether a system of statements is a conventional system of irrefutable implicit definitions, or whether it is a system which is empirical in my sense; that is, a refutable system. Yet this only shows that my criterion of demarcation cannot be applied immediately to a system of statements—a fact I have already pointed out in sections 9 and 11. The question whether a given system should as such be regarded as a conventionalist or an empirical one is therefore misconceived. Only with reference to the methods applied to a theoretical system is it at all possible to ask whether we are dealing with a conventionalist or an empirical theory. The only way to avoid conventionalism is by taking a decision: the decision not to apply its methods. We decide that if our system is threatened we will never save it by any kind of conventionalist stratagem. Thus we shall guard against exploiting the ever open possibility just mentioned of ‘. . . attaining for any chosen . . . system what is called its “correspondence with reality” ’.

In order to formulate methodological rules which prevent the adoption of conventionalist stratagems, we should have to acquaint ourselves with the various forms these stratagems may take, so as to meet each with the appropriate anti-conventionalist counter-move. Moreover we should agree that, whenever we find that a system has been rescued by a conventionalist stratagem, we shall test it afresh, and reject it, as circumstances may require.

The anti-capitalist mentality in action

There is an anti-capitalist Tumblr post by a person working in a restaurant being quoted on Twitter by various people. The person in question makes $12 an hour. This person claims the restaurant makes $30,000 per week. Then the person writes:

i’m not going to go into details, but after the costs of production (payroll for employees, rent for the building, maintenance, and wholesale food purchasing) are accounted for, the restaurant makes an estimated profit of $20,000 per week.

It is very unlikely that those are the only costs of running the restaurant. Other costs will include taxes, spoilage of raw ingredients, employee theft, the cost of looking for and hiring staff, the cost of marketing, the cost of borrowing money to keep the place running, the cost of inspections, electricity, gas, phones, laundry for staff clothing and a load of other stuff I don’t know about. Also, even if the profit from some of the owner’s restaurants is high he may have made other attempts to open restaurants, failed and lost a load of money on them: restaurants have a high failure rate.

More speculation follows:

the owner purchases rice at a very low bulk price of about 25 cents a pound. i cook the rice, and within a few minutes, that pound of rice is suddenly worth about $30. the owner did not create this value, i did. the owner simply provided the initial capital investment required to start the process.

The owner of the restaurant picked the location, which is very important to how much money the restaurant makes. The owner may also have decided what kind of food should be cooked, e.g. – Indian, Chinese, Italian, Vietnamese etc. He may decide what kind of clothing waiters and other staff wear, which affects what kind of customers will want to go to the restaurant. He may have made a load of other decisions too. And the owner has the option of reconsidering those decisions in the light of changes of circumstances. All of those decisions contributed to what people are willing to pay for that food.

The post writer continues:

the owner of my restaurant pays me the current minimum wage of my area, because to them, i am not a person. i am an investment. i am an asset. i am a means to create more money.

The owner of the restaurant isn’t treating his employee as an asset. If the owner was doing that he would lock the employee up at night with his property. Also, the owner doesn’t offer employment to the oven at the restaurant. He does offer his employee a job on certain terms and the employee could decline those terms. The employee accepted those terms. If the employee accepted terms he doesn’t like that’s not the employer’s fault.

One final quote:

when you are paid minimum wage, the message your boss is sending you is this: “legally, if i could pay you less, i would.”

That’s not true. It’s impossible for an employer to tell how much money an employee will make before hiring him. The employer has to guess and hope he doesn’t screw up too badly. He can sometimes criticise his guesses in advance by looking at the employee’s past record and so on, but people change and some people have no past record of employment. Maybe he would like to pay some people more and some people less but doesn’t want to put up with workplace politics that might result. Also, the employer has stuff to do apart from sit around thinking about his employees. After all, an employee is an adult human who is capable of standing up for his own value, or ought to be able to do that. And the employer isn’t responsible for fixing his employees.

The author of this Tumblr post has overreached: I know nothing about restaurants but found loads of stuff by thinking and doing Google searches that the post writer didn’t mention. The post writer only considers the parts of the restaurant business he wants to see. He likes being angry and having a high opinion of himself. He’s not doing well by his own standards and he prefers to blame other people rather than fix his problems. This is a common reason for anti-capitalism, as pointed out by Mises in The Anti-capitalist Mentality.

The writer of the post could learn stuff about salary negotiation if he wants more money. Part of successful salary negotiation involves being good at your job and understanding the market. He could learn more about how to run a restaurant and run his own restaurant. Or he could learn about some other occupation that would please him more or make him more money. Writing Tumblr posts about how his boss is screwing him won’t do him any good.

Problems with Bayesian epistemology

The hotness in philosophy of science is currently Bayesian epistemology. The idea behind Bayesian epistemology involves Bayes’ theorem, which sez that

P(a | b) = \frac{P(b | a) P(a)}{P(b)},

where P(a | b) is the probability of a given b.

Philosophers who practice Bayesian epistemology like to say that b is some evidence e and a is a hypothesis h and write:

P(h | e) = \frac{P(e | h) P(h)}{P(e)}.

Philosophers then like to imagine that it is possible to use this equation to increase the probability of a hypothesis h by finding suitable evidence.

Popper spent a lot of space on pointing out that the rules of probability can’t be used like this, see Section VI of the introduction to Realism and the Aim of Science, as well as Part II Chapters I and II.

But there is another objection. The rules of probability apply to a space of events. Where does this event space come from? It can only come from an explanatory theory. That explanatory theory can’t be put into Bayes’ formula: it is an assumption required to apply the formula at all. There is no such thing as the probability of a theory.

An associated problem is that explanatory theories apply to the whole of physical reality. Some theories are explicitly universal: it applies to everything that happens anywhere in reality. The general theory of relativity isn’t the theory of gravity on Earth at 2.30 pm on Friday 25 August 2017. Rather, it is supposed to apply to everything happening everywhere all the time. But probabilities are tested using relative frequencies. So to test general relativity you would need multiple copies of the whole of physical reality. But let’s suppose that you’re talking about an explanation of some particular event. For example, there are some instances in which a sustained nuclear fission reaction occurred naturally. The explanation for that event is that wherever circumstances occur that some set of properties a fission reaction will take place. So every instance in the universe where those properties occur will give rise to fission. So to test the probability of that theory you would need to have access to multiple copies of the whole of physical reality.

The last I’ll raise is that the point of assessing a theory is that you will either use the theory to solve some problem or reject it. So any epistemology should give you a yes or no answer to the question, as explained here.