The Nature of Scepticism

No, its a conclusion. They happen at the end. The assumptions go at the beginning. In this case the assumption is that one can infer general statements from specific observations (ie., induction is the assumption). We also assume that we can know truth. We assume that we can arrive at truth through observation.It isn't proven beyond all doubt that the boy is lying: but one can (and often must) reach conclusions based on a balance of probabilities. It is a tentative conclusion based on all the evidence we have that personality traits are largely stable over time and pranksters and liars will prank and lie.

{oooh: post 6000, nice round number.} All conclusions are based on assumptions. Take a physics exam and in answering the questions, part of your marks rely on you identifying the assumptions you had to make to reach your conclusions. Newton's laws have assumptions, Einstein's do - your computer is built based on conclusions derived from making assumptions. You make assumptions that are life and death every day. Assumptions are not bad, they are necessary. You just have to be aware of what assumptions you are making, why you made them, and where they might fail. So we should believe pathological liars and act on those beliefs (such as getting weapons and running to protect the herd) just in case its the one time they're telling the truth?IF you had a friend who regularly yelled 'Fire!' when he makes an entrance at parties - would you always evacuate and call the fire brigade and not return to the building until they had checked it out?All knowledge is tentative, and we weigh the costs of believing a claim (ie the actions we take as a result of such a belief) by the probability of the claim being true versus the costs of not believing the claim based on the probability of it being false. This is basic decision making, right? We know we need to make decisions, and in order to make decisions we have to make assumptions. Edited by Modulous, : No reason given.Edited by Modulous, : No reason given.

A mad genius builds a 'wolf detector'.Every day the 'wolf detector' goes off, but no wolves are evident.After 365 days, only one wolf is found after the alarm went off on one day.If this is representative - does this not imply that the chances of the wolf alarm correctly detecting a wolf is 1/365 and the chances of it being a false positive are 364/365?Therefore - would it not be true that multiple false positives actually do effect the probability that the next alarm will be correct?

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"The race of man, while sheep in credulity, are wolves for conformity." - Carl Van Doren

Of course it is. It doesn't prove it with 100% certainty. But evidence isn't about certainty. It's about increasing the probability that something is true. No discovered dead prey animals, no tracks, no furs by someone who knows where to look to find these kinds of things - these things increase the probability of the proposition being true. Yes you do. We have evidence that personalities and abilities are broadly consistent over time. That's why, for example, convicted rapists and murderers have a hard time getting elected to high office. There is an increased probability over others that they will commit serious offences in the future. Then that would be evidence against the proposition that there will be future false alarms. Well because I believe that personalities are consistent over time - I would believe the boy genuinely thought he saw a wolf.However, if the boy is regular in calling an alarm - and sheep almost always don't get attacked after an alarm is raised - we have reason to doubt the boy's alarms. Just as you would have reason to doubt your car would start in the morning if it had failed to do so on 10 previous mornings.

I'm afraid I'm not an expert in wolf predation. What is the purpose of this question? How does it address what I said about how something that increases the probability of a proposition being true is evidence, even if it doesn't lead to certainty or near certainty? Well if that weren't the case, we'd be using a different example right now wouldn't we? If you read my post, I explicitly said the exact opposite. Because I believe personalities are broadly consistent, I wouldn't deduce he was a liar if I knew he was honest. Over what period? If it happened two times in an hour, there might be an inclination toward suspicion where two times over a full human lifetime wouldn't. Coming to any conclusion about the real world is based on 'invalid logic'. It wasn't an assumption of lying, it was an evidenced based conclusion of lying. Evidenced based conclusions can be false. The villagers, if they were robots, should have weighed the relative costs of action and inaction versus the probabilities of false positives and true positives. As they are human, and thus imperfect reasoners, they no doubt erred in acquiring an adequate sampling size and instead relied on heuristics to guide their decisions. But then, the story is meant to highlight the danger of falsely raising the alarm given the fact that people are likely to conclude you are a false alarm raiser prematurely (in your view) - which can have real world negative consequences. One should not trust people who habitually raise false alarms. Granted, the more rational response of the villagers upon doubting the veracity of the boy's alarms would be to replace the boy with a more reliable person who doesn't muck about.Remember, unlike us, the villagers explicitly knew there was no wolf. So they knew the alarm was false. Not a true alarm with an undetected wolf. The story isn't really about wolves of course. It is about emergencies in general. So you could replace crying 'wolf' with crying 'fire!' - where it is much easier to ascertain the truth of the matter.

Nobody was denying the existence of the wolf. It was denied there was a wolf threatening the sheep. Because the story explicitly says there was no wolf threatening sheep when he called the alarm. Here it is:

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when his neighbors came to help him, laughed at them for their pains.

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So he was doing it to laugh at them, not because he thought there was a wolf threatening the sheep. Then:

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The Wolf, however, did truly come at last.

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That is before it was falsely claimed, now it was truly there.Now, once you've absorbed that, perhaps you could address the meat of my post rather than mangle Aesop's story.

Indeed, you might say nobody believes a liar...even when he is telling the truth. Of course, as I said earlier. But that wouldn't really have the literary punch would it? Yes. So what is the best solution based on your skeptical approach? Give me a few seconds, I'll reveal a simple model in my next post.

So, let us consider proposition p.What is the probability that p?There are a number of approaches one could take.One could say 'It is unknown.' This is approximately the position RAZD says should be taken.Another approach I will elucidate here.P(p) = Number of true propositions/Number of propositions.For instance. If there were only 10 propositions that could be made, and only one of them was true the chance would beP(p) = 1 / 10But of course the real numbers are much much bigger. I submit that there are more false claims than true claims. Indeed, most propositions can be rephrased so as to be untrue in many different ways.For instance: G = 6.67384 10^-11 m³ kg^-1 s^-2 is, as far as we can tell, a true proposition (within the accuracy provided). There are an infinite number of other values we could propose for G.I therefore propose that the fraction N_{true claims}/N_{all possible claims} is very small.Therefore, at the start of our process we conclude that P(p) is low.But of course, we know that this is just a general result. It is, in a sense, answering the question 'If we entered every possible proposition into a hat and drew one, what are the chances that it is true?'And this is where evidence comes in. Evidence is any fact which if true would raise the probability of the truth of a certain proposition. So now we have the question 'What is P(p) given evidence, E?'We're almost as far as we need to go. There is also falsifying evidence. This is any fact that if true, lowers the probability of a proposition.'What is P(p) given affirming evidence, E and doubt causing evidence, D?'Let us turn to inaudible elephants. We start the process off by considering that its one claim among countless and is thus improbable. Then we look to the affirming evidence. We find none.But of course we're not done. What about doubting evidence, D? Well we have evidence that people believe false things, strange things, paradoxical things, bizarre things, contradictory things with regularity. This raises the doubt that perhaps this person is delusional. There is no way for him to have acquired the knowledge of the causal relationship to his proposed elephants and brain damage through inspection of the exterior world, which lends strength to the doubting evidence in that this elephant belief might be one of many cases of the human brain confabulating.We start with a small number. We can add nothing (or if we're being incredibly generous, a negligible amount) to the probability based on verifying facts, ie evidence. Then we subtract some because we know human brains naturally and constantly confabulate. And thus we end up with the conclusion that it is incredibly improbable.P(p) (small) + E (negligible to zero)- D (comparatively huge) = very small probability.In the wolf story, as it progresses the D component rises.Let's say the flock is worth 10000. Let's say to rally a wolf defence costs 1000. This is going to be kept simple.First alarm: Probability given E (an alarm is called) - D(5%) = 95%Second alarm: Probability given E - D(10%) = 90%Third alarm: P, E - d (40%) = 60%
There is a 60% chance now we reckon. Let's run a 100 trials.
60 times we defend the sheep. This costs us 60,000. But saves us 600,000
40 times it costs us 40,000.
Total: 500,000 benefit over 100 trials or 5000 per trial.Fourth alarm = 10%
100 trials
10 times defend the sheep. This costs us 10,000. It saves us 100,000.
90 times it costs us 90,000
Total: 0Eventually it becomes foolish to act given the doubt causing evidence, as you will soon be spending more resources protecting than the resources are worth. Even if we wish to postulate that with one set of variables, the villagers should have acted in some other way, it becomes clear there is always some point that our doubt in the veracity of a persons claims rises to the point we deem it unworthy to act upon them.Edited by Modulous, : minor maths boo boo

I'm sorry - how are you determining that the previous 3 rolls were a 4 a 1 a and a 5? Because we're talking about the reliability of detectors to give accurate reports which you have failed to take into account here. Conditional probabilities, sir. If the dice reader says it is a six then what is the probability that the dice rolled a six? If I told you that my dice reader is designed to never display the correct result (and it works as designed) , I contend the chances are not 1 in 6 but 0 (or close to it).The probability I am a murderer might be 1 in 100,000. If I have been convicted of murder, the probability is different. Exactly. Where did this number come from? Did you derive this number from the number of false positives? If so, then you agree that the number of false positives do effect the probability that the next alarm will be correct. This can be easily confirmed by changing the number from 365 to 1000 in my example. Then suddenly you would be saying the chances of it being correct are 1 in 1000. This shows that the probability of being correct is dependent on the number of times it is incorrect.This is not the same as saying the number of false positives impacts the frequency of wolf attacks. Obviously it does not. But can you not see that as the number of false reports goes up, our confidence in the reports goes down? The entire point of an alarm is to increase your confidence that a wolf is attacking, right?Let us say that the probability at any given arbitrary time period that there will be a wolf attack is 1 in 1000.The alarm sounds. What is the probability that a wolf is attacking?If you say 1 in 1000 then the alarm is useless. We could have deduced that without the alarm.It could be that the alarm is reliable enough that it is better than guessing, no different from guessing or worse than guessing. Agreed?Edited by Modulous, : No reason given.

So now are you agreeing with the statement 'multiple false positives actually do effect the probability that the next alarm will be correct'?

Largely what I said in Message 236, right?

I don't see the need to privilege any particular point. In order to have confidence in the true ratio of true to false positives, we'd need several true positives. But if you set a fire alarm in your house that goes off every 10 seconds, you don't need to wait for the day an actual fire occurs to conclude the fire alarm is unreliable and gives off too many false positives. And it would still be the case that an alarm that gives a false positive every 10 seconds is worse than an alarm that gives a false positive every six months.

And if a replacement was not possible at the time? Should we always go on wolf alert when the boy cries an alarm, or does there come a time when we should just ignore the boy until such time as a replacement can be arranged? What evidence would cause you to change your mind, to cease being sceptical of this conclusion?

I disagree. You could be making a social fuck up, allowing your time be dictated by dishonest people. You might be making a survival fuck up - burning all your calories protecting sheep only a small number of which you'll eat. Are you saying there is no amount of wasted time and sleep which would justify just ignoring the boy as worse than useless? If the boy cried wolf every ten minutes, would you still think it wise to go running every time?I mean, you have a livelihood too presumably, beyond your communal interest in preserving the sheep, maybe you have cows and fields to attend to. Surely, your time has an actual value? And surely too the flock has only finite value to you? Would it make sense to invest more and more and more of your time in preserving one flock of sheep while your cows went unmilked and your field unharvested? If you felt that strongly about preserving the sheep to the point of physical exhaustion why aren't you just the shepherd, saving you all the time running back and forth!?