How do we know X existed?

[Paul the Uncertain]

No, the evidence cited tells us that we have a trusted contemporary eyewitness of Pythagoras. That tells us he existed. There is no 80% probability he existed on that evidence. It's either/or. (Unless, as I pointed out about being theoretical, in which case we would say it is 99% certain he existed as it is 99% certain the moon is made of rock and not cheese and 99% certain ScoMo is PM of Australia. That's nice for a theoretical discussion but historians' data is real; it is not theoretical like their hypotheses may be.)

So, why not use 100% in your Bayesian calculation on that point? Why do you have to use 99%? If it's one element amongst many others that goes against it, it will come out in the wash.

The difference is that 100% means that you believe that any new evidence you encounter will not inspire doubt, nor even the shadow a doubt (e.g. no evidence could move you from 100% to 99.99%).

There is no "Bayesian calculation" to do on anything that's 100%, and if 100%, then you believe there never will be. You're stuck there, and you fully believe that you're never going to change.

I find it very difficult to believe that any professional evidential reasoner would confine their inquires to matters for which they could never ever be persuaded they're wrong - not even be persuaded that they may be wrong. For one thing, there just aren't enough things in the tangible world that are both certain and interesting.

I conjecture that part of the problem is that some accounts of historical deliberation may invite the reader to conflate two different categorical states of mind, acceptance and certainty. Certainty is immune to change by observation; acceptance acknowledges uncertainty and anticipates that it may well change as information changes.

I can accept things of which I am nowhere near certain (Socrates was a real man who actually lived). Acceptance and certainty are two different issues. And I can accept all sorts of things which are interesting (Socrates had a distinctive viewpoint on the human condition), but of which I am uncertain (he didn't have a viewpoint on anything if he didn't exist).

I can believe that historians may strongly prefer to work with propositions which they can accept. I cannot believe that they confine their attention to things of which they are certain.

[GakuseiDon]

No, the evidence cited tells us that we have a trusted contemporary eyewitness of Pythagoras. That tells us he existed. There is no 80% probability he existed on that evidence. It's either/or. (Unless, as I pointed out about being theoretical, in which case we would say it is 99% certain he existed as it is 99% certain the moon is made of rock and not cheese and 99% certain ScoMo is PM of Australia. That's nice for a theoretical discussion but historians' data is real; it is not theoretical like their hypotheses may be.)

So, why not use 100% in your Bayesian calculation on that point? Why do you have to use 99%? If it's one element amongst many others that goes against it, it will come out in the wash.

The difference is that 100% means that you believe that any new evidence you encounter will not inspire doubt, nor even the shadow a doubt (e.g. no evidence could move you from 100% to 99.99%).

No, that's not correct. You can be 100% certain that ScoMo is the Prime Minister of Australia, but if you get evidence that you may be living in a Matrix (silly example, but for argument's sake), you might reduce the odds. The "100%" is important when carried forward in evaluating the probability of something else, where the importance of who was PM at the time needs to be considered.

Example: the impact of evangelism on federal politics, since the current PM is a committed evangelist. Though "100%" means it would be redundant in the calculation, but you get the idea. There is no need to set the "ScoMo is PM" odds to 99% in order to use it in Bayes, which is what Neil Godfrey seems to be suggesting (I hope he will correct me if I am reading him wrong).

There is no "Bayesian calculation" to do on anything that's 100%, and if 100%, then you believe there never will be. You're stuck there, and you fully believe that you're never going to change.

True. You don't need Bayes on anything that's already 100%. If one thinks that Pythagoras existing is at 100%, then we can leave that out of the equation if we are considering evaluations of what he said or did.

I can believe that historians may strongly prefer to work with propositions which they can accept. I cannot believe that they confine their attention to things of which they are certain.

Well put. Theses written by doctoral students of history aren't simply a recitation of accepted facts!

[Paul the Uncertain]

The difference is that 100% means that you believe that any new evidence you encounter will not inspire doubt, nor even the shadow a doubt (e.g. no evidence could move you from 100% to 99.99%).

No, that's not correct. You can be 100% certain that ScoMo is the Prime Minister of Australia, but if you get evidence that you may be living in a Matrix (silly example, but for argument's sake), you might reduce the odds. The "100%" is important when carried forward in evaluating the probability of something else, where the importance of who was PM at the time needs to be considered.

I am 100% that I am not living in the Matrix. I therefore do not believe that I will encounter evidence that will erode my confidence about that. If I am mistaken about that prediction, then that will be a problem if, as, and when it occurs, and Bayes will not help me. Which doesn't (and shouldn't) change my current belief that I will never have the problem.

BTW, I am strictly less confident that Scott Morrison is the Prime Minister of Australia than that I don't live in the Matrix. So I'm not really 100% about Morrison, except in the sense that the difference from 100% is too small to bother measuring, and probably won't ever make any difference in my life.

Otherwise, we seem to be in general agreement.

[neilgodfrey]

Bayes is simply a formalisation of what you have done with Pythagoras.

No. (Unless we acknowledge that all sound reasoning is Bayesian at some level, in which case the term loses any useful meaning.)

All sound reasoning IS Bayesian. If it can't be expressed in Bayesian terms, it probably isn't sound.

From Dr Richard Carrier's "Proving History", page 68:

As one analyst put it, BT actually explains “what are regarded as sound methodological procedures” and reveals “the infirmities of what are acknowledged as unsound procedures” in almost any empirical field. 1 In other words, Bayes's Theorem underlies all other methodologies and thus explains why certain methods are regarded as sound, and others not—even when advocates or detractors of various methods are unaware of BT's capability in this regard. This entails a testable prediction, that all valid empirical methods reduce to BT: any method you propose will either be logically invalid or it will be described by BT.

No, the evidence cited tells us that we have a trusted contemporary eyewitness of Pythagoras. That tells us he existed. There is no 80% probability he existed on that evidence. It's either/or. (Unless, as I pointed out about being theoretical, in which case we would say it is 99% certain he existed as it is 99% certain the moon is made of rock and not cheese and 99% certain ScoMo is PM of Australia. That's nice for a theoretical discussion but historians' data is real; it is not theoretical like their hypotheses may be.)

So, why not use 100% in your Bayesian calculation on that point? Why do you have to use 99%? If it's one element amongst many others that goes against it, it will come out in the wash.

If you are going to conflate the concept of valid reasoning entirely with explicit Bayesean claims then the concept of Bayesean reasoning loses any significance or meaning when addressing a particular type of knowledge.

The reason one does not use 100% in reasoning with probabilities is because the maths doesn't work. There is no longer any equation or balancing of probabilities involved at all.

But in everyday life we consider "reality" to be something other than theoretical mathematics. When I hear it raining outside, and know from earlier weather reports to expect rain, and had seen the buildup of rain-clouds and felt the temperature suddenly drop only moments earlier, and then went out to have a look and saw rain falling -- then mathematically I would factor in 99.9999% confidence it is really raining and I am not in some sort of dream world or makebelieve movie-set. But in real life I would say it is raining. No doubt. 100%.

[GakuseiDon]

If you are going to conflate the concept of valid reasoning entirely with explicit Bayesean claims then the concept of Bayesean reasoning loses any significance or meaning when addressing a particular type of knowledge.

Can you explain why, please?

But in everyday life we consider "reality" to be something other than theoretical mathematics. When I hear it raining outside, and know from earlier weather reports to expect rain, and had seen the buildup of rain-clouds and felt the temperature suddenly drop only moments earlier, and then went out to have a look and saw rain falling -- then mathematically I would factor in 99.9999% confidence it is really raining and I am not in some sort of dream world or makebelieve movie-set. But in real life I would say it is raining. No doubt. 100%.

Sure, and then that would factor into whatever you want to use that figure for. For example, "do I need to take an umbrella outside on my walk to the car?" You might factor in "100% it is raining now" with "I am adequately protected from the rain with my raincoat". The fact that you are using "100%" doesn't make the calculation invalid, if that's what you are saying.

[neilgodfrey]

If you are going to conflate the concept of valid reasoning entirely with explicit Bayesean claims then the concept of Bayesean reasoning loses any significance or meaning when addressing a particular type of knowledge.

Can you explain why, please?

If reasoning = bayesian processes and there is no difference then there is no benefit in preferring one term over another.

But in everyday life we consider "reality" to be something other than theoretical mathematics. When I hear it raining outside, and know from earlier weather reports to expect rain, and had seen the buildup of rain-clouds and felt the temperature suddenly drop only moments earlier, and then went out to have a look and saw rain falling -- then mathematically I would factor in 99.9999% confidence it is really raining and I am not in some sort of dream world or makebelieve movie-set. But in real life I would say it is raining. No doubt. 100%.

Sure, and then that would factor into whatever you want to use that figure for. For example, "do I need to take an umbrella outside on my walk to the car?" You might factor in "100% it is raining now" with "I am adequately protected from the rain with my raincoat". The fact that you are using "100%" doesn't make the calculation invalid, if that's what you are saying.

But that's not a probability calculation. No ratio is involved at all.

[neilgodfrey]

Bayesian calculations do not tell you where the airplane crashed. They tell you where the probabilities indicate is the most likely place to look for it given known factors at the time of calculation.

When you are standing where the airplane crashed and are standing in the middle of the wreckage you are not using Bayesian analysis to see if that is where the airplane crashed.

Refer back to what we have covered about the difference between real life knowledge and theoretical knowledge.

[neilgodfrey]

If you are going to conflate the concept of valid reasoning entirely with explicit Bayesean claims then the concept of Bayesean reasoning loses any significance or meaning when addressing a particular type of knowledge.

Can you explain why, please?

As already stated here or in another related thread, there is a difference between real-life experiences and theoretical calculations. At a theoretical level all "rational reasoning" is Baysian, true. But in the real world we draw a distinction between Bayesian reasoning and real life responses to testimonies etc.

Hence one finds in works discussing history and reasoning and believing etc at a general level subsections on Bayesian analysis as one kind of reasoning and responding to evidence, testimonies etc. Two works I'm thinking of are Testimony by Coady and Our Knowledge of the Past by Tucker. There's a blog you've recommended to others; all of this and more has been addressed in some depth there. (You should read it, too ). There has been some discussion of both works there, though I don't recall off-hand of Bayesian analysis is the subject of both posts. Bayesian analysis is certainly addressed by both authors, though, in their larger respective discussions of how historians know stuff.

[Paul the Uncertain]

But in everyday life we consider "reality" to be something other than theoretical mathematics. When I hear it raining outside, and know from earlier weather reports to expect rain, and had seen the buildup of rain-clouds and felt the temperature suddenly drop only moments earlier, and then went out to have a look and saw rain falling -- then mathematically I would factor in 99.9999% confidence it is really raining and I am not in some sort of dream world or makebelieve movie-set. But in real life I would say it is raining. No doubt. 100%.

As opposed to what Bayesians, near-Bayesians, and quite a few non-Bayeisan uncertaintists would do: accept that it is raining.

It is not that there is "no doubt," but rather what doubt there is too small to measure and there is no prospect of it actually ever making any difference in any aspect of the decisionmaker's life. It's much more like this than "theoretical mathematics:"

Sure, and then that would factor into whatever you want to use that figure for. For example, "do I need to take an umbrella outside on my walk to the car?" You might factor in "100% it is raining now" with "I am adequately protected from the rain with my raincoat". The fact that you are using "100%" doesn't make the calculation invalid, if that's what you are saying.

All real world measurements without any exceptions are to finite precision. Even an atomic clock reports an estimate of the time it measures, and by the time you've perceived its output, then it isn't that time any more. Nobody has a problem with this. Nobody pretends that it isn't an error. Everybody recognizes it is an inconsequential error - I can read the clock well enough to use my reading to good effect. In particular, I can manage time this way, minuscule error and all, much better than if I tried to tell time without any artificial aid.

Somehow, the same kind of difficulty is supposed to be some critical problem for uncertaintists, whether Bayesian or otherwise.

It isn't a problem.

But that's not a probability calculation. No ratio is involved at all.

It is isomorphic to a probability calculation. That is the most that any "theoretical mathematics" model can claim about its relationship to real-world activities (in this case, whether deploying an umbrella is a cost-effective response to the weather).

I was walking with a dog yesterday, he likes to play fetch with a ball or stick. He moves in a trajectory in four dimenensional space to intercept a moving three dimensional object. Whenever he succeeds, his feat is isomorphic to solving a partial differential equation with variable boundary conditions. Given that there are college graduates who don't even know what the last seven words of the previous sentence mean, I'm thinking no "partial differential equation with variable boundary conditions" was involved in the dog's success.

Nor is any such thing claimed. Never. Nevertheless, the model in question agrees with what the dog does. We may validly state that the dog reasons in exquisite accurate agreement with Newtonian physics. How the dog does so is an interesting problem, but irrelevant to the conclusion that the observed peformance and the model agree.

When you are standing where the airplane crashed and are standing in the middle of the wreckage you are not using Bayesian analysis to see if that is where the airplane crashed.

Nevertheless, in the real world, if I am an air safety investigator, insurance adjuster, coroner ... then I will put you to the trouble of documenting your basis for identifying this wreckage as the wreckage of the specific plane.

"Doubt" includes one person's awareness that other people will not effortlessly share one's own confidence. The usefulness of uncertainty management has not ended when you accept that you've found the right plane, but moves on to your next problem, convincing others to agree with your conclusion.

Of course, convincing other scholars has no place in the academy. Oh wait - don't historians publish arguments on behalf of their conclusions? And then there's Polya's domain: mathematics, where evidence doesn't exist - you prove or you fail. Ah, but you do have to choose what to try to prove, to discern what conjectures are worth the effort of following up on - and suddenly, even the mathematician can use Bayes in pursuit of their profession.

[neilgodfrey]

It isn't a problem.

Carrier says the same as you about everything having a measure of doubt, however infinitesimal. But I don't buy it.

Standing in the rain I know it is raining. Not even a 0.01% doubt. No doubt at all. Your mileage may differ.

But when a jury decides unanimously and "without reasonable doubt" that so-and-so is guilty then the effect is a real-life absolute. The 0.01% doubt is meaningless. It only exists in the minds of theoreticians.

Sure, new evidence may emerge that overturns the verdict. But that's a new situation. Until that time and on the available evidence there is no doubt.