A discussion on weighing up two sides of an argument

[JeffHamm]

Are you an Aspie?

No, I'm just genuinely interested in all sorts of things. Why did you ask? Are you?

- Jeff

[DJA]

Yes, that's a good example. Basically, it's how extremely rare and unlikely events are, by their very nature of being very rare and unlikely, impossible to predict, almost by definition. One can, however, make a meta-prediction type statement that "If you always choose the most probable, and make a large enough number of choices, the number of errors you will make can be predicted within a certain range, 95% of the time. But, regardless, it will be impossible a priori to predict if an individual choice will be one of them."

"Black swan" events do occur, but by definition they occur very very rarely, which means if one decides "This is the time for a black swan event", you have a very very high chance of being wrong.

It's basically an example of how probabilistic statements are not 100% truth statements, which is why they are stumbling blocks for pure reason - you cannot make a 100% new truth statements when one of the premises is of the "some X are Y", not matter how close to 100% that "some X" is. Even if it's off by only 1 in a billion, that means 1 in a billion times the most probable choice will be wrong. I just wouldn't want to bet that a given instance is that 1 in a billion.

We see this sort of thing in actual court cases too, which shows up as wrongful convictions even in the absence of corruption. Beyond reasonable doubt is not beyond all doubt, making the criterion for conviction less than perfection. It's set to a high bar, but not an infallible one. To set it at an infallible level creates an impossible one to reach.

On the other hand, a true "black swan" occurrence effectively requires the current underlying theory to be wrong as well. There are examples of theories that have predicted what were considered to be such improbable events that had to occur that it became important to confirm them. Einstein's theory of relativity (of which I am no expert by any means) predicted the bending of light around large masses, and this was at the time considered highly improbable but his theory required it to happen. It was eventually confirmed, as were other things, such as gravitational waves (which took much longer to confirm as it required huge advances in technology to do it). So, just because something is considered highly improbable in one sense, according to theory that highly improbable event might be considered highly probable (as in the above examples). When something is considered highly probable to occur by a theory, and yet the highly unexpected happens, that is a signal the theory (or at least our understanding of its implications) is somehow flawed.

Thanks DJA, that was a really interesting point to bring in.

- Jeff

Are you an Aspie?

[DJA]

Meh.
White swans are found in cold miserable countries .
Black swans are found in Oz!

[JeffHamm]

Black swan theory - Wikipedia

Yes, that's a good example. Basically, it's how extremely rare and unlikely events are, by their very nature of being very rare and unlikely, impossible to predict, almost by definition. One can, however, make a meta-prediction type statement that "If you always choose the most probable, and make a large enough number of choices, the number of errors you will make can be predicted within a certain range, 95% of the time. But, regardless, it will be impossible a priori to predict if an individual choice will be one of them."

"Black swan" events do occur, but by definition they occur very very rarely, which means if one decides "This is the time for a black swan event", you have a very very high chance of being wrong.

It's basically an example of how probabilistic statements are not 100% truth statements, which is why they are stumbling blocks for pure reason - you cannot make a 100% new truth statements when one of the premises is of the "some X are Y", not matter how close to 100% that "some X" is. Even if it's off by only 1 in a billion, that means 1 in a billion times the most probable choice will be wrong. I just wouldn't want to bet that a given instance is that 1 in a billion.

We see this sort of thing in actual court cases too, which shows up as wrongful convictions even in the absence of corruption. Beyond reasonable doubt is not beyond all doubt, making the criterion for conviction less than perfection. It's set to a high bar, but not an infallible one. To set it at an infallible level creates an impossible one to reach.

On the other hand, a true "black swan" occurrence effectively requires the current underlying theory to be wrong as well. There are examples of theories that have predicted what were considered to be such improbable events that had to occur that it became important to confirm them. Einstein's theory of relativity (of which I am no expert by any means) predicted the bending of light around large masses, and this was at the time considered highly improbable but his theory required it to happen. It was eventually confirmed, as were other things, such as gravitational waves (which took much longer to confirm as it required huge advances in technology to do it). So, just because something is considered highly improbable in one sense, according to theory that highly improbable event might be considered highly probable (as in the above examples). When something is considered highly probable to occur by a theory, and yet the highly unexpected happens, that is a signal the theory (or at least our understanding of its implications) is somehow flawed.

Thanks DJA, that was a really interesting point to bring in.

- Jeff

[DJA]

Black swan theory - Wikipedia

[DJA]

Dunno.

Surmised he was a male.

Was on a few sites,banned from at least two.

Let's face it,made a **** of it's self.

[John Wheat]

Bayes's ideas were popularized by some dude named Pierre.

Didn't Pierre turn out to be female?

[DJA]

Difference Between Condescending and Patronizing

[JeffHamm]

Meh,it's back

Hi DJA,

You do realize that you are not obliged to read a thread you're not interested in.

- Jeff

P.S. Yes, as I noted, black swans are common in Australia and New Zealand. Quite possibly elsewhere as well, but I had never even heard of them when I lived in Canada.

[DJA]

I fear we may have derailed this thread...

Meh,it's back

[DJA]

Most swans hereabouts are black.Last white swan I saw was in the Melbourne Zoo 40 years ago.

We learnt most of this soon after reading "John and Betty" (and Fluff and Scottie).

Not really.

Crikey though,keep this thread running.Winter is not far away.

[JeffHamm]

Hmmm, I suppose there is one other aspect of debate and discussion that I should mention.

Rational approaches to debate and argumentation, which is what I've been focusing on above, is not the only approach available. The underlying goal, however, of reason is to get to the "truth." This is why pure reason focuses on those "All X are Y" ideals, because from those situations one can absolutely derive a true statement. Again, with the swans, if it were true that All swans are white, and it were true that I saw a swan yesterday, I never have to tell you that the swan I saw was white. You do not need my statement to that effect to prove the swan I saw was white. It had to be, purely through logical reasoning.

Those "some swans are white" type constructions don't allow for absolute truth to be derived at purely through logical reasoning, and because rare events do happen sometimes, pure reason throws a hissy fit and says we can't get to pure truth. The approach about how to deal with those is uncomfortable to the extremist of pure reason because of that - the objective can never be reached, similar to Achilles and the tortoise. However, just as calculus solved that paradox, philosophers have worked on rational rules for probabilistic premises in a similar way (while one cannot reach pure truth, one can try and estimate which limit of true/false is being approached by the asymptote).

In contrast, debates and discussion can introduce techniques from the school of sophistry. The goal of sophistry in a debate is not to discover truth, but rather only to persuade others to one's way of thinking. Eloquence, for example, is a technique emphasized by sophistry. See, the truth value of a statement doesn't change just because it is phrased awkwardly. It might not be clear, or easy to understand, but that doesn't necessarily make it any less true (or false, if you prefer). Granted, poorly phrased statements often introduce unintended meanings, which in turn would impact the truth value, but it does not have to. Sophistry emphasizes presentation techniques to win over listeners without adding any truth value to the statements. As such, in a debate where the rational argument is true, but presented awkwardly might fare more poorly by an elegant, but false, counter argument.

While eloquence is beneficial to the presentation, as it makes it easier to evaluate the truth values, it can also be used as a technique to persuade listeners to false conclusions.

Other sophistry techniques involve the use of pejorative language, particularly directed at the other speaker rather than their arguments per se. The idea is that if one can make the listeners view the other speaker more poorly, then the reasoning behind their arguments will be ignored. (Pointing out spelling or grammatical mistakes, for example, is a great distraction from the truth content of a statement) Again, the goal of sophistry is not to persuade by the strength of one's arguments, but rather to persuade through techniques of speech that do not contain or contribute to the truth value of what is said.

I am not a proponent of this form of counter-argument, although I recognize that clarity of presentation is beneficial I only recognize that provided it is the truth aspect of the statement that is clarified. When eloquence is used to mask a false statement as true, then it because a bad thing, in my view.

However, those of the sophistry school of debate do not agree with that last comment, because sophistry has a different set of "winning conditions", if you will. The objective is not to be true, but to convince, regardless of the truth.

So, while it is my opinion that sophistry should be avoided, I'm not espousing that the boards prohibit someone whose approach is of the sophistry school of debate. Indeed, I know for a fact I have entered into sophistry styles of debating on occasion, and while it can be emotionally satisfying, I also recognize it does not advance our progress in understanding what happened in 1888. Only fools would disagree with me there! (That, for example, is sophistry).

- Jeff

P.S. And to the great relief of what I suspect is not an entirely small number, I think I'm done.

P.P.S. I've been wrong before about that though.

[JeffHamm]

Ok, why I think the above post contains some useful points with respect to JtR type discussions.

First, beyond the trivial, in a murder case, historical or current, we are never in the situation where we have starting premises of the "all X are Y" type. Rather, we have statements of the "some X are Y", where some might be replaced with "most" or some other description indicating a probability. Things like "the vast majority of murders are committed by someone known to the victim". But that, of course, means that not all murders are committed by someone known to the victim.

We see this come up in suspect focused debates, where if a known link can be made between the suspect and the victim this is put forth as positive evidence for the case. Barnett comes to mind for example (just introducing a concrete example, with no desire to debate the merits of any individual case here, there are threads for that). Despite that, I'm going to just stick with Barnet in my example here, but the focus in on where I think such a debate would be most fruitful in terms of getting us somewhere.

So yes, as a starting point, that would be a fair argument, there is often a link between a victim and their murderer, and Barnet has such a link with the last victim. Other examples, such as Kemper, can even be pointed to illustrating that very point. For those arguing against, they need to bring arguments as to why, in this particular case, they believe the JtR cases are more likely to be an example of either the less common "stranger murder" (and so arguing against any theory that posits a relationship) or, the more focused situation of bringing in evidence against the specific link between Barnet and the murders. But it is not sufficient to just say "but some murders do not have that link.", that's just restating the "some X are Y" in a reverse statement of "some X are not Y", and in this case the weight is in favour of the first formulation (more are related than that not related).

Now, for other aspects of a discussion, we get into more subjective areas of the weight we might assign to that "some X are Y" type starting point. I might argue "it is highly likely that X are Y", but if I can't show some objective data to support that indeed "most X are Y", the counter argument should focus on my claim of "high probability". One could simply say "well, in your opinion most X are Y, but unless you can demonstrate that is the case, it could be that few X are Y".

But we now reach a point where neither side can claim they are right because neither side is presenting evidence of the underlying probability X are Y. What it does, though, is focus us both on what evidence we need to be looking for. Because, if we are both rational, then knowing the relative probabilities between "X are Y" and "X are not Y", would then lead us both to agreement. Rationally, we should end up both coming to a common conclusion once that weighting is determined.

Of course, if upon determining that weighting we see that both conclusions still have a high support (let's say half of X are Y and half are not Y), then we we would rationally have to agree that "hmmm, it appears knowing X is not the important piece of the puzzle we thought it was", again leaving us without a rational conclusion to choose in the bigger topic.

None of this limits what we can or cannot put forward for consideration. Rather, knowing how rational arguments "work" when dealing with probabilistic premises can make us focus on how to bolster our case, and also how to recognize when someone has pointed out where our case is weak and needs work. We always have in a murder case probabilistic premises, and even a match with DNA evidence is always testified as having a probability of being "not the suspect", it's just so very small we reject it as unreasonable to consider.

And, of course, it's also totally fine if people want to stick with their idea, despite it being the case that their idea falls on the less probable side of the final evaluations. By keeping in mind how rational decisions are made using this type of information, it can guide people to look for evidence that would end up changing the balance (such as finding out I was interested in rare birds, and was in the area of the 1 in a billion black swan example I used in the post above; combine that with information about how people will do things that reflect their interests, and suddenly we're building a case that makes it more and more reasonable to suggest the swan I saw was indeed a rare black swan).

The more and more specific a case gets, meaning the more and more suspect focused it gets, the more it becomes important to have that sort of evidence, that only has a high probability of leading to that rare case because there are more people that are not Barnet than are Barnet, so the probability (without any other information to guide us) is that JtR was not Barnet (again, only used as an example; put anything other name in there if Barnet is your chosen favorite suspect. I'm not suspect focused myself, but if I were, I would have used my own personal top choice).

Anyway, as I say, nothing about understanding how rational argument "works" in any way limits the topics one can discuss. But I believe it can greatly benefit everyone to take a moment to consider it because it will aid one in choosing what aspects of their case need the most focus of improvement.

The case isn't solved, after all, so any and all solutions could be wrong. So finding how to rationally tip the balance towards or away from a given solution is a useful thing to know. It's about knowing the tool, not limiting what what builds with them, but how to build that thing more easily and creating a sturdier item.

- Jeff

[JeffHamm]

Hi,

Ok, it appears that I've jumped too far into the topic for it to make sense. And, due to the nature of philosophical discussions, they often result in lengthy posts.

Here's sort of the crux of what I'm trying to get at.

Logic, or reason, operates on proving things by indisputable combinations of truth statements.

For example, given the following:

All swans are white.
Yesterday I saw a swan.

If both of those are true, we can create the new statement:

The swan I saw yesterday was white.

That has to be true beyond all doubt provided the first two statements are also true.

The problem we face, is that we never have statements of the "All swans are white", we have statements like "Most swans are white." And, given there are black swans, we know that first statement is not true (some swans are black).

That means, while both of these statements can be true:

Most swans are white.
Yesterday I saw a swan.

We cannot say that beyond all doubt "The swan I saw yesterday was white" because the first premise is not of the "all swans" construction.
Through the application of pure reason, it doesn't matter how rare non-white swans might be. There could be only 1 in a billion swans that are not white, and we still cannot, through the application of the rules of pure logic and reason, draw that conclusion beyond all doubt. But can we get to "beyond reasonable doubt"?


What if we knew that 99.9999999% of all swans were white (1 in a billion), and that I saw a swan yesterday. With no other information to work with, what would we consider the weight of evidence towards the conclusion?


So in this situation (call it Situation Minimal data), Rationally, we should consider that the swan I saw was, in all probability, one of the white ones. It's not proven, but that would be the safe bet which would satisfy "beyond reasonable doubt" given the information we have.

What if we add more information to work with (Situation more data)? Can we change that level of doubt? (given it's not 100%, it should, rationally, be open to change, either increasing or decreasing that level of confidence).

What sort of information might change our view on that? Well, if you had evidence that I was in a location known to have those extremely rare swans yesterday, and you knew I had some sort of interest in swans, or birds in general, or even just animals in general, then now you have new information, still not sufficient to meet the strict rules of pure logic and reasoning, but information that you could argue increases the likelihood I would have gone to specifically see that black swan. You don't know for sure I did go, but you would have grounds (based upon knowledge of how humans make choices) to argue there is a high probability that I would take the opportunity to satisfy my interest in animals by going to view an extremely rare example.

So, now, despite how rare our black swans may be, we then have an argument that could very well lead to the conclusion that it is more likely that the swan I saw was, in fact, not white. But it's still not proven 100%, but this would probably at least meet the criterion of reasonable doubt.

While none of it leads to the kind of "proof" in the absolute sense, reasoning based upon statements of the "Most X are Y" formulations can still follow rational rules of reasoning, with the end result not being of the "beyond all doubt" conclusion (which we could do if All swans were white) but it shows how probabilistic premises (Most swans are white) can be used rationally to weigh two possible conclusions despite the two possible conclusions ever being ruled out entirely beyond all doubt).

What is important to notice, however, is that to shift the weight of evidence from our conclusion of a white swan in the "situation minimal" example towards our opposite conclusion of a black swan in "situation more data", requires we have more data, not simply emphasizing that 1 in a billion swans are black. That emphasis alone is not an argument, it's just restating why the evidence is in favour of the safer conclusion in the first place.

None of the above limits what arguments we can consider, or put forth, or debate over. What it does, however, is focus us as to what sort of evidence we might need to provide when we're suggesting that a rare option is the one to consider as the most likely conclusion. We need to find and present evidence that shifts the weight of evidence towards to the more improbable side of that "Most X and Y" side of the equation. We can't just say "But not all X are Y therefore the answer is not Y despite X being the case. If most X are Y, then the safe conclusion is Y, unless something evidential comes into play that shifts the probability that we are, in fact, dealing with an example of the more unlikely situation of "not Y".

- Jeff

Oh, by the way, black swans are pretty common in New Zealand and Australia. I had never seen or even heard of one before I moved here, and often wondered why examples in logic lectures often used things like "All swans are white" in their examples. It was never actually pointed out that this starting premise was wrong, so the first time I saw one I was pretty surprised. I've called them "logic swans" ever since, but that, perhaps, is a level of geek too far.

[DJA]

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