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View Full Version : Logical Fallacy, does it have a name?

Eckelston
2006-Sep-03, 02:39 PM
Let's say you have 2 hypotheses A and B which are complementary. One of them is true but not both. Somehow you find out that A is unlikely and conclude that B is likely true. Now let's say you can somehow find that B is unlikely too (as long as you ignore your previous finding about A being unlikely), thus making A as likely to be true as B.

I'm not even sure if this is a logical fallacy but it surely is a wrong way of thinking to ignore the evidence of B being unlikely in itself. I guess you call it jumping to conclusion, but I'm wondering if there's another term.

grant hutchison
2006-Sep-03, 02:47 PM
It seems that the situation you describe can't exist.
If A and B are complementary, then finding that the probability of A is 1% immediately places the probability of B at 99%. Likewise, if A is impossible, B is certain.
If A and B are both found to be unlikely, then they can't be complementary possibilities in the way you describe, or the information you've been given about A and B is faulty.

Grant Hutchison

Ken G
2006-Sep-03, 02:54 PM
He may be describing some looser sense of "complementary", defined by him as "if one is true then the other isn't". Like who was the murderer, that kind of thing. Originally you thought it had to be one or the other, but if you find they are both unlikely, you have to accept new possibilities (what Grant means by "faulty information", or as my Dad would say, "if you've searched every place it could be, start searching the places it couldn't."). It's not strictly a fallacy, because logic and probability/information are a bit different, but it's clearly bad to assume that A and B are strictly complementary (in the correct sense Grant described) when you don't in fact know that to be true.

Nereid
2006-Sep-03, 03:00 PM
I'm not even sure what domain the OP might be referring to.

In mathematics, it's all cut and dried - there are systems, axioms, definitions of what constitutes proof, etc, etc, etc. Perhaps the closest you could come might be "the number n is either positive (A) or negative (B)", and if you later found out that n = 0, then neither A nor B is true. This is, of course, trivial, but no doubt there are far more subtle variations on this kind of theme.

In physics, no matter how crazy, or illogical, something might seem to be, the universe could care less; no matter what tests you apply for you to decide that A and B are complementary, no matter how good your determinations of the 'unlikliness' of A or B are, if a later experiment or observation* rules them both out, then the universe has spoken (and the judges decision is final).

*To be sure, you'd want multiple, independent validation and verification.

Ilya
2006-Sep-03, 03:00 PM
Keep in mind that probability of an event is not some fixed quantity, but merely a measure of the evaluator's ignorance. In Ken G's example obviously someone is the murderer, and probability of him being that is 100%. Probability can be anything less only as long as you have incomplete information -- and it can have different values depending on how much information you have.

grant hutchison
2006-Sep-03, 03:04 PM
He may be describing some looser sense of "complementary ...I wondered about this, but the OP stipulates "One of them is true but not both," which seems to specify a standard complementarity arrangement.
Eckelston?

Grant Hutchison

Ken G
2006-Sep-03, 03:14 PM
Yeah, it seems the new information developed along the way is that they are not complementary. At some point, that becomes more likely than either A or B, which is why logic must be flexible to apply to reality.

Eckelston
2006-Sep-03, 03:40 PM
I definitely meant that exactly one of the two hypotheses is true.

I'll try to give an example. It's what inspired the question.

A: It is very likely that intelligent civilizations existed.
B: It is very likely that if intelligent civilizations existed some of them have colonized the whole galaxy.
C: It is very unlikely that aliens had colonized Earth.

My point is that it is much easier to argue A AND B than NOT C. Basically someone could make the argument:

With hundreds of billions of stars in the Galaxy there must have been countless civilizations in the last billion years and a few of them almost surely colonized the whole galaxy. Therefore aliens almost surely lived on Earth some time in the past.

Now it may be that A and B are actually not that likely but you only know that becouse you know C is likely true.

So I guess the problem is that the assumptions are contradictory or inclomplete but not obviously so. You only know that becouse they seem to lead to unlikely results.

If there was certainty one could use reductio ad absurdum as a counter-argument. Just point out that since C is true A and B can't both be.

hhEb09'1
2006-Sep-03, 10:17 PM
I definitely meant that exactly one of the two hypotheses is true.

I'll try to give an example. It's what inspired the question.

A: It is very likely that intelligent civilizations existed.
B: It is very likely that if intelligent civilizations existed some of them have colonized the whole galaxy.
C: It is very unlikely that aliens had colonized Earth.Obviously, some of the confusion is that you can't count. :)

Another is that in that example, there are scenarios where none of the three are true, but I also get the impression that the Hypothesis A is meant to be "Intelligent civilizations existed," not "It is likely that intelligent civilizations existed," which would change things I think.

grant hutchison
2006-Sep-03, 10:30 PM
Yes, to form the sort of complementary pair you first described, you'd need something as follows:
A Alien civilizations have colonized every habitable world in the galaxy
B Earth has not been colonized by an alien civilization

But you're trying to freight option A with too many other conditions for the simple logical dichotomy to pertain. As soon as you start making subsidiary claims about the probability of civilizations arising and the likelihood of them behaving like mad colonizers, the probability space fragments into lots of little options that break your simple complementarity.

So I would say that you have built your own false dichotomy, which is maybe the fallacy you're looking for.

Grant Hutchison

Ken G
2006-Sep-03, 11:13 PM
Yes as Grant points out, it appears that proposition A is not important, it is B and C that are the two in question. One way to consider B without C is to ask if we should expect the Andromeda galaxy to be crawling with alien colonists. It is quite hard to argue that either way, given what we know about intelligent life and interstellar travel, which is basically zilch. Since we do have proposition C, I would say that is one of the only actual pieces of information we can bring to bear on the issue at all.

Lord Jubjub
2006-Sep-03, 11:19 PM
How about Douglas Adams 'girl who quoted the stock market' from his book "The Long Dark Tea Time of the Soul?"

Dirk Gently was investigating wierd happenings when he runs across Kate. Kate tells him of a girl in an institution who is quoting the stock market exactly 24 hours out of sync. But because the prices being quoted are yesterday's prices, the doctor in charge dismisses the feat as merely a magician's trick.

Dirk points out that however impossible it might be for the girl to be channelling yesterday's prices, it is equally as impossible that the girl is somehow getting a hold of and memorizing, second by second, the stock ticker in exactly a 24-hour delay.

Eckelston
2006-Sep-04, 06:25 PM
Hm, looks like I didn't say exactly what I wanted to say. Lord Jubjub still got it, though I have no idea how :)

The correct way to describe the statements is:

A: Intelligent civilizations have existed in the galaxy.
B: If intelligent civilizations existed some of them have colonized the whole galaxy.
C: Aliens had not colonized Earth.
D: A and B are both true.

(Yeah, I know, that's 4 already ;) )

Now the two complementary statements are C and D. There is no room for a false dichtomy any more, I think. And now it makes sense to talk about D and C as both being very likely.

Now it may be the case that you can never make two complemetary cases look both very probable, since at the very least you should find out that you know very little about the subject.

I'll try to come up with another example since some of you seem to think it's flawed, becouse A and B are just not very likely to be true. Actually I think I know one.

An airliner crashes after liftoff killing all passengers and crew on board. The model has flown for decades without any incidents and the pilot and crew were experienced and had a distinguished record.

The producers of the aircraft make the point that the model has flown for years without incident so it's extremely unlikely that the crash was caused by design or mechnical error.

The Pilots' Union points out that it's just improbable that such a good pilot would do something that could have caused the crash.

Anyway, for the record I realize that the arguments are fallacious. But they do occur in real world situations, perhaps most commonly in blame games after freak accidents.

grant hutchison
2006-Sep-04, 06:49 PM
A: Intelligent civilizations have existed in the galaxy.
B: If intelligent civilizations existed some of them have colonized the whole galaxy.
C: Aliens had not colonized Earth.
D: A and B are both true.I think this is a rephrasing of my dichotomous construction, with the subsidiary information put back in again. The trouble is, if C is true (making D false), then A or B may be false. The dichotomy is false because you've squeezed two propositions into a single statement (D).

An airliner crashes after liftoff killing all passengers and crew on board. The model has flown for decades without any incidents and the pilot and crew were experienced and had a distinguished record.

The producers of the aircraft make the point that the model has flown for years without incident so it's extremely unlikely that the crash was caused by design or mechnical error.

The Pilots' Union points out that it's just improbable that such a good pilot would do something that could have caused the crash.This one is a bit of false logic, indeed, but rather different from your original example.
The error here is that plane crashes are rare of themselves, so reasoning from the rarity of possible causes is an error. One has to use posterior probabilities:
The likelihood of pilot error, given that a crash occurred.
The likelihood of mechanical failure, given that a crash occurred.
Both of these turn out to be quite likely, but not complementary (as I'm sure you know) since things like wind-shear close to the ground can also lead to crashes with moderate posterior probability.

There may well be a name for an error in reasoning about rare events in this way, but I don't know it.

Grant Hutchison

Ken G
2006-Sep-04, 07:50 PM
Yes, I think the airplane example just muddies the waters even more, because it is not clear in the debate between the manufacturer and the union which of the two fallacies Grant mentioned is causing the problem: either neglecting the third possibility ("act of God", we can call it), or forgetting that when you already know that something unlikely happened, the issue is relative likelihoods rather than absolute likelihoods. People certainly make a hash of probability.

I think the key issue in the original example, the alien colonization, is that if you believe that most galaxies are colonized, then you already know that something unusual is going on for us. So immediately you must compare the relative unusualness of a galaxy going uncolonized versus colonization happening and us not noticing. Let's say that 1/100 of all galaxies in the universe have gone uncolonized, and within the colonized ones, 1/100 planets have been visited without the "locals" noticing. Now I hand you a random planet on which the locals don't see evidence for colonization. What can you say about whether their galaxy was colonized? Nothing!

Of course, I personally would expect the fraction of uncolonized galaxies to be much higher than the fraction of visited planets that "didn't notice", so I think the fact that Earth has not apparently been colonized is a very likely indicator that our galaxy does not contain a colonizing species (yet). Thus to me the argument carries no weight that we must have been visited and didn't notice. Anyone who suspects that the fraction of uncolonized galaxies is much smaller than the chance of not knowing you've been visited would of course conclude that the Earth has likely been visited. So one must argue the relative probabilities, and that's certainly not easy given all we don't know here!

Ken G
2006-Sep-04, 08:09 PM
And here's more food for thought, to show how much we really don't know. For someone who thinks that almost all galaxies have been colonized, they might imagine that the colonizing species is highly benevolent. Perhaps they would have a kind of "noninterference directive", which could explain why we might not know of their presence. Note that also means that the evidence that is cited for visitation would have to be spurious-- none of it exemplifies a species that is trying to not be discovered (UFO sightings and the like). However, a somewhat interesting wild speculation that can come from this is that if such a species had a strict noninterference, nondiscovery principle, they might have picked up and left when humanity started to evolve, leaving no trace a million years ago. As this hypothesis requires no evidence (indeed, it requires a lack of evidence), it cannot be considered scientific, merely amusing.

beepbeepitsme
2006-Sep-07, 04:21 AM
Sounds like the logical fallacy of the false dilemma or the false dichotomy.

The suggestion that only 2 options are available and you must make one of the two presented choices.

Commonly called the "you are either for us or against us fallacy."

RE: logical fallacy

What Is Evidence?
http://beepbeepitsme.blogspot.com/2006/09/what-is-evidence_07.html

Ken G
2006-Sep-07, 04:54 AM
Actually, that was suggested in post #10, but it was found that this is a true dichotomy, but it is a dichotomy between two (arguably) normally unlikely options that have become a truly complementary system by virtue of acquired knowledge. Like if you have looked for your keys everywhere in your house except for the two least likely places, but since you didn't find them anywhere else, you are now comparing relative likelihoods of two things that both earlier seemed unworthy of attention. And welcome to the forum beepbeepitsme, you seem to combine a knowledgeable and concise style, moreso than the norm here, present company included!