Logical Fallacies

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Re: Logical Fallacies

Postby Kemosabe-TBC » Mon Sep 14, 2009 5:24 pm

davar55 wrote:Evolution is far and away the best explanation for all
biological origins and interconnections. I didn't say accept
by blind faith, I said defend.


Perhaps, but I don't believe in best explanations. I believe in correct or incorrect explanations.
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Postby bill » Mon Sep 14, 2009 5:29 pm

Kemo can you prove what you believe in is correct or incorrect :lol: :lol: :lol: :roll: :roll: :roll: :wink: :wink: :wink:
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Postby Kemosabe-TBC » Mon Sep 14, 2009 5:46 pm

bill wrote:Kemo can you prove what you believe in is correct or incorrect :lol: :lol: :lol: :roll: :roll: :roll: :wink: :wink: :wink:


I believe nothing in the Universe can be proven, we are always in a quest for the truth. Except for controlled systems, like math, where we make the "rules of the game". We dictate the axioms and how everything works together, and then anything that abides by the rules of those systems can be proven true, or false, under the definition of a particular system only.
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Postby bill » Mon Sep 14, 2009 5:54 pm

Kemo is that your best explanation and can you prove it is your best :D :D :D :lol: :lol: :lol: :roll: :roll: :roll:

Can you prove the "rules fo the game" are correct or incorrect :D :D :D :lol: :lol: :lol: :roll: :roll: :roll:

Of course you realize I am busting you a bit here.
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Postby Kemosabe-TBC » Mon Sep 14, 2009 6:19 pm

bill wrote:Kemo is that your best explanation and can you prove it is your best


No, and I don't want to, but I'll try :D
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Postby bill » Mon Sep 14, 2009 6:27 pm

Kemo the simple fact that we are talking to one another is concrete proof that the rules are correct. :D :D :D

A rock cannot prove it exists until it is discovered by a sentient being. Can a sentient being prove his/her own existence. :D :D :D

I guess all that would take are our common sense's :D :D :D
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Postby Kemosabe-TBC » Mon Sep 14, 2009 6:29 pm

bill wrote:Kemo the simple fact that we are talking to one another is concrete proof that the rules are correct. :D :D :D

Are we? Maybe we're inside the Matrix :roll:

A rock cannot prove it exists until it is discovered by a sentient being. Can a sentient being prove his/her own existence. :D :D :D

I don't believe in rocks, I think they're product of your imagination.
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Postby bill » Mon Sep 14, 2009 6:35 pm

Prove you do not believe in rocks prove that you know what the product of my imagination equals. :D :D :D :shock: :shock: :shock: 8) 8) 8)
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Postby Kemosabe-TBC » Mon Sep 14, 2009 6:38 pm

All I know is that I know nothing
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Postby bill » Mon Sep 14, 2009 6:42 pm

Prove you know nothing :D :D :D I say you do not know enough about nothing to say you know it :D :D :D nothing I say "is talking to you now" :D :D :D

Nothing is an AI program I developed :D :D :D

Therefore I am nothing :D :D :D

Who would know nothing better than nothing itself :D :D :D
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Postby davar55 » Fri Apr 22, 2011 1:06 pm

One hopes that Marilyn didn't overlook the fallacy of
medio fortelovatium in her otherwise thorough analytic
article. That's the argument from rational emotion.
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Re: Logical Fallacies

Postby drrosslg » Thu Sep 01, 2011 4:32 pm

Marilyn wrote:Logical Fallacies

Readers often ask about critical thinking and how to reason better. One of the best ways is to learn about logic, which is both fun and useful. Following are examples of the most common logical fallacies. You can use them as exercises to find the flaws in your own thinking.

Simple errors arising from ambiguity.

The same word may be used in different senses (called equivocation): “Marriage is a subject of great gravity, so getting married will make us gain weight.” Or a sentence construction may produce a double meaning (amphiboly): “We’re having some friends for dinner.” Or a word may be emphasized inappropriately (accent): Contrast “I just love my dog!” with “I just love my dog!” Or words that are similar in form may not be similar in sense (figure of speech): “Does he have cold feet?” Who asked: Your husband’s mother or his doctor?!

Confusing the parts with the whole.

We may mistakenly assume that what is true of the parts must be true of the whole (composition): “A chimpanzee is an intelligent animal and even grasps certain numerical concepts, such as the difference between one and two. So a dozen chimpanzees probably would be able to divide a dozen bananas among themselves equally.” Not too likely, right?! But what about this? “Every member of a congressional committee is bright and understands fiscal policy. So the committee likely would be able to successfully restructure the country’s fiscal policy.” It’s the same fallacy.
And sometimes we assume that what is true of the whole must be true of the parts (division): “A group of musicians is wildly popular. Therefore, if they break up, each will be wildly popular.” Of course, that’s incorrect. But how about this? “A corporation consisting of several subsidiaries produces goods of high quality and is profitable. Therefore, each subsidiary can be expected to produce goods of high quality and be profitable.” Again, it’s the same fallacy.

Considering the form of an argument.

We’ve all heard of “if-then” arguments: If this is so, then that must be so. One source of error is assuming “this” defines the only way in which “that” can occur (affirming the consequent): “If a person has full-blown AIDS, then his or her T-cell count will be low.” True. But the following is false: “A person has a low T-cell count. Thus, he or she has AIDS.” Other conditions cause low T-cell counts. A twin error occurs in the opposite manner (denying the antecedent): “A person does not have AIDS. Thus, he or she does not have a low T-cell count.” False, and for the same reason: Other conditions cause low T-cell counts.

Learning about deductive reasoning.

Have you ever heard this? “Every man is mortal; Socrates is a man; therefore, Socrates is mortal.” It’s a famous “syllogism,” a form of deductive reasoning that consists of a major premise, a minor premise, a “middle,”and a conclusion. (The “middle” appears in both premises, linking them.)
An error occurs when the middle contains a term used in two different senses (four terms): “Wool coats shrink if they get wet. Sheep have wool coats. Thus, sheep get smaller when they stand in the rain.” Obvious, right? But what about this? “Many people pay no taxes. The working class is composed of many people. Thus, the working class pays no taxes.” Obviously wrong!
Or the middle term may be used inappropriately to link the two premises (undistributed middle): “Truffles often are found by dogs trained to locate them by scent. Illegal drugs often are found by dogs trained to locate them by scent. Thus, truffles are often illegal drugs.” Oops! This is wrong, just as wrong as the following. “Executives often are ambitious and want to make a lot of money. Criminals often are ambitious and want to make a lot of money. Thus, successful executives are criminals.”
One error occurs when the conclusion is broader than the major premise allows (illicit major): “Politicians are actually reasonable people and not biased nitwits. All politicians are human beings. Therefore, no human beings are unreasonable or biased nitwits.” Another error occurs when the conclusion is broader than the minor premise allows (illicit minor): “Politicians love power. All politicians are human beings. Therefore, all human beings love power.”

Considering the fabric of an argument.

Capital punishment is the source of many an argument, both good and bad. Following are some bad ones, all containing an irrelevant conclusion (ignoratio elenchi). In this one, the opponent is attacked instead of the premise of the debate (argumentum ad hominem): “Capital punishment is wrong because people who favor it tend to be less religious.” And in this one, the opponent is attacked by means of a countercharge (tu quoque): “Capital punishment is right because those who oppose it are more likely to be criminals themselves.”
Abortion is also the source of many bad arguments. The following contain irrelevant conclusions, too. This form uses an appeal to pity (argumentum ad misericordium): “Abortion is wrong; what have these innocent babies ever done to deserve such a cruel fate?” And this form uses an appeal to popular passion (argumentum ad populum): “Pro-choice is right; if your daughter became pregnant as the result of a rape, should she be forced to bear the child?” This form relies on an authority (argumentum ad verecundiam): “Abortion is wrong because my religion says so.”
One last form of irrelevant conclusion is used by just about everyone, so let’s look at an example that is hard to criticize. This form maintains that because a premise is not known to be untrue, it may indeed be true (argumentum ad ignorantium): “No one has ever disproved the existence of the Tooth Fairy. Therefore, it won’t hurt to put your grandfather’s previous set of false teeth under your pillow every night. After all, she may be easy to fool.”

Circular Arguments

Scientists and creationists are always at odds, of course. The following fallacy is called “vicious circle.” In it, the conclusion also appears as an assumption (circulus in probando): “The story of divine creation as related in Genesis must be true because God would not deceive us.” Another fallacious argument is called “begging the question.” The conclusion appears as an assumption, but in a different form (petitio principii): “Miracles cannot occur because they would defy the laws of nature.” (All those talk show hosts who say, “And that begs the question...” when they mean, “And that prompts the question...” are simply wrong.)

Errors of Principles

Evolution has long been the target of illogical arguments that use presumption (secundum quid). One is called “direct accident,” in which the truth of an abstract principle is applied to a specific circumstance: “The theory of evolution maintains that man evolved from apes. Thus, the apes in our wildlife preserves will someday be found reading the newspaper.” Wrong, right?! So is the one called “converse accident,” which is the reverse: “Because the apes in our wildlife preserves will never be found reading the newspaper, man did not evolve from apes.”

Contradiction, Diversion, and Superstition

In one fallacy, the argument declares that an assumption is false if a contradiction can be drawn from it (reductio ad absurdum): “Intelligent people have open minds. Politicians are supposed to be intelligent. But anyone who says that recreational drugs should not be legalized has a closed mind. Therefore, politicians are not intelligent people.” In another fallacy, the argument takes the form of a question phrased so that a direct reply (instead of a denial) supports the implications of the question (plurimum interrogationum): “How many family members have you put at risk with the handgun you bought for self-defense?” Yet another fallacy (“after this, therefore because of it”) is the source of much of the world’s superstition, a legacy from early times (post hoc, ergo propter hoc). Can you imagine the audience reaction if a speaker were to be struck by lightning while denouncing creationism from an outdoor podium? It would make news all over the world!

That just doesn’t follow!

And in the notorious fallacy of non sequitur, the conclusion doesn’t follow from the argument, as in this example: “Because fish have gills and birds have wings, because dinosaurs are extinct and snakes are not, because the duckbilled platypus and the spiny anteater have characteristics of both reptiles and mammals, because animals need the waste products of plant respiration to survive and plants need the waste products of animal respiration, because plenty of plants need insects for fertilization but earthworms don’t even need another earthworm, because dolphins are intelligent and whales can sing, because crustaceans look so much like big bugs and primates look so much like humans, and because nearly every meat on the planet doesn’t taste all that much different from chicken, the theory of evolution is correct.” That just doesn't follow!
[quote]
tHE FALLACY IN MARILYN'S GAME SHOW SOLUTION
The foundational question is not whether you should switch or not
(here used as a creation of audience tension through delay). The question is whether the events are independent of each other or not. In fact the events (here each possible choice is an event) are here independent of each other. Whether it is a shell game or any game with three independent choices (one of which is a winning choice), the gamemaster removing one of the losing choices does not eliminate the independence of the original choices. This lack of recognition of whether or not the events are independent of each other or not is the most common error among amateurs of probability theory.
If you could prove that the goat-car choices are not independent of each other, then you must avoid the use of a probability theory that was designed for independent events.
For mutually dependent choices you might try Bayes who was one of the first to design a probability theory for mutually dependent events (conditional dependencies).
Best regards,
Ross Lee Graham, PhD
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Postby Kemosabe-TBC » Fri Sep 02, 2011 4:43 pm

I didn't understand exactly what is the fallacy you're referring to in Marilyn's Solution. If the gamemaster must remove a losing choice then her solution is correct, if the gamemaster removes a random choice, and it happens to be a losing choice, then her answer is incorrect. I'm sure she knows about this.
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Re: Logical Fallacies

Postby JeffJo » Tue Sep 06, 2011 11:03 am

drrosslg wrote:The foundational question is not whether you should switch or not
(here used as a creation of audience tension through delay)

Ummm... yes it is. That's what was asked, a fact which will become important below. Do you mean "The underlying issue behind whether you should switch is something else" ?
The question is whether the events are independent of each other or not. In fact the events (here each possible choice is an event) are here independent of each other.

Not really. The issue that causes controversy in the answer, is one of creating the proper sample space. That begins by properly defining what the words "outcome" and "event" mean. I'm not quite sure what you think they mean, but whatever it is, isn't right. It seems that by "dependent event" you mean that the actions are related to one another, because the possibilities for one action depend on the results of another. That's not what "dependent" means in probability theory.
If you could prove that the goat-car choices are not independent of each other, then you must avoid the use of a probability theory that was designed for independent events.
For mutually dependent choices you might try Bayes who was one of the first to design a probability theory for mutually dependent events (conditional dependencies).

There is no such thing as "a theory that was designed for independent events." Bayes' Theorem is part of all probability theory. You are right that the issue can be one of understanding how and when to apply it, but it isn’t necessary if you do things carefully. But that's the tricky part, and too many people ignore the need because they think their intuition is sufficient.

I think that what you are calling an "event" is what is called an "outcome" in probability theory. It is the actual result of some action that could have more than one result based on unknown factors. The actual contestant's choice (C), the actual placement of the automobile (A), and the actual host's choice (H) are all outcomes. We can describe the outcome of any one game fully, by writing those three numbers like this: CAH. So if the contestant chooses door #1, the auto is behind door #2, and the host opens door #3, that outcome is represented 123.

Ignoring how the choices are made, there are 27 combinations. But the set where C=2 is identical, in principle, to the set where C=1 if you just add 1 to A and H (and change "4" to "1"); as is the set where C=3. So I'll just use the nine where C=1: {111, 112, 113, 121, 122, 123, 131, 132, 133}. But five of those are not really possible; H is never going to be equal to C or A. That's what it seems you mean by "dependent events." That one action is predicated on the outcome of another. So dependency is not the issue here.

A probability is not assigned to an outcome; since it represents an actual results the idea of probability is meaningless for an outcome. Probability is assigned to an event. An "event" is a set of possible outcomes for a process. Anyone who says "The probability of outcome 123" really means "the probability of the set of possibilities {123}." It is written P({123}). But an event can include any number of possible outcomes. The event where you win by staying is {111,112,113}. (Yes, I mean all three - hold your objection a moment)

A probability can be any number between 0 and 1, including 0 and 1. That's one concept that often eludes non-mathematicians. They usually will try to "ignore" impossible outcomes completely, when the proper thing to do is ignore only the probability of the corresponding atomic event. You do that by saying its probability is 0, as in P({111})=0. That way, 111's inclusion in the event "win by staying" has no effect on other probabilities.

Two events are independent if they don’t duplicate any possible outcomes, and dependent if they do. Different atomic events are always independent. The probability of any event is the sum of the probabilities of any collection of independent events comprising it. It is usually easiest to use the atomic events for this. Then, all you need to do to solve a probability problem is assign a probability to every atomic event in the sample space. From that, you can derive any probability you need. And the way you do, is to use the information you are calling "dependent."

So now, finally, I'll get to your point. You seem to be arguing that the outcome H is dependent on the outcomes C and A, since it can't be equal to either. The correct way to express that thought, in probability theory, is that the probability of any atomic event where H=C or H=A is 0. Starting from that, we can use our knowledge of how some outcomes rely on others to get our atomic probabilities.

Since the placement of the car does not rely on other decisions, and we assume it is equally likely to be any door. Thus, we know that:
  • 1/3=P({111,112,113})=P({111})+P({112})+P({113})=0+P({112})+P({113})=P({112})+P({113})
  • 1/3=P({121,122,123})=P({121})+P({122})+P({123})=0+0+P({123})=P({123})
  • 1/3=P({131,132,133})=P({131})+P({132})+P({133})=0+P({132})+0=P({132})
Two of the unknown probabilities are now solved: P({123})=P({132})=1/3. If we make an assumption, Bayes' theorem is not needed. The event where you win by switching is {123,132}, and has probability 2/3. We don’t know for sure what the other two unknown probabilities are; but with that assumption, we don’t need to. The event where you win by staying is their union {112,113}, and has probability 1/3.

What assumption did we make there? That we can't distinguish the outcomes where H=2, from those where H=3. In practice, we will always see what door the host opened, whether or not the problem mentions it. So this is a bad assumption. Bayes' Theorem is now needed to determine the conditional probabilities, given what H is. Symmetry again lets us assume a value without losing any generality, so say H=3. Then,
    P(win by switching|host opens door #3 knowing it has a goat)
    = P({123}|{113,123})
    = P({113,123}|{123})*P({123})/P({113,123})
    = 1*P({123})/[P({113})+P({123})]
    = (1/3)/[P({113}+(1/3)]
    = 1/[3*P({113})+1]
So now we do need to know what P({113}) is, when all we know for sure is P({112})+P({113})=1/3. If we can assume those two are equal, and there is no way we can assume anything else, then each is 1/6 and this evaluates to 2/3, just like before.

But what if they aren't equal? Suppose the host always opens the door that lets Lovely Linda lead the goat offstage, to the right, without leading it in from of the other goat. Otherwise, the goats may "baa" at each other, revealing the surprise. It may be true wether or not we can assume it. In that case, P({113})=1/3 and P({112})=0, and the answer is 1/2. Buit it turns out that, no matter what you assume for P({113}) between 0 and 1/3, that P({123}|{113,123})>=P({113}|{113,123}). So you can never do worse by switching, and probably will do better.
Kemosabe-TBC wrote:If the gamemaster must remove a losing choice then her solution is correct, ...

Her answer that you should switch is; but not necessarily her answer that it doubles the probability. That depends, as I showed above, on how he chooses a door when the contestant originally picks correctly. And the way she obtained an answer - her "solution" - is quite flawed.
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Postby robert 46 » Wed Sep 07, 2011 11:48 am

JeffJo wrote:...the probability of any atomic event where H=C or H=A is 0

This is to assume a bias within the problem; as does P(H=null)=0.
So you can never do worse by switching, and probably will do better.

If the host only gives the opportunity to switch when the player has chosen the car then it is impossible to win by switching; P(H=null|C<>car)=1. This bias is just as much a matter of the host's motives as is any bias toward which door with a goat he may choose to open. If we assume non-bias then the host will give the opportunity to switch under both circumstances of the player choosing a door with goat or car, and there will be no bias as to which door with a goat to open (i.e. the host chooses a door randomly).
Kemosabe-TBC wrote: If the gamemaster must remove a losing choice then her solution is correct, ...

Her answer that you should switch is; but not necessarily her answer that it doubles the probability. That depends, as I showed above, on how he [the host] chooses a door [to open] when the contestant originally picks correctly [the door with the car].

JeffJo hypothesizes the relevancy of the host's motives which are unknown and unknowable.

I explained how the expected statistics prove the probability on Aug 04, 2008 9:49 am, page 62, Game Show Problem topic:
http://www.marilynvossavant.com/forum/v ... &start=915

All JeffJo could argue with is that the game combinations are not expected to happen equally often, and that this would change in the aggregate the statistics of winning the car by switching. (It is impossible to change the 1/3 probability of winning the car by staying.) But he cannot assert this unequal expectation without knowledge of specified conditions necessarily provided by the problem statement. However, there aren't any such explicit conditions. The only question of relevancy is whether the stated one-time occurrence of the host opening a door with a goat and giving the player the opportunity to switch should be considered generic to the problem. Whereas there is no information to the contrary from within the problem statement, this is a logically inferred necessary assumption; for otherwise the problem cannot give a definitive answer, but only an ad hoc answer based on unjustified assumptions imposed on the problem from outside the problem statement.
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