## Logical Fallacies

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**4**of**5**• 1, 2, 3,**4**, 5robert 46 wrote: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.

Did you even read what I wrote? It seems not, since the "bias" you claim I assume (and I only use the word because you did) is that the host won't open the contestant's door, or the door with the car, which is what you always insist must be assumed.

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

Who said anything about "the host only gives the opportunity to switch when the player has chosen the car" ? Certainly not me. I was talking about something entirely different. Go back, and try reading for a change.

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.

No, that's what you do. I allowed for any motive.

I explained how the expected statistics ...

There is no such thing as "expected statistics." So anything you think you "proved" by them is wrong.

- We don't know the host's motives.
- But we assume he always opens a door, always opens a goat door, and always offers the switch. These assumptions cannot be proven by any means, but are good assumptions. As are many others you refuse to make.
- We probably can also assume he chooses randomly if there are two doors he can choose between. It's actually required by law, which is why it's a good assumption. But it isn't necesssary to answer the question "Should You Switch?"
- But it is necessary to get the ansswer you give, of 1/3 : 2/3. You make that assumption.

All JeffJo could argue with ...

I presume you are speaking hypothetically, since that was posted two years before I joined the list. But it is another example of who you try to give false impressions, if they serve to promote your own ego.

But there are many things wrong with your "proof." It completely fails to adhere to any known principles of probability. While the prior probability for each door is equal as you claim, the posterior probability depends on the motives of the host, which you claim are unknowable. It is only by making certain assumptions that a value for that probability can be assigned. You even describe how you do it, but you leave one motive out.

- JeffJo
- Intellectual
**Posts:**2609**Joined:**Tue Mar 10, 2009 11:01 am

JeffJo wrote:We don't know the host's motives.

Agreed.

But we assume he always opens a door, always opens a goat door, and always offers the switch. These assumptions cannot be proven by any means, but are good assumptions.

Agreed.

As are many others you refuse to make.

If we assume that there is a new player for each game then any consistency on the part of the host which each new player doesn't know about is irrelevant to the calculated probability. For example: the host might always put the car behind the door to the right (circular) of the door the car was behind during the previous game. If the new player does not know this, or does not know which door the car was behind during the prior game, then this consistency is irrelevant.

We probably can also assume he chooses randomly if there are two doors he can choose between.

Again, if the current player does not know about a consistent pattern the host uses for choosing between goat doors it is irrelevant to the probability.

While the prior probability for each door is equal as you claim, the posterior probability depends on the motives of the host, which you claim are unknowable. It is only by making certain assumptions that a value for that probability can be assigned. You even describe how you do it, but you leave one motive out.

Presumed to mean "Method of selecting between goat doors".

- robert 46
- Intellectual
**Posts:**2841**Joined:**Mon Jun 18, 2007 9:21 am

robert 46 wrote:If we assume that there is a new player for each game then any consistency on the part of the host which each new player doesn't know about is irrelevant to the calculated probability.

Unknown, but not irrelevant. You have to assume something to answer.

The assumptions that are made here are (1) that the car placement is random, (2) the contestant's choice is un-informed (which makes it random), (3) the host always opens a door (4) to reveal a goat, (5) the host always offers a switch, and (6) maybe that the host chooses randomly from all available goat doors. #6 is not necessary to answer the question "should you switch," but it is necessary to place a value on the probability.

Again, if the current player does not know about a consistent pattern the host uses for choosing between goat doors it is irrelevant to the probability.

It affects the probability; it is the the contestant's ability to calculate it that you describe. And this is an argument you yourself have used in other "discussions." Assuming the host favors one door is equivalent to assuming, in the TCP, that you "always" know about a boy.

- JeffJo
- Intellectual
**Posts:**2609**Joined:**Tue Mar 10, 2009 11:01 am

JeffJo wrote:robert 46 wrote: If we assume that there is a new player for each game then any consistency on the part of the host which each new player doesn't know about is irrelevant to the calculated probability.

Unknown, but not irrelevant. You have to assume something to answer.

Then we assume there is no *hypothetical* "consistency on the part of the host" to which we need give any consideration.

The assumptions that are made here are (1) that the car placement is random, (2) the contestant's choice is un-informed (which makes it random), (3) the host always opens a door (4) to reveal a goat, (5) the host always offers a switch, and (6) maybe that the host chooses randomly from all available goat doors. #6 is not necessary to answer the question "should you switch," but it is necessary to place a value on the probability.

It cannot be "necessary" if it cannot be determined. The point is to calculate a probability relative to the current player, so a determination must be made as to what the player can be reasonably expected to know. Nothing in the problem statement implies host bias in the selection of a door with a goat to open at such times as there is an option. The player would reasonably think that, whereas he had a 2/3 chance of picking a door with a goat, it is twice as likely that the host has no option as to which door to open in the current game; but if he does have an option, as far as the player can determine the choice is irrelevant.

Quote: Again, if the current player does not know about a consistent pattern the host uses for choosing between goat doors it is irrelevant to the probability.

It affects the probability; it is the the contestant's ability to calculate it that you describe.

Contestant has no ability to factor in the effect of unknown details. You have said that a probability is relative to what the person calculating the probability knows.

Whereas the host knows where the prizes are and what the player's choice of door is, the probability determined by the host of the player switching to the remaining door and winning the car is a certainty- either 0 or 1 depending on the circumstances of the game. But this trivial viewpoint is not the one of importance. Only the player's viewpoint is relevant to the sought for probability answer.

And this is an argument you yourself have used in other "discussions." Assuming the host favors one door is equivalent to assuming, in the TCP, that you "always" know about a boy.

I don't see it that way. Assuming the host always *opens a door with a goat* is the same as always *knowing about a boy*. However, if "boy" is everywhere in the TCP replaced with "girl" then the numeric answer must be the same consequent to the assumption of equi-probability of the births of boys and girls. So it doesn't matter whether we *always* know about boys or *always* know about girls.

But if we randomly know about boys or girls and wish to know the probability of *two boys*, it is isomorphic to randomly opening a door with goat or car and wishing to know the probability of *winning the car by switching*. When we know about a girl it is impossible for the family to have two boys, and when the door with the car is opened it is impossible to win the car by switching. These occurrences change the statistics of winning the car by switching over multiple games, and change the statistics of having two boys over multiple families. A probability problem has been converted into a statistical problem by introducing the random element of reporting boys or girls, or random element of opening a door with goat or car. It is this added random element introduced into the problem from outside which morphs the problem into something different from what we were given.

I assert it converts to a statistical problem just because the given one-time occurrence has been changed to heterogeneous multiple occurrences by the introduction of the new random element which is *only* effectual over multiple occurrences. So the real difference is between a homogeneous multiple occurrence problem (given) vs. a heterogeneous multiple occurrence problem (introduced). But we are necessarily tasked with solving the *given* problem, not the *introduced* problem.

- robert 46
- Intellectual
**Posts:**2841**Joined:**Mon Jun 18, 2007 9:21 am

robert 46 wrote:Then we assume there is no *hypothetical* "consistency on the part of the host" to which we need give any consideration.

Assumption is not knowledge. You said that.

The point is that we don't need to make that assumption, even if it is a very good one, to answer the question. And that you implicitly make it in everything you've ever said about the problem, without acknowledging that you are doing it. Most of what you wrote is wrong because of that, even if (by serendipity) it gets the right answer. Just like you assume "you always know there is a boy" in the TCP, where it is NOT a good assumption.

The fact is that how information is obtained changes the relative values of the probabilities of what remains possible in both problems. The probability that your original choice is the car does not stay at 1/3 because it started there, it is because of the assumptions you make about the host's motivations. The probability of BB and BG remain equal only if you assume a bias in teh process by which you learned of the boy.

Other assumptions, which are not contraindicated in any way, can and do produce other values. Your solutions are wrong because they do not handle this fact. The answers may be right, but the solutions are wrong.

It cannot be "necessary" if it cannot be determined. The point is to calculate a probability relative to the current player, so a determination must be made as to what the player can be reasonably expected to know.

No, that determination does not need to be made. Haven't you been reading?

Whereas the host knows where the prizes are and what the player's choice of door is, the probability determined by the host of the player switching to the remaining door and winning the car is a certainty- either 0 or 1 depending on the circumstances of the game. But this trivial viewpoint is not the one of importance. Only the player's viewpoint is relevant to the sought for probability answer.

Right - and the answer is that switching wins with probability 1/(1+Q), where Q is the probability in the player's viewpoint for the host's bias. We don't know if that player has some information about it - specifically, we don't know for a fact that the player hasn't noticed that the host prefers to open Door #3 on Tuesdays.

I don't see it that way.

Of course you don't - you never see things in the way that shows how wrong you are.

Assuming the host always *opens a door with a goat* is the same as always *knowing about a boy*.

Why? Why isn't it the same as "knowing about one gender - in this one case, 'boy'" ? There is part of the wording of the TCP that makes either interpretation preferable to the other. In the GSP, there is a difference - we assume the host is tantalizing the contestant, because in our experinece that is what game show hosts always do.

However, if "boy" is everywhere in the TCP replaced with "girl" then the numeric answer must be the same consequent to the assumption of equi-probability of the births of boys and girls. So it doesn't matter whether we *always* know about boys or *always* know about girls.

There is no justification for "always know 'boy'" over "always know one gender that is appropriate."

I assert it converts to a statistical problem

And again, you do not understand what the term "statistical" means. Go ahead - try to formulate your definition. I'll tell you where it is wrong.

What you mean is that the Bayesian probability - for a one-time occurrence - can be modeled as a frequentist probability - for repeated occurrences. But you have to figure out what gets repeated to do that, and you do it wrong.

- JeffJo
- Intellectual
**Posts:**2609**Joined:**Tue Mar 10, 2009 11:01 am

### Response in GSP and TCP topic

I have responded in the GSP and TCP topic, Magazine Column forum, because this thread has gone off-topic from logical fallacies.

- robert 46
- Intellectual
**Posts:**2841**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Response in GSP and TCP topic

robert 46 wrote:I have responded in the GSP and TCP topic, Magazine Column forum, because this thread has gone off-topic from logical fallacies.

Still, that digression is a great example of a logical fallacy discussed. "If the family is appropriate to the context of the problem, then it includes at least one boy" is not the same as "If the family includes at least one boy, then it is appropriate to the context of the problem." That would be an example of affirming the consequant.

- JeffJo
- Intellectual
**Posts:**2609**Joined:**Tue Mar 10, 2009 11:01 am

It occured to me recently that the logical fallacy argument from incredulity is flawed.

I have seen it used mainly against religous people who are skeptical of evolution.

'I can't believe fish could gradually mutate into man.'

The problem I see is that the opposing view, 'I can't believe a super intelligent entity exists and created all life', is equally disqualified by argument from incredulity.

The basic logic still stands, but since it can knock down both opposing views, it's useless for gaining any ground in a debate.

I have seen it used mainly against religous people who are skeptical of evolution.

'I can't believe fish could gradually mutate into man.'

The problem I see is that the opposing view, 'I can't believe a super intelligent entity exists and created all life', is equally disqualified by argument from incredulity.

The basic logic still stands, but since it can knock down both opposing views, it's useless for gaining any ground in a debate.

- JO 753
- Intellectual
**Posts:**625**Joined:**Tue Mar 16, 2010 6:54 pm**Location:**IL NOEEZ

### Re: Logical Fallacies

I think the most common lojik error iz appeal to authority.

Even tho it may not be the most common in debates, it iz ubiquitously utilized in the form uv quotes and attribution. It iz standard operating proceedure in journalizm.

An article intended to persuade readerz to believe a particular opinion andor conclusion will often contain quotes from experts, providing their name and credentialz az evidens that such a knowledgeable person believz it, therefor so shoud the prezumably less qualified readerz.

I can understand that a reporter cant become an expert overnite on a subject he haz no previous experience in, so it makes sens for him to just report wut the experts say.

A problem I see iz that many popular 'opinionatorz' will call on authority figurez rather that explain the lojik behind their opinion.

Even tho it may not be the most common in debates, it iz ubiquitously utilized in the form uv quotes and attribution. It iz standard operating proceedure in journalizm.

An article intended to persuade readerz to believe a particular opinion andor conclusion will often contain quotes from experts, providing their name and credentialz az evidens that such a knowledgeable person believz it, therefor so shoud the prezumably less qualified readerz.

I can understand that a reporter cant become an expert overnite on a subject he haz no previous experience in, so it makes sens for him to just report wut the experts say.

A problem I see iz that many popular 'opinionatorz' will call on authority figurez rather that explain the lojik behind their opinion.

- JO 753
- Intellectual
**Posts:**625**Joined:**Tue Mar 16, 2010 6:54 pm**Location:**IL NOEEZ

### Re: Logical Fallacies

Using references - books or quoting people - is only an appeal to authority if

the source is not identified. If the source is identified, then the logic of the

point in the presentation is made transparent and can be evaluated.

the source is not identified. If the source is identified, then the logic of the

point in the presentation is made transparent and can be evaluated.

- davar55
- Intellectual
**Posts:**728**Joined:**Tue Jun 13, 2006 4:24 pm**Location:**New York City

### Re: Logical Fallacies

Identifying the sours duznt make the lojik transparent.

- JO 753
- Intellectual
**Posts:**625**Joined:**Tue Mar 16, 2010 6:54 pm**Location:**IL NOEEZ

### Re: Logical Fallacies

Identifying sources makes the logic or illogic accessible.

- davar55
- Intellectual
**Posts:**728**Joined:**Tue Jun 13, 2006 4:24 pm**Location:**New York City

### Re: Logical Fallacies

Suppoze to, anyway. How many peepl will actually bother?

Its an effort that woud only be made if sumwun wuz sufficiently inspired, pozitivly or negativly, to try to find source material or the person.

Its an effort that woud only be made if sumwun wuz sufficiently inspired, pozitivly or negativly, to try to find source material or the person.

- JO 753
- Intellectual
**Posts:**625**Joined:**Tue Mar 16, 2010 6:54 pm**Location:**IL NOEEZ

### Re: Logical Fallacies

sumTymz tha athorti iz juhhhst comn sens.

- davar55
- Intellectual
**Posts:**728**Joined:**Tue Jun 13, 2006 4:24 pm**Location:**New York City

### Re: Logical Fallacies

KoMN SeNS IZ U MIx. XeR oR PEPL WIx GuD SeNS, BUT XA oR NoT KoMN.

- JO 753
- Intellectual
**Posts:**625**Joined:**Tue Mar 16, 2010 6:54 pm**Location:**IL NOEEZ

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