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The Counter-Point Guide to Logic


DZComposer

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If you've have no experience with logic, this thread is here to help!

NOTE: This was originally written for The Pub. Some of the examples are political or religious. Please do not debate them in this thread, create a thread in The Pub if you want to do that.

Logic basics:

Let's start with some terms.

Argument - an argument is a set of declarations, called premises, followed by a conclusion based on said premises. In other words, you take some points, for example "it is raining outside" and "I do not have an umbrella," and derive a conclusion from those points, "I will get wet." So, the example argument: It is raining outside and I do not have an umbrella, thus I will get wet.

Validity - A valid argument is an argument that is free from logical fallacies (more on those later). Truth of the premises does not matter. This argument is valid, despite it's absurd premises: If it is raining outside, I will die in a fire. It is raining outside. Thus, I will die in a fire.

Soundness - an argument is sound if the argument is valid, and the premises are true. A sound argument: It is raining outside and I do not have an umbrella, thus I will get wet.

Logical Fallacy - A misconception caused by incorrect reasoning

For discussing arguments, I will use logical notation.

Logical Symbols:

Variables (P,Q, R, S, A, B, X, Z, Etc.) - A variable is a letter of the alphabet. It represents a phrase. Variables remove the contents of the statements so that you can focus solely on the logic rather than the premises themselves.

->  conditional, also known as an If Statement.  The Antecedent of an If Statement is the condition that must be met for the statement to be true. The Consequent is the result of the antecedent being true. A -> C

= equality - the statement is true if both premises are true or both premises are false. A = B

!  not - negates a premise. Rarely used by itself. !A

* and - the statement is true if both premises are true. A * B

v or - the statement is true if one or both premises are true A v B

? xor - the statement is true if one of the premises is true, BUT NOT BOTH. A ? B

Logical symbols are laid out like elementary math problems, for example:

P -> Q

P

-------

Q

This reads "If P, then Q. P. Therefore, Q."

Arguments:

Arguments can be complex, but here are some basic valid arguments:

Modus Ponens

P -> Q

P

-------

Q

This reads "If P, then Q. P. Therefore, Q."

Modus Ponens is your basic If Statement argument. For an If statement to be true, the antecedent, P, must be true in order for the consequent, Q, to happen. Modus Ponens states the If Statement, and then affirms the antecedent, thus validating the conclusion that the consequent is also true.

Modus Tollens

P -> Q

!Q

-------

!P

This reads "If P, then Q. Not Q. Therefore, not P."

Modus Tollens is the basic negative if statement argument. It denies the consequent, and as a result states that the antecedent must not have occured.

This argument is an easy one to get tripped-up on in the validity vs. soundness difference. A common challenge to this form is "what if P happens anyway?" Such an action would render Q to NOT be a consequent of P, thus making the conditional premise false. But, the argument is still valid because that criticism is one for soundness, not validity.

MPT

I will not define the acronym, as it would lead to confusion.

!(A * B)

A

--------

!B

This reads "Not both A and B. A. Therefore, not B.

MPT is a basic AND argument. A good way to think of it is "there is only one winner." The first premise states that A and B cannot both be true. The second premise affirms A, thus the conclusion is that B is untrue since A and B cannot both be true.

Hypothetical Syllogism

P -> Q

Q -> R

-------

P -> R

"If P, then Q. If Q, then R. Thus, if P, then R."

This is a more complex conditional, and is designed to prove a point by proxy. The consequent of the first conditional is the antecedent of the second. Since the first antecedent determines the truth of Q, it also determines the truth of the second consequent R since the truth or R is dependent on the truth of Q. Thus the conclusion that the truth of P leads to the truth of R.

Categorical syllogism

All P have Q.

All R are P.

-----------

All R have Q.

All P have Q. All R are P. Thus, All R have Q.

This is a form of deductive reasoning. Premise 1 states that all P have Q. Premise 2 states that all R are P. Since all R are P, and all P are Q, it can be safely deduced that all R have Q.

There are many more arguments. I will add more to the thread over time.

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Logical Fallacies

This is the bread and butter of this thread.

Formal fallacy - Formal fallacies are always wrong. They are usually invalid, meaning no matter the text of the premise, it is wrong.

Informal fallacy - Informal fallacies are fallacies where the premises fail to support the conclusion, even though the argument may be technically valid.

Formal Fallacies:

Affirming the Consequent

P -> Q

Q

-------

P

If P, then Q. Q. Therefore, P.

This is a bastardization of Modus Tollens. This is fallacious because the occurrence of Q is not sufficient to prove the occurrence of P as P is not stated as the exclusive cause of Q. This is similar to the informal fallacy "Confusing necessary and sufficient conditions"

Denying the antecedent

P -> Q

!P

-------

!Q

If P, then Q. Not P. Thus, not Q.

This is fallacious for the same reason affirming the consequent is: P is not stated as the exclusive cause of Q.

Affirming a disjunct

P v Q

P

------

!Q

P or Q. P. Therefore, not Q.

This fallacy is a great explanation of the difference between OR and XOR. Or means that one or both of the premises is true. So, the claim that Q is not true is fallacious because the OR statement could still be true if Q is true as well as P. On the other hand, if the original statement was P ? Q, then the argument would be valid as XOR cannot be true if both P and Q are true.

The Fallacy Argument

P -> Q

P is fallacious.

--------

!Q

If P, then Q. P is fallacious. Thus, not Q.

We all love to bat someone over the head when they make a logic error, but it is easy to fall into this trap and make one yourself while in the process of calling your opponent. Just because your opponent commits a fallacy does not mean their conclusion is false.

False Dilemma

Also known as False Dichotomy

It is usually presented thusly:

P ? Q

!P (implied)

------

Q (implied)

This is one of those rare formal fallacies which is technically valid. To spot the fallacy, we have to go beyond logical notation, as this is a valid XOR statement. A common way of seeing it: "Well, Either you support the war in Afghanistan or you support Terrorism. Which is it?" Basically you are misusing XOR to force your opponent to choose between two options that are not mutually exclusive, or even the only two options.

Appeal to Probability

Possibly P

------

P

P is possible, thus P.

If there is a possibility P is true, assume it is true. Of course the problem with this is that it is also possible that P is false. This one likes to pop-up during debates about social programs. You'll often see the claim that since there is a potential for fraud, fraud will happen, so we shouldn't do it.

Bare Assertion

X says P.

X says X is not a lair.

-------

P

Person X says P. X says X is not a liar. Therefore, P.

And how do we know X is not lying about being a not being a liar?

Circular Reasoning

P -> P

P

---

P

Circular reasoning means the conclusion depends upon itself. "Potheads smoke lots of weed. Thus, people who are potheads smoke a lot of weed."

Proof by Example

X is part of B.

X has P.

----------

All Bs have P.

X is a member of group B. X has attribute P. Thus, all members of B have attribute P.

An example showing how ridiculous this line of reasoning is explains it best: My car is a Corvette. My car is blue. Thus, all Corvettes are blue.

Quantifier Shift

For each A there is B as C.

-------

Thus, there is a B that A and C.

I will give an easier to understand example:

Everybody has something to believe in. Therefore, there is something that everybody believes in.

Accident

P does Q.

R does Q.

----

R is P.

This fallacy claims that because one entity does something another one does, they are related. Of course that is not the case with most things. This is a favorite form to use while invoking Godwin's law: "Hitler was a good speaker. Obama is a good speaker. Thus, Obama is like Hitler."

Converse Accident

Each P I see is Q.

-------

All P are Q.

This fallacy assumes that because you have not seen differently, all of a group must be the same. Ex: All Corvettes I have seen are blue. Thus, all Corvettes are blue.

Exclusive Premises

No P are Q.

Some Q are !R

--------

Thus, some R are !P.

This fallacy assumes that because no P are Q, and that some Q are not R, that some R are not P. Ex: No fish are mammals. Some fish are not whales. Thus, some whales are not mammals.

Four Terms

Ex:

All P have Q.

All R have P.

----

All S have Q

This is a bastardization of the Categorical Syllogism. Because this fallacy in pure logical form is quite obviously fallacious, it is usually paired with the informal fallacy Equivocation. Example:

Nothing is greater than eternal enlightenment.

$5.00 is better than nothing.

This, $5.00 is better than eternal enlightenment.

Undistributed Middle

All P are Q.

A is Q.

---------

A is P

This incorrectly asserts that Q defines P, and thus all Q are P. Example: All Corvettes are Sports Cars. This Lotus Elise is a Sports Car. Thus, all Lotus Elises are Corvettes.

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Sorry to interrupt DZ, and feel free to remove this post if it's bugging you, but I do think one can sum all that up in three words.

Use common sense. Wink-2.gif

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Informal Fallacies

Since these fallacies may appear in many logical forms, I will not diagram them.

Ad Hominem

This fallacy attacks you opponent instead of their argument.

Example: Of course you would want to legalize marijuana. You are a pothead, afterall.

Appeal to Ignorance

This fallacy attempts to shift the burden of proof off of the argument and onto the rebuttal. It argues that since there is no evidence against a claim, it must be true.

Ex: You can't prove that God doesn't exist, thus it is acceptable to assume that he does.

Begging the Question

This fallacy bases its premises on the truth of the conclusion.

Ex: The Bible is the word of God because the Bible says God says the Bible is the Word of God.

Confusing necessary and sufficient conditions

This one can be hard to spot. The fallacy assumes that a necessary condition is sufficient for an event to occur.

Ex: Chernobyl happened because nuclear reactions are difficult to control.

Equivocation

Equivocation is a confusion of meanings for a word.

Ex: Pain isn't generic. For example, muscle tension causes headaches, and damaged cartilage causes arthritis pain. Since pain isn't generic your pain medicine should not be a generic brand, either. Use Tylenol, the number one doctor recommended brand. (This is from an actual Tylenol radio ad, BTW)

Faulty Analogy

This fallacy assumes that because there is one similarity between two things, that they must be alike.

This is another favorite for Godwin's Law. Ex: "Hitler was an artist, thus Picasso hated Jews."

Inconsistency

This one is simple: One commits this fallacy if their argument is inconsistent with itself.

Ex: "I don't think the government should be rounding up so many people for drug crimes, but I do think the government needs to be as tough as possible to prevent the filth of drugs from spoiling our society."

Irrelevant Authority

This fallacy occurs when you take the word of someone as an authority on a subject, when the person is, in fact, NOT an authority on that subject.

The authority can be anyone, be it a family member: "Well, my dad says 9/11 was an inside job..." or a professional speaking about a field that is not theirs: "As a PhD candidate in Molecular Chemistry, I can say that running after meals will give you leg cramps"

Is-Ought

This fallacy is the assumption that because something is a certain way, that is the way it ought to be.

Ex: Government is not regulating carbon emissions now, so there is no need for them to regulate carbon emissions.

Ought-Is

This is the opposite of Is-Ought: The assumption that because something ought to be a certain way, it is that way. Ought-is is usually tied with an appeal to emotion.

Ex: "I know he has been gone for five years, but he must be alive! I know he is!"

Questionable Cause

Assuming that one thing is caused by another without sufficient proof. Mere correlation is not proof. A well-know statistical adage is "correlation is not causation."

Ex: "The economy always does better when Republicans are in power, thus we need more Republicans in power."

Red Herring

This is a broad category of fallacy. Basically, a red herring is an attempt to draw you opponent off of the issue by focusing on something only marginally related.  This is sometimes called the "Chewbacca Defense" though technically that is a subset of the red herring that goes completely off-topic.

Examples:

A: Carbon acts as an insulator, trapping warmth inside the planet.

B. Warmth is nice. Nothing like a warm apple pie to sooth your nerves.

A: Corn-based Ethanol is a useful fuel, and it can be produced entirely within our borders.

B: I think the corn would be better used to help starving children in Africa.

Slippery Slope

Slippery Slope arguments are actually considered sound by many people, but, in fact, they are not. A slippery slope is used to argue against something by claiming that doing that will lead to a series of events with a less-than-fortunate outcome. This chain of events is not backed-up by evidence.

Ex: "First they will make us register to be gun owners. Then they will make us register our guns. Then they will take them away."

Sometimes this fallacy is accidentally stumbled-into during an attempt to do a reductio ad absurdium, which is a legitimate debate tactic to draw your opponent's line of thinking to it's absurd extreme.

Strawman

A strawman is an argument that re-frames your opponents argument as an argument that is easier to counter, and then mercilessly destroying it. This is fallacious because instead of debunking your opponents argument, you are debunking something they did not say.

Ex:

A. Gays should have just as much right to marry the one they love as straights.

B. No. Homosexuality is a sin, and such promiscuous lifestyles should be banned, as they are sins in the eyes of The Lord.

Two Wrongs

Two wrongs don't make a right. One commits a fallacy if they respond to a claim by pointing out something wrong their opponent did instead of debunking the point.

Ex:

A: You shouldn't smoke, it's bad for your lungs.

B: And you shouldn't drink, it's bad for your liver.

Unwarranted Generalization

This fallacy occurs when you make a generalization without sufficient supporting evidence.

Ex: "This class is going to be easy. The first lecture was all stuff I already knew!"

No true Scotsman

This fallacy is committed by one who holds a universal opinion about something. When that universal opinion is challenged with a counter example, the response is that that example is not one of the group.

Ex:

A: Every programmer loves C.

B: My uncle's been a programmer for 15 years, and he hates C.

A: Pfft. No REAL programmer would hate C.

Denying the correlative

This is the opposite of the false dilemma. There actually are cases where there is a binary choice between two mutually exclusive items. This fallacy occurs when one tires to add another choice that does not really exist.

Ex:

A: You either killed the girl or you didn't, stop stalling.

B: Are you sure the girl is really dead?

Texas Sharpshooter

This fallacy occurs when you design your evidence around your intended conclusion, instead of finding supportive evidence. The name comes from a joke about a Texas farmer who shot-up his barn, and then painted a target around his shots to make him appear to be a sharpshooter. It can be a tough one to spot. It is popular among believers in Nostradamus and things like the Bible Code.

A: Using this complex forumula, I can prove that there are hidden satanic messages in the Beatles' Yellow Submarine lyrics.

B: Does that forumula work on other songs?

A: No. I have to design a formula for each song.

Continuum

This occurs when one rejects a conclusion because a premise is vague. Vagueness of a premise does not guarantee that the conclusion is false.

A: Wood products are biodegradable, thus railroad ties will eventually rot away.

B: You're being to vague. Just because some wood products are biodegradable doesn't mean that my railroad needs to periodically replace ties.

False Attribution

This fallacy occurs when you cite a source that is unqualified, irrelevant, unidentified, or fabricated.

Ex: "My father's cousin works at Nintendo and he says there is a Star Fox game coming out next year for Wii."

Loki's Wager

This fallacy occurs when you claim that something is not defined, and thus, cannot be discussed.

Ex: "God is above human knowledge and reason, thus it is fallacious to discuss him in that manner"

Quoting out of context

This is when you quote somebody incompletely, removing context that could be counter to your point.

A: The weapons used by this group are being passed around. If we take away the guns, the murders will stop.

B: A is anti-gun: "If we take away the guns, the murders will stop."

Appeal to Emotion

This occurs when you use emotions to sway people to your side. IT IS NOT ALWAYS A FALLACY. Appeal to emotion is only fallacious if the appeal is unwarranted.

Ex:

"If you elect a Democrat, there will be a terrorist attack within three months."

"Pornography must be banned! Think of the children!"

Appeal to Morality

This fallacy occurs when you claim that a premise is immoral, and thus false.

Ex:

A: Strip clubs should not be discriminated against. They have just as much right to exist as christian book stores.

B: Lusting for women is immoral, so these clubs do not have a right to exist.

Non-sequitur

This fallacy occurs when your premises do not lead to your conclusion. Note that many of the other fallacies are special cases of non-sequitur.

Ex:

"HP printers are utter crap, and the ink is way too expensive. Thus the ex-CEO of HP should not be a senator."

Godwin's Law

AKA Reductio ad Hitlerum

This fallacy occurs when you needlessly attach your opponent's claim to Hitler, Nazis, Nazi Germany, or The Holocaust. It is usually used as an appeal to emotion or a red herring.

A: I think registering for a driver's license is a good idea. It makes sure that those who are on the road know the rules and how to operate a motor vehicle.

B: Hitler made all the Jews register so he could take them away. What's to stop the government from doing the same thing to drivers?

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Sorry to interrupt DZ, and feel free to remove this post if it's bugging you, but I do think one can sum all that up in three words.

Use common sense.

These seem common sense because I am using obvious examples. These fallacies are everywhere. The only way to avoid making them is to be aware of them, and even then you slip-up. I don't claim to be perfect at this. I've dropped my fair share of fallacies in my time, but knowing them has reduced it.

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To help with the guide, I will periodically post some things from around the internet and identify the fallacy.

This comes for a Huffington Post comment thread about Obama forcing Gen. McChrystal's resignation today:

Another Obama mistake. The military has to live up to a code of ethics and display proper protocol but politicians, in general, have no such expectations of themselves and spout their mouths off without repercussions. While McCrystal should have held his tongue, Obama is WRONG.

This is an inconsistency with a touch of two wrongs. On the one hand, this person claims that military personnel should be held to a standard of ethics, yet his conclusion is that the president was wrong in holding McChrystal accountable for his remarks, while mentioning that politicians are not held to the same standard.

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Sorry to interrupt DZ, and feel free to remove this post if it's bugging you, but I do think one can sum all that up in three words.

Use common sense. Wink-2.gif

The problem with common sense is people tend to forget they have it when politics and religion is involved.

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Guest Julius Quasar

The problem with common sense is people tend to forget they have it when politics and religion is involved.

...and emotions run high, clouding judgment.

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DZ, what a detailed deconstruction of debate theory. ^_^ Which all but guarantees most people won't understand. :P:trollface:

Asper Sarnoff, not all of us have common sense. :3 I mean, I have my own common sense, but it's very different from most other people's.  It's often like not having common sense at all. X3

Phil: Use common sense!

Hilary: I don't have any common sense!

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I already PMed DZ about this, but I think his explaination isn't difficult because it's detailed, but rather to complex. You don't need faux programing lingo or horrible, hard to follow asci graphs. A simple explaination will sufice.

Also, I disagree that the chewbacca defence is a red herring. The goal of the chewbacca defence is to confuse your opponent into giving up, not mislead them away from the topic.

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Also, I disagree that the chewbacca defence is a red herring. The goal of the chewbacca defence is to confuse your opponent into giving up, not mislead them away from the topic.

I know of at least one debate book that mentions the Chewbacca defense as a term for the red herring: http://www.amazon.com/Thank-You-Arguing-Aristotle-Persuasion/dp/0307341445/ref=sr_1_1?ie=UTF8&s=books&qid=1277404976&sr=1-1

I learned logic using those symbols. They make the argument easier to understand by removing the content of the argument and focusing on the raw logic. If symbols bamboozle you for some reason, I did describe them in more detail underneath.

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So, one guy says that it should simply be called a red herring, and that somehow trumps popular usage. The goal of a red herring is to descract, mislead, or dodge a question. Chewbacca defence doesn't have to do any. It can be off topic, or on topic. The goal is to confuse.

As for being 'bamboozled', I understand them mainly from how logic works. That's doesn't mean it couldn't be simpler. It's a bit like those guys who say 'intiger' instead of number, or use the long versions of words for no reason. It doesn't add anything other then confusion. It makes it harder to read (though that is partly due to crap asci) and makes you seem like a smug psudo intellectual tosser.

I was big in the school math circuit. I'm a trained computer tech. I am a novice programmer. I know how to animate in both 2D and 3D and thus know some of the lingo that goes into those. As such I see this kind of thing alot. The point of jargon is to make talking about specifics within a field quicker and more clear. It's NOT about exclusion and making yourself look smart. That is why I have issue with how you did the op. It's needless.

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When we were on the subject of common-sense, I'd like to share something I got in an E-mail recently about him.Laugh.gif

Today, we mourn the loss of our good friend, common sense, who has been with us for many years. No one know for sure how old he was, since his birth records have long ago been lost in bureaucratic red tape. He will be remembered as having cultivated such valuable lessons as:

-knowing when to come in out of the rain

-why the early bird gets the worm

-life isnt always fair

-and maybe it was my fault

Common Sense lived by simple, sound financial policies (don't spend more than you can earn) and reliable strategies (adults, not children, are in charge)

His health began to deteriorate rapidly when well-intentioned but overbearing regulations were set in place. Reports of a 6 year old boy charged with sexual harassment for kissing a classmate; teens suspended from school for using mouthwash after lunch; and a teacher being fired for reprimanding an unruly student, only worsened his condition

Common Sense lost ground when parents attacked teachers for doing the job that they themselves had failed to do in disciplining their unruly children.

He declined even further when schools were required to get parental consent to administer sun lotion or an aspirin to a student; but could not inform parents when a student became pregnant and wanted to have an abortion.

Common Sense lost the will to life as the churches became businesses; and criminals recived better treatment than their victims.

Common Sense took a beating when you couldn't defend yourself from a burglar in your own home and the burglar could sue you for assault.

Common Sense finally gave up the will to live, after a woman failed to realize that a steaming cup of coffee was hot. She spilled a little on her lap, and was promptly awarded a huge settlement

Common Sense was preceeded in death, by his parents, Truth and Trust, by his wife, Discretion, by his daughter, Responsibility, and by his son, Reason.

He is survived by his 4 step-brothers:

-I know my rights

- Someone else is to blame

- Im a victim

-I want it now

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When we were on the subject of common-sense, I'd like to share something I got in an E-mail recently about him.Laugh.gif

...I smell right-wing slant in that email. :lol: Seriously though, it has some good tongue-in-cheek humor. :3

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So, one guy says that it should simply be called a red herring, and that somehow trumps popular usage. The goal of a red herring is to descract, mislead, or dodge a question. Chewbacca defence doesn't have to do any. It can be off topic, or on topic. The goal is to confuse.

As for being 'bamboozled', I understand them mainly from how logic works. That's doesn't mean it couldn't be simpler. It's a bit like those guys who say 'intiger' instead of number, or use the long versions of words for no reason. It doesn't add anything other then confusion. It makes it harder to read (though that is partly due to crap asci) and makes you seem like a smug psudo intellectual tosser.

I was big in the school math circuit. I'm a trained computer tech. I am a novice programmer. I know how to animate in both 2D and 3D and thus know some of the lingo that goes into those. As such I see this kind of thing alot. The point of jargon is to make talking about specifics within a field quicker and more clear. It's NOT about exclusion and making yourself look smart. That is why I have issue with how you did the op. It's needless.

Is there anything you agree with around here? I am getting sick of your negativity. I am trying my best to be helpful, and you are going around accusing me if trying to be overly intellectual. STOP.

If you feel you can explain a concept better than I can, then do so. That is why I unlocked the thread. Don't bitch at me for trying to help people learn the way I learned.

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DZ, you're doing an awesome job at explaining this stuff.

These fallacies happen all over the place everyday, and a lot of people go through life not knowing what they are.

It's amazing the sheer number of instances that we can stumble argumentatively.

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Is there anything you agree with around here? I am getting sick of your negativity. I am trying my best to be helpful, and you are going around accusing me if trying to be overly intellectual. STOP.

If you feel you can explain a concept better than I can, then do so. That is why I unlocked the thread. Don't bitch at me for trying to help people learn the way I learned.

You are doing a GrEaT job DZ,

this data is going to be really

helpful. At least to me and a load

of people. :wink:

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Oh boy...

What do you call a case that was about to be closed,

yet a statement just blows everything away

and people are too stunned to counter that statement?

And I think this board is like a courthouse.

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Oh boy...

What do you call a case that was about to be closed,

yet a statement just blows everything away

and people are too stunned to counter that statement?

And I think this board is like a courthouse.

Fatality.

And nah, its a pub. We even have a bar.

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Oh boy...

What do you call a case that was about to be closed,

yet a statement just blows everything away

and people are too stunned to counter that statement?

And I think this board is like a courthouse.

Depends on what the statement is, really.

If it's off topic, it is likely a Chewbacca Defense form of the Red Herring.

It could be appeal to emotion.

Or, it could be completely sound argument with just a shocking conclusion.

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One that's cropped up alot recently I'm trying to find a name of, if not there should be one made up.

Basicly the idea of worst case justifies the rest. Examples

"This DRM is good because at least it's not the Ubisoft DRM."

"That was a sexist comment, but it wasn't as bad as the comment by person X so it's fine."

"I might have thrown an orphan under a train, but at least I'm not Hitler."

Update. It's called Moral equivalence falacy.

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I have another. Trying to find a name for it. Where A and B are arguing. Person B is losing, and so claims that "This conversation is over" and doesn't reply to any more posts, comments, questions ect.

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