A Little Logic is a Dangerous Thing

[Username17]

Rant Ahead!

You know what's really pissing me off these days? People calling shit "fallacies" and calling people on using fallacies. In fact, even the word "fallacy" hacks me right off. Because you know what? Most of this shit isn't a fallacy, and even if it was the fact of something being a fallacy doesn't actually stop it from being a good argument in all cases.

Let's go back for a moment to what a Fallacy actually is: it is an argument where the conclusions are not 100% contained in the premises. This means for example that absolutely every single piece of scientific investigation is always a fallacy because total truth does not exist in the real world and actual sense data has margins of error. That doesn't make it wrong that just makes it logically invalid. I am confident that if I were to drop a pencil that it would fall in accordance with gravity but that is not a logically sound conclusion because there is chance that my experience up to date has all been atypical and the gravity generators that have been laughing at me for nearly three decades could stop right before I loose the pencil. That's possible, so my argument in favor of gravity is technically fallacious.

The fact is that Logical Truth does not really exist in the real world. It's a fundamentally bankrupt philosophy that cannot address anything outside the narrow confines of mathematics. And only some maths at that. Even within the spheres that Logic applies to, it is almost invariably applied incorrectly. After all, we often talk about game mechanics which actually are mathematical constructs made out of rules. But that's exactly the problem. They are made out of rules. Not declarative true statements. Logic that applies to rules is not the same as logic that applies to declarative statements.

For example: In Sentential Logic (that's the easiest kind of logic), you have cool little "Fallacies" like this one:

"If A then B" therefore:
"Not A, therefore Not B" - WRONG!

Under sentential logic, this argument is false. You only know if A or B is true if it is stated in one of the statements that are assumed to be true (the Premises). So because we don't have A we have no statement saying is definitely True, but we also have no statement that it is False. We are in coin flip territory.

But most games are not written like that. They are written in rules. And that means that B is generally speaking false unless a rule comes in to make it true. So if you have the rule "If A then B." and you don't have A, you don't have B either. While such a statement is formally a "Denying the Antecedent Non Sequitur Formal Fallacy" for purposes of sentential logic, within the confines of a game's set of rules it is actually true.

Furthermore, sentential logic gets its panties all knotted up if you have contradictions. Rule logic doesn't. Seriously, once you have a contradiction of any kind in sentential logic things go south hard:

1. ~A * A
2. ~A
3. A
   --------
4. ~A v B (2, Addition)
5. B (3, 4, Disjunction)

Oh snap! You just proved that B is true for any B no matter how ridiculous. And that's the kind of thing that will plague you constantly if you try to apply the rigid rules of sentential logic to a set of directives.

But directive logic doesn't break under that strain. If you have a rule that tells you "If A then B" and another rule that says "If C then Not B" then you can totally have A and C and not explode your head. The rules just get applied in some order and B ends up ether being true or false and not both and you move on with your life.

---

In conclusion: Logic isn't particularly helpful a lot of the time. Frankly, it's a largely discredited epistemological system. Since you can't really know anything "for sure" pretty much everything you ever say is technically a logical fallacy and calling attention to that fact is a waste of everyone's time. Hopefully we're all mature enough to realize that we aren't completely certain that the sun will rise tomorrow or that other people are real or that you aren't in The Matrix right now. Hopefully we're all also mature enough to accept that fact and move on with our lives as if the highly probable were in fact "true" and adaptable enough to change our view of what is highly probable in the face of evidence.

But even within the context of the highly probable, rules of sentential logic are a waste of my damn time. And yours. Affirming a Disjunct Non Sequitur is something that frickin works, because most of the time people use exclusive "or" when speaking and/or writing things down. We use and/or for a reason.

-Username17

[Judging__Eagle]

What caused this?

[RandomCasualty2]

Furthermore, sentential logic gets its panties all knotted up if you have contradictions. Rule logic doesn't. Seriously, once you have a contradiction of any kind in sentential logic things go south hard:

1. ~A * A
2. ~A
3. A
   --------
4. ~A v B (2, Addition)
5. B (3, 4, Disjunction)

Oh snap! You just proved that B is true for any B no matter how ridiculous. And that's the kind of thing that will plague you constantly if you try to apply the rigid rules of sentential logic to a set of directives.

But directive logic doesn't break under that strain. If you have a rule that tells you "If A then B" and another rule that says "If C then Not B" then you can totally have A and C and not explode your head. The rules just get applied in some order and B ends up ether being true or false and not both and you move on with your life.

Well yeah, obviously if your premises include the fact that A is true and ~A is true, which means that A is both true and false, then you're not going to be able to make any real judgments about that, because your basic premises are illogical, therefore any conclusions you get from that are going to be illogical. Why do you consider that a bad thing?

The moment you say that Professor Plum is the murderer and also not the murderer, you're no longer living in a sane universe anymore. And thus anything can now be true, because you've invalidated the accuracy of your starting premises. But this doesn't actually prove anything except the fact that one or more of your premises is false. If your premises themselves are a contradiction, then any conclusion you reach will be garbage. The fact that you're trying to draw conclusions from an illogical universe should be reason enough to throw up a red flag.

All the times i can find a fallacy being used in a debate, it usually means that the person really is using faulty logic. Really the only problem I've seen is that sometimes someone accuses someone of a fallacy when they really haven't made that fallacy.

I'm curious as to what fallacies you think have a relevant place in debate?

[Surgo]

Damn good post. I've tried to inform people that all of scientific evidence ever was, technically, fallacious before and they looked at me with those strange questioning glances people get when they're confused and wondering what the hell you're going on about.

What really gets me is how people are willing to throw around the Ad Hominem fallacy when most of the time nobody's actually doing it.

[Count Arioch the 28th]

I thought Ad Hominem attacks weren't considered a fallacy? The way I was always using was "Your opinions about my mother's sexual encounters are not relevant to the discussion, stop being a douche."

[RandomCasualty2]

I thought Ad Hominem attacks weren't considered a fallacy? The way I was always using was "Your opinions about my mother's sexual encounters are not relevant to the discussion, stop being a douche."

The main "fallacy" to ad hominem is an implied one. Namely it's that "This guy is a douchebag, therefore what he says is automatically false."

It's the basic mudslinging political theory, where if you don't like someone you're less likely to think that what they're saying is accurate.

[Username17]

Well yeah, obviously if your premises include the fact that A is true and ~A is true, which means that A is both true and false, then you're not going to be able to make any real judgments about that, because your basic premises are illogical, therefore any conclusions you get from that are going to be illogical. Why do you consider that a bad thing?

Because rules are not premises. So if you have a rule that says something like:

• Characters get their Dexterity Bonus to Armor Class (formalizes to "A").

and another rule that says something like:

• Characters who are blind do not get their Dexterity Bonus to Armor Class (formalizes to "If B then ~A")

then you're totally fine if your character gets blinded. While at that point you have two directives which state A and Not A, that's not problematic.

It's illogical, because it's not logic, but it parses fine. One rule contradicts the other and you don't get your Dexterity to AC. The contradiction doesn't break anything because it's not a sentential logic system and is not amenable to sentential logic operations. Rules aren't "true" or "false" - they are just rules. And they are weighted accordingly.

-Username17

[Surgo]

I thought Ad Hominem attacks weren't considered a fallacy? The way I was always using was "Your opinions about my mother's sexual encounters are not relevant to the discussion, stop being a douche."

The main "fallacy" to ad hominem is an implied one. Namely it's that "This guy is a douchebag, therefore what he says is automatically false."

It's the basic mudslinging political theory, where if you don't like someone you're less likely to think that what they're saying is accurate.

Ad hominem is not formal, no, but it's really just part of a more abstract concept than that which is formal: irrelevance. IE, say I need to prove that A => B, and suppose that A =|=> Z. Then saying if A, then Z, thus B would be quite incorrect.

But what it actually means is saying that someone is wrong because they like to eat babies. Just because they like to eat babies doesn't make their view on whether or not wizards can learn spells off of arcane scrolls made by dragons wrong. And all the internet warriors out there seem to get it wrong, and think that any personal attack is argument ad hominem. Which it isn't.

[Psychic Robot]

To summarize: armchair logicians suck.

[RandomCasualty2]

It's illogical, because it's not logic, but it parses fine. One rule contradicts the other and you don't get your Dexterity to AC. The contradiction doesn't break anything because it's not a sentential logic system and is not amenable to sentential logic operations. Rules aren't "true" or "false" - they are just rules. And they are weighted accordingly.

Well, yes the rules statements can't immediately be assumed to be sentential logic statements. This is because rules statements in an exception based system always have the implied statement "Unless there's an exception."

thus all you really know sententally is that "A character not getting his dexterity bonus to AC implies some kind of exception has occured." and by extension that if there is no exception, then a character gets his dex bonus to AC.

So basically every statement you read is ~E -> X, where E is the existence of an exception to that rule and X is the rule itself.

So the prior dexterity based example you gave would look like the following sententially:

• ~E1 -> A
• ~E2 -> (B -> ~A)
• ~E2 -> (B -> E1)

And that's pretty complicated, but that's what an exception based system looks like logically. And basically when you resolve anything, unless you can prove the existence of an exception, you add ~Ex as one of your premises.

So solving the dex rule sententially for a situation where you were blind, you'd add:
~E2
B

to your premises.

Then from there you'd get that B->~A.


Now since in an exception based system, there can be lots of exceptions, and some we may not even know about, what exceptions don't exist are always part of our premises, since basically you have to assume that there isn't some exception that you don't know about to resolve the rule, since there is no way we can ever prove that an exception doesn't exist in such a system. But by introducing a new exception into the proof, it will create a contradiction that can invalidate the old assumption that the exception doesn't exist. But that's basically consistent with the an exception based system, because you are supposed to assume the exception doesn't exist unless it is specifically proven to exist.

If you accidentally add in a premise claiming that an exception does not exist, like assuming ~E1 and ~E2 in the prior example, you'd get a contradiction, since ~E2-> (B->E1) and ~E1 and E1 form a contradiction. This warns you that one of your premises is false, which in this case would be ~E1, since blindness is an exception to the rule about A. So it's impossible to reach a false conclusion without creating a contradiction.

And you can do that if you want for all the rules in the book. It'd get complicated as hell, but you could do it. And sometimes it can be beneficial to do that, since you learn something about the rules that way. In fact, most problematic rules would be unable to be written in sentential notation.

It's not so much that sentential logic is useless, so much that people tend to apply it incorrectly.

[Caedrus]

What really gets me is how people are willing to throw around the Ad Hominem fallacy when most of the time nobody's actually doing it.

That really gets me too. People don't seem to understand for it to be a fallacy the ad hominem attack has to be wrongly used as part of the premises (and of course, "you're a douchebag" is irrelevant to the subject of "your argument does not hold water").

[Absentminded_Wizard]

Damn good post. I've tried to inform people that all of scientific evidence ever was, technically, fallacious before and they looked at me with those strange questioning glances people get when they're confused and wondering what the hell you're going on about.

This statement confuses me, too. I thought a fallacy was the use of a bad form of argument or dirty tricks (e.g., attemepting to refute an argument without addressing its actual premises), and that this was a separate issue from whether or not the premises were true. In the basic philosophy classes I took, I was taught that there were two ways to refute an argument: prove one of the premises false *or* show that the argument was fallacious. You and Frank seem to have conflated both concepts into the word "fallacious."

Edit: According to Wikipedia: "An informal fallacy is an argument whose stated premises fail to support their proposed conclusion." So basically, a fallacy is either a flaw in the form of an argument or a factual disconnect between premises and conclusion. Neither of these definitions has anything to do with the truth of the premises.

[JonSetanta]

To summarize: armchair logicians suck.

More like: bitchmoaning effectively with an eager audience.

[Caedrus]

Damn good post. I've tried to inform people that all of scientific evidence ever was, technically, fallacious before and they looked at me with those strange questioning glances people get when they're confused and wondering what the hell you're going on about.

This statement confuses me, too. I thought a fallacy was the use of a bad form of argument or dirty tricks (e.g., attemepting to refute an argument without addressing its actual premises), and that this was a separate issue from whether or not the premises were true. In the basic philosophy classes I took, I was taught that there were two ways to refute an argument: prove one of the premises false *or* show that the argument was fallacious. You and Frank seem to have conflated both concepts into the word "fallacious."

Edit: According to Wikipedia: "An informal fallacy is an argument whose stated premises fail to support their proposed conclusion." So basically, a fallacy is either a flaw in the form of an argument or a factual disconnect between premises and conclusion. Neither of these definitions has anything to do with the truth of the premises.

To summarize: armchair logicians suck.

More like: bitchmoaning effectively with an eager audience.

+1. My understanding of a fallacy is that it is a separate way of invalidating an argument from discrediting the premises, instead identifying a flaw in the form of an argument.

[Surgo]

Damn good post. I've tried to inform people that all of scientific evidence ever was, technically, fallacious before and they looked at me with those strange questioning glances people get when they're confused and wondering what the hell you're going on about.

This statement confuses me, too. I thought a fallacy was the use of a bad form of argument or dirty tricks (e.g., attemepting to refute an argument without addressing its actual premises), and that this was a separate issue from whether or not the premises were true. In the basic philosophy classes I took, I was taught that there were two ways to refute an argument: prove one of the premises false *or* show that the argument was fallacious. You and Frank seem to have conflated both concepts into the word "fallacious."

Edit: According to Wikipedia: "An informal fallacy is an argument whose stated premises fail to support their proposed conclusion." So basically, a fallacy is either a flaw in the form of an argument or a factual disconnect between premises and conclusion. Neither of these definitions has anything to do with the truth of the premises.

The problem is that the premises (scientific data) do fail to logically support the conclusion because you don't have data for every single possible case. That doesn't mean it's wrong, it just means it's not logically proven.

[Gelare]

This probably needs to be cross-posted to Wizards, ENWorld, Paizo, et al, because the rate at which those idiots shout "LOGICAL FALLLACYOMG!" to make themselves feel smart is excruciating, as though it's an automatic "I win" button. Also, it is extremely important for people, including quite a few folks here, to note that:

the fact of something being a fallacy doesn't actually stop it from being a good argument in all cases.

People make logically invalid arguments seriously all the time. Some people haven't taken classes in first-order predicate calculus, and don't realize that the logical form of the argument they're trying to make reduces to a contridiction, but that doesn't mean that everything they've said is immediately stupid and irrelevant. That is to say, pointing at someone's argument and saying "Look, it's a contradiction LOL!" does not mean that the position they're trying to defend is necessarily wrong.

[Caedrus]

The problem is that the premises (scientific data) do fail to logically support the conclusion because you don't have data for every single possible case. That doesn't mean it's wrong, it just means it's not logically proven.

No, scientific data does support a conclusion, it's just limited to being inductive logic, rather than absolute proof. Premises supporting conclusion != unassailable proof of the truth of a position. It just makes for a better case.

[Absentminded_Wizard]

The problem is that the premises (scientific data) do fail to logically support the conclusion because you don't have data for every single possible case.

But isn't this just saying, "Your premises may be wrong"? Which is a separate question from "Is the argument fallacious?".

Galere: Right on. I think you expressed the concept even better than Frank. Proving an argument fallacious only invalidates that particular argument; it doesn't automatically invalidate the conclusion. There may be a valid argument that proves your adversary's conclusion.

[Surgo]

The problem is that the premises (scientific data) do fail to logically support the conclusion because you don't have data for every single possible case. That doesn't mean it's wrong, it just means it's not logically proven.

No, scientific data does support a conclusion, it's just limited to being inductive logic, rather than absolute proof. Premises supporting conclusion != unassailable proof of the truth of a position. It just makes for a better case.

Term confusion abounds, because you most certainly can have an absolute proof with mathematical induction (though it's generally restricted to the natural numbers), but that's not relevent. My point here was specifically that scientific reasoning is not an absolute proof and is not formal logic (or rather that it is not strictly rigorous).

[IGTN]

Mathematical induction != inductive logic, if I remember right.

[Surgo]

I know, hence "term confusion abounds".

[Username17]

But isn't this just saying, "Your premises may be wrong"? Which is a separate question from "Is the argument fallacious?".

Absolutely not. Let's talk about formal fallacies, specifically the "Non Sequitur" Fallacy. What it is is a statement that the argument does not show that the conclusion is true from the premises. It may show that given the premises that the conclusion is very likely and still be a "Fallacy." But so long as all the premises could be true and the conclusion still be false, your argument is technically a nonsequitur as far as Logic is concerned.

And the ironic thing is that in Science and Law there aren't any absolute truths. There's just the most likely answer and you go with that until you get new evidence.

---

Let's say that you find some one's finger prints all over a gun that had recently been fired and you find powder burns on that person consistent with firing that gun and ballistics matches the gun in question to the gun that shot a recent murder victim three times in the back of the head and you found a dry cleaning receipt that puts this person within a block and a half of the murder 15 minutes before neighbors reported gun shots. Sounds like a good case right? Like, a stupidly awesome case that would be a calm dream to prosecute. It's a fallacious argument.

What it reduces to is a series of If,Then statements where if the evidence didn't fit them then they didn't commit the crime. No matter what the ballistics tells you, if you placed the suspect in Chicago on the night of the murder in Houston then he is innocent. Now all those pieces do fit this guy but that just means you haven't found any reason to throw the case out. It's still technically possible that some other murderer shot the victim several times while wearing gloves and dropped the gun while running out and the suspect grabbed the gun off the street with bare hands and fired after the assailant. Or whatever. The fact that any set of events fits the data (premises) and not the verdict (conclusion) means that we haven't made a valid argument.

---

Or how about those stars? We see them every night and we can use angles and red shifts to estimate their distance and their speed. We can ascribe minimum ages to them based on those distances because the speed of light is constant. But that's a logically invalid argument.

See it turns out that the speed of light is a constant every single time we ever measure it, to the point that we can use it to make horrendously accurate clocks. But we don't "know" that it was constant at every point in the past. What if it went a lot faster a few thousand years back? What if the light from stars doesn't come from stars at all and is instead created as giant beams in a divine sound stage just a few thousand light years around us in a giant crystalline sphere? What then smart boy!?

Those are dumb things to believe, but they are technically possible ways to explain all the data (premises) while still invalidating our scientific model (conclusion). And because such things exist, our model is based on fallacious reasoning.

---

Anything which is not merely the best explanation but in fact the only explanation is not a Logically Valid explanation. And every explanation which is not Logically Valid is based on reasoning that is a Logical Fallacy.

Literally all Scientific truth is derived fallaciously. The Scientific Method is an alternate theory of epistemology from Logic that functions differently. It accepts lesser degrees of certainty in exchange for being able to make light bulbs, penicillin, and jet planes. Logic cannot build things. Science cannot give us absolute certainty.

-Username17

[Draco_Argentum]

That really gets me too. People don't seem to understand for it to be a fallacy the ad hominem attack has to be wrongly used as part of the premises (and of course, "you're a douchebag" is irrelevant to the subject of "your argument does not hold water").

Of course even when you're a douche isn't a premise its still an attempt to shift the conversation into rhetoric rather than something that is worth my time reading.

[RandomCasualty2]

Literally all Scientific truth is derived fallaciously. The Scientific Method is an alternate theory of epistemology from Logic that functions differently. It accepts lesser degrees of certainty in exchange for being able to make light bulbs, penicillin, and jet planes. Logic cannot build things. Science cannot give us absolute certainty.

Well sentential logic doesn't require certainty either. It's why each proof has premises, which are basically things that you accept to be true for the purpose of the proof. And premises are not proven anywhere, they're simply accepted to be true for the purposes of the proof. And the reason for this is exactly what you're talking about, because otherwise we couldn't prove anything with logic, because the only time you can have a generalized statement like "All light travels at C" is by making it a premise, because you can't physically measure light at every time and every place.

Now, if you run into a contradiction in your logic, it tells you that one of your premises are false.

All logic really states is that "if your premises are true, then the following is true."

But that can be pretty important for a lot of applications.

[Hey_I_Can_Chan]

I'm gonna share.

So I'm the high school teacher and Bill, a former student of mine, shows up after school to have me read his college English paper. Yet it's not quite after school yet. There's, like, 7 minutes left in the school day. But Bill shows up. Moments later I get a phone call from the front office, asking if Bill had signed in. I ask Bill. He says no. I tell him to go sign in. He leaves my classroom.

He returns a few minutes later. "Did you sign in?" I ask. "I didn't need to; the bell rang--school's out," he says. Not 5 minutes later the school cop shows up at my room. He has a gun.

"This person hasn't signed in," says the cop.

"School's out," I say.

"He still needs to sign in," cop says.

"I understand that. But this is a former honors student, class president, lead in the school play; is there any way we can let this slide?" I ask.

"Listen, you don't like policy, you take it up with the principal," cop says.

"I just think it's a fallacy to assume that everyone who is on campus is an evildoer, y'know," I say.

"Hey, hey," says cop, "speak English! I don't want to hear about this whole fallacy thing."

Seriously.