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Logical Fallacies

The study of logical fallacies is useful in learning how to think instead of what to think. In learning how to deconstruct an argument, you learn how to efficiently construct your own thoughts, ideas, and arguments. You learn how to find fallacies in your own line of reasoning before they're even presented, which is a valuable methodology for learning how to think. Which is a lot more honest, liberating, and possibly more objective than simply regurgitating what society, teachers, parents, preachers, friends, or politicians tell us what to think.

Most debates utilize the format of deductive reasoning. Premises are outlined, and conclusions are drawn from those premises. A premise can either be accepted or rejected by another debater so it's up to the person positing those premises to provide evidence for their premise.

Arguments can be put into the format of a syllogism. A syllogism is a point-by-point outline of a deductive or inductive argument. Syllogisms usually have 2 premises and a conclusion:
Premise1: "..."
Premise2: "..."
Conclusion: "..."

If premise 1 or 2 is not accepted by another person, then the conclusion necessarily would not be accepted. Example:
Premise1: Souls exist
Premise2: Souls are created by god
Conclusion: God exists

The conclusion of this argument is logically sound -- that is, if a person accepts premises 1 and 2. If someone doesn't accept premise 1, for example, then it's up to the person positing P1 to provide some form of evidence or logical proof that "souls exist".

Premises are never conclusions in and of themselves. Premises only serve as a function of guiding a logical debate. However, a premise of one argument can be a conclusion of another.

Continuing the syllogism above:
Conclusion: God exists
Premise3: God says that walking backwards on Tuesdays after 6pm is a sin
Premise4: You were walking backwards Tuesday night at 8:43 pm
Conclusion: You're a sinner.

Implication in detail

An argument is valid if the conclusion follows necessarily from the premises. An argument is sound when it's valid and all of the premises are true.

Clearly you can build a valid argument from true premises, and arrive at a true conclusion. You can also build a valid argument from false premises, and arrive at a false conclusion.

The tricky part is that you can start with false premises, proceed via valid inference, and reach a true conclusion. For example:
Premise: All fish live in the ocean
Premise: Sea otters are fish
Conclusion: Therefore sea otters live in the ocean

There's one thing you can't do, though: start from true premises, proceed via valid deductive inference, and reach a false conclusion. In the case above, if you reject the fact that sea otters live in the ocean soley based on the premises, that disagreement would technically be a Logical Fallacy called Argument ad Logicam, or an Argument from Fallacy. The best thing to do in the case above would to simply say that the argument doesn't prove that sea otters live in the ocean, not that sea otters simply don't live in the ocean.

Many debates in the internet are terribly poor - most people's "arguments" are nothing but assertions. Others simply contain logical fallacies. "Non-Sequitur" simply means "It does not follow". All logical fallacies are non-sequiturs, but there are certain categories to logical fallacies depending upon the premises stated, conclusions, or the deductive process that joins them.

Here are some common fallacies:

Affirming the Consequent
The phrase "if... then" is a common inference made in casual conversation. However, it can be used mistakenly in an argument. The "consequent" in the "if... then" is the subject of the "then". Saying "if God isn't a Penn State fan, then why is the sky blue and white?", the consequent would be "the sky is blue and white".

An example in an argument:
Premise 1: If God is a Penn State fan, then the sky would be blue and white
Premise 2: God is a Penn State fan
Conclusion: Therefore, the sky is blue and white

This argument is valid. However, the fallacy of affirming the consequent would be asserting the consequent of P1 is true in P2, and then concluding that God is indeed a Penn State fan.
Premise 1: If God is a Penn State fan, then the sky would be blue and white
Premise 2: The sky is blue and white
Conclusion: Therefore, God is a Penn State fan

This is fallacious because there could be other reasons why the sky is blue and white - like most of the visible spectrum of light is absorbed by particles in the air and only the shortest wavelength (blue) reaches our eyes.

Denying the Antecedent
The phrase "if... then" is a common inference made in casual conversation. However, it can be used mistakenly in an argument. The "antecedent" in the "if... then" is the subject of the "if". Saying "if I live in a mansion, then I am really rich" the antecedent would be "if I live in a mansion".

An example in an argument:
Premise 1: If I live in a mansion, then I'm really rich
Premise 2: I live in a mansion
Conclusion: Therefore, I'm really rich

This argument is valid. However, the fallacy of denying the antecedent would be asserting the antecedent of P1 is false in P2, and then concluding that I'm not really rich.
Premise 1: If I live in a mansion, then I'm really rich
Premise 2: I don't live in a mansion
Conclusion: Therefore, I'm not really rich

This is fallacious because I could simply not want to live in a mansion if I had a lot of money.


The reasoning for the logic behind both Denying the Antecedent and Affirming the Consequent can be seen if one were to draw up a Truth Table. A Truth Table is a visual heuristic for determining the truth of an argument. The Truth Table for "if... then" is as follows:

Notice that the only time that the conditional "if... then" is false is when the antecedent is true and the consequent is false. In any other arrangement, "if... then" is true no matter what - which is why Denying the Antecedent and Affirming the Consequent are fallacies... there's no way to determine what the other value would be. For example, in Affirming the Consequent, once the consequent has been affirmed (the sky is blue and white) there's no way to differentiate between God being and not being a Penn State fan, since both instances would make the "if... then" true:
It should also be noted that "if.. then" (the material conditional) doesn't necessarily have to be a causal relationship. The statement "If I live in the U.S.A., then Mars is the fourth planet from the Sun" is true, since both antecedent and consequent are true. This is can be seen as a modal relationship and not a causal (ie A causes B) relationship. However, in common understanding the statement is obviously false. To further confuse yourself, click here to learn more about "if... then". I think of the antecedent of the material conditional as sort of "turning on" or "instantiating" (to borrow OOP terminology) the material conditional. The antecedent is the power button - once it's on (its value is "true") then you can find out if the whole thing is true. If the antecedent is NOT on (ie false) then you aren't going to be able to evaluate the whole statement.

Special Pleading
Special pleading occurs when someone makes a statement and then later makes an ad hoc exception to the statement to prevent their stance from being included. An example:

  • Person A: Everything that exists needs a creator
  • Person B: What about the creator of everything?
  • Person A: Well... he doesn't count

Begging the Question
Begging the question occurs when the conclusion of an argument is already implicitly assumed in one of the premises. Begging the question can also be called circular logic - because it's circular. An example:

  • Person A: The Bible is the word of god
  • Person B: How do you know?
  • Person A: Because it says so
  • Person B: How do you establish that what the Bible says is true?
  • Person A: Obviously god wouldn't lie

Another humorous example:

Complex Question
A complex question is a question that has a hidden assumption underlying it which hasn't been agreed upon between the questioner and the person receiving the question. Answering the question forces the answerer to agree with the hidden premise. Some examples:

  • Have you stopped beating your wife?
    • (The assumption being that the person beats their wife)
  • Who's going to pay for the dinner you're taking me to?
    • (The assumption being that the person is taking them to dinner in the first place)
  • Who else besides Jesus can save you from sin?
    • (The assumption being that 'sin' exists and the person actually 'sins' to begin with)
  • What book other than the Qur'an satisfactorily identified the real objective for the human life?
    • (The assumption being that there's a real objective for human life and the Qur'an satisfactorily demonstates this)
  • Where do you go when you die?
    • (The assumption being that there's a 'you' after you die, and that you have to go 'somewhere')

Fallacy of Equivocation
This fallacy occurs when a word can have two possible, yet distinct definitions. The person committing this mistake usually navigates between the two different uses of the word in the same context. Example:

"There are many theories about the origin of life. Evolution is only one of them"

The equivocation is between the layman use of the word theory (a guess or hunch) and the scientific definition of the word theory (A coherent statement or set of tested hypotheses that attempt to explain observed phenomena and functions as a model of whatever it is the "theory" of)

Fallacy of Reification
This fallacy occurs when someone takes an abstract concept and attempts to "reify" or "solidify" it. Example:

"There are things in the world that are unknown. God is unknown, so since the unknown exists, God exists"

This fallacy is slightly related to the fallacy of equivocation. However, this differs in that the "unknown" isn't an actual thing, and doesn't have a physical referant. The "unknown" is an abstract concept. Abstractions in our language simply serve as descriptions of certain types of knowledge - or maybe even "meta-data".

Just like this webpage has some meta-data associated with it that can be viewed by looking at the source code for this page. That meta-data has nothing to do with what is "real" - the conent of the page. It's just a description of what's going to be displayed. The "unknown" doesn't exist in the same manner that this computer screen exists. Just like "love" or "justice" serve as abstractions and don't physically exist.

Naturalistic Fallacy
This is the fallacy that assumes everything that's "natural" is ethically or morally "good". Consequently, this means that everything that's "unnatural" is bad. I see this argument frequently in debates about homosexuality, but the fallacy is invoked in other contexts as well.

For example, it is sometimes argued that sex solely as a means for procreation is what nature intended. This would mean that oral and/or anal sex are "unnatural" and therefore "immoral" or "bad". However, rape is also a phenomenon that is natural - it's practiced by many species besides humans. Ducks sometimes engage in rape flights where a group of male ducks will rape a female duck - sometimes even other male ducks.

It simply does not follow that all that is "natural" is inherently "good". This is in many ways related to David Humes Is-Ought Problem. Just because something "is", doesn't mean that's how it "ought" to be.

Prosecutor's Fallacy
In this fallacy, the user will apply the rationale of "low probability" to formulate their case. This is expressed in simple conditional probability formats like P(A | B) = 1. This reads "The probability of A given B equals 1" (or 100%). The prosecutor's fallacy reads that since something has "low odds" of happening, that some alternative - that has a higher probability - must be chosen.

Say for instance someone wins the lottery. Since there is a low probability for winning the lottery, the lotto winner is accused of having cheated. Since P(winning the lottery | rigging the test) = 1, the accuser concludes that the lotto winner MUST have cheated. However, just because something has a low probability of happening, doesn't mean that events were rigged in their favor. The "prosecutor" would have to provide other evidence that shows that the lotto winner actually did rig the lotto.

Simply introducing a scenario that has a higher probability in no way proves that this alternative is true.

Gambler's Fallacy
The gambler's fallacy is that which encompasses any of the following misconceptions:

  • A random event is more likely to occur because it has not happened for a period of time
  • A random event is less likely to occur because it has not happened for a period of time
  • A random event is more likely to occur because it recently happened
  • A random event is less likely to occur because it recently happened

These are common misunderstandings that arise in everyday reasoning about probabilities, many of which have been studied in great detail. Many people lose money while gambling due to their erroneous belief in this fallacy. Although the gambler's fallacy can apply to any form of gambling, it is easiest to illustrate by considering coin-tossing; its rebuttal can be summarised with the phrase "the coin doesn't have a memory".

The gambler's fallacy can be illustrated by considering the repeated toss of a coin. With a fair coin the chances of getting heads are exactly 0.5 (a half). The chances of it coming up heads twice in a row are 0.5 x 0.5=0.25 (a quarter). The probability of three heads in a row is 0.5 x 0.5 x 0.5= 0. 125 (an eighth) and so on.

Now suppose that we have just tossed four heads in a row. A believer in the gambler's fallacy might say, "If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is 0.55 = 0.03125; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads."

This is the fallacious step in the argument. If the coin is fair, then by definition the probability of tails must always be .5, never more (or less), and the probability of heads must always be .5, never less (or more). While a run of five heads is only 1 in 32 (0.03125), it is 1 in 32 before the coin is first tossed. After the first four tosses the results are no longer unknown, so they don't count. The probability of five consecutive heads is the same as four successive heads followed by one tails. Tails is no more likely. Each of the two possible outcomes has equal probability no matter how many times the coin has been flipped previously and no matter what the result. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses is the fallacy. The fallacy is the idea that a run of luck in the past somehow influences the odds of a bet in the future.

Ad Hoc
Ad Hoc means in Latin "For this purpose". In logic, this means that something on the part of the debater has been made up on the spot - usually to prevent their stance from being falsified.

For example, ESP researchers have been known to blame the hostile thoughts of onlookers for unconsciously influencing pointer readings on sensitive instruments. The hostile vibes, they say, made it impossible for them to duplicate a positive ESP experiment. Being able to duplicate an experiment is essential to confirming its validity. Of course, if this objection is taken seriously, then no experiment on ESP can ever fail. Whatever the results, one can always say they were caused by paranormal psychic forces, either the ones being tested or others not being tested.

False Dilemma / False Dichotomy / Fallacy of the Excluded Middle
A False Dilemma occurs when someone claims that there are only two options to a question or solution when in fact there are many more options. Usually termed "seeing the world in black and white". Some examples:

  • Matthew 12:30 / Luke 11:23 :
    He who is not with me is against me, and he who does not gather with me scatters.

  • All human emotions can be put into one of two categories: Love or Fear.

Hasty Generalization
A Hasty Generalization is a fallacy of Induction. Induction would be the following process:

  • Crow #1 is black
  • Crow #2 is black
  • Crow #3 is black
  • Crow #4 is black
  • ...
  • Crow #N is black
  • I will therefore conclude that Crow #N + 1 is also black

Induction is not a sure thing, and by its nature never claims to be. Induction is along the lines of saying "it is reasonable to conclude" or "Due to its track record, I can safely assume...". A Hasty Generalization occurs when someone views, in the situation above, crow #1 being black and then concludes that all crows are black. That is fallacious because no track record has been established. Some other examples:

  • I never had any experience with black people until I met Tony, and he was an asshole. Therefore, ALL black people are assholes
  • All women are lying manipulative whores. I know this because my past 2 girlfriends cheated on me
  • I met this one Jew who was a penny pincher. Therefore, ALL Jews are penny pinchers
This fallacy is the reasoning behind racism, sexism, and all other types of prejudices/bigotry.

Post Hoc, Ergo Propter Hoc / The Fallacy of Correlation / Correlation Does Not Imply Causation
The Fallacy of Correlation, or Fallacy of Coincidence - in Latin "Post Hoc, Ergo Propter Hoc" literally "It happened after, so it was caused by" - is another fallacy of Induction. People utilize this fallacy when they notice that one event happens after doing another unrelated event and then conclude that the prior event caused the second event. This fallacy is tricky because it's not always fallacious, and a lot of our knowledge comes from seeing correlations and / or coincidences. The only way to differentiate between a fallacious "Post Hoc" and a non-fallacious Post Hoc is by utilizing the methodology of falsifiability.

For example:
Person A: "Every time I make a sacrifice to the Flying Spaghetti Monster on Tuesday nights, I always get good pasta when I go to Olive Garden"

As human beings, we tend to only look for data that confirms our pet superstitions and disregard data that contradicts it. This is called Confirmation Bias. Also, when recalling events to prove a correlation, we might recall only the positive hits and forget the negative hits. This is called Selection Bias. As an easy way to see if something really is a causal relationship, the person in the quote above could try not doing a sacrifice and then going to Olive Garden to see if the pasta is still good, or maybe even doing a sacrifice to a deity that the person thinks is obviously fiction.

However, since it is a fallacy of induction, when attempting to falsify our pet superstitions we should be weary of hasty generalizations (ie the one time I didn't sacrifice to the Flying Spaghetti Monster I got bad pasta, therefore every time I don't sacrifice to the Flying Spaghetti Monster I'll get bad pasta).

Fallacy of Composition
A person makes this fallacy when they assume that the properties of individual elements are the same as the properties of the whole, which is another fallacy of induction. For example, a person might claim:

"A building is built by a builder, a painting is painted by a painter, a watch is made by a watchmaker - therefore the Earth/Universe was made by someone"

Following the reasoning above, we'd arrive at the obviously false conclusions:
Sodium is poisonous if you eat it
Chloride is poisonous if you eat it
Therefore Sodium Cloride (also known as table/edible salt) is poisonous if you eat it

H2O (dihydrogen monoxide) freezes at 32 F
Therefore hydrogen freezes at 32 F (hydrogen actually freezes at -434 F)

This occurs when someone misrepresents another's argument and refutes the misrepresentation and then concludes that the original argument is also unsound.

Person A: "Evolution says we all decended from monkeys. If this is true, then how come there are still monkeys around? Evolution must be false then."

The strawman is the statement "...we all descended from monkeys". Since the theory of Evolution doesn't say this, Person A has misrepresented the ToE to make it easier to refute.

Person A: [paraphrased] "You say plants grow when you use water on them. How come I've never seen a plant grow out of a toilet??? [Therefore, plants don't need water to grow]"

Obviously, plants do need water to grow. The strawman is asserting that plants have to grow in toilets if plants need water to grow.

Ad Hominem
Ad Hominem (Ad hom) is Latin for "against the man". Ad homs are tricky. Ad hom basically means attacking the validity of an argument based on the characteristics of the person presenting the argument. There's also a difference between an ad hom and a pesonal attack. Ad homs, depending on their context, also aren't always logical fallacies - just like others listed here.

Example of a fallacious ad hom:

Person A: "All rectangles are squares, my house is a rectangle, therefore it's a square"

Person B: "Your house isn't a square because you're a fucking liar!!"

Example of a NON fallacious ad hom:

Person A: "All rectangles are squares, my house is a rectangle, therefore it's a square"

Person B: "All rectangles aren't squares because you're a fucking liar!!"

Notice the difference between the two. Premises can be accepted or rejected for any reason. If a person positing a premise is known to be a liar, then it might be reasonable to reject a liar's premises based on the fact that the person is known to be a liar. While in this case it might not be very classy, an untrustworthy source isn't to be trusted - that's axiomatic. However in the first example, the validity of the argument itself and/or the conclusion is rejected on the basis of the person's characteristics. That is a fallacious ad hom, and it's fallacious due to the same reasons as Argument Ad Logicam.

An example of a personal attack:
Person A: "All rectangles are squares, my house is a rectangle, therefore it's a square"

Person B: "You're house isn't a rectangle because I counted 5 sides. You're a fucking moron!!"

This is a personal attack because the attack has no bearing on the validity of the premises or conclusions of the argument.