SFA: Not an argument.

Please note:
Not ALL fallacious arguments are listed below, purely the ones I have studied, I will look into the ones on Sythe's sticky when I have the time.​

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The Basics...

Standard Form​

First of all, I shall quickly explain the basics of constructing an argument. Arguments can be written in a form we call standard form. We write them in this form so they are easier to make sense of. Let me demonstrate by using this simple example:​

Cats are all warm-blooded. I know this because all cats are mammals and all mammals are warm-blooded.

Now, we write this in standard form:​

P1) All cats are mammals.
P2) All mammals are warm-blooded.

C) All cats are warm-blooded.

Notice the use of "P1)", "P2)" and "C)". These stand for 'premise one', 'premise two' and 'conclusion', respectively.
A premise is simply a statement put forward in support of a central claim (the conclusion, in this case, "all cats are warm-blooded" is the central claim).

I will use this form to demonstrate the fallacies that follow, so it is important you understand the above.
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Validity and Soundness

Validity is concerned with the structure of the argument. Validity is nothing to do with the truth of an argument.
Soundness is concerned with the truth of the argument's premises. Sound arguments are also valid.

Valid Arguments:
What makes an argument reliable? There are two major virtues that an argument can have: the argument has true premises and is well structured.

A well structured argument is known as a valid argument.
A badly structured argument is known as an invalid argument.

Example of a valid argument:

P1) All men are mortal (All A's are B's)
P2) Socrates is a man (X is an A)

C) Therefore, Socrates is mortal (Therefore, X is a B)

And another, slightly different one:

P1) All cats are mammals (All A's are B's)
P2) All mammals are vertebrates (All B's are C's)

C) Therefore, all cats are verterbrates (Therefore all A's are also C's)

A Valid argument is one which forces you to accept the conclusion if you accept the premises.​

Invalid Arguments:
An invalid argument is one where the premises do not tie you in to the conclusion. In an invalid argument, we are not forced to accept the conclusion, even on the occasion where we have completely accepted the premises as being true.

An example of an invalid argument:

P1) All Doctors are humans (All A's are B's)
P2) Mr Smith is a human (X is a B)

C) Therefore, Mr Smith is a Doctor (Therefore, X is an A)

You can see here that although we fully accept the premises, accepting them does not necessarily guarantee the truth of the conclusion.

An invalid argument is one which does not force us to accept the conclusion even if we accept all of the premises.​

Sound Arguments:
An argument is said to be 'sound' when the premises are true and it has a valid structure. A sound argument is therefore the best argument you can have. As sound arguments also have a valid structure, we are therefore guaranteed a true conclusion or central claim.

An example of a sound (and valid) argument:

P1) All bachelors are male (All A's are B's + true premise)
P2) Mr Smith is a bachelor (X is an A + true premise)

C) Therefore, Mr Smith is a male (Therefore, X is a B + true conclusion)

As you can see, we are forced to accept the conclusion if we accept the premises (valid) and the premises are true (sound).


Unsound arguments:
As you can guess, an unsound argument is one which either has a false premise, invalid structure, or both. If you read a premise that is as a matter of fact, false then the argument is automatically unsound. If all the premises are true, then we must look to the structure of the argument to see if it is unsound.

An example of an unsound (+ valid) argument:

P1) All parrots are cats (All A's are B's + false premise)
P2) All cats have feathers (All B's are C's + false premise)

C) Therefore, all parrots have feathers (all A's are also C's + false conclusion)

This argument is unsound as it has false premises but it is valid as acceptance of the premises guarantees the truth of the conclusion.

An example of an unsound (+ invalid) argument:

P1) All parrots are birds (All A's are B's + true premise)
P2) All parrots have feathers (All A's are C's + true premise)

C) Therefore, all birds have feathers (Therefore, all B's are also C's + true conclusion)

This argument is unsound as although it has true premises and conclusion, it is of invalid structure.


Inductive and Deductive Arguments

Some arguments are said to be inductive in nature and others are said to be deductive.
Deductive arguments are more likely to be valid and sound which means that they are more likely to be believed.
Inductive arguments are less reliable. Inductive arguments are based on a limited amount of experience and therefore less likely to be believed.

An example of a deductive argument:

P1) All cats have tails
P2) Felix is a cat

C) Therefore, felix has a tail

A deductive argument begins with a general premise and then goes on to deduce the truth of some particular fact based on this (a specific conclusion).

Deductive arguments do not go beyond what is contained in the premises. A deductive argument is one that attempts to guarantee the truth of the conclusion.​

An example of an inductive argument:

P1) This cat is black
P2) That other cat is black
P3) A third cat is black

C) Therefore, all cats are black

This is an inductive argument as the assumption that all cats are black has come from a limited experience of only three cats. It is cogent (convincing and coherent) but it doesn't mean to say it is reliable and offering a true conclusion. Just because three cats are black doesn't mean to say that all cats are black. A good way to remember the difference is likening the word inductive to induction (induction training is given to new employees with limited experience.

Another, different example of induction in an argument:

My cat just hates getting wet so I wouldn't give your cat a bath if I were you.

This example could be said to be inductive because it is basing the fact your cat wont like a bath on the fact one cat didn't like it.

An inductive argument, therefore, goes beyond what is contained in the premises by generalising from limited experience. ​

What is a fallacy?

A fallacy is simply defined as follows: A fallacy is an error in reasoning that occurs in an argument.

Fallacies can be divided into two groups known as formal fallacies and informal fallacies. An informal fallacy can be structurally valid but relies on false premises whereas a formal fallacy is an argument which usually has an informal stucture.


Formal Fallacies

There are two formal fallacies:

• Denying the antecedent
• Affirming the consequent

It is important we can distinguish between antecedents and consequents. This is how we determine the difference:

We can remember this easily by likening the word 'consequent' to consequence (what comes after).

The premise may not be in a straight forward layout like the example above, consider this:

You are British because you are Scottish.

We can re-write this as:

IF you are Scottish THEN you are British.

Traditionally, we write this as "If P then Q", where P is the antecedent and Q is the consequent.

Denying the antecedent:
This name is given to any argument which follows this structure:

If P then Q
NOT P

Therefore, NOT Q

You can see here, we are denying (calling false) the antecedent, which then follows that the consequence is also false.

Example:

P1) If Queen Elizabeth is an American Citizen, then she is a human being (If P then Q)
P2) Queen Elizabeth is not an American Citizen (Not P)

C) Therefore, Queen Elizabeth is not human (Therefore, not Q)

You can see clearly from this type of fallacious reasoning that it is flawed. Just because Queen Elizabeth is not American, does not mean she is not human. She could be German, British, Swedish or Russian etc etc.

You can see this fallacy is invalid because the conclusion is false.

Affirming the consequent:
This fallacy looks very similar to denying the antecedent, but is slightly different.

If P then Q
Q

Therefore, P

You can see here we affirm (calling true) the consequent, which then follows the antecedent is also true.

Example:

P1) If I have the flu then I have a sore throat (If P then Q)
P2) I have a sore throat (Q)

C) Therefore, I have the flu (Therefore, P)

We can see clearly from this type of fallacious reasoning that it is flawed. There are other reasons someone may have a sore throat other than the flu, for example, burning your throat on a hot beverage.

Do not mix these fallacies with 'Affirming the Antecendent' and 'Denying the Consequent' - these are not fallacies, these are possible and are valid.
Formal fallacies usually have an invalid structure.​

Informal Fallacies​

Informal fallacies are not recognised by their structure or validity, but by their use of non-rational means to win the argument.
They are perfectly capable of being valid but mostly always will be unsound because of their reliance on dubious premises.


I shall focus on the 6 main informal fallacies I have studied:

• Post hoc ergo propter hoc (After this therefore because of this)
• False dilemma
• Argument from ignorance
• Ad hominem (Attacking the person)
• Illigitimate appeals to authority
• Slippery slope

Post hoc ergo propter hoc (After this therefore because of this):
This fallacy is commited if it is assumed, in the course of an argument, that because 'x' and 'y' occur one after the other, that one causes the other. We cannot assume that all things that follow up one another are causally related.

Example:

P) The cockerel crows before the sun comes up every day.
C) So, the cockerel must cause the Sun to come up

We can see in this extreme example what we mean by fallacious reasoning.


False dilemma:
This fallacy is committed if, in an argument, it is assumed that X and Y are the only two possibilities, when in fact there are other possibilities. As the name suggests, creating a dilemma which is fact not a real dilemma. Although do note: there are possible dilemmas where there are only X and Y, for example, either you are pregnant or you're not pregnant.

Example:

P1) Either you support Manchester United or Manchester City
P2) You don't support Manchester United

c) Therefore, you must support Manchester City

We can see from this example, it contains fallacious reasoning. It is possible for example to support Chelsea. This argument is also unsound as the first premise is false.

Argument from ignorance:
An argument from ignorance can be written in two forms, both the exact opposite of each other. This fallacy is committed when we argue either:

• True because it hasn't been proven false.
  
  OR​
• False because it hasn't been proven true.

Example:

P) You cannot prove that God doesn't exist.

C) Therefore, God must exist.

AND

P) You cannot prove that God exists.

C) Therefore, God doesn't exist

Ad hominem (Attacking the person):
This fallacy is committed when it is argued that X is false on the grounds that it is put forward by a particular person who may benefit from our acceptance of the argument. This type of fallacy focuses on the character of the arguer rather than the statement that their opponent supports.

Example:

P) How can you believe the testimony of that witness?

C) He's an unemployed layabout who has never done an honest day's work in his life.

Another, slightly different example:

P1) Bill: "I believe that abortion is morally wrong."
P2) Dave: "Of course you would say that, you're a priest."
P3) Bill: "What about the arguments I have given to support my argument?"
P4) Dave: "Those don't count. Like I said, you're a priest, so you have to say that abortion is morally wrong. Further, you are just a lackey to the Pope, so I can't believe what you say."

Clearly Dave is attacking the character of Bill, rather than his arguments he had put forward beforehand. He's dismissing Bill's arguments which may in fact be fully justified on the basis that he is a priest and apparently a lackey to the Pope.

Illegitimate appeal to authority:
This fallacy is committed if a conclusion decided based on the fact that a person(s) said this to be true despite the person in question not being authoritative in the matter.

Example:

I read in a book once that there is no highest prime number. Oscar Award winning actor, Denzel Washington says that there is no highest prime number. Therefore, there must be no highest prime number.

We cannot accept the fact, although it may be true, when it is based upon the fact that a certain person said so when the person is not authoritative in the matter (e.g. Denzel Washington is not a Mathematics Professor).

Slippery Slope
This is the last informal fallacy and this claims that one thing will inevitably lead to another, usually worse, state of affairs, without further argument.

Example:

The US shouldn't get involved militarily in other countries. Once the government sends in a few troops, it will then send in thousands to die.

We can see here, no further argument was given to support the fact that thousands will be sent in to die, and was said to inevitably happen.

Another example:

If we ban religion in schools it wont be long before we ban philosophy and history, too. If we ban philosophy and history we will soon have a state controlled curriculum. Once we have a state controlled curriculum we will no longer be freethinking students. A society without freethinking students is a totalitarian state. So, we must defend the teaching of religion at all costs.

We can see how ridiculous this extreme example sounds.

Please let me know if I have made any mistakes and such. I probably have done as I'm still leaning myself. - Thanks.​

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Please let me know if I have made any mistakes and such. I probably have done as I'm still leaning myself. - Thanks.​

Hey I found one! I've been taking this more seriously recently, and I'd like to thank you for this guide. Don't know why it's been buried for six years.