argument forms

7/27/2019 Argument Forms

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Consider, for example, what happens when we construct a truth-table that lists each of the four combinations

of truth-values that the component statements could exhibit in the simple argument form that we identified at the top

of this page.

p q

p_______

q

This truth-table shows that (no matter what statements we substitute

for p and q ) both of the premises of the argument will be true

only on the first line (when both component statements are true). But

on that line, the conclusion is also true, so the inference is valid. Whenever we come across an argument that shares

this basic structure, we can be perfectly certain of its logical validity. In fact, arguments of this form are so common

that the form itself has a name,Modus Ponens, which we will usually abbreviate as M.P.

On the other hand, consider what happens when we construct a truth-table for testing the validity of a distinct,

though superficially similar, argument form:

p q

q_______

p

In arguments of this form, both premises are true on the first and on

the third lines of the truth-table. While the conclusion is true on the

first line, on the third line it is false. Since it is therefore possible for

the premises to be true while the conclusion is false, the inference is invalid. This unreliable argument form is called

the fallacy ofaffirming the consequent. Although it might be mistaken for M.P. at a casual glance, the fallacy

unlike its valid cousin

does not guarantee the truth of its conclusion.

Modus Toll ens

Another common argument form with a valid inference isModus Tollens(abbreviated as M.T.), which has the

form:

p q

~ q

_______

~ pAs the truth-table shows, the premises are true only when both of the

component statements are false, in which case the conclusion is also

true. There is no line on which both premises are true and the

conclusion false, so the inference is valid, as are all substitution-instances of this argument form.

As with M.P., there is an argument form superficially similar to M.T. that yields entirely different results.

1st Premise 2nd Premise Conclusion

p q pq p q

T T T T T

T F F T F

F T T F T

F F T F F


p q pq q p

T T T T T

T F F F T

F T T T F

F F T F F


p q pq ~ q ~ p

T T T F F

T F F T FF T T F T

F F T T T
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p q

~ p

_______

~ q

This is the fallacy ofdenying the antecedent. As the truth-table to the

right clearly shows, it is an unreliable inference, since it is possible

(on the third line) for both of its premises to be true while its

conclusion is false. Substitution-instances of this argument form may not be valid.

Hypothetical Syllogism

A larger truth-table is required to demonstrate the validity of

the argument form called Hypothetical Syllogism (H.S.), since it

involves three statement variables instead of two, and we must

consider all eight of the possible combinations of their truth-

values:

p q

q r

_______

p r

Despite its greater size, this truth-table establishes validity in

exactly the same way as its more compact predecessors: both

premises are true only on the first, fifth, seventh, and eighth lines, and the conclusion is also true on each of these

lines. It follows that all arguments sharing in thisgeneral form must be valid.

Disjunctive Syllogism

Finally, consider the argument form known as Disjunctive

Syllogism or D.S.

p q

~ p

_____

q

The truth-table demonstration of its validity should look familiar by

now. Whenever the premises are true (on the third line of the truth

table), so is the conclusion.

Once again, however, there is a similar form that embodies an invalid inference, the fallacy of affirming the

alternative:


p q pq ~ p ~ q

T T T F F

T F F F T

F T T T FF F T T T


p q r pq qr pr

T T T T T T

T T F T F F

T F T F T T

T F F F T F

F T T T T T

F T F T F T

F F T T T T

F F F T T T


p q pq ~ p q

T T T F T

T F T F F

F T T T T

F F F T F

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p q

p

_____

~ q

In this case, the first line of the truth-table shows that (with ourinclusive sense of the ) it is possible for the premises to be true

and the conclusion false.

p q pq p ~ q

T T T T F

T F T T T

F T T F F

F F F F T


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Constructing a Logical Argument

Introduction

There is a great deal of argument on Usenet. Unfortunately, most of it is of very poor quality. This document

attempts to provide a gentle introduction to logic, in the hope of improving the general level of debate.

Logic is the science of reasoning, proof, thinking, or inference [Concise OED]. Logic allows us to analyze a piece of

reasoning, and determine whether it is correct or not. To use the technical terms, we determine whether the

reasoning is valid or invalid.

One does not need to study logic in order to reason correctly. However, a little basic knowledge of logic is often

helpful when constructing or analyzing an argument.

Note that I am not claiming that logic is universally applicable. That issue is very much open to debate. This

document only explains how to use logic; you must decide whether logic is the right tool for the job.

Note also that this document deals only with simple boolean logic. Other sorts of mathematical logic, such as fuzzy

logic, obey different rules. When people talk of logical arguments, though, they generally mean the type being

described here.

Basic concepts

The building blocks of a logical argument are propositions, also called statements. A proposition is a statement

which is either true or false; for example:

"The first programmable computer was built in Cambridge."

"Dogs cannot see colour."

"Berlin is the capital of Germany."

Propositions may be either asserted (said to be true) or denied (said to be false). Note that this is a technicalmeaning of "deny", not the everyday meaning.

The proposition is the meaning of the statement, not the particular arrangement of words used. So "A God exists"

and "There exists a God" both express the same proposition.

What is an argument?

An argument is, to quote the Monty Python sketch, "a connected series of statements to establish a definite

proposition". There are three stages to an argument: Premises, inference, and conclusion.

Stage one: Premises

One or more propositions will be are necessary for the argument to continue. They must be stated explicitly. They

are called the premises of the argument. They are the evidence (or reasons) for accepting the argument and its

conclusions.

Premises (or assertions) are often indicated by phrases such as "because", "since", "obviously" and so on.


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(The phrase "obviously" is often viewed with suspicion, as it can be used to intimidate others into accepting dubious

premises. If something doesn't seem obvious to you, don't be afraid to question it. You can always say "Oh, yes,

you're right, it is obvious" when you've heard the explanation.)

Stage two: Inference

The premises of the argument are used to obtain further propositions. This process is known as inference. Ininference, we start with one or more propositions which have been accepted. We then derive a new proposition.

There are various forms of valid inference.

The propositions arrived at by inference may then be used in further inference. Inference is often denoted by phrases

such as "implies that" or "therefore".

Stage three: Conclusion

Finally, we arrive at the conclusion of the argument, another proposition. The conclusion is often stated as the

final stage of inference. It is affirmed on the basis the original premises, and the inference from them. Conclusions

are often indicated by phrases such as "therefore", "it follows that", "we conclude" and so on.

Types of argument

There are two traditional types of argument, deductive and inductive. A deductive argument provides conclusive

proof of its conclusions; if the premises are true, the conclusion must also be true. A deductive argument is either

valid or invalid.

A valid argument is defined as one where if the premises are true, then the conclusion is true.

An inductive argument is one where the premises provide some evidence for the truth of the conclusion. Inductive

arguments are not valid or invalid, but we can talk about whether they are better or worse than other arguments. We

can also discuss how probable their premises are.

There are forms of argument in ordinary language which are neither deductive nor inductive. However, this

document concentrates on deductive arguments, as they are often viewed as the most rigorous and convincing.

Here is an example of a deductive argument:

Every event has a cause (premise) The universe has a beginning (premise) All beginnings involve an event (premise) This implies that the beginning of the universe involved an event (inference) Therefore the universe has a cause (inference and conclusion)

Note that the conclusion of one argument might be a premise in another argument. A proposition can only becalled a premise or a conclusion with respect to a particular argument; the terms do not make sense in isolation.

Recognizing an argument

Sometimes an argument will not follow the order described above. For instance, the conclusions might be stated

first, and the premises stated afterwards in support of the conclusion. This is perfectly valid, if sometimes a little

confusing.
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Arguments are harder to recognize than premises or conclusions. Many people shower their writing with assertions

without ever producing anything which one might reasonably describe as an argument. Some statements look like

arguments, but are not.

For example:

"If the Bible is accurate, Jesus must either have been insane, an evil liar, or the Son of God."

The above is not an argument, it is a conditional statement. It does not assert the premises which are necessary to

support what appears to be its conclusion. (Even if we add the assertions, it still suffers from a number of other

logical flaws -- see the section on this argument in "Alt.Atheism Frequently Asked Questions".)

Another example:

"God created you; therefore do your duty to God."

The phrase "do your duty to God" is neither true nor false. Therefore it is not a proposition, and the sentence is

not an argument.

Causality is important. Suppose we are trying to argue that there is something wrong with the engine of a car.

Consider two statements of the form "A because B". The first statement:

"My car will not start because there is something wrong with the engine."

The statement is not an argument for there being something wrong with the engine; it is an explanation of why the

car will not start. We are explaining A, using B as the explanation. We cannot argue from A to B using a statement

of the form "A because B".

However, we can argue from B to A using such a statement. Consider:

"There must be something wrong with the engine of my car, because it will not start."

Here we are arguing for A, offering B as evidence. The statement "A because B" is then an argument.

To make the difference clear, note that "A because B" is equivalent to "B therefore A". The two statements then

become:

"There is something wrong with the engine, therefore my car will not start."

And:

"My car will not start, therefore there is something wrong with the engine."

If we remember that we are supposed to be arguing that there is something wrong with the engine, it is clear that

only the second statement is a valid argument.

Implication in detail

There is one very important thing to remember: The fact that a deductive argument is valid does not imply that its

conclusion holds. This is because of the slightly counter-intuitive nature of implication, which we must now

consider more carefully.
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Obviously a valid argument can consist of true propositions. However, an argument may be entirely valid even if it

contains only false propositions.

For example:

All insects have wings (premise) Woodlice are insects (premise) Therefore woodlice have wings (conclusion)

Here, the conclusion is not true because the argument's premises are false. If the argument's premises were true,

however, the conclusion would be true. The argument is thus entirely valid.

More subtly, we can reach a true conclusion from one or more false premises, as in:

All fish live in the sea (premise) Dolphins are fish (premise) Therefore dolphins live in the sea (conclusion)

However, the one thing we cannot do is reach a false conclusion through valid inference from true premises.

We can therefore draw up a "truth table" for implication. The symbol "=>" denotes implication; "A" is the premise,

"B" the conclusion. "T" and "F" represent true and false respectively.

Premise Conclusion Inference

A B A=>B----------------------------

F F T

F T T

-- If the premises are false and the inference valid, the conclusion can be true or false.

T F F-- If the premises are true and the conclusion false, the inference must be invalid.

T T T

-- If the premises are true and the inference valid, the conclusion must be true.

A sound argument is a valid argument whose premises are true. A sound argument therefore arrives at a true

conclusion. Be careful not to confuse sound arguments with valid arguments.

Of course, we can criticize more than the mere soundness of an argument. In everyday life, arguments are almost

always presented with some specific purpose in mind. As well as criticizing the argument itself, one can criticize the

apparent intent of the argument. Such criticism is outside the scope of this document, however!

Further reading

For a readable introduction to logic, try Flew's "Thinking Straight", listed in the atheist resources document. The

document also lists LOGIC-L, a LISTSERV mailing list devoted to discussing the teaching of elementary logic.
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Fallacies

To delve further into the structure of logical arguments would require lengthy discussion of linguistics and

philosophy. It is simpler and probably more useful to summarize the major pitfalls to be avoided when

constructing an argument. These pitfalls are known as fallacies.

In everyday English the term "fallacy" is used to refer to mistaken beliefs as well as to the faulty reasoning that leads

to those beliefs. This is fair enough, but in logic the term is generally used to refer to a form of technically incorrect

argument, especially if the argument appears valid or convincing.

So for the purposes of this discussion, we define a fallacy as a logical argument which appears to be correct, but

which can be seen to be incorrect when examined more closely. By studying fallacies we aim to avoid being misled

by them.

Below is a list of some common fallacies, and also some rhetorical devices often used in debate. The list is not

intended to be exhaustive.

Argumentum ad baculum / Appeal to force

The Appeal to Force is committed when the arguer resorts to force or the threat of force in order to try and push

the acceptance of a conclusion. It is often used by politicians, and can be summarized as "might makes right". The

force threatened need not be a direct threat from the arguer.

For example:

"... Thus there is ample proof of the truth of the Bible. All those who refuse to accept that truth will burn in Hell."

Argumentum ad hominem

Argumentum ad Hominem is literally "argument directed at the man".

The Abusive variety of Argumentum ad Hominem occurs when, instead of trying to disprove the truth of an

assertion, the arguer attacks the person or people making the assertion. This is invalid because the truth of an

assertion does not depend upon the goodness of those asserting it.

For example:

"Atheism is an evil philosophy. It is practised by Communists and murderers."

Sometimes in a court of law doubt is cast upon the testimony of a witness by showing, for example, that he is a

known perjurer. This is a valid way of reducing the credibility of the testimony given by the witness, and not

Argumentum ad Hominem; however, it does not demonstrate that the witness's testimony is false. To conclude

otherwise is to fall victim of the Argumentum ad Ignorantiam.

The circumstantial form of Argumentum ad Hominem is committed when a person argues that his opponent ought to

accept the truth of an assertion because of the opponent's particular circumstances. For example:

"It is perfectly acceptable to kill animals for food. How can you argue otherwise when you're quite happy to wear

leather shoes?"

This is an abusive charge of inconsistency, used as an excuse for dismissing the opponent's argument.
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This fallacy can also be used as a means of rejecting a conclusion. For example:

"Of course you would argue that positive discrimination is a bad thing. You're white."

This particular form of Argumentum ad Hominem, when one alleges that one's adversary is rationalizing a

conclusion formed from selfish interests, is also known as "poisoning the well".

Argumentum ad ignorantiam

Argumentum ad ignorantiam means "argument from ignorance". This fallacy occurs whenever it is argued that

something must be true simply because it has not been proved false. Or, equivalently, when it is argued that

something must be false because it has not been proved true. (Note that this is not the same as assuming that

something is false until it has been proved true, a basic scientific principle.)

Examples:

"Of course the Bible is true. Nobody can prove otherwise."

"Of course telepathy and other psychic phenomena do not exist. Nobody has shown any proof that they are real."

Note that this fallacy does not apply in a court of law, where one is generally assumed innocent until proven guilty.

Also, in scientific investigation if it is known that an event would produce certain evidence of its having occurred,

the absence of such evidence can validly be used to infer that the event did not occur.

For example:

"A flood as described in the Bible would require an enormous volume of water to be present on the earth. The

earth does not have a tenth as much water, even if we count that which is frozen into ice at the poles. Therefore

no such flood occurred."

In science, we can validly assume from lack of evidence that something has not occurred. We cannot conclude with

certainty that it has not occurred, however. See also Shifting the Burden of Proof

Argumentum ad misericordiam

This is the Appeal to Pity, also known as Special Pleading. The fallacy is committed when the arguer appeals to pity

for the sake of getting a conclusion accepted. For example:

"I did not murder my mother and father with an axe. Please don't find me guilty; I'm suffering enough through

being an orphan."

Argumentum ad populum

This is known as Appealing to the Gallery, or Appealing to the People. To commit this fallacy is to attempt to win

acceptance of an assertion by appealing to a large group of people. This form of fallacy is often characterized by

emotive language. For example:

"Pornography must be banned. It is violence against women."
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"The Bible must be true. Millions of people know that it is. Are you trying to tell them that they are all mistaken

fools?"

Argumentum ad numerum

This fallacy is closely related to the argumentum ad populum. It consists of asserting that the more people who

support or believe a proposition, the more likely it is that that proposition is correct.

Argumentum ad verecundiam

The Appeal to Authority uses the admiration of the famous to try and win support for an assertion. For example:

"Isaac Newton was a genius and he believed in God."

This line of argument is not always completely bogus; for example, reference to an admitted authority in a

particular field may be relevant to a discussion of that subject. For example, we can distinguish quite clearly

between:

"Hawking has concluded that black holes give off radiation"

and

"Penrose has concluded that it is impossible to build an intelligent computer"

Hawking is a physicist, and so we can reasonably expect his opinions on black hole radiation to be informed.

Penrose is a mathematician, so it is questionable whether he is well-qualified to speak on the subject of machine

intelligence.

The fallacy of accident

The Fallacy of Accident is committed when a general rule is applied to a particular case whose "accidental"

circumstances mean that the rule is inapplicable. It is the error made when one goes from the general to the

specific. For example:

"Christians generally dislike atheists. You are a Christian, so you must dislike atheists."

This fallacy is often committed by moralists and legalists who try to decide every moral and legal question by

mechanically applying general rules.

Converse accident / Hasty generalization

This fallacy is the reverse of the Fallacy of Accident. It occurs when one forms a general rule by examining only a

few specific cases which are not representative of all possible cases. For example:

"Jim Bakker was an insincere Christian. Therefore all Christians are insincere."

Sweeping generalization / Dicto simpliciter
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A sweeping generalization occurs when a general rule is applied to a particular situation in which the features of

that particular situation render the rule inapplicable. A sweeping generalization is the opposite of a hasty

generalization.

Non causa pro causa / Post hoc ergo propter hoc

These are known as False Cause fallacies.

The fallacy of Non Causa Pro Causa occurs when one identifies something as the cause of an event but it has not

actually been shown to be the cause. For example:

"I took an aspirin and prayed to God, and my headache disappeared. So God cured me of the headache."

The fallacy of Post Hoc Ergo Propter Hoc occurs when something is assumed to be the cause of an event merely

because it happened before the event. For example:

"The Soviet Union collapsed after taking up atheism. Therefore we must avoid atheism for the same reasons."

Cum hoc ergo propter hoc

This fallacy is similar to Post Hoc Ergo Propter Hoc. It asserts that because two events occur together, they must be

causally related, and leaves no room for other factors that may be the cause(s) of the events.

Petitio principii / Begging the question

This fallacy occurs when the premises are at least as questionable as the conclusion reached.

Circulus in demonstrando

This fallacy occurs when one assumes as a premise the conclusion which one wishes to reach. Often, the

proposition will be rephrased so that the fallacy appears to be a valid argument. For example:

"Homosexuals must not be allowed to hold government office. Hence any government official who is revealed to

be a homosexual will lose his job. Therefore homosexuals will do anything to hide their secret, and will be open to

blackmail. Therefore homosexuals cannot be allowed to hold government office."

Note that the argument is entirely circular; the premise is the same as the conclusion. An argument like the above

has actually been cited as the reason for the British Secret Services' official ban on homosexual employees.

Another example is the classic:

"We know that God exists because the Bible tells us so. And we know that the Bible is true because it is the word

of God."

Complex question / Fallacy of interrogation / Fallacy of presupposition

This is the interrogative form ofBegging the Question. One example is the classic loaded question:

"Have you stopped beating your wife?"
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The question presupposes a definite answer to another question which has not even been asked. This trick is often

used by lawyers in cross-examination, when they ask questions like:

"Where did you hide the money you stole?"

Similarly, politicians often ask loaded questions such as:

"How long will this EC interference in our affairs be allowed to continue?"

or

"Does the Chancellor plan two more years of ruinous privatization?"

Another form of this fallacy is to ask for an explanation of something which is untrue or not yet established.

Ignoratio elenchi

The fallacy of Irrelevant Conclusion consists of claiming that an argument supports a particular conclusion when it

is actually logically nothing to do with that conclusion.

For example, a Christian may begin by saying that he will argue that the teachings of Christianity are undoubtably

true. If he then argues at length that Christianity is of great help to many people, no matter how well he argues he

will not have shown that Christian teachings are true.

Sadly, such fallacious arguments are often successful because they arouse emotions which cause others to view the

supposed conclusion in a more favourable light.

Equivocation / Fallacy of four terms

Equivocation occurs when a key word is used with two or more different meanings in the same argument. For

example:

"What could be more affordable than free software? But to make sure that it remains free, that users can do what

they like with it, we must place a license on it to make sure that will always be freely redistributable."

Amphiboly

Amphiboly occurs when the premises used in an argument are ambiguous because of careless or ungrammatical

phrasing.

Accent

Accent is another form of fallacy through shifting meaning. In this case, the meaning is changed by altering which

parts of a statement are emphasized. For example, consider:

"We should not speak ill of our friends"

and

"We should not speak ill of our friends"


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Fallacies of composition

One Fallacy of Composition is to conclude that a property shared by the parts of something must apply to the

whole. For example:

"The bicycle is made entirely of low mass components, and is therefore very lightweight."

The other Fallacy of Composition is to conclude that a property of a number of individual items is shared by a

collection of those items. For example:

"A car uses less petrol and causes less pollution than a bus. Therefore cars are less environmentally damaging than

buses."

Fallacy of division

The fallacy of division is the opposite of the Fallacy of Composition. Like its opposite, it exists in two varieties. The

first is to assume that a property of some thing must apply to its parts. For example:

"You are studying at a rich college. Therefore you must be rich."

The other is to assume that a property of a collection of items is shared by each item. For example:

"Ants can destroy a tree. Therefore this ant can destroy a tree."

The slippery slope argument

This argument states that should one event occur, so will other harmful events. There is no proof made that the

harmful events are caused by the first event.

For example:

"If we legalize marijuana, then we would have to legalize crack and heroin and we'll have a nation full of drug-

addicts on welfare. Therefore we cannot legalize marijuana."

"A is based on B" fallacies / "...is a type of..." fallacies / Fallacy of the Undistributed Middle

These fallacies occur when one attempts to argue that things are in some way similar without actually specifying in

what way they are similar. Examples:

"Isn't history based upon faith? If so, then isn't the Bible also a form of history?"

"Islam is based on faith, Christianity is based on faith, so isn't Islam a form of Christianity?"

"Cats are a form of animal based on carbon chemistry, dogs are a form of animal based on carbon chemistry, so

aren't dogs a form of cat?"

Affirmation of the consequent
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This fallacy is an argument of the form "A implies B, B is true, therefore A is true". To understand why it is a fallacy,

examine the truth table for implication given earlier.

Denial of the antecedent

This fallacy is an argument of the form "A implies B, A is false, therefore B is false". The truth table for

implication makes it clear why this is a fallacy. Note that this fallacy is different from Non Causa Pro Causa. The

latter has the form "A implies B, A is false, therefore B is false", where A does not in fact imply B at all. Here, the

problem is not that the implication is invalid; rather it is that the falseness of A does not allow us to deduce

anything about B.

Converting a conditional

This fallacy is an argument of the form "If A then B, therefore if B then A".

Argumentum ad antiquitatem

This is the fallacy of asserting that something is right or good simply because it is old, or because "that's the way

it's always been."

Argumentum ad novitatem

This is the opposite of the Argumentum ad Antiquitatem; it is the fallacy of asserting that something is more

correct simply because it is new or newer than something else.

Argumentum ad crumenam

The fallacy of believing that money is a criterion of correctness; that those with more money are more likely to be

right.

Argumentum ad lazarum

The fallacy of assuming that because someone is poor he or she is sounder or more virtuous than one who is

wealthier. This fallacy is the opposite of the argumentum ad crumenam.

Argumentum ad nauseam

This is the incorrect belief that an assertion is more likely to be true the more often it is heard. An "argumentum ad

nauseam" is one that employs constant repetition in asserting something.

Bifurcation

Also referred to as the "black and white" fallacy, bifurcation occurs when one presents a situation as having only

two alternatives, where in fact other alternatives exist or can exist.

Plurium interrogationum / Many questions
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This fallacy occurs when a questioner demands a simple answer to a complex question.

Non sequitur

A non-sequitur is an argument where the conclusion is drawn from premises which are not logically connected

with it.

Red herring

This fallacy is committed when irrelevant material is introduced to the issue being discussed, so that everyone's

attention is diverted away from the points being made, towards a different conclusion.

Reification / Hypostatization

Reification occurs when an abstract concept is treated as a concrete thing.

Shifting the burden of proof

The burden of proof is always on the person making an assertion or proposition. Shifting the burden of proof, a

special case ofArgumentum ad Ignorantiam, is the fallacy of putting the burden of proof on the person who denies

or questions the assertion being made. The source of the fallacy is the assumption that something is true unless

proven otherwise. For further discussion of this idea, see the "Introduction to Atheism" document.

Straw man

The straw man fallacy is to misrepresent someone else's position so that it can be attacked more easily, then to

knock down that misrepresented position, then to conclude that the original position has been demolished. It is a

fallacy because it fails to deal with the actual arguments that have been made.

The extended analogy

The fallacy of the Extended Analogy often occurs when some suggested general rule is being argued over. The

fallacy is to assume that mentioning two different situations, in an argument about a general rule, constitutes a

claim that those situations are analogous to each other.

This fallacy is best explained using a real example from a debate about anti-cryptography legislation:

"I believe it is always wrong to oppose the law by breaking it."

"Such a position is odious: it implies that you would not have supported Martin Luther King."

"Are you saying that cryptography legislation is as important as the struggle for Black liberation? How dare you!"

Tu quoque

This is the famous "you too" fallacy. It occurs when an action is argued to be acceptable because the other party

has performed it. For instance:
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"You're just being randomly abusive."

"So? You've been abusive too."

This is a personal attack, and is therefore a special case ofArgumentum ad Hominem.

Audiatur et altera pars

Often, people will argue from assumptions which they do not bother to state. The principle of Audiatur et Altera

Pars is that all of the premises of an argument should be stated explicitly. It is not strictly a fallacy to fail to state all

of one's assumptions; however, it is often viewed with suspicion.

Ad hoc

There is a difference between argument and explanation. If we're interested in establishing A, and B is offered as

evidence, the statement "A because B" is an argument. If we're trying to establish the truth of B, then "A because

B" is not an argument, it is an explanation.

The Ad Hoc fallacy is to give an after-the-fact explanation which does not apply to other situations. Often this ad

hoc explanation will be dressed up to look like an argument. For example, if we assume that God treats all people

equally, then the following is an ad hoc explanation:

"I was healed from cancer."

"Praise the Lord, then. He is your healer."

"So, will He heal others who have cancer?"

"Er... The ways of God are mysterious."

Argumentum ad logicam

This is the "fallacy fallacy" of arguing that a proposition is false merely on the grounds that it has been presented

as the conclusion of a fallacious argument. Remember always that fallacious arguments can arrive at true

conclusions.

mathew
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Philosophical Terms and Methods

Vocabulary Describing Arguments

Contents

Valid Arguments Sound Arguments Persuasive Arguments Conditionals

o Necessary and sufficient conditions Consistency

Most of the arguments philosophers concern themselves with are--or purport to be--deductive arguments.

Mathematical proofs are a good example of deductive argument.

Most of the arguments we employ in everyday life are not deductive arguments but rather inductive arguments.

Inductive arguments are arguments which do not attempt to establish a thesis conclusively.Rather, they cite evidence

which makes the conclusionsomewhat reasonable to believe. The methods Sherlock Holmes employed to catch

criminals (and which Holmes misleadingly called "deduction") were examples of inductive argument. Other

examples of inductive argument include: concluding that it won't snow on June 1st this year, because it hasn't

snowed on June 1st for any of the last 100 years; concluding that your friend is jealous because that's the best

explanation you can come up with of his behavior, and so on.

It's a controversial and difficult question what qualities make an argument a good inductive argument. Fortunately,

we don't need to concern ourselves with that question here. In this class, we're concerned onlywith deductive arguments.

Philosophers use the following words to describe the qualities that make an argument a good deductive argument:

Valid Arguments

We call an argument deductively valid (or, for short, just "valid") when the conclusion is entailed by, or logically

follows from, the premises.

Validity is a property of the argument'sform. It doesn't matter what the premises and the conclusion actually say. It

just matters whether the argument has the right form. So, in particular, a valid argument need nothave true premises,

nor need it have a true conclusion. The following is a valid argument:

1. All cats are reptiles.2. Bugs Bunny is a cat.3. So Bugs Bunny is a reptile.

Neither of the premises of this argument is true. Nor is the conclusion. But the premises are of such a form

that ifthey were both true, then the conclusion would also have to be true. Hence the argument is valid.
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To tell whether an argument is valid, figure out what the form of the argument is, and then try to think of some other

argument ofthat same form and having true premises but a false conclusion. If you succeed, then every argument of

that form must be invalid. A valid form of argument can neverlead you from true premises to a false conclusion.

For instance, consider the argument:

1. If Socrates was a philosopher, then he wasn't a historian.2. Socrates wasn't a historian.3. So Socrates was a philosopher.

This argument is of the form "If P then Q. Q. So P." (If you like, you could say the form is: "If P then not-Q. not-Q.

So P." For present purposes, it doesn't matter.) The conclusion of the argument is true. But is it a valid form of

argument?

It is not. How can you tell? Because the following argument is of the same form, and it has true premises but a false

conclusion:

1. If Socrates was a horse (this corresponds to P), then Socrates was warm-blooded (this corresponds to Q).2. Socrates was warm-blooded (Q).3. So Socrates was a horse (P).

Since this second argument has true premises and a false conclusion, it must be invalid. And since the first argument

has the same form as the second argument (both are of the form "If P then Q. Q. So P."), both arguments must be

invalid.

Here are some more examples of invalid arguments:

The Argument Its Form

If there is a hedgehog in my gas tank, then my car will not start.My car will not start.

Hence, there must be a hedgehog in my gas tank.

If P then Q.Q.

So P.

If I publicly insult my mother-in-law, then my wife will be angry

at me.

I will not insult my mother-in-law.

Hence, my wife will never be angry at me.

If P then Q.

not-P.

So not-Q.

Either Athens is in Greece or it is in Turkey.

Athens is in Greece.

Therefore, Athens is in Turkey.

Either P or Q.

P.

So Q.

If I move my knight, Christian will take my knight.

If I move my queen, Christian will take my knight.

Therefore, if I move my knight, then I move my queen.

If P then Q.

If R then Q.

So if P then

R.


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Invalid arguments give us no reason to believe their conclusions. But be careful: The fact that an argument is

invalid doesn't mean that the argument's conclusion is false. The conclusion might be true. It's just that the invalid

argument doesn't give us any good reason to believe that the conclusion is true.

If you take a class in Formal Logic, you'll study which forms of argument are valid and which are invalid. We won't

devote much time to that study in this class. I only want you to learn what the terms "valid" and "invalid" mean, and

to be able to recognize a few clear cases of valid and invalid arguments when you see them.

Exercise

For each of the following arguments, determine whether it is valid or invalid. If it's invalid, explain why.

Either Colonel Mustard or Miss Scarlet is the culprit.

Miss Scarlet is not the culprit.

Hence, Colonel Mustard is the culprit.

Your high idle is caused either by a problem with the transmission, or by too

little oil, or both.

You have too little oil in your car.

Therefore, your transmission is fine.

If the moon is made of green cheese, then cows jump over it.

The moon is made of green cheese.

Therefore, cows jump over the moon.

Sometimes an author will not explicitly state all the premises of his argument. This will render his argument invalid

as it is written. In such cases we can often "fix up" the argument by supplying the missing premise, assuming thatthe author meant it all along. For instance, as it stands, the argument:

1. All engineers enjoy ballet.2. Therefore, some males enjoy ballet.

is invalid. But it's clear how to fix it up. We just need to supply the hidden premise:

1. All engineers enjoy ballet.2. Some engineers are male.3. Therefore, some males enjoy ballet.

You should become adept at filling in such missing premises, so that you can see the underlying form of an

argument more clearly.

Exercise

Try to supply the missing premises in the following arguments:


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If you keep driving your car with a faulty carburetor, it will eventually

explode.

Therefore, if you keep driving your car with a faulty carburetor, you will

eventually get hurt.

Abortion is morally wrong.Abortion is not a constitutional right.

Therefore, abortion ought to be against the law.

Sometimes a premise is left out because it is taken to be obvious, as in the engineer argument, and in the

exploding car argument. But sometimes the missing premise is very contentious, as in the abortion argument.

Sound Arguments

An argument is sound just in case it's valid andall its premises are true.

The argument:

1. If the moon is made of green cheese, then cows jump over it.2. The moon is made of green cheese.3. Therefore, cows jump over the moon.

is an example of a valid argument which is not sound.

We said above that a valid argument can never take you from true premises to a false conclusion. So, if you have a

sound argument for a given conclusion, then, since the argument has true premises, and since the argument is valid,

and valid arguments can never take you from true premises to a false conclusion, the argument's conclusion mustbe

true. Sound arguments always have true conclusions.

This means that if you read Philosopher X's argument and you disagree with his conclusion, then you're committed

to the claim that his argument is unsound. Either X's conclusion does not actually follow from his premises--there is

a problem with his reasoning or logic--or at least one of X's premises is false.

When you're doing philosophy, it is never enough simply to say that you disagree with someone's conclusion, or that

his conclusion is wrong. If your opponent's conclusion is wrong, then there must be something wrong with his

argument, and you need to say what it is.

Exercise

Here are some sample arguments. Can you tell which ones are valid and which of the valid arguments are also

sound? (There are 5 valid arguments and 2 sound arguments.)

I. If Socrates is a man, then Socrates is mortal. Socrates is a man. So,

Socrates is mortal.

II. If Socrates is a horse, then Socrates is mortal. Socrates is a horse. So,

Socrates is mortal.


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III. If Socrates is a horse, then Socrates has four legs. Socrates is a

horse. So, Socrates has four legs.

IV. If Socrates is a horse, then Socrates has four legs. Socrates doesn't

have four legs. So, Socrates is not a horse.

V. If Socrates is a man, then he's a mammal. Socrates is not a mammal. So

Socrates is not a man.

VI. If Socrates is a horse, then he's warm-blooded. Socrates is warm-blooded.

So Socrates is a horse.

VII. If Socrates was a philosopher then he wasn't a historian. Socrates

wasn't a historian. So, Socrates was a philosopher.

Persuasive Arguments

Unfortunately, merely having a sound argument is not yet enough to have the persuasive force of reason on your

side. For it might be that your premises are true, but it's hard to recognize that they're true.

Consider the following two arguments:

Argument A Argument B

1. Either God exists, or 2+2=5.2. 2+2 does not equal 5.3. So God exists.

1. Either God does not exist, or 2+2=5.2. 2+2 does not equal 5.3. So God does not exist.

Both of these arguments have the form "P or Q. not-Q. So P." That's a valid form of argument. So both of these

arguments are valid. What's more, at least one of the arguments is sound. If God exists, then all the premises of

Argument A are true, and since Argument A is valid, it must also be sound. If God does not exist, then all the

premises of Argument B are true, and since Argument B is valid, it must also be sound. Either way, one of the

arguments is sound. But we can't tell which of these arguments is sound and which is not. Hence neither argument is

very persuasive.


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In general, when you're engaging in philosophical

debate, you don't just want valid arguments from premises that happen to be true. You want valid arguments from

premises that are recognizable as true, or already accepted as true, by all parties to your debate.

Hence, we can introduce a third notion:

Apersuasiveargument is a valid argument with plausible, or obviously true, or

antecedently accepted premises.

These are the sorts of arguments you should try to offer.

Conditionals

A claim of the form "If P then Q" is known as a conditional. P is called the antecedent of the conditional, and Q is

called the consequent of the conditional.

In this class, you can take all of the following to be variant ways of saying the same thing:

If P then Q P implies Q P -> Q P is sufficient (or: a sufficient condition) for Q If you've got P you must have Q A necessary condition for having P is that you have Q Q is necessary for having P It's only the case that P if it's also the case that Q P only if Q
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Note the terms sufficient condition and necessary condition.

To say that one fact is a sufficient condition for a second fact means that, so long as the first fact obtains,

that's enough to guarantee that the second fact obtains, too. For example, if you have ten children, that is

sufficient for you to be a parent.

To say that one fact is a necessary condition for a second fact means that, in order for the second fact to be

true, it's required that the first fact also be true. For example, in order for you to be a father, it's necessary

that you be male. You can't be a father unless you're male. So being male is a necessary condition for being

a father.

When P entails Q, then P is a sufficient condition for Q (if P is true, that guarantees that Q is true, too); and

Q is a necessary condition for P (in order for P to be true, Q also has to be true).

Exercise

Consider the following pairs and say whether one provides sufficient and/or necessary conditions for the other.

1. a valid argument, a sound argument

2. knowing that it will rain, believing that it will rain

Now, just because P entails Q, it doesn't follow that Q entails P. However, sometimes it's both the case that P

entails Qandalso the case that Q entails P. When so, we write it as follows (again, all of these are variant ways of

saying the same thing):

P if and only if Q P iff Q P just in case Q P Q if P then Q, and if Q then P P is both sufficient and necessary for Q P is a necessary and sufficient condition for Q

For example, being a male parent is both necessary and sufficient for being a father. If you're a father, it's required

that you be a male parent. And if you're a male parent, that suffices for you to be father. So we can say that someone

is a father if and only if he's a male parent.

Consistency

When a set of propositions cannot all be simultaneously true, we say that the propositions are inconsistent. Here

is an example of two inconsistent propositions:

1. Oswald acted alone when he shot Kennedy.2. Oswald did not act alone when he shot Kennedy.

When a set of propositions is notinconsistent, then they're consistent. Note that consistency is no guarantee of truth.

It's possible for a set of propositions to be consistent, and yet for some or all of them to be false.


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Sometimes we say that a proposition P is incompatible with another proposition Q. This is just another way of

saying that the two propositions are inconsistent with each other.

A contradiction is a proposition that's inconsistent with itself, like "P and not-P."

Sometimes it's tricky to see that a set of propositions is inconsistent, or to determine which of them you ought to

give up. For instance, the following three propositions all seem somewhat plausible, yet they cannot all three be true,for they're inconsistent with each other:

1. If a person promises to do something, then he's obliged to do it.2. No one is obliged to do things which it's impossible for him to do.3. People sometimes promise to do things it's impossible for them to d

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