Introduction
There's a lot of debate on the net. Unfortunately, much of it is
of very low quality. The aim of this document is to explain the
basics of logical reasoning, and hopefully improve the overall
quality of debate.
The Concise Oxford English Dictionary defines logic as "the
science of reasoning, proof, thinking, or inference." Logic will
let you analyze an argument or a piece of reasoning, and work out
whether it is likely to be correct or not. You don't need to know
logic to argue, of course; but if you know even a little, you'll
find it easier to spot invalid arguments.
There are many kinds of logic, such as fuzzy logic and
constructive logic; they have different rules, and different
strengths and weaknesses. This document discusses simple Boolean
logic, because it's commonplace and relatively easy to understand.
When people talk about something being 'logical', they usually mean
the type of logic described here.
What logic isn't
It's worth mentioning a couple of things which logic is not.
Firstly, logical reasoning is not an absolute law which
governs the universe. Many times in the past, people have
concluded that because something is logically impossible (given the
science of the day), it must be impossible, period. It was also
believed at one time that Euclidean geometry was a universal law;
it is, after all, logically consistent. Again, we now know that the
rules of Euclidean geometry are not universal.
Secondly, logic is not a set of rules which govern human
behavior. Humans may have logically conflicting goals. For
example:
-
John wishes to speak to whoever is in charge.
-
The person in charge is Steve.
-
Therefore John wishes to speak to Steve.
Unfortunately, John may have a conflicting goal of avoiding
Steve, meaning that the reasoned answer may be inapplicable to real
life.
This document only explains how to use logic; you must decide
whether logic is the right tool for the job. There are other ways
to communicate, discuss and debate.
Arguments
An argument is, to quote the Monty Python sketch, "a
connected series of statements to establish a definite
proposition."
Many types of argument exist; we will discuss the deductive
argument. Deductive arguments are generally viewed as the
most precise and the most persuasive; they provide conclusive proof
of their conclusion, and are either valid or
invalid.
Deductive arguments have three stages: premises, inference, and
conclusion. However, before we can consider those stages in detail,
we must discuss the building blocks of a deductive argument:
propositions.
Propositions
A proposition is a statement which is either true or
false. The proposition is the meaning of the statement, not the
precise arrangement of words used to convey that meaning.
For example, "There exists an even prime number greater than
two" is a proposition. (A false one, in this case.) "An even prime
number greater than two exists" is the same proposition,
re-worded.
Unfortunately, it's very easy to unintentionally change the
meaning of a statement by rephrasing it. It's generally safer to
consider the wording of a proposition as significant.
It's possible to use formal linguistics to analyze and re-phrase
a statement without changing its meaning; but how to do so is
outside the scope of this document.
Premises
A deductive argument always requires a number of core
assumptions. These are called premises, and are the
assumptions the argument is built on; or to look at it another way,
the reasons for accepting the argument. Premises are only premises
in the context of a particular argument; they might be conclusions
in other arguments, for example.
You should always state the premises of the argument explicitly;
this is the principle of audiatur et altera
pars. Failing to state your assumptions is often viewed as
suspicious, and will likely reduce the acceptance of your
argument.
The premises of an argument are often introduced with words such
as "Assume...", "Since...", "Obviously..." and "Because...." It's a
good idea to get your opponent to agree with the premises of your
argument before proceeding any further.
The word "obviously" is also often viewed with suspicion. It
occasionally gets used to persuade people to accept false
statements, rather than admit that they don't understand why
something is 'obvious'. So don't be afraid to question statements
which people tell you are 'obvious' -- when you've heard the
explanation you can always say something like "You're right, now
that I think about it that way, it is obvious."
Inference
Once the premises have been agreed, the argument proceeds via a
step-by-step process called inference.
In inference, you start with one or more propositions which have
been accepted; you then use those propositions to arrive at a new
proposition. If the inference is valid, that proposition should
also be accepted. You can use the new proposition for inference
later on.
So initially, you can only infer things from the premises of the
argument. But as the argument proceeds, the number of statements
available for inference increases.
There are various kinds of valid inference - and also some
invalid kinds, which we'll look at later in this document.
Inference steps are often identified by phrases like "therefore..."
or "...implies that..."
Conclusion
Hopefully you will arrive at a proposition which is the
conclusion of the argument - the result you are trying to prove.
The conclusion is the result of the final step of inference. It's
only a conclusion in the context of a particular argument; it could
be a premise or assumption in another argument.
The conclusion is said to be affirmed on the basis of
the premises, and the inference from them. This is a subtle point
which deserves further explanation.
Implication in detail
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.
We can summarize these results as a "truth table" for implication. The symbol
"=>" denotes implication; "A" is the premise, "B" the
conclusion. "T" and "F" represent true and false respectively.
Truth Table for Implication
| Premise |
Conclusion |
Inference |
| A |
B |
A => B |
| false |
false |
true |
| false |
true |
true |
| true |
false |
false |
| true |
true |
true |
'
|
- If the premises are false and the inference valid, the
conclusion can be true or false. (Lines 1 and 2.)
- If the premises are true and the conclusion false, the
inference must be invalid. (Line 3.)
- If the premises are true and the inference valid, the
conclusion must be true. (Line 4.)
So the fact that an argument is valid doesn't necessarily
mean that its conclusion holds -- it may have started from
false premises.
If an argument is valid, and in addition it started from true
premises, then it is called a sound argument. A sound
argument must arrive at a true conclusion.
Example argument
Here's an example of an argument which is valid, and which may
or may not be sound:
-
Premise: Every event has a cause
-
Premise: The universe has a beginning
-
Premise: All beginnings involve an event
-
Inference: This implies that the beginning of the universe
involved an event
-
Inference: Therefore the beginning of the universe had a
cause
-
Conclusion: The universe had a cause
The proposition in line 4 is inferred from lines 2 and 3. Line 1
is then used, with the proposition derived in line 4, to infer a
new proposition in line 5. The result of the inference in line 5 is
then re-stated (in slightly simplified form) as the conclusion.
Spotting arguments
Spotting an argument is harder than spotting premises or a
conclusion. Lots of people shower their writing with assertions,
without ever producing anything you might reasonably call an
argument.
Sometimes arguments don't follow the pattern described above.
For example, people may state their conclusions first, and then
justify them afterwards. This is valid, but it can be a little
confusing.
To make the situation worse, some statements look like arguments
but aren't. For example:
"If the Bible is accurate, Jesus must either have been insane,
an evil liar, or the Son of God."
That's not an argument; it's a conditional statement. It doesn't
state the premises necessary to support its conclusion, and even if
you add those assertions it suffers from a number of other flaws
which are described in more detail in the Atheist Arguments document.
An argument is also not the same as an explanation. Suppose that
you are trying to argue that Albert Einstein believed in God, and
say:
"Einstein made his famous statement 'God does not play dice'
because of his belief in God."
That may look like a relevant argument, but it's not; it's an
explanation of Einstein's statement. To see this, remember that a
statement of the form "X because Y" can be re-phrased as an
equivalent statement, of the form "Y therefore X." Doing so gives
us:
"Einstein believed in God, therefore he made his famous
statement 'God does not play dice'.
Now it's clear that the statement, which looked like an
argument, is actually assuming the result which it is supposed to
be proving, in order to explain the Einstein quote.
Furthermore, Einstein did not believe in a personal God
concerned with human affairs -- again, see the Atheist Arguments document.
Further reading
We've outlined the structure of a sound deductive argument, from
premises to conclusion. But ultimately, the conclusion of a valid
logical argument is only as compelling as the premises you started
from. Logic in itself doesn't solve the problem of verifying the
basic assertions which support arguments; for that, we need some
other tool.
The dominant means of verifying basic assertions is scientific
enquiry. However, the philosophy of science and the scientific
method are huge topics which are quite beyond the scope of this
document.
For a more comprehensive introduction to logic, try Flew's
"Thinking Straight",
listed in the Atheist Media
document. A much more detailed book is Copi's "Introduction to Logic." The
Electronic Resources document also lists LOGIC-L, a LISTSERV mailing list
devoted to discussing the teaching of elementary logic.
Fallacies
There are a number of common pitfalls to avoid when constructing
a deductive argument; they're known as fallacies. In
everyday English, we refer to many kinds of mistaken beliefs as
fallacies; but in logic, the term has a more specific meaning: a
fallacy is a technical flaw which makes an argument unsound or
invalid.
(Note that you can criticize more than just the soundness of an
argument. Arguments are almost always presented with some specific
purpose in mind -- and the intent of the argument may also be
worthy of criticism.)
Arguments which contain fallacies are described as
fallacious. They often appear valid and convincing;
sometimes only close inspection reveals the logical flaw.
Below is a list of some common fallacies, and also some
rhetorical devices often used in debate. The list isn't intended to
be exhaustive; the hope is that if you learn to recognize some of
the more common fallacies, you'll be able to avoid being fooled by
them.
The Nizkor Project at
<http://www.nizkor.org/> has another excellent list of logical
fallacies. The reference works mentioned above also all contain
fallacy lists.
Sadly, many of the examples below have been taken directly from
Usenet, though some have been rephrased for the sake of
clarity.
List of fallacies
Accent is a form of fallacy through shifting meaning. In this
case, the meaning is changed by altering which parts of a statement
are emphasized. For example:
"We should not speak ill of our
friends"
and
"We should not speak ill of our
friends"
Be particularly wary of this fallacy on the net, where it's easy
to misread the emphasis of what's written.
As mentioned earlier, 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's an
explanation.
The Ad Hoc fallacy is to give an after-the-fact explanation
which doesn't 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."
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. Here's an example:
"If the universe had been created by a supernatural
being, we would see order and organization everywhere. And we do
see order, not randomness -- so it's clear that the universe had a
creator."
This is the converse of Denial of the
Antecedent.
Amphiboly occurs when the premises used in an argument are
ambiguous because of careless or ungrammatical phrasing. For
example:
"Premise: Belief in God fills a much-needed
gap."
One of the simplest fallacies is to rely on anecdotal evidence.
For example:
"There's abundant proof that God exists and is still
performing miracles today. Just last week I read about a girl who
was dying of cancer. Her whole family went to church and prayed for
her, and she was cured."
It's quite valid to use personal experience to illustrate a
point; but such anecdotes don't actually prove anything to anyone.
Your friend may say he met Elvis in the supermarket, but those who
haven't had the same experience will require more than your
friend's anecdotal evidence to convince them.
Anecdotal evidence can seem very compelling, especially if the
audience wants to believe it. This is part of the
explanation for urban legends; stories which are verifiably false
have been known to circulate as anecdotes for years.
This is the fallacy of asserting that something is right or good
simply because it's old, or because "that's the way it's always
been." The opposite of Argumentum ad
Novitatem.
"For thousands of years Christians have believed in
Jesus Christ. Christianity must be true, to have persisted so long
even in the face of persecution."
An Appeal to Force happens when someone resorts to force (or the
threat of force) to try and push others to accept a conclusion.
This fallacy is often used by politicians, and can be summarized as
"might makes right." The threat doesn't have to come directly from
the person arguing. 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."
"... In any case, I know your phone number and I know where you
live. Have I mentioned I am licensed to carry concealed
weapons?"
The fallacy of believing that money is a criterion of
correctness; that those with more money are more likely to be
right. The opposite of Argumentum ad
Lazarum. Example:
"Microsoft
software is undoubtedly superior; why else would Bill Gates have
got so rich?"
Argumentum ad hominem literally means "argument directed at the
man"; there are two varieties.
The first is the abusive form. If you refuse to accept a
statement, and justify your refusal by criticizing the person who
made the statement, then you are guilty of abusive argumentum ad
hominem. For example:
"You claim that atheists can be moral -- yet I happen
to know that you abandoned your wife and children."
This is a fallacy because the truth of an assertion doesn't
depend on the virtues of the person asserting it. A less blatant
argumentum ad hominem is to reject a proposition based on the fact
that it was also asserted by some other easily criticized person.
For example:
"Therefore we should close down the church? Hitler and
Stalin would have agreed with you."
A second form of argumentum ad hominem is to try and persuade
someone to accept a statement you make, by referring to that
person's particular circumstances. For example:
"Therefore it is perfectly acceptable to kill animals
for food. I hope you won't argue otherwise, given that you're quite
happy to wear leather shoes."
This is known as circumstantial argumentum ad hominem. The
fallacy can also be used as an excuse to reject a particular
conclusion. For example:
"Of course you'd argue that positive discrimination is
a bad thing. You're white."
This particular form of Argumentum ad Hominem, when you allege
that someone is rationalizing a conclusion for selfish reasons, is
also known as "poisoning the well."
It's not always invalid to refer to the circumstances of an
individual who is making a claim. If someone is a known perjurer or
liar, that fact will reduce their credibility as a witness. It
won't, however, prove that their testimony is false in this case.
It also won't alter the soundness of any logical arguments they may
make.
Argumentum ad ignorantiam means "argument from ignorance." The
fallacy occurs when it's argued that something must be true, simply
because it hasn't been proved false. Or, equivalently, when it is
argued that something must be false because it hasn't been proved
true.
(Note that this isn't the same as assuming something is
false until it has been proved true. In law, for example, you're
generally assumed innocent until proven guilty.)
Here are a couple of 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."
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 didn't
occur. It does not prove it with certainty, however.
For example:
"A flood as described in the Bible would require an enormous
volume of water to be present on the earth. The earth doesn't have
a tenth as much water, even if we count that which is frozen into
ice at the poles. Therefore no such flood occurred."
It is, of course, possible that some unknown process occurred to
remove the water. Good science would then demand a plausible
testable theory to explain how it vanished.
Of course, the history of science is full of logically valid bad
predictions. In 1893, the Royal Academy of Science were convinced
by Sir Robert Ball that communication with the planet Mars was a
physical impossibility, because it would require a flag as large as
Ireland, which it would be impossible to wave. [Fortean Times
Number 82.]
See also Shifting the Burden of
Proof.
The fallacy of assuming that someone poor is sounder or more
virtuous than someone who's wealthier. This fallacy is the opposite
of the Argumentum ad Crumenam. For
example:
"Monks are more likely to possess insight into the meaning of
life, as they have given up the distractions of wealth."
This is the "fallacy fallacy" of arguing that a proposition is
false because it has been presented as the conclusion of a
fallacious argument. Remember always that fallacious arguments can
arrive at true conclusions.
"Take the fraction 16/64. Now, cancelling a six on top and a six
on the bottom, we get that 16/64 = 1/4."
"Wait a second! You can't just cancel the six!"
"Oh, so you're telling us 16/64 is not equal to 1/4, are
you?"
This is the Appeal to Pity, also known as Special Pleading. The
fallacy is committed when someone 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."
This is the incorrect belief that an assertion is more likely to
be true, or is more likely to be accepted as true, the more often
it is heard. So an Argumentum ad Nauseam is one that employs
constant repetition in asserting something; saying the same thing
over and over again until you're sick of hearing it.
On Usenet, your argument is often less likely to be heard if you
repeat it over and over again, as people will tend to put you in
their kill files.
This is the opposite of the Argumentum
ad Antiquitatem; it's the fallacy of asserting that something
is better or more correct simply because it is new, or newer than
something else.
"BeOS is a far better choice of operating system than OpenStep,
as it has a much newer design."
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. For example:
"The vast majority of people in this country believe that
capital punishment has a noticeable deterrent effect. To suggest
that it doesn't in the face of so much evidence is ridiculous."
"All I'm saying is that thousands of people believe in pyramid
power, so there must be something to it."
This is known as Appealing to the Gallery, or Appealing to the
People. You commit this fallacy if you 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."
"For thousands of years people have believed in Jesus and the
Bible. This belief has had a great impact on their lives. What more
evidence do you need that Jesus was the Son of God? Are you trying
to tell those people that they are all mistaken fools?"
The Appeal to Authority uses admiration of a famous person to
try and win support for an assertion. For example:
"Isaac
Newton was a genius and he believed in God."
This line of argument isn't always completely bogus when used in
an inductive argument; for
example, it may be relevant to refer to a widely-regarded authority
in a particular field, if you're discussing 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.
Often, people will argue from assumptions which they don't
bother to state. The principle of Audiatur et Altera Pars is that
all of the premises of an argument should be stated explicitly.
It's not strictly a fallacy to fail to state all of your
assumptions; however, it's often viewed with suspicion.
Also referred to as the "black and white" fallacy and "false
dichotomy", bifurcation occurs if someone presents a situation as having
only two alternatives, where in fact other alternatives exist or can
exist. For example:
"Either man was created, as the Bible tells us, or he evolved
from inanimate chemicals by pure random chance, as scientists tell
us. The latter is incredibly unlikely, so..."
This fallacy occurs if you assume as a premise the conclusion
which you wish to reach. Often, the proposition is 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.
Circular arguments are surprisingly common, unfortunately. If
you've already reached a particular conclusion once, it's easy to
accidentally make it an assertion when explaining your reasoning to
someone else.
This is the interrogative form of Begging the
Question. One example is the classic loaded question:
"Have you stopped beating your wife?"
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 EU 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.
The Fallacy of Composition is to conclude that a property shared
by a number of individual items, is also shared by a collection of
those items; or that a property of the parts of an object, must
also be a property of the whole thing. Examples:
"The bicycle is made entirely of low mass components, and is
therefore very lightweight."
"A car uses less petrochemicals and causes less pollution than a
bus. Therefore cars are less environmentally damaging than
buses."
A related form of fallacy of composition is the "just" fallacy, or
fallacy of mediocrity. This is the fallacy that assumes that any given member
of a set must be limited to the attributes that are held in common with all
the other members of the set. Example:
"Humans are just animals, so we should not concern ourselves
with justice; we should just obey the law of the jungle."
Here the fallacy is to reason that because we are animals, we can have
only properties which animals have; that nothing can distinguish us as a
special case.
This fallacy is the reverse of the Fallacy
of Accident. It occurs when you form a general rule by
examining only a few specific cases which aren't representative of
all possible cases. For example:
"Jim Bakker was an insincere Christian. Therefore all
Christians are insincere."
This fallacy is an argument of the form "If A then B, therefore
if B then A."
"If educational standards are lowered, the quality of argument
seen on the Internet worsens. So if we see the level of debate on
the net get worse over the next few years, we'll know that our
educational standards are still falling."
This fallacy is similar to the Affirmation
of the Consequent, but phrased as a conditional statement.
This fallacy is similar to post hoc ergo
propter hoc. The fallacy is to assert that because two events
occur together, they must be causally related. It's a fallacy
because it ignores other factors that may be the cause(s) of the
events.
"Literacy rates have steadily declined since the advent of
television. Clearly television viewing impedes learning."
This fallacy is a special case of the more general non causa pro causa.
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. That 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 isn't that the implication is invalid;
rather it's that the falseness of A doesn't allow us to deduce
anything about B.
"If the God of the Bible appeared to me, personally, that would
certainly prove that Christianity was true. But God has never
appeared to me, so the Bible must be a work of fiction."
This is the converse of the fallacy of Affirmation of the Consequent.
A sweeping generalization occurs when a general rule is applied
to a particular situation, but the features of that particular
situation mean the rule is inapplicable. It's the error made when
you go 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 people who try to decide
moral and legal questions by mechanically applying general
rules.
The fallacy of division is the opposite of the Fallacy of Composition. It consists of
assuming that a property of some thing must apply to its parts; or
that a property of a collection of items is shared by each
item.
"You are studying at a rich college. Therefore you must be
rich."
"Ants can destroy a tree. Therefore this ant can destroy a
tree."
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."
One way to avoid this fallacy is to choose your terminology
carefully before beginning the argument, and avoid words like
"free" which have many meanings.
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.
Here's real example from an online 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!"
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 undoubtedly 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, these kinds of irrelevant arguments are often successful,
because they make people to view the supposed conclusion in a more
favorable light.
The Appeal to Nature is a common fallacy in political arguments.
One version consists of drawing an analogy between a particular
conclusion, and some aspect of the natural world -- and then
stating that the conclusion is inevitable, because the natural
world is similar:
"The natural world is characterized by competition; animals
struggle against each other for ownership of limited natural
resources. Capitalism, the competitive struggle for ownership of
capital, is simply an inevitable part of human nature. It's how the
natural world works."
Another form of appeal to nature is to argue that because human
beings are products of the natural world, we must mimic behavior
seen in the natural world, and that to do otherwise is
'unnatural':
"Of course homosexuality is unnatural. When's the last time you
saw two animals of the same sex mating?"
Robert Anton Wilson deals with this form of fallacy at length in
his book "
Natural Law." A recent example of "Appeal to Nature"
taken to extremes is The Unabomber
Manifesto.
Suppose I assert that no Scotsman puts sugar on his porridge.
You counter this by pointing out that your friend Angus likes sugar
with his porridge. I then say "Ah, yes, but no true
Scotsman puts sugar on his porridge.
This is an example of an ad hoc change
being used to shore up an assertion, combined with an attempt to shift the meaning of the words used
original assertion; you might call it a combination of
fallacies.
The fallacy of Non Causa Pro Causa occurs when something is
identified 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."
This is known as a false cause fallacy. Two specific forms of
non causa pro causa fallacy are the cum hoc ergo
propter hoc and post hoc ergo propter
hoc fallacies.
A non sequitur is an argument where the conclusion is drawn from
premises which aren't logically connected with it. For example:
"Since Egyptians did so much excavation to construct the
pyramids, they were well versed in paleontology."
(Non sequiturs are an important ingredient in a lot of humor.
They're still fallacies, though.)
This fallacy occurs when the premises are at least as
questionable as the conclusion reached. Typically the premises of
the argument implicitly assume the result which the argument
purports to prove, in a disguised form. For example:
"The Bible is the word of God. The word of God cannot be
doubted, and the Bible states that the Bible is true. Therefore the
Bible must be true.
Begging the question is similar to circulus
in demonstrando, where the conclusion is exactly the same as
the premise.
This fallacy occurs when someone demands a simple (or
simplistic) answer to a complex question.
"Are higher taxes an impediment to business or not? Yes or
no?"
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 that event. For example:
"The Soviet Union collapsed after instituting state
atheism. Therefore we must avoid atheism for the same
reasons."
This is another type of false cause
fallacy.
This fallacy is committed when someone introduces irrelevant
material to the issue being discussed, so that everyone's attention
is diverted away from the points made, towards a different
conclusion.
"You may claim that the death penalty is an ineffective
deterrent against crime -- but what about the victims of crime? How
do you think surviving family members feel when they see the man
who murdered their son kept in prison at their expense? Is it right
that they should pay for their son's murderer to be fed and
housed?"
Reification occurs when an abstract concept is treated as a
concrete thing.
"I noticed you described him as 'evil'. Where does this 'evil'
exist within the brain? You can't show it to me, so I claim it
doesn't exist, and no man is 'evil'."
The burden of proof is always on the person asserting something.
Shifting the burden of proof, a special case of Argumentum ad Ignorantiam, is the fallacy
of putting the burden of proof on the person who denies or
questions the assertion. The source of the fallacy is the
assumption that something is true unless proven otherwise.
"OK, so if you don't think the grey aliens have gained control
of the US government, can you prove it?"
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
more people would start to take crack and heroin, and we'd have to
legalize those too. Before long we'd have a nation full of
drug-addicts on welfare. Therefore we cannot legalize
marijuana."
The straw man fallacy is when you misrepresent someone else's
position so that it can be attacked more easily, knock down that
misrepresented position, then conclude that the original position
has been demolished. It's a fallacy because it fails to deal with
the actual arguments that have been made.
"To be an atheist, you have to believe with absolute
certainty that there is no God. In order to convince yourself with
absolute certainty, you must examine all the Universe and all the
places where God could possibly be. Since you obviously haven't,
your position is indefensible."
This is the famous "you too" fallacy. It occurs if you argue
that an action is acceptable because your opponent has performed
it. For instance:
"You're just being randomly abusive."
"So? You've been abusive too."
This is a personal attack, and is therefore a special case of Argumentum ad Hominem.
These fallacies occur if you attempt to argue that things are in
some way similar, but you don't actually specify 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?"
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