How to Argue Logically

“Does Australia Exist?”, or
Introduction to Argumentation

Imagine …
• Imagine you were having a discussion with a friend of
yours, and in the middle of the chat they said to you “I
don’t believe Australia exists. I’ve never been there,
have you?”, what would you say?

Imagine …
• If you have been there, that makes life easy, you get to
say “yes” and you can tell various stories about your
adventures in Australia (and they would be a form of
evidence for the existence of Australia). But if you
haven’t been there, what do you say?

Imagine …
• You’d have to say “No, but…” and then you’d have to
offer various forms of evidence for the existence of
Australia, maybe that you’ve met people from
Australia, and people who have been there. You could
show maps of the world, and photographs from
space, TV shows from Australia, and the millions of
books that mention Australia (including history books,
geography books, travel books, biographies, etc.), you
could show passports and other legal documents, etc.

Imagine …
• So, how do we know whether or not a belief is
justified?
• Being able to demonstrate some forms of evidence is
a good way of justifying our beliefs.

How to Argue
• Evidence:
• Facts that support a particular claim can be considered
very strong evidence.
• The fact could be in some form of documentation, like a
contract, a passport, a medical report, a letter, a book, or
a documentary; it could also be the testimony of someone
who is very knowledgeable about a particular aspect of
the claim (they can be called an expert).

“The Ground Rules”, or
How to Argue

How to Argue
• To have a discussion with someone, there are a few
things you both have to agree to, and without those,
it’s really hard to have a fair chat.
• So, we typically call these discussions an argument,
but that doesn’t mean we are actually fighting, it just
means we are having a discussion that follows some
rules.

How to Argue
• To call an argument “reasonable”, the first thing we
have to do is to follow the three basic laws of reason
(or “laws of logic”). These are:
1. the law of Identity
2. the law of Non-contradiction
3. the law of Excluded Middle

How to Argue
• The Law of Identity:
•This one is really easy, it just means something is
what it is. Or we could also say that until something
is changed, it is what it is.
•So “a rock is a rock”, or more formally “A is A”.

How to Argue
• The Law of Non-contradiction:
•This is also really easy, it just means two
contradictory statements can’t be true at the same
time, so if something is, then it can’t be isn’t.
•So, we can either say “something is completely
made of rock”, or “something isn’t completely
made of rock”, but not both. Or more formally
“nothing can be both A and not A”. Also “nothing
can be both true and not true”.

How to Argue
• The Law of Excluded Middle:
•This is also really easy, it just means if something is,
then it can’t be isn’t (and there’s no in-between).
•So, if something is “completely made of rock”, it
can’t be “not completely made or rock” at the same
time, or more formally “everything is either A or
not A”. Also, “everything is either true or not true”.

How to Argue
• We have to take these three laws for granted when we
are having a discussion, if we are talking about a rock
and our friend says: “Well it’s a rock, but it isn’t really
a rock”, we have to say “Well, it’s either is a rock or it
isn’t, which is it?” (Non-contradiction), and if they say
“Well, it’s a mix of rock and glass”, then you say, “Well
then, it’s not a rock, because it’s either fully a rock or
not, and that’s not fully a rock” (Excluded Middle).

How to Argue
• Also, because we have to take these three laws for
granted, before we even start the argument (we can
say that we “suppose” they are true before the
argument), we can say we “presuppose” them to be
true (or we can say that they are presuppositions).

How to Argue
• So, an argument could work as follows:
• Your friend tells you something they believe (making a claim).
• If you don’t believe their claim, you ask for evidence.
• They present their evidence to you as clearly as possible.
• You either choose to accept the claim or reject the claim.
• It’s worth remembering that it’s up to your friend to prove
their claim; you don’t have to prove the opposite to be true,
they have the burden of proof because they made the claim.

How to Argue
• The Burden of Proof:
• The person making a claim has the burden of proof to
prove their claim, in other words, they have to provide
sufficient evidence to justify that belief
• You don’t have to prove the opposite to be true, why not?
• If your friend claims “the Loch Ness monster is real”, and
you say, “show me the evidence”, and they say, “can you
prove the Loch Ness monster isn’t real?”, you answer is
“You are making the claim, can you prove it? If not, I have
the right to reject it, until sufficient evidence is provided.”

“What would Judge Judy do?”, or
The Courtroom Analogy

How to Argue
• In some ways arguments are a bit like a court case. The
courts are designed to check if someone is guilt or not guilty.
• You have two sides to the argument, the prosecution, who is
trying to prove that the person is guilty, and the defense,
whose job it is to raise doubts that the prosecution have
provided enough evidence to prove the guilt of the person.

How to Argue
• The job of the prosecution is to present enough evidence to
convince the jury of the claim that the accused person is
guilty, they have the burden of proof, in other words they
have to present the evidence in a clear way to convince the
jury of their claim.

How to Argue
• The job of the defense is to raise doubt that prosecution has
presented enough evidence to convince you that the person
is guilty.
• They don’t have to prove that the accused person is
innocent, just that the prosecution haven’t made their case.
• They have no burden of proof to show that the accused
person is innocent (because it’s very difficult to prove a
negative).

How to Argue
• As a member of the jury, you review the evidence, and if you
feel sufficient evidence was presented by the prosecution
that wasn’t refuted by the defense, then you choose to
accept the claim that the person is guilty. And if you feel the
prosecution didn’t present sufficient evidence, or the
defense refuted that evidence then you reject the claim that
the person is guilty.

How to Argue
• It is worth noting that there can be any number of
technicalities as to why a jury might have to find someone
not guilty, and even if the jury did believe that the accused
committed the crime they are accused of, they have to find
that person not guilty.
• So, if a jury finds an accused person not guilty, that doesn’t
mean that they believe the person is innocent, it just means
that the prosecution didn’t present the evidence correctly or
sufficiently to convince them.

How to Argue
• Technicalities:
• If the arresting office puts the wrong date on the arrest
record, or some important item of evidence goes
temporarily missing and is later located, the jury may have
to find the accused person not guilty.
• This is because the quality of evidence is important, if
there are even small issues with the evidence, it reduces
the how much faith the jury can have in that evidence,
and therefore they must find the accused not guilty.

How to Argue
• So, courts look at the question of guilt, whether someone is
guilty or not guilty, they don’t look at whether someone is
innocent or not innocent. And most importantly the court
does not look at if someone is guilty or innocent, because
that’s too complicated, and it’s two different concepts, or
two different prongs of the argument.
• So, courts focus on guilt.

How to Argue
• Obviously, if it is possible to prove that someone innocent,
then that clearly helps address the issue of whether they are
guilty or not, so the two prongs are related, but in a lot of
cases it’s not possible to prove someone innocent (because
it’s hard to prove a negative), so the defense shouldn’t have
to do it.

“I don’t believe you”, or
Rejecting the Claim

Rejecting the Claim
• If your friend says, “I have a €500 note in my wallet”, and you
say, “I don’t believe you”, and they say, “Are you saying I
don’t have a €500 note in my wallet?”, your answer is “No,
I’m saying I am withholding my belief in your claim until I see
some evidence”.
• So, it’s worth highlighting there is a different between “I
don’t believe that you have a €500 note until I see some
evidence” is different from “I believe that you don’t have a
€500 note in your wallet”.

Rejecting the Claim
• So, it’s important to recognize there are two different
things happening here, your friend is saying that they
have this note. So, the two issues are:
1. THE FACT: Whether, or not, there is, in fact, a €500 note
in their wallet.
2. YOUR BELIEF: Whether or not you believe them, that’s a
belief that may or may not be justified (which means
that they have a legitimate reason for your belief).

Rejecting the Claim
• The FACT is that they either do or don’t have a €500 note in
their wallet, there’s only two possibilities.
• Your BELIEF can be one of three things; that you believe they
have the note, that you believe they do not have the note, or
that you don’t know, and are choosing not to believe their
claim until you see evidence.

Rejecting the Claim
• So, if you friend makes the claim of having the note, and you
say, “No, I’m saying I am withholding my belief in your claim
until I see some evidence”, if their answer is, “Can you prove I
don’t have a €500 note?”, your answer has to be “I’m not
saying you don’t have it, all I’m saying is that I don’t know if
you do, or not, until I see some evidence.”
• So, in other words, rejecting a claim is not a positive
assertion of the opposite claim, it is just a rejection of the
claim.

“Drama starts where logic
ends”, or Logical Fallacies

Logical Fallacies
• Sometimes when you are chatting to your friend they
will make an argument, that sounds very convincing,
but there is a flaw in their reasoning, and these are
called logical fallacies.
• There are hundreds of fallacies, and here a few of the
most common ones.

Logical Fallacies
• Appeal to Probability:
• This is when someone argues that something is true
because it probably could be the case.
• For example:
If I do not bring my umbrella, then it will
rain.
It will rain. (invalid conclusion).
If I do not bring my umbrella (premise)

Logical Fallacies
• Argument to Moderation:
• This is when someone argues that a compromise between
two positions is always correct.
• For example:
You say my house is worth €100.
I say my house is worth €100,000.
Therefore, my house is worth €50,050.

Logical Fallacies
• Equivocation Fallacy:
• Using a term with more than one meaning in a statement
without specifying which meaning.
• For example:
Elvis Presley is a star.
A giant ball of gas is a star.
Therefore, Elvis is a giant ball of gas.

Logical Fallacies
• False Equivalence:
• Describing two or more statements as virtually equal
when they are not.
• For example:
Dogs have tails and feet.
Cats have tails and feet.
Therefore, dogs are equivalent to cats.

Logical Fallacies
• Slippery Slope:
• An argument that a small, first action will inevitably lead
to a final negative event and, therefore, should not be
permitted.
• For example:
If we lower the drinking age by 1 year, next
thing we know children will get to drive at
age ten years old.

Logical Fallacies
• Begging the Question:
• Using the conclusion of the argument in support of itself
in a premise.
• For example:
The Apple iPhone is the best smartphone on
the planet because no one makes a better
smartphone than Apple does.

Logical Fallacies
• Argument from Ignorance:
• This is assuming that a claim is true because it has not
been or cannot be proven false, or vice versa.
• For example:
Don’t move to Ireland because it rains all
the time.

Logical Fallacies
• Argument from Incredulity:
• This is arguing that if the person cannot imagine how
something could be true; it must be false.
• For example:
I can’t think of any other reason how this
could happen, so it must be true.

Logical Fallacies
• Ad hominem Argument:
• This is arguing that attacks the arguer instead of the
argument.
• For example:
Socrates' arguments about human excellence
are no good because what would a guy with a
beard know about human excellence.

Logical Fallacies
• Ad populum Argument:
• This is arguing that a proposition is true solely because
the majority of people believe it to be so.
• For example:
Everybody else believes this, shouldn't you?

“Elementary, My Dear Watson”,
or Syllogistic Arguments

Types of Arguments
• A common way to structure an argument is with two
statements that lead to a conclusion, the classic
example is as follows:
All people are mortal.
Socrates is a person.
Therefore, Socrates is mortal.

Types of Arguments
• The first line is a general statement, and is called the
major premise

Types of Arguments
• The second line is a specific statement, and is called
the minor premise

Types of Arguments
• The third line is the conclusion, and is as a result of
the two premises:

Deductive Arguments
• This form of argument is also called a syllogism.
Major premise.
Minor premise.
Therefore, Conclusion.

Types of Arguments
• There are two standard types of arguments:
•Deductive Arguments
•Inductive Arguments
• The type of argument we have just seen is usually
associated with Deductive arguments.

Deductive Arguments
• Well-formed Deductive Arguments always lead to a
true conclusions as long as the two premises are true,
as we’ve seen in the Socrates example, another
example is:
All birds have feathers.
Robins are birds.
Therefore, robins have feathers.

Deductive Arguments
• So the basic principle is that we go from “the general
to the specific”, another example could:
It's dangerous to drive on icy roads.
The roads are icy now.
Therefore, it is dangerous to drive.

Deductive Arguments
• Well-formed:
• An argument is well-formed if it is both Valid and Sound.
• An argument is Valid if it is structured correctly, so it has a
major premise and a minor premise that leads to a
conclusion.
• An argument is Sound if the premises are true, e.g. “All
birds can fly. Penguins are birds.
Therefore, penguins can fly” is not sound
because the major premise is not true, because not all
birds can fly.

Inductive Arguments
• Inductive Arguments often lead to a true conclusions,
but they are not always true, it is probable based on
the premises supplied, for example:
Mary is left-handed and uses left-handed
scissors.
Bill is also left-handed.
Therefore, Bill also uses left-handed
scissors.

Inductive Arguments
• So the basic principle is that we go from “the specific
to the general”, another example could:
90% of graduates of School-X go to
University.
Anne is a graduate of School-X.
Therefore, Anne will go on to
University.

Inductive Arguments
• The Inductive approach is the way people learn most
of the time, e.g.
• For the past 5 years the post (letters)
almost always gets delivered sometime
between 8:05am and 8:20am, so today I
predict the post will be get delivered
sometime between 8:05am and 8:20am, it
might not, but chances are it will.

Inductive Arguments
• An inductive argument is categorized as either being
Strong or Weak.
• If the premises are true or highly probability, then the
argument is Strong.
• If the premises have a low (or unknown) probability,
then the argument is Weak.

Types of Arguments
• In summary:
General Specific
Deductive Argument
Specific General
Inductive Argument

Types of Arguments
• Other Types of Arguments include:
•Abductive Argument
•Argument by analogy

Abductive Argument
• Abductive Arguments are ones where the major premise is
true, but the minor premise is only probable, therefore the
conclusion is only probable.
The dog comes into the house wet.
It looks like rain water.
Therefore, it’s raining outside.
• We note that the sprinklers might have wet the dog.

Abductive Argument
• Abductive reasoning is used in medical diagnosis or by
police detectives, where not all the information is
known, so the best guess is all you can do.

Argument by Analogy
• Argument by analogy looks at the truth of a particular
premise, and identifies a similar premise, and argues
toward the truth in the similar premise (as a
conclusion).
Dolphins are mammals who are sea
creatures who give live birth.
Whales are sea creatures who give
live birth.
Therefore, Whales are mammals.

Argument by Analogy
• This type of argument goes “from the specific to the
specific”, for example:
Plato is mortal.
Socrates was like Plato in other
respects.

Acknowledgements
#CheckYourTech
The authors of these slides and the participants of the Ethics4EU project gratefully acknowledge the
support of the Erasmus+ programme of the European Union. The European Commission's support for
the production of this publication does not constitute an endorsement of the contents, which reflect
the views only of the authors, and the Commission cannot be held responsible for any use which may
be made of the information contained therein.
www.Ethics4EU.eu
#Ethics4EU

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