Logical Arguments
Activity #1:“What is a Logical Argument?”


Discuss as a whole group what they think a logical argument is.
Start discussion by asking them to describe what the terms “logical” and “argument” are.
Activity # 2: “Associated Vocabulary”
1. Divide into buzz groups of ~4 people.
2. Distribute handout #1a Logical Argument Terms. One per group.
3. Discuss and write as many definitions as possible for the vocabulary words associated with
logical arguments (Handout #1a Logical Argument Terms).
4. Optional (n.b. Providing answers might discourage discussion.) When the groups have done
as much as possible (or after 10min) provide each person with the answers (Handout #1b
Logical Argument Terms Answers). It is alright if this activity is not completed as they can
look at the answers in their own time.
Activity # 3: “Logical Arguments”
1. Activity to be done in the same buzz groups
2. Give each person Handout #2a: Logical Arguments Exercise.
3. Go through example 1 with them as a whole group (the answer is b) then ask them to do the
rest of the problems in their buzz groups.
4. Allow 15min to complete. As much as possible promote discussion.
5. Optional (n.b. Providing answers might discourage discussion.) Hand out answers (Handout
#2b: Logical Arguments Exercise Answers). It is alright if this activity is not completed as they
can look at the answers in their own time.
Handout #1a Logical Argument Terms
Define the following terms in your buzz group to the best of your ability:
1. Proposition
2. Argument
3. Premise
4. Conclusion
5. Inference
6. Deduction
7. Induction
8. Evidence
9. Valid
10. Invalid
11. Sound
12. Unsound
Reference
Access date 30th July 2007
KEMERLING, G. (2001) Arguments and Inference. URL:http://www.philosophypages.com/lg/e01.htm
Handout #1b Logical Argument Terms
Answers
Proposition
Something which is asserted or avowed; a sentence or form of words in which this is
done; a statement, an assertion. A proposition is either true or false, though in a
particular instance we may not know which it is.
Argument
A statement or fact advanced for the purpose of influencing the mind; a reason urged in
support of a proposition.
A collection of two or more propositions, all but one of which are the premises supposed
to provide inferential support—either deductive or inductive—for the truth of the
remaining one, the conclusion. The structure of arguments is the principal subject of
logic.
Premise
An assertion or proposition which forms the basis for a work, theory, etc.; an initial or
basic assumption; a starting point for reasoning.
A statement whose truth is used to infer that of another statement.
Conclusion
A proposition deduced by reasoning from previous propositions.
A proposition whose truth has been inferred on the basis of other propositions assembled
with it in a logical argument.
Inference
The action or process of inferring; the drawing of a conclusion from known or assumed
facts or statements; esp. in Logic, the forming of a conclusion from data or premisses,
either by inductive or deductive methods; reasoning from something known or assumed
to something else which follows from it.
The relationship that holds between the premises and the conclusion of a logical
argument, or the process of drawing a conclusion from premises that support it
deductively or inductively.
Deduction
The process of deducing or drawing a conclusion from a principle already known or
assumed; inference by reasoning from generals to particulars.
Distinction in logic between types of reasoning, arguments, or inferences. In a deductive
argument, the truth of the premises is supposed to guarantee the truth of the
conclusion.
Induction
The process of inferring a general law or principle from the observation of particular
instances (as opposed to deduction).
Distinction in logic between types of reasoning, arguments, or inferences. In an inductive
argument, the truth of the premises merely makes it probable that the conclusion is
true.
Evidence
Support for the truth of a proposition, especially that derived from empirical observation
or experience.
Valid
The most crucial distinction among deductive arguments and the inferences upon which
they rely.
In a valid argument, if the premises are true, then the conclusion must also be true.
Alternatively: it is impossible for the premises of a valid argument to be true while its
conclusion is false.
Invalid
The most crucial distinction among deductive arguments and the inferences upon which
they rely. All other arguments are invalid; that is, it is possible for their conclusions to be
false even when their premises are true. Thus, even the most reliable instances of
inductive reasoning fall short of deductive validity.
Sound
Distinction among deductive arguments. A sound argument both has true premises and
employs a valid inference; its conclusion must therefore be true.
Unsound
Distinction among deductive arguments. An unsound argument either has one or more
false premises or relies upon an invalid inference; its conclusion may be either true or
false.
References
KEMERLING, G. (2001) Arguments and Inference.
URL:http://www.philosophypages.com/lg/e01.htm Access date 30th July 2007
Oxford English Dictionary
Handout #2a: Logical Arguments Exercise
This handout is based on material by Harry J. Gensler, John Carroll University
(http://www.jcu.edu/philosophy/gensler/).
A good argument should be convincing. An argument is a set of statements consisting of premises
(the data/information) and a conclusion (inferred from the data). You should find yourself believing
the claim, or at least finding the conclusion reasonable. This entails several things:
 that the premises are acceptable or reasonable (likely to be true)
 that the evidence or reasons are relevant to the claim
 that the reasons provide sufficient grounds to lead us to accept the claim.
These things are based on logic. Logic is the analysis and appraisal of arguments. The best
introduction to logic is to DO some logic problems, give them a try – DON’T WORRY most people get
a lot of them wrong.
Each problem gives you premises (data/information) and asks which conclusion follows logically.
Don't worry about whether the premises are true; instead, ask yourself, "If these premises WERE true,
then what else would HAVE to be true?"
Here's an example:
All humans are mortal.
Socrates is human.
So ??? _______________
a) Socrates is mortal. (CORRECT ANSWER)
b) Socrates is Greek.
c) None of these validly follows.
1.
Some cave dwellers use fire.
All who use fire have intelligence.
So ???______________________
a)
b)
c)
d)
2.
All who have intelligence use fire.
Some cave dwellers have intelligence.
All cave dwellers have intelligence.
None of these validly follows.
No one held for murder is given bail.
Smith isn't held for murder.
So ???________________
a)
Smith is given bail.
b)
Smith isn't given bail.
c)
Smith is innocent.
d)
None of these validly follows.
3.
If you overslept, you'll be late.
You didn't oversleep.
So ???______________________
4.
a)
You aren't late.
b)
You did oversleep.
c)
You're late.
d)
None of these validly follows.
Anyone who has just lost a lot of blood is likely to faint.
No one who is likely to faint is a safe pilot.
So ???__________________________________
5.
a)
Everyone who has just lost a lot of blood is a safe pilot.
b)
No one who has just lost a lot of blood is a safe pilot.
c)
All safe pilots have just lost a lot of blood.
d)
None of these validly follows.
No person desiring to help others is reluctant to make sacrifices.
Some masochists aren't reluctant to make sacrifices.
So ???____________________________________
6.
a)
Some masochists don't desire to help others.
b)
All masochists desire to help others.
c)
Some masochists desire to help others.
d)
None of these validly follows.
Only language users employ generalizations.
Not a single animal uses language.
At least some animals reason.
So ??? ___________________________________
a)
Not all reasoning beings employ generalizations.
b)
Only reasoning beings employ generalizations.
c)
No reasoning beings employ generalizations.
d)
None of these validly follows.
This one is difficult!
This test was designed to test gender-differences in reasoning. Despite the common belief that
females are less logical than males, the results found that both groups did equally well.
Analysing arguments for validity
Here's a simple example:
All humans are mortal. VALID
Socrates was human.
So Socrates was mortal.
This argument is VALID. This means that the conclusion follows from the premises. Equivalently, it
would be impossible for the premises to be true while the conclusion was false. The opposite of
"valid" is "invalid." An argument can be “valid” without the premises being “true”.
Validity and truth
When we try to prove something, we try to give a SOUND argument -- one that is valid (the
conclusion follows from the premises) and has true premises. The conclusion of a sound argument
will always be true.
When we attack an argument, we usually try to show that it's UNSOUND. We try to show that the
conclusion doesn't follow from the premises or that one or more of the premises are false. Showing
that the argument is unsound doesn't refute the conclusion. The conclusion might still be true - and
our opponent might later find a better argument for it.
1.
Suppose you show that Barbara's conclusion doesn't follow from her premises. Have you
thereby shown that her conclusion is false?
A)
Yes
B)
2.
No
All dogs are animals.
You are a dog.
So you are an animal.
3.
A)
Valid
B)
Invalid
All dogs are animals.
You aren't a dog.
So you aren't an animal.
4.
5.
A)
Valid
B)
Invalid
Suppose that Barbara gives you an argument, but her conclusion is definitely false. We can
conclude that
A)
one or more of her premises is false.
B)
her conclusion doesn't follow from her premises.
C)
one of the other of these things happened.
D)
none of the above.
Suppose that Barbara gives you a valid argument. Must her conclusion then be true?
A)
Yes
B)
6.
No
Bob’s enjoyment of another's misfortune is pleasure.
Bob’s enjoyment of another's misfortune isn't intrinsically good.
So not all pleasure is intrinsically good.
A)
Valid
B)
Invalid
7.
All logicians are millionaires.
Gensler is a logician.
So Gensler is a millionaire.
8.
A)
Valid
B)
Invalid
Suppose you show that one of Barbara's premises are false. Have you thereby shown that her
conclusion is false?
A)
Yes
B)
9.
Suppose that Barbara shows you that her premises are true and that her conclusion follows
from her premises. Has she thereby shown that her conclusion is true?
A)
Yes
B)
10.
No
No
If God created the world, then the world would be perfect.
The world isn't perfect.
So God didn't create the world.
11.
A)
Valid
B)
Invalid
The trail goes to the left or to the right.
The trail doesn't go to the left.
So the trail goes to the right.
A)
Valid
B)
Invalid
References:
Student learning centre brochure:
http://www.flinders.edu.au/SLC/Brochures/writg_argument.pdf
Genslers logic pretest
http://www.jcu.edu/philosophy/gensler/fe/fe-0--00.htm
Handout #2b: Logical Arguments Exercise: Answers
1.
a)
This is invalid (try plugging in "calculus" for "..."):
All who use ... have intelligence.
So all who have intelligence use ....
b)
Correct! If SOME of them use fire, and ALL who do this have intelligence, then SOME of
them have intelligence. It might be that they ALL have intelligence. But we can't conclude this
from the premises, since we only know that SOME of them use fire.
c)
d)
"All" in the conclusion is too strong. Maybe only a few cave dwellers use fire -- and only
these few have intelligence.
No, we can draw a conclusion.
2.
a)
b)
c)
d)
Maybe Smith isn't given bail -- because maybe he's held for something else (like kidnapping)
for which bail is denied. Or maybe he's not held for anything at all.
Maybe he's held for a minor offence and so is given bail
Are you his lawyer?
We can't tell from the premises whether he is given bail. For all we know, he might be a
kidnapper and the law might deny bail to kidnappers.
3.
a)
b)
c)
d)
4.
a)
b)
c)
d)
The first premise only tells us what happens if you oversleep. It doesn't say what happens if
you DON'T oversleep. You still might be late for some other reason -- maybe your car didn't
start.
Huh? The second premise says that you didn't oversleep!
Given the premises, you might still be on time!
Correct. An IF-THEN only tells us what follows if the IF-part is TRUE. It doesn't tell us what
follows if the IF-part is FALSE.
No! Such people might faint!
By the first premise, if you just lost a lot of blood then you might faint. By the second premise,
if you might faint then you wouldn't make a safe pilot. So if you just lost a lot of blood then
you wouldn't make a safe pilot. You might faint!
No! Such pilots might faint!
No, we can draw one of the conclusions.
5.
This one is difficult!
a)
We can't conclude this from the premises. Maybe ALL masochists desire to help others
b)
We can't conclude this from the premises.
c)
Not necessarily! The second premise tells us that SOME masochists aren't reluctant to make
sacrifices. These masochists might not care about others. They might make sacrifices just
because they like to do so. The premises don't tell us that they desire to help others.
d)
Given our premises, we can't draw any of these conclusions.
6.
This one is difficult!
a)
Correct. John Stuart Mill used this to argue that reasoning doesn't require generalizations
(statements using "all" or "no"). We could rephrase the conclusion as "Some reasoning beings
don't employ generalizations."
b)
To draw this conclusion, we'd need a further universal premise linking reasoning beings with
language users or with animals.
c)
"No" in the conclusion is too strong. Notice that the last premise is about SOME reasoning
beings.
d)
No, we can draw one of these conclusions.
Analysing arguments for validity
1.
A)
You've shown that her argument is unsound and thus doesn't prove its conclusion. But she
might find a better argument later. To show that her conclusion is false, you have to develop your
own argument against it.
B)
You've shown that her argument is unsound and thus doesn't prove its conclusion. But she
might find a better argument later. To show that her conclusion is false, you have to develop your
own argument against it.
2.
A)
B)
This is valid. Unless you are a very exceptional dog, however, the second premise is false!
Bow, wow! You don't really think that this is invalid, do you?
3
A)
B)
Maybe you're a cat! Then you'd be an animal.
Correct This is invalid. Maybe you're a cat! Then you'd be an animal.
4
A)
Maybe her premises are all true, but her conclusion doesn't follow from her premises.
B)
Maybe her conclusion follows, but one or more of her premises is false.
C)
Correct. If her conclusion is false, then something is wrong with her argument. Either one or
more of her premises is false, or else her conclusion doesn't follow from her premises.
D)
If her conclusion is false, then something is wrong with her argument.
Either one or more of her premises is false, or else her conclusion doesn't follow from her premises.
5.
A)
“Valid" just means that the conclusion follows from the premises. The conclusion might be
false if a premise is false.
B)
Correct Valid" just means that the conclusion follows from the premises. The conclusion
might be false if a premise is false.
Here's an example of a valid argument with a false conclusion:
All logicians are millionaires. (False!)
Gensler is a logician.
So Gensler is a millionaire. (False!)
6.
A)
Correct This is valid, but the second premise is controversial.
Clearly stated philosophical arguments often are valid but have controversial premises.
B)
This is valid, but the second premise is controversial.
Clearly stated philosophical arguments often are valid but have controversial premises.
7.
A)
Correct This argument is VALID -- because this just means that the conclusion follows from
the premises. Calling an argument "valid" doesn't say whether its premises are true. Here the first
premise is false -- and so the argument doesn't prove its conclusion.
B)
This argument is VALID -- because this just means that the conclusion follows from the
premises. Calling an argument "valid" doesn't say whether its premises are true. Here the first
premise is false -- and so the argument doesn't prove its conclusion.
8.
A)
You've shown that her argument is unsound and thus doesn't prove its conclusion. But she
might find a better argument later. To show that her conclusion is false, you have to develop your
own argument against it.
B)
Correct You've shown that her argument is unsound and thus doesn't prove its conclusion.
But she might find a better argument later. To show that her conclusion is false, you have to develop
your own argument against it.
9.
A)
B)
Correct Since her argument is sound (valid with true premises), her conclusion has to be true.
Since her argument is sound (valid with true premises), her conclusion has to be true.
10.
A)
Correct This is valid, but the first premise is controversial. Clearly stated philosophical
arguments often are valid but have controversial premises.
B)
This is valid, but the first premise is controversial. Clearly stated philosophical arguments
often are valid but have controversial premises.
11.
A)
Correct. This is valid. It has this valid form: "A or B, not-A, so B."
The author was hiking on the Appalachian Trail in West Virginia during the great snowstorm of 1993
(which killed over 150 people). The trail was covered by several feet of snow and was hard to follow.
The author used the above form of reasoning many times as he tried to get back to civilization. The
premises represented "educated guesses" rather than firm knowledge. Reasoning can be useful even if
the premises aren't known with certitude.
B)
Incorrect Where else could the trail go? The premises exclude any other possibility.
References:
Student learning centre brochure:
http://www.flinders.edu.au/SLC/Brochures/writg_argument.pdf
Genslers logic pretest
http://www.jcu.edu/philosophy/gensler/fe/fe-0--00.htm