Logic Slides 1

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Logic Slides 1

• Propositions and Rules for Writing Short
  Arguments
• PHIL 211
• Cosmos to Citizen
• Dr. Mike Miller
• Mount St. Marys College

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Logic and Arguments

• Logic is all about arguments and reasoning well.
  In particular, the study of logic teaches how to
  make convincing arguments, to evaluate those of
  others, and (if you deem it necessary) to defeat
  them.

Knowing these skills has always been important,
for if you can reason well you can protect
yourself from those trying to dupe you. You can
also greatly influence others with your own
persuasive arguments. And finally, you may even
learn the truth the goal of many philosophers.
So, what is an argument?
An Argument is a series of propositions with a
form or structure such that one proposition (the
conclusion) is affirmed on the basis of the
others (the premises).
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What is a Proposition?
Fine, thats the definition of an argument. But
what does it mean? And what does proposition,
conclusion and premise mean? Lets find out . . .
In other words, a proposition is a declarative
sentence that is either true or false (that is,
it has what is called a truth value), but not
both. Somebody is almost always willing to agree
or disagree with every proposition, even if they
cant prove it right or wrong. So, if it is
possible to claim that a given sentence is true
or false even if it may be silly to do so
then its probably a proposition!
A Proposition is the meaning of a declarative
sentence and, as such, is either true or false.
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Are the following propositions?

• Plato is the greatest philosopher ever.
• 2) Close your notes and begin writing.
• 3) Why must every person eventually die?
• 4) Mount St. Marys is located in Texas.

Yes. You may not know if this declarative
sentence is true or false, but this kind of
sentence must be either true or false. So, this
sentence is a proposition.
No. This is not a proposition because this
sentence does not have a truth value. That is,
it is just a command. You may say No, I dont
want to, but you cant logically respond False
or True.
No. Questions are never propositions because
they are not declarative sentences.
Yes, because this declarative statement is either
true or false. We all know that the proposition
is false, but someone in another part of the
country may not. What matters here is that the
sentence must be either true or false.
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Objective or Subjective?
Every proposition is either objective or
subjective.
A proposition is objective if it is true or false
independently of what anyone thinks, believes, or
feels.
1 1 2 Objective, because it can be proven
true. 1 1 3 Also objective because it can
be proven false. Christmas 2002 was on a
Tuesday. I dont remember, but that doesnt
matter. The proposition is objective. Hydrogen
has 4 atoms. I dont have a clue, but the
proposition is still objective. I trust someone
can prove the answer.
Objective propositions are about things that can
generally be proven true or false, even if you
cant prove it yourself. For example, look at
the following 4 propositions
It is important to realize that objective
propositions are not necessarily true.
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A proposition is subjective if it is not
objective.
Subjective propositions are generally about what
people think, believe or feel. These
propositions cant be proven like objective
claims. A proposition remains subjective (even
if someone is really sure it is true) if the
proposition isnt something that can be proven by
an independent and credible source. The
following propositions are all subjective
I love to eat pizza. Fine, that may be true, but
the truth of this proposition depends fully upon
your feelings. Your preferences may change
tomorrow. I think the Yankees are great. I
strongly disagree (I think they are all jerks!),
but the strength of our opinions doesnt make
either proposition objective. I believe in
aliens. It may be an objective fact that aliens
do or do not exist, but the meaning of this
sentence depends upon a belief, so the
proposition is subjective.
So . . .
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Are the following propositions objective or
subjective?
Emmitsburg was founded in 1785.
Objective historians disagree about when the
town was founded, but this is the kind of
proposition that is true or false independent of
anyones feeling, thoughts or beliefs.
Therefore, the proposition is objective.
Britney Spears is ugly.
Subjective. Is there one universal standard
of beauty? It varies from one person to another.
So this proposition is subjective.
Still subjective.
Britney Spears is beautiful.
John said Britney Spears is ugly.
Objective, because the truth of the proposition
(whether John really said what he said) is not
dependent upon any opinion, belief or thought.
Did he say Britney is ugly or not? Dont know?
Your ignorance doesnt change anything. Its
still objective.
Today is Friday.
Objective, because the sentence is true or false
independently of what day of the week you think
it is.
God Exists.
Wow, this is a tough one. Some people would say
objective because they believe Gods existence
can be proven. Others will say subjective
because people either choose to believe God
exists or not. This example just shows that not
everything even in logic is always clear cut.
NB Please note that the issue separating
objective and subjective propositions is not
whether a proposition is true or false, but if
the meaning of the proposition is dependent upon
feelings, beliefs or thoughts and not
independent verification. Also, please note
that subjective claims can be true or false.
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OK, you now know what a proposition is, but what
is an argument?
Our Logic Handout defines an argument as a series
of propositions with a form or structure that one
proposition (the conclusion) is affirmed on the
basis of the others (the premises). According
to Anthony Weston, to give an argument means to
offer a set of reasons or evidence in support of
a conclusion.
Given these definitions it should remain obvious
that before you can understand the point of any
argument you must first determine which
proposition is being supported and which
propositions are doing the support. Likewise,
when you are writing arguments you should follow
Westons first rule in A Rulebook for Arguments
(p. 1-9) . . .
Rule 1 Distinguish premise and conclusion.
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Premise and Conclusion
Every argument contains a conclusion and at least
one premise.
A Premise is a proposition on whose basis another
proposition is affirmed.
Every time this semester I go to Patriot Hall
after my 1100 class they never have french
fries. They will not have french fries today
either.
A Conclusion is a proposition affirmed on the
basis of other propositions.
The person making the argument above is trying to
convince us that the dining hall will not have
french fries because they were not available when
he wanted them in the past. The reasons why you
should believe something are the premises. What
you should believe is the conclusion.
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Indicator Words
An indicator word is a word or phrase added to a
proposition that helps make clear the role the
proposition plays in the argument.
A conclusion indicator tells us which proposition
is the conclusion. A premise indicator tells us
which proposition is the premise.
Common premise indicators Since . . . Because
. . . For . . . In as much as . . . Given
that . . . It follows from . . .
Common conclusion indicators Therefore . . .
Hence . . . So . . . Thus . . .
Consequently . . . It follows that . . .
See the chart on Page 7 of the logic handout for
more indicator words.
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In order to make your arguments convincing, you
need to make the argument as clear as possible.
One of the most important rules to follow is . .
. Rule 2 Present your ideas in natural
order Generally, in a short argument either the
premises come first and then the conclusion, or
the argument starts with the conclusion and the
premises follow. Both forms are acceptable. Make
use of premise and conclusion indicators to
highlight to your reader what you are arguing.
Without these indicator words your argument is
often much harder to understand.
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Underline the conclusion in the following
arguments
Aristotle left Platos Academy in 410 BC because
he was upset that Plato did not leave the school
in his charge.
Aristotle left Platos Academy in 410 BC because
he was upset that Plato did not leave the school
in his charge. (Notice the premise indicator in
blue.)
Given that those that who do their home work get
better grades and better grades usually means a
higher paying job, it follows that you should
always do your homework.
Given that those that who do their home work get
better grades and better grades usually means a
higher paying job, it follows that you should
always do your homework. (Once again, indicators
make it easy.)
President Clinton was born in Michigan. All
people from Michigan have Buzz as their middle
name. Therefore, President Clintons middle name
is Buzz.
President Clinton was born in Michigan. All
people from Michigan have Buzz as their middle
name. Therefore, President Clintons middle name
is Buzz.
Note this is an argument, even though both of
the premises and the conclusion are false.
Arguments dont have to be good to be
arguments. Bad arguments are still arguments.
As long as someone intends to support one
proposition with another you have an argument.
Over 1,000 people in MD receive burns on their
body each year because they misuse lighter fluid.
Burns are very painful and leave ugly scars.
All of these injuries can be avoided. Always
follow safety rules when using lighter fluid.
Over 1,000 people in MD receive burns on their
body each year because they misuse lighter fluid.
Burns are very painful and leave ugly scars.
All of these injuries can be avoided. Always
follow safety rules when using lighter fluid.
Even though the first sentence is a very brief
argument it is not the conclusion of the entire
paragraph because the first three sentences all
support the last sentence.
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Even if your premises do give reasons why your
conclusion is true, your conclusion will probably
not be accepted if your premises are implausible.
So, . . .
Rule 3 Start with reliable premises
Consider the following argument
Since all children love to eat chocolate, Lucy
should make chocolate cake for Billys 7 year old
birthday party.
Is the premise reliable? No. Not every kid I
know loves to eat Chocolate. Since this premise
claims too much its unreliable and the argument
is bad.
Although the following argument is very similar,
it is more successful because the premise is more
reliable. Since most children like chocolate,
Lucy should make chocolate cake for Billys 7
year old birthday party. The argument is still
not perfect, but it is better.
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It is very important to realize that just because
something sounds plausible, it doesnt make it
true.
Plausibility does not equal truth!
Did you know that the government is hiding
information about UFOs and alien life forms in
Area 51 in Groom Lake, Nevada? Think about it
they let no one in Area 51, they refuse to answer
questions about it, and they are now increasing
security. Besides, people have seen things that
they deny for obvious reasons!
OK, its possible that aliens are in Area 51, but
I dont think its plausible. So, I wont
believe it is true.
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When writing arguments always follow . . .
Rule 4 Be concrete and concise Long complex
sentences and wordy expressions will often lose
your readers. As one of my favorite teachers in
college often said, Omit needless words! Omit
needless words! Omit needless words!
Vague expressions also confuse your readers.
A sentence is too vague when it is unclear what
the speaker intended.
That is, when you hear a sentence that is too
vague, you end up asking, what do you mean?
Without additional explanation, you simply cant
understand what the person is saying so you cant
determine if the proposition is true or false.
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Why are the following sentences too vague?
Lasagna is the best. Lets interview an old
person. Tall people need help. Ferrets are
wonderful.
The best what? Dinner? Italian dish?
What do you mean by old?
Whos tall? What kind of help?
Wonderful at what? Digging? Running? Singing?
Note The issue isnt whether a sentence is
vague, but whether its too vague, given the
context, for us to be justified in saying it has
a truth value.
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Spin Doctors at Work
Arguments that distort or mock your claims or
those of others are to be avoided. Language that
is used to do this is intended to sway the
emotions and is called loaded. So, always . .
. Rule 5 Avoid loaded language
When you give an argument, you should strive to
stick to the evidence. If you resort to playing
games with words and phrases to make your point
rather than the reasons themselves, you really
are not making an argument. You are trying to
deceive your reader. There are several ways to
deceive with loaded language in the premises or
conclusions of arguments . . .
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Unfortunately, we often try to make some claims
or arguments sound better or worse than they
really are.
A Euphemism is a word or phrase that makes
something sound better than its neutral
description.
Better take the prisoners to their jail cells.
Warden Bring our guests to the pacification
center.
Spy Director I sent an insurgent eradicator to
terminate a soft target.
Why not say it like it is? I sent an assassin to
kill a rebel.
It is not always clear if some words or phrases
are deceptive.
President Reagan I sent the troops to rescue
the people of Granada.
Did Reagan use the word rescue to make an
invasion of a foreign nation sound better than
it was? Or, was it really a rescue operation?
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The opposite of an Euphemism is called a
Dysphemism
A Dysphemism is a word or phrase that makes
something sound worse than its neutral
description.
flower
John put a pollen-producing, bee-attracting
organism on your desk. Biff monopolized the votes
to become class president Hey, your ball and
chain is on the phone and wants to talk to you.
earned the most
spouse
A lie usually is not considered a euphemism or a
dysphemism unless it uses an emotionally
charged word inplace of a neutral one. And
not every euphemism is bad. For example, many
consider it more polite to say that a loved one
passed away than died. It is important to
recognize that in this situation you are not
tying to deceive anyone. Euphemisms and
dysphemisms are always problems, however, when
they ask you to accept a dubious concealed claim.
Can you replace each Dysphemism with a more
neutral word?
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A Down-player is a word or phrase that minimizes
the significance of a claim.
But your Honor, I only shot him in the head once!
Our new Dishwasher is just 699.99.
Qualifier words, italics, and even the tone of
our voice are all used to downplay a claim.
Qualifiers are often called weasel words because
they suck most of the content out of statements.
High debt could be one of the possible causes of
the recession. Peer pressure arguably is the
greatest influence on young kids. Janice Smith
has won one of our two 1,333,333 prizes!
If she returns the grand prize entry, we
will be pleased to announce that . . . .
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An Up-player is a word or phrase that exaggerates
the significance of a claim.
Good news! You get to clean the bathrooms
today. Doctor to patient You have what few men
ever have a chance to put things in order
before you leave this world.
An extreme version of an Up-player is called an
hyperbole.
My daughters goal in the closing minute of her
kindergarten soccer game had to be the greatest
moment in sports history! Come and get your
mile-high ice cream cones!
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If you do not use consistent terms in your
premises and conclusion you have violated . . .
Rule 6 Use Consistent Terms Arguments depend
upon connections between the premises and the
conclusion. If your reader cant easily see the
connection between the two parts he or she will
likely not understand your argument. Even though
you can legitimately call one thing by several
names, dont do it if doing so confuses your
audience.
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When arguments slide from one meaning of a term
to another in order to make their case they have
broken . . . Rule 7 Stick to one meaning for
each term.
A proposition suffers from equivocation if there
are at least two clear ways to understand it.

• Equivocation is a problem because two very
  different but correct meanings can be taken
  from the sentence. Although one meaning may be
  silly, it is still a possible meaning. For
  example
• Dogs smell better than horses.
• I shot an elephant in my pajamas.
• I went to the bank to get money.
• Biff hit the waiter with the glasses.

Do you catch the two possible meanings in each
sentence? Which meaning is the true meaning?
Are you sure?
Although we can tolerate some vagueness in
arguments, we can never tolerate equivocation in
reasoning.
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Heres a example of an argument that breaks the
rule against equivocation
Peggy said she has a frog in her throat. Frogs
live on lily pads. Therefore, Peggy must have a
lily pad in her throat as well.
The example above is rather silly, but more
serious mistakes in reasoning can also be made
through equivocation. For example
It is lawful to keep an animal is a pen and to
feed it once a day. Ozzy Osborn is a real animal.
Therefore, it is lawful to keep Ozzy in a pen and
feed him once a day as well.
OK, this example of equivocation (on the term
animal) wasnt very serious, but the mistake was
serious. How about this one . . .
Since the Constitution declares all men were
created equal the government must give me a
million dollar house like my neighbor so we are
both equal.
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• It should now be apparent that if you want to
  argue well you must pay attention to the
  meaning of words.
• In the Appendix (p. 79-85), Weston makes several
  important comments about Definitions
• D1 When terms are unclear, get specific
• D2 When terms are contested, work from the clear
  cases
• D3 Dont expect definitions to do the work of
  the argument.

It may surprise you how hard it is to define
something well. Try it out . . . define chair
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If you said something to sit on doesnt that
also include the following
If you narrowed down your definition to a piece
of furniture with four legs intended for sitting
that supports the back arent you still
including the following
How can you improve the definition?
Are these items really chairs? What do you need
to add to the definition to make it work?
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But does your new definition end up excluding the
following examples?
Should these items be excluded from any
definition of chair? Does your definition exclude
them?
I hope it is clear that it takes time and effort
to make a good definition. Never rush when
giving a definition, especially when your
argument depends upon it. Try some more . . .
Define cup and fork.
Make sure to test the definitions to ensure they
include all the correct items and exclude those
that do not belong.
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• In the second set of slides we will discuss
  different types of arguments. In the third set
  we will discuss common mistakes in reasoning,
  called fallacies.
• Please contact me with any questions about the
  information in these slides or the related
  assigned reading
• Weston, Introduction, Chapter 1 and the Appendix
• Logic Handout, pages 1-3 and the chart on page 7