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Logic Slides 1. Propositions and Rules for Writing Short Arguments PHIL 211 Cosmos to Citizen Dr. Mike Miller Mount St. Mary’s University. Logic and Arguments.

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logic slides 1
Logic Slides 1

Propositions and Rules for Writing Short Arguments

PHIL 211

Cosmos to Citizen

Dr. Mike Miller

Mount St. Mary’s University


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).

what is a proposition
What is a Proposition?

Fine, that’s the definition of an argument. But what does it mean? And what does proposition, conclusion and premise mean? Let’s 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 can’t 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 it’s probably a proposition!

A Proposition is the meaning of a declarative sentence and, as such, is either true or false.

are the following propositions
Are the following propositions?

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.

  • Plato is the greatest philosopher ever.

2) Close your notes and begin writing.

3) Why must every person eventually die?

4) Mount St. Mary’s is located in Texas.

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 don’t want to,’ but you can’t 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.

objective or subjective

Every proposition is either objective or subjective.

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 don’t remember, but that doesn’t matter. The proposition is objective.

Hydrogen has 4 atoms.

I don’t 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 can’t prove it yourself. For example, look at the following 4 propositions:

* It is important to realize that objective propositions are not necessarily true.


A proposition is subjective if it is not objective.

Subjective propositions are generally about what people think, believe or feel. These propositions can’t be “proven” like objective claims. A proposition remains subjective (even if someone is really sure it is true) if the proposition isn’t 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 doesn’t 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 . . .


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 anyone’s 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? Don’t know? Your ignorance doesn’t change anything. It’s 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 God’s 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.


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 Weston’s first rule in A Rulebook for Arguments (p. 1-9) . . .

Rule 1: Distinguish premise and conclusion.

premise and conclusion
Premise and Conclusion

Every argument contains a conclusion and at least one premise.

A Premiseis a proposition on whose basis another proposition is affirmed.

Every time this semester I go to Patriot Hall after my 11:00 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.

indicator words
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.


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.


Underline the conclusion in the following arguments:

Aristotle left Plato’s Academy in 410 BC because he was upset that Plato did not leave the school in his charge.

Aristotle left Plato’s Academy in 410 BCbecause 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 thatyou 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 Clinton’s middle name is Buzz.

President Clinton was born in Michigan. All people from Michigan have “Buzz” as their middle name. Therefore,President Clinton’s middle name is Buzz.

Note: this is an argument, even though both of the premises and the conclusion are false. Arguments don’t 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.


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 Billy’s 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 it’s 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 Billy’s 7 year old birthday party.

The argument is still not perfect, but it is better.


It is very important to realize that just because something sounds plausible, it doesn’t make it true.

Plausibility does not equal truth!

Did you know that the government is hiding information about UFO’s 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, it’s possible that aliens are in Area 51, but I don’t think it’s plausible. So, I won’t believe it is true.


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 vaguewhen 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 can’t understand what the person is saying so you can’t determine if the proposition is true or false.


Why are the following sentences too vague?

Lasagna is the best.

Let’s interview an old person.

Tall people need help.

Ferrets are wonderful.

The best what? Dinner? Italian dish?

What do you mean by old?

Who’s tall? What kind of help?

Wonderful at what? Digging? Running? Singing?

Note: The issue isn’t whether a sentence is vague, but whether it’s too vague, given the context, for us to be justified in saying it has a truth value.


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 . . .


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?


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.


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


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?


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 . . . .


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 daughter’s 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!


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 can’t 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, don’t do it if doing so confuses your audience.


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.

Here’s 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) wasn’t 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.

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: Don’t 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’


If you said ‘something to sit on’ doesn’t 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’ aren’t 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?


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.


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