Notes on Argument Basics 
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Table of Contents

The Basic Elements of an Argument
Definition of an Argument
Definition of a Claim
Definition of a Conclusion
Definition of a Premise
Definition of an Inference
Verbal Indicators
Arguments without Verbal Indicators
The Two Structural Types of Arguments: Simple and Complex
The Two Semantic Types of Arguments: Non-deductive and Deductive
Some Hints about Deductive and Non-Deductive Arguments
An Exercise in a Stupid Argumentation (with a serious intention)
Truth Vs. Validity
Evaluation Vs. Classification of Arguments
Evaluation of Arguments
Evaluation of Non-deductive Arguments
Evaluation of Deductive Arguments 
The Analysis of Arguments
The Process of Analyzing Argument in Standard Form Analysis
A Sample Analysis of an Argument in Standard Form and its Numerical Analysis
Writing a One-sentence Description of the Argument 

Definition of an Argument
An argument is a set of claims that include a (final) conclusion, one or more premises, and an inference.

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Definition of a Claim
A claim is a statement of alleged fact. 

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Definition of a Conclusion
A conclusion is a claim supported by one or more premises in the argument. 

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Definition of a Premise
A premise is a claim offered as a reason for a conclusion. It answers the critical question "why" about the conclusion.

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Definition of Inference
Every argument will have one inference. The infererence means "leads to." Without the sense that one claim "leads to" another, as a reader or listener, you are not sensing argument.

The parentheses ( ) around the word "premise" mean implied, suggesting that both stated and unstated or implied premises may "lead to" a conclusion. 

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Verbal Indicators
The use of certain words in texts often indicate an argument. Some are markers for premises, others for conclusions.

Some Premise Indicators
since, because, on account of, given that, if . . . then, either . . . or, etc.

Some Conclusion Indicators
therefore, as a result, in conclusion, hence, (you) can expect that, etc.

Of course, in everyday speech, we use informal markers as well:

Some Informal Premise Indicators
Mama! She said . . . ! 
Now, look a'here! 
Because I said so!

Some Informal Conclusion Indicators
Let met tell you som'thin', son! 
Would you believe! 
Hello! 
What did I say?!!

Here is one example of the appearance of verbal markers in arguments:

Since it is wrong to kill a human being, it stands to reason that capital punishment is wrong because it takes the life of a human being.

In this complex sentence, the words "since" and "because" function as premise markers while the phrase "it stands to reason that" signals a conclusion. Note that three different claims are contained in the framework of this single sentence. An important step in analyzing texts in arguments will be the analysis and isolation of each discrete claim within a text.

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Arguments without Verbal Indicators
While many texts contain both standard and more familiar, or informal, verbal markers, many do not. It will be necessary for you to sense that one claim "leads to" another without the crutches of such markers. Read the following two claims: do you sense an argument?

Claim 1: The train derailed in Albuquerque.

Claim 2: The price of eggs will increase in Dallas.

Well? Probably not. But let's add an additional claim:

Claim 1: The train derailed in Albuquerque.

Claim 2: The train that derailed in Albuquerque was carrying a month's supply of eggs for Dallas.

Claim 3: The price of eggs will increase in Dallas.

Well? Probably yes. You probably sense that claims 1 and 2 "lead to" claim 3. If that's the case, you are sensing argumentation in which claims 1 and 2 are premises for claim 3, the conclusion.

Notice something else: The only way for you "to get that" these claims are, in fact, an argument is if two other unstated--implied--claims are operating in your mind:

Claim 4: When supply decreases, prices increase.

and

Claim 5: When the train carrying a month's supply of eggs for Dallas derailed in Albuquerque, the supply of eggs in Dallas decreased.

In other words, you remember something, at least, from high school economics: the law of supply and demand. If the principle of the "Law of Supply and Demand" were not operating in your consciousness, you would never sense that claims 1 and 2 "lead to" claim 3.

Here is an example, then, of an argument that includes both stated and implied claims. That's not uncommon in arguments. In fact, your greatest challenge will be to identify the unstated or implied claims that must be operating in the mind of the author as you read for argument in texts.

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Two Structural Types of Arguments: Simple and Complex

For purposes of this course, we will rely on classifying arguments as either "simple" or "complex." A "simple argument" is any argument that has one--and only one--conclusion, the final conclusion. A "complex argument" is any argument that has more than one conclusion; that is, it will have a final conclusion and one/more than one intermediate conclusions. An intermediate conclusion reflects a "sub argument" within the main argument. In each case, an intermediate conclusion will be the premise of yet another sub argument or a premise for the final conclusion.

Below is a graphic illustrating the structure of simple and complex arguments:

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Non-Deductive Arguments
Non-deductive arguments are arguments the premises of which make the conclusion "likely" or "probable." For this reason, they are sometimes referred to as "probability arguments." Here is an example:

Premise: Turner Falls is a popular campsite. 
Premise: People sleep outside at campsites. 
Premise: The motel rooms are full. 
Premise: We'll get a discount if we sleep outside. 
Conclusion: We'll sleep outside.

Note that in the argument above, the premises "lead to" the conclusion; that is, they make the conclusion "likely" or "probable"--well, at least more likely than unlikely, more probable than improbable, no? (I like the "discount" option!) Nevertheless, the premises do not guarantee that "we'll sleep outside." We still have choices, perhaps.

Deductive Arguments
Deductive arguments are arguments the premises of which guarantee the conclusion--word for word (synonymous words or phrases acceptable).

Here is an example of a deductive argument:

Premise: If it is cold, we'll sleep outside. 
Premise: It will be cold. 
Conclusion: We'll sleep outside.

Notice the difference between the "semantics" of the two arguments. The first argument derives its meaning (conclusion) from premises that make the conclusion likely or probable. The latter, however, derives its meaning (conclusion) from premises that actually guarantee the conclusion; note that the two premises give us no choice. If the condition of the first premise is fulfilled, "we'll sleep outside." The condition is fulfilled, in fact, by the second premise. Therefore, "we'll sleep outside."

Okay, all right! I know it's a stupid argument, already! But stupidity (your text calls it "worthlessness") has nothing to do with the argument's semantic type. Stupid or not--even false or not--if the premises of an argument guarantee the conclusion--your scruples aside!--the argument is deductive. The same thing for "truth"! It doesn't matter whether either the premises are true or false in determing the semantic type (it has everything to do with your evaluation of the argument). Get it? Once again--if the premises guarantee the wording of the final conclusion, the argument is deductive. Period!

Question: Which is the stronger of the two semantic types: deductive? or non-deductive? Of course! It's the deductive argument. Now here's a "Grimes" axiom for you:

Every probability argument wants to grow up some day to be a deductive argument! All kidding aside, however: In a court of law, what does every prosecuting attorney's team try to create for a jury? Sure! A deductive argument! One that will lock in a guilty verdict, right? Of course! At best, however, most prosecuting teams are stuck with the task of developing--as convincingly as possible--a non-deductive or probability argument. 

Okay--you try it ..............................................turn the page 

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An exercise in stupid argumentation (with a serious intention):

Instructions: Create a deductive argument containing two claims (premises) that will guarantee the following conclusion: 

Premise 1: ________________________________________________

Premise 2: ________________________________________________

Therefore: Men are women.

(Here ........... here's some workspace:)

.

.

.

.

Okay: A Hint Try using the word "roaches" in both of the premises. Like this:

Premise 1: ___________________________________ roaches.

Premise 2: ___________________________________ roaches.

Therefore: Men are women!

How's that? Did you get it?............................................................................... NO!????

O-kay! (Geezzz!): A Second Hint 
Try placing the word "women" in the subject position of the first premise and the word "men" in the subject position of the second premise. Now, only a verb in each claim and one additional word in the first claim will guarantee the conclusion. Try it! (Like this:)

Premise 1: _________ women _____________________ roaches.

Premise 2: Men ________________________ roaches.

Therefore: Men are women!

How's that? ....................................................................................... No?!

Well ............... all right! (By the way-- "all right" is always two words! Alright! Alright! I know! You've seen it all over the place spelled "alright"! It doesn't matter. Everybody is wrong!--Signed, "English Department" Grimes). Here's the answer--several of them:

Example One: 
Premise 1: Only women are afraid of roaches. 
Premise 2: Men are afraid of roaches. 
Therefore: Men are women.

Example Two: 
Premise 1: If men are afraid of roaches, men are women. 
Premise 2: Men are afraid of roaches. 
Therefore: Men are women

Example Three: 
Premise 1: Either men are men or men are women. 
Premise 2: Men are not men. 
Therefore: Men are women.

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Of course, every non-deductive argument--with even a whiff of pride and self-respect--is, in disguise, a "deductive wannabe!" Every non-deductive argument would like to grow up to be a deductive argument in which the premises guarantee the conclusion. And I mean just that--the premises, by the way they are worded, guarantee the exact wording of the conclusion--word for word!

In fact, many seemingly non-deductive arguments are supported by authors' implied premises which actually make the argument deductive. The implied premises usually lie behind the stated premises as reasons for the stated premises. In other words, what often appears to be a simple, non-deductive argument in stated form is, in reality, a complex, deductive-argument once the reader has identifed both the stated and implied premises.

How do you tell which is which? It's often really a matter of correctly interpreting the author's intention. To get at the implied premises, you have to ask the critical question "why?" twice, once to discover the stated claims and then a second time to identify the unstated claims--these are the assumptions that the author must be making in order to justify, in his own mind, the reasons (premises) stated in support of the conclusion. Sometimes it's a matter of interpreting the author's strength of opinion in offering a conclusion. Ask yourself, "Does this writer really intend a deductive argument here? If your answer is "yes," then it is necessary for you to identify both the stated and the unstated conclusions that must be leading to the final conclusion in a way in which the final conclusion is guaranteed--word for word.

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Truth vs. Validity 
What you have witnessed in the examples above is something about the relationship between truth and validity. "Validity" means "deductive." That is, if the premises, both stated and implied (if any), guarantee the wording of the conclusion, then the argument is said to be valid or deductive (same thing).

Of course, we would prefer that each element of a deductive argument (the premises and conclusions) be true. In fact, we are moved to reject such arguments as those above because either the premises or conclusions or both are worthless, but that's the problem of evaluation, and we'll get to that right now.

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Evaluation vs. Classification of Arguments
Certainly, we've heard arguments many times that we reject offhand as wrongheaded or worthless. It is important to remember that whether we accept or reject an argument has nothing to do with our classification of the argument either structurally (simple or complex) or semantically (non-deductive or deductive). A general tendency is for students new to the analysis of argumentation to asume that "deductive" means "true" and "non-deductive" means "untrue." Be careful not to make this mistake. Remember: your willingness to accept or reject an argument is a function of evaluation, not classification of either the structural or semantic types.

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Evaluation of Arguments: Some Important Terms 
We will evaluate non-deductive arguments as either "successful" or "unsuccessful." We will evaluate deductive arguments as either "sound" or "unsound." Don't confuse these sets of terms!

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Evaluation of Non-deductive Arguments 
The evaluation of non-deductive arguments rests on two factors: 1) the amount of support given in the premises, and 2) the quality of the premises. We will evaluate a non-deductive argument as "successful" if the premises make the conclusion more likely than unlikely, more probable than improbable. We will evaluate a non-deductive argument as "unsuccessful" if the premises make the conclusion more unlikely than likely, more improbable than probable.

Adding More Support to Non-deductive Arguments
One way of strengthening a non-deductive argument is to add more premises. The more reasons you can provide a non-deductive conclusion, generally the more support you build on its behalf.

Qualifying the Premises
One bad premise can sometimes undermine the credibility of all the others in a non-deductive argument. While integrity demands that we tell the whole story--give all the reasons, in other words, you need to remember that contradictory or otherwise unacceptable premises weaken the probability or likelihood of a non-deductive conclusion. Generally, we will seek to add premises that are 1) true, 2) acceptable, or at least 3) unquestioned. If the premises meet one or more of these criteria, then a non-deductive argument will be strengthened. If one or more of the premises offered in support of a non-deductive argument are found to be 1) false, 2) unacceptable, or even 3) questionable, the quality of the argument diminishes and reduces its probability or likelihood. The same criteria are applicable to deductive arguments as well.

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Evaluation of Deductive Arguments
The evaluation of deducive arguments rests on the quality of the premises. While, by definition, we know that the premises guarantee the conclusion, as we have seen above, premises may serve unworthy arguments as a whole.

We will find a deductive argument "sound" if the premises are 1) true, 2) acceptable, or at least 3) unquestioned.

We will find a deductive argument "unsound" if any one of the premises is determined to be 1) false, 2) unacceptable, or even 3) questioned. 

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The Analysis of Arguments
Arguments are analyzed in a format called "standard form" analysis. Conway and Munson's The Elements of Reasoning introduces four models, citing the third and fourth models as the more desirable since both are rich enough to account for the relationships in both simple and complex arguments as well as non-deductive and deductive arguments (pp. 17-18). Important: For our purposes, we will use "Standard Form 3" and argument "Diagramming" (Standard Form 4). From here on, I will simply refer to Standard Form analysis (meaning "Standard Form 3") and numerical analysis (meaning "Diagramming"--Standard Form 4). 

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The Process of Analyzing Argument in Standard Form Analysis 
To analyze any argument found in either short or longer texts, employ the following steps:

1) Identify a claim that sounds like it might be a conclusion. To do that, read any claim and then ask "why?" If you find a claim that seems "to lead to" that claim, then you have identified a conclusion and at least one stated premise.

2) Then, isolate each stated claim in the passage as a simple sentence (note that complex sentences contain more than one claim, and each must be isolated as a separate claim.

3) Number each claim starting with the first claim found in the passage through the last claim found in the passage.

4) Translate each claim into conventional (standard) English and all question forms into declarative sentences.

5) Delete any repeated claims unless their interpretation is distinctly different.

6) Clarify all vagueness and ambiguities (for example, replace relative pronouns like "that" with their references (to whom or what they refer).

7) Delete any unnecessary claims (claims that do not function as either premises or conclusions) as well as any merely transitional or other unnecessary words and phrases in those claims which are part of the argument..

8) Identify and number any unstated claims operating in the argument. To do that, after reading each claim, ask yourself, "Why?" "Why is this claim so?" "What must the author be assuming to make such a statement?"

9) Reorganize the entire argument now, renumbering each of the remaining discrete claims with the premises on top and the conclusion at the end.

10) Place at the end of each conclusion (intermediate and final) the number(s) of the claims meant to read as premises.

11) As a last step, construct the numerical analysis.

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A Sample Analysis of an Argument in Standard Form and its Numerical Analysis
Here is an example of standard form analysis and numerical analysis of our earlier "train derailment" argument as it might have appeared in a casual observation or informal text:

Text What a mess! Can you imagine? I read in the paper today that a train derailed outside of Albuquerque. It was really some accident, the paper said. It was carrying a month's supply of eggs for Dallas. You can bet the price of eggs will increase in Dallas next month.

Step 1: Identify any claim that sounds like a conclusion.
(Note: Most conclusions in argumentative paragraphs will be found as a topic sentence for the paragraph and will usually be placed at the beginning of the paragraph. In the case of the "exploratory paragraph," it may come at the end.)

What a mess! Can you imagine? I read in the paper today that a train derailed outside of Albuquerque. It was really some accident, the paper said. It was carrying a month's supply of eggs for Dallas. You can bet the price of eggs will increase in Dallas next month.

Step 2: Isolate each stated claim as a simple sentence.

What a mess! 
Can you imagine? 
I read in the paper today that a train derailed outside of Albuquerque.
It was carrying a month's supply of eggs for Dallas. 
You can bet the price of eggs will increase in Dallas next month.

Step 3: Number each claim.

1) What a mess! 
2) Can you imagine? 
3) I read in the paper today that a train derailed outside of Albuquerque. 
4) It was carrying a month's supply of eggs for Dallas. 
5) You can bet the price of eggs will increase in Dallas next month.

Step 4: Translate each claim into standard English and all questions into declarative sentences.

1) What a mess was caused when the train, carrying eggs, derailed outside of Albuquerque. 
2) You can imagine what a mess occurred when the train derailed carrying a month's supply of eggs for Dallas.

Step 5: Delete any repeated claims. 
(There appears to be none in this passage.)

Step 6: Clarify all vagueness or ambiguities.

4) [The train that derailed outside of Albuquerque] was carrying a month's supply of eggs for Dallas.

Step 7: Delete any unnecessary claims as well as any merely transitional or other unnecessary words and phrases in those claims which are part of the argument.

1) What a mess was caused when the train, carrying eggs, derailed outside of Albuquerque. 
2) You can imagine what a mess occurred when the train derailed carrying a month's supply of eggs for Dallas. 
3) I read in the paper today that a train derailed outside of Albuquerque.
4) [The train that derailed outside of Albuquerque] was carrying a month's supply of eggs for Dallas. 5) You can bet the price of eggs will increase in Dallas next month.

Step 8: Identify and number any unstated claims operating in the argument.
(Note: place implied claims inside parentheses to distinguish them in standard form analysis from stated claims in the original text.)

6) (When the supply decreases, prices increase.)
7) (The train derailment outside of Albuquerque decreased the supply of eggs for Dallas next month.)

Step 9: Reorganize the entire argument now, renumbering each of the remaining discrete claims with the premises on top and the conclusion at the end.

1) A train derailed outside of Albuquerque. 
2) [The train that derailed outside of Albuquerque] was carrying a month's supply of eggs for Dallas. 3) (When the supply decreases, prices increase.)
4) (The train derailment outside of Albuquerque decreased the supply of eggs for Dallas next month.) 
5) The price of eggs will increase in Dallas next month.

Step 10: Place at the end of each conclusion (intermediate and final) the number(s) of the claims meant to read as premises.

1) A train derailed outside of Albuquerque. 
2) [The train that derailed outside of Albuquerque] was carrying a month's supply of eggs for Dallas. 3) (When the supply decreases, prices increase.)
4) (The train derailment outside of Albuquerque decreased the supply of eggs for Dallas next month.) 
5) The price of eggs will increase in Dallas next month. 1, 2, 3, 4

Note: For an example of the standard form analysis of a complex argument, see p. 18.

Step 11: Construct the numerical analysis of the argument.

or you may omit the arrow, if you wish, using the underline to suggest "leads to":

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Writing a One-sentence Description of the Argument 
A one-sentence description of an analyzed argument will include three elements: 1) the structural type, 2) the semantic type, and 3) your evaluation of the argument.

For example, a one-sentence description of the argument above might read like this:

The claim that "the price of eggs will increase in Dallas next month" is the final conclusion of a simple, deductive, though unsound argument.

An example of a paragraph explaining your evaluation might read as follows:

As a reader of this argument myself, I find the argument to be "unsound" in my evaluation. I find questionable and unacceptable the claim that "the train that derailed in Albuquerque was carrying a month's supply of eggs for Dallas." My experience in the marketplace suggests that an entire month's supply of eggs for Dallas wouldn't be shipped on one train. Therefore, I find the argument unsound.

Note, however, that the evaluation doesn't effect the classification of the argument as deductive since the premises actually guarantee the conclusion.