# What is an argument in logic?

What is an argument in logic?

What is standard form and how are sub-arguments included in standard form?

What is an argument in logic? (see reserves article on “Argument”)

“An argument in logic is a group of statements or propositions, one or more of which (the premises) are claimed to provide support for, one of the other statements (the conclusion).” Premises + conclusion = argument

An argument can have only one conclusion, and needs at least one premise.

If there is more than one conclusion, then there is more than one argument.

If there is no conclusion, then there is no argument.

Notice that the language of “statements” is the same language that Feynman uses in his quotation on the first page of the syllabus, when he characterizes the knowledge (or lack thereof) of scientists.

5. Premises are the reasons that support the conclusion, and, therefore, include the evidence. We will discuss types of evidence later in the course.

6. The conclusion is the position that the arguer holds and is trying to support. “If you don’t know the conclusion, you cannot analyze the argument.” (p. 65, text, Wanda Teays)

What is a statement?

A statement is a complete sentence which is potentially true or false.

As we learned in the power point presentation for Week 2, value claims can also be treated as potentially true or false, even if it is difficult to ascertain when they are actually true or false.

What is not a statement?

“Shut the door.” – command (which you may do or not do, but is not true or false, although, if I then say “You shut the door”, this is a statement that can be true or false.)

“What time is it?” – question (which is itself neither true or false, although the answer to this question may be a statement that is true or false, if it is in a complete sentence, “It is now 7 pm in Philadelphia, PA.”)

“Ouch” – interjection (which is itself neither true or false, although if I then say “You must be in pain”, this is a statement that can be true or false.)

Identifying & Reconstructing an argument

An argument may appear trivial or not well supported, yet may still be an argument, if it fits the definition on the previous slide:

It is important to either identify or reconstruct an argument of an article, video, essay, etc., before evaluating it.

In reconstructing an argument, you need not rely only on direct quotes, but you do need to use complete sentences (that is, statements).

In reconstructing an argument, we aim for clarity, by omitting any unnecessary language, and by identifying any implicit assumptions, especially as regards definitions of terms (reality assumptions) or value assumptions.

You should be charitable in your reconstruction of the argument, which means that you reconstruct in its best possible light before evaluating or criticizing it.

A reconstruction of an argument that distorts the position of the arguer in order to make it easier to knock down or criticize, commits the fallacy of “straw man”.

An essay/article/movie may contain elements, such as description & sometimes explanation, that are not part of the argument & can be omitted from reconstructing the argument unless relevant to supporting the conclusion.

We will address explanations later in the course, when we discuss cause and effect reasoning, although there can also be causal arguments.

Arguments in logic versus persuasive essays

Although your text (p. 42) states that argument is “one of the more significant means of persuasion”, it revises this later on p. 44, when it says that [argument] “is different from a creating a persuasive argument, given that we might be persuaded by a threat (“Agree with me or I’ll step on your sore toe”), by a celebrity’s testimonial (e.g., Bozo likes red balloons why don’t you?), by appeal to patriotism, and so on.”

We will treat argument as a means to convince a person through reasons, rather than persuade them through threats, etc. I might persuade you to give me your wallet if I hold a gun to your head, but have good reasons actually been given by me to convince you that it is right that I demand money, even if, under the circumstances, you are willing to turn over your wallet?

Therefore, an argument in logic is concerned with logos, not ethos or pathos. Reasons are supposed to govern, and not appeals to emotion.

Premise indicators & conclusion indicators: pp. 62 – 64 of text

“Remember: Premises don’t always appear before the conclusion [in an essay, article or video] – they could follow it. Alternatively, the conclusion could be sandwiched between premises.” Moreover, the conclusion might not be stated at all, but implied, as we shall see in an example later in these slides.

Therefore, it is helpful to look for premise and conclusion indicators (which are only clues as to what the premises and conclusion might be, and not formulas):

Some conclusion indicators: Therefore, In conclusion, Accordingly, So, As a result, Consequently, Hence, It follows that, Subsequently, Thus (See the chart and examples on p. 63 of the text)

Some premise indicators: Because, Whereas, In light of, For (if it means because), Given that, For the reason that, Since (if it means because); (See the chart and examples on p. 63 of the text)

Some examples of arguments from the reserves article on “Argument”

Abraham Lincoln: I have come to the conclusion never again to think of marrying, and for this reason: I can never be satisfied with anyone who would be blockhead enough to marry me.

Conclusion: Therefore, I shall never again think of marrying. (Indicator words: “I have come to the conclusion”): You should try to identify the conclusion first.

Premise: I can never be satisfied with anyone who would be blockheaded enough to marry me. (Indicator words: “for this reason”:

This might not sound to you like much of an argument, but it is an argument, according to the definition of argument in logic.

Examples of arguments (continued)

V) : French essayist Voltaire (1694 – 1778): If it were permitted to reason consistently in religious matters, it is clear that we all ought to become Jews, because Jesus Christ was born a Jew, lived a Jew, and died a Jew, and because he said that he was accomplishing and fulfilling the Jewish religion.

What is the conclusion of this argument? At first glance, it might seem to be “We all ought to become Jews” with the premises indicated by the premise indicator “because”, “Jesus Christ was born a Jew, lived a Jew, and died a Jew, and because he said he was accomplishing and fulfilling the Jewish religion.

However, the conclusion of this argument is unstated. Clues to the conclusion are indicated by the “If, then” statement, which is a conditional or hypothetical statement (that is, under the condition that, or under the hypothesis that…), and by Voltaire’s frame of reference, which is that of a satirist (that is, he often uses satire in his essays and novels). What is the condition that Voltaire states under which “it is clear that we all ought to become Jews”? Do you think that Voltaire seriously believes that people fulfill this condition? (See the next slide)

Voltaire’s argument, its conclusion and intended audience

The conclusion of Voltaire’s argument is probably: “It is not permitted to reason consistently in religious matters.” The unstated premise, or implicit (hidden) assumption is that “For most people, it is not clear that we all ought to become Jews, regardless of the evidence.” Therefore, we do not reason consistently in religious matters (conclusion).

Notice that Voltaire also seems to take for granted that his audience is Christian. In logic, we often act as if an argument does not appeal to a particular audience, and that reasons and rationality can make general appeals to any audience.

However, most essays and articles and movies have a particular audience in mind, which is why they often omit some of their implicit assumptions. They often presume these implicit assumptions are shared by their audience and do not need to be articulated, but if the audience should change or broaden, these implicit assumptions might become very controversial.

Does the movie, “Half the Sky” have an intended audience in mind, and, if so, who is it? How might this influence what is actually said and not said?

Another example from the reserves article on “Argument”

VI): It is absurd to bring back a runaway slave. If a slave can survive without a master, is it not awful to admit that the master cannot live without the slave? (Diogenes of Sinope).

This argument refers to ancient slavery and not American slavery, and so it might not have a familiar ring to it. I might have a different set of implicit assumptions than those with which we are familiar or which the abolitionists used in fighting American slavery.

What is the conclusion of the argument? “It is absurd to bring back a runaway slave.”

Restate the premises in a statement: A master should not admit that he cannot live without a slave, if a slave, by running away, can show he can live without a master.

What are some of the implicit assumptions here? A person should be able to control his or her own life? (Independence is important?) A person who is independent is superior to one who is dependent upon other people? A master should never put himself in a position in which he is inferior to a slave, even if it means letting an escaped slave go free? Any others?

Standard Form

Since in logic we are interested in clarity rather than literary style, one simple, clear method of stating an argument (and indicating which statements are the premises and which the conclusion) is preferred to the rich variety of forms available in writing essays. There are actually several ways to clearly visualize an argument, but we will use the method of putting an argument in standard form.

We put an argument in standard form by listing the premises, labeled P1, P2, P3…and then the conclusion C.

These should be listed underneath each other, with each premise (P1, P2, P3, etc.) on a separate line, and the conclusion (C) on a separate line.

2. Do not use bullet points, because it is important to be able to identify which premise is which by #, when we start evaluating the argument.

Examples of arguments in standard form from p. 43 of text

P1: Cutting a pet bird’s wings limits or eliminates the bird’s ability to fly.

P2: Birds that can’t fly are like guinea pigs with feathers.

P3: Only someone who is cruel would turn the bird into the equivalent of a guinea pig.

C: Therefore, cutting a pet bird’s wings is cruel.

What implicit assumptions are omitted from the above argument?

There are no good reasons for cutting a pet bird’s wings (such as to protect it from crashing into a window or flying into a ceiling fan).

The life of a pet bird with cut wings is inferior to that of a bird that can fly.

We might also consider whether or not there is an implicit assumption about what is “natural” and that a “natural way of life is better than an unnatural way of life”.

See also pp. 76, 134, & 136 in your text for examples of standard form in longer arguments.

Incorporating sub-arguments into standard form

In putting an argument in standard form, first identify the conclusion.

Then identify those reasons (which can be reality or value assumptions) that might provide support for this conclusion. These are the premises. The main premises usually include the most general reasons that support the conclusion.

Then identify further evidence for these main premises, and use this further evidence to set up sub-arguments within the standard form. This further evidence may be more concrete, such as examples or statistics, or anecdotes, or testimony. (We will be discussing these in more detail later in the course.)

See the next slide for examples of how to incorporate this last step of setting up sub-arguments into standard form.

The further evidence for the main premises will be statements that are called sub-premises.

The main premise then is treated as if it were a conclusion to a mini-argument that is embedded in the larger argument.

The sub-argument is not a separate argument from the main argument.

Examples of standard form that includes sub-arguments

P1a: In a democracy, all adult citizens have

an equal right to vote

P1. A democracy promotes certain types of equality.

P2. Equality is a good thing.

C: Therefore, democracy is a good thing.

In the above argument, P1a is a sub-premise that tries to give support to the main premise (P1), which is acting as a conclusion to this sub-argument.

“P1a” indicates that the sub-premise supports “P1”. It is important to use a numbering system that shows which main premise the sub-premise is supporting. Do not use bullet points.

“P1a” answers the question, what type of equality does democracy promote? Notice that this statement, “In a democracy, all adult citizens have an equal right to vote” has not been historically true, and is not true of most of those with a felony record today. However, this is still is an argument, even if it is not a strong argument.

We could also try to build a sub-argument for P2. Do so, if you want.

However, you do not need to build a sub-argument for every main premise.

Examples of standard form that includes a sub-argument (continued)

See the reserves article, “Thinking Clearly” by Jill Leblanc: “Standardizing Arguments”, p. 35:

Notice that this author numbers the main premises and sub-premises somewhat differently than I have done and your text does. It is acceptable to use this alternative numbering system, but it is not acceptable to use bullet points.

Without proper medical evidence we may never know whether [former President] John Kennedy was killed by a single gunman.

2.1 There is controversy about the location and size of the wounds in Kennedy’s head.

2.2. Some experts believe that X-rays of the head wounds have been faked.

2.3. Some experts charge that the X-rays are inconsistent with one another.

The evidence is far from satisfactory.

C: Therefore, we may never know whether John Kennedy was killed by a single gunman.

In the above argument “2.1, 2.2, & 2.3” are all sub-premises which support the main premise 2, which then acts as the conclusion of this sub-argument. Notice that each sub-premise starts with “2” so that you know what it supports (premise #2.

We will not use the alternative system of mapping arguments introduced on p. 35.

Standard form is not an outline

Although standard form looks like an outline (in reverse), it is not an outline.

Unlike an outline, you must complete sentences (that is, statements) that include the content that could potentially be true or false. Therefore, do not say, “Statistics about rape”, but rather state in a complete sentence what some of those statistics are. Do not use short phrases, such as “Education in Vietnam”, but rather make a statement that contains content about education in Vietnam.

Unlike an outline, the sub-premises (P1a, P1b, etc) must support the main premise (P1), and not simply elaborate on that premise or retell a story about the premise. Likewise, do not simply use the main premises (P1, P2, etc.) to retell a story. This is why indicator words can be helpful – see slide #6.

Unlike an outline, try to set forth the logical connections between the sub-premises and the main premise that the sub-premises support; and between the main premises and the conclusion.

This is why the sub-premises are listed above the sub-premise, and the premises are listed above the conclusion. In that way, we are reconstructing the argument in a linear fashion in a way that it might not appear in the original article, essay, or movie.