Weeek 2 Discussion 2

Week 2 Discussion Hint

This document is so long because I address all of the types of arguments discussed this week.

Remember, you only have to give two examples (and explanations) for one type of argument.

Deductive arguments

Deductive arguments are all about how the ideas in the standard form argument are related to

each other in the statements making up the premises and the conclusion. The goal is to create an

argument such that if the reader believes the premises are true, then they absolutely must also

accept the conclusion is true. So, it’s not just about the ideas presented (the content of the

argument), it’s about the structure (or form) of the argument. All of the ideas in the conclusion

have to be explicitly stated in the premises and related to each other in a way that forces the

reader to accept the conclusion. There are specific structures of deductive arguments that do this,

and they are called valid forms.

Valid deductive argument forms

Below are the most common basic valid deductive forms. They are so common they’ve been

given names. I present them as templates for basic deductive arguments, and any more complex

deductive argument—what the text calls sorties—is simply a combination of these forms. For

each form, IF the premises are true (note I’m not saying they actually are true), then the

conclusion MUST also be true—that’s the definition of validity. (The truth of the premises is a

separate idea and deals with the soundness of the argument.) To create examples of these forms,

you would replace the information in brackets with ideas or concepts consistently (i.e., exactly

the same words) throughout the template. You should look at each one and make sure you

understand why they are valid.

A. Modus ponens:

P1. If [something is true], then [conclusion of the argument]

P2. [something is true]

C. Therefore, [conclusion of the argument]

B. Modus tollens:

P1. If [opposite of the conclusion of the argument], then [something is true]

P2. Not-[something is true]

C. Therefore, not-[opposite of the conclusion of the argument]

If you use information from this document in any of your posts, you are required to cite it

following APA requirements. You must also provide the following reference:

Munns, C. A. (2018, March 27). PHI103: Informal Logic, week 2 discussion hint [Class

handout]. Division of General Studies, Ashford University, San Diego, CA.

C. Disjunctive Syllogism:

P1. Either [something is true] or [conclusion of the argument]

P2. Not-[something is true]

C. Therefore, [conclusion of the argument]

D. Hypothetical Syllogism:

P1. If [something #1 is true], then [something #2 is true]

P2. If [something #2 is true], then [conclusion of the argument]

C. Therefore, if [something #1 is true], then [conclusion of the argument]

E. Categorical Syllogism

P1. All [something #1] are [something #2]

P2. All [something #2] are [something #3]

C. Therefore, all [something #1] are [something #3]

Examples of valid arguments

Because the forms above are necessarily valid, any information you use to replace the

information in brackets, as long as you’re consistent, will give you a valid argument regardless

of what those ideas are. Consider this slightly modified flat earth argument from my week 1

discussion hint post:

P1. If the earth is not flat, then the curvature of the earth would be visible in the distance.

P2. There is no curvature of the earth visible in the distance.

C. Therefore, the earth is flat.

The words in bold help us pick out the form of the argument. As you can see this is an example

of modus tollens (see the form above). The first part of premise 1 (the part following the word

‘if’—called the antecedent) and the conclusion express opposite ideas. The second part of the

first premise (the part following the word ‘then’—called the consequent because it’s a

consequence of the first part) is the opposite of the idea in premise two. So, you should be able to

recognize that this argument follows the form modus tollens, but why is it valid?

The first premise sets up a relationship between potential events or conditions (in fact, an if-then

statement is called a conditional statement). It doesn’t say that the earth is not flat, but it tells us

that if the “the earth is not flat” is true, the second part, “the curvature of the earth is not visible”

must also be true. Consider another example. If I say, “If it rains, then the grass will get wet,”

what I’m telling you is not that it actually is raining, but that grass gets wet when it rains. Notice

that doesn’t preclude the grass getting wet for other reasons (e.g., sprinklers).

To assess the validity of the argument we need to temporarily accept the truth of the premises

(i.e., pretend they are true). So, if premise 1 is true, then we know a consequence of the earth

being flat (i.e., “the curvature of the earth won’t be visible”) is also true. This is important

because premise 2 gives us a factual claim: “The curvature of is not visible,” which is the

opposite of the consequence of premise one. Since we’ve temporarily assumed the premises are

true, that means that if premise 2 is true, the antecedent in premise 1 cannot also be true. Thus,

the opposite of the first part of premise 1 (the antecedent) must be true, which gives us the

conclusion of the argument, “The earth is flat.” [Once we’ve determined the argument is valid,

then we would evaluate whether the premises are true. If they are, then the argument is sound,

and we have to accept the conclusion is true. If not, then the argument is unsound, and we reject

the conclusion.]

Here’s a bad (invalid) example of a deductive argument:

P1. If it is raining, then the grass is wet.

P2. The grass is wet.

C. Therefore, it is raining.

Since I’ve already told you this argument is invalid, you know it doesn’t follow any of the valid

forms above (go ahead and compare it to the forms above). See if you can figure out where the

problem with the form is (remember, it’s not about the ideas themselves, it’s about how they are

related to each other). You can post your thoughts on why it’s invalid as a reply to this post, and

I’ll comment on them. A deductive argument would also be considered “bad” if it’s valid, but

any of the premises are false. That argument would also be unsound, even if the premises happen

to be true.

Statistical syllogisms

Statistical arguments are very common, particularly in science and politics. If you want to be a

good critical thinker, it would be a good idea to gain a basic understanding of statistics and

statistical analysis by taking a dedicated course or two. Unfortunately, that’s beyond the scope of

this course. For now, you just need to understand the basics of arguments based on statistics. The

basic form for a statistical syllogism is:

P1. X% of [group #1] are [members of group #2].

P2. [individual] is an [group #1].

C. Therefore, [individual] is (probably/probably not) a [member of group #2].

Like all inductive arguments, what makes such an argument good or bad is how strong the

evidence is in support of the conclusion. Unlike the deductive arguments discussed above, the

premises of an inductive argument don’t guarantee the truth of the conclusion; they only make it

more or less likely to be true. For statistical syllogism the strength comes from how likely it is

the individual in premise two is going to be a member of group and whether the conclusion says

that individual is (or isn’t) part of that group. For that reason, statistical syllogisms—and all

inductive arguments—are said to be either strong or weak arguments.

Here’s a good (i.e., strong) statistical syllogism:

P1. 95% of Republicans are anti-Gun control.

P2. John is a Republican.

C. Therefore, John is (probably) anti-Gun control.

Even though this is an argument I made up, it is a strong argument because the higher the

percentage of the first group (Republicans) belong to the second group (Pro Life) the greater the

chance that the individual in question, John, will be a member of the second group based on his

membership in the first group. However, there is still 5% possibility that he is not a member of

the second group, so the premises, if true, do not guarantee the conclusion is true. That’s why it’s

better to say he is probably a member of the second group. If the conclusion said, “John is

probably not Pro Life,” then it would be a weak argument. (Note that if the percentage is 100%,

the argument becomes deductive, not inductive. Can you explain why?)

Here’s a bad (i.e., weak) statistical syllogism:

P1. 5% of Democrats are anti-Gun control.

P2. John is a Democrat.

C. Therefore, John is (probably) anti-Gun control.

Again, the statistics here are completely made up (don’t do that in your papers, but it’s okay for

the discussion), but it should be clear why this is a weak argument. Basing John’s membership in

the second group on only 5% of Democrats being in that group is not enough evidence. If the

conclusion said, “John is probably not anti-Gun control,” the argument would be much stronger.

I would recommend that if you give statistical arguments you include the words “probably” or

“probably not” (or some equivalent) in your conclusion. These words strengthen your argument

because you are including the possibility that the evidence might not fully support your claim—

you’re not overstating your position.

Also, you need to make sure you have gotten your statistics from credible and recent sources. For

example, in a recent section of PHI208 Ethics and Moral Reasoning, a student submitted a paper

on sexual harassment in the workplace. The statistics supported her argument, but they were

from a government published in 2000. While that may seem recent, with changes in social

attitudes toward sexual harassment and the recent #metoo movement, there is likely to have been

an increase in reported incidents over the past 18 years, so more current statistics would give a

better picture of how things are in the workplace.

Arguments from analogy

Like statistical arguments, arguments from analogies are common. We often make connections

and comparisons between things (that’s an analogy—thing A is like thing B in qualities x and y)

and then extend that comparison to other aspects of those things (B must also be like A by

having quality z). The form for an argument from analogy is:

P1. [Unfamiliar case] is similar to [Familiar case] because they both have [qualities x,

and y].

P2. [Familiar case] has [quality z].

C. Therefore, [Unfamiliar case] probably also has [quality z].

The key to a good (i.e., strong) argument from analogy is to show that the things being compared

are actually alike in ways that are relevant to the conclusion. These arguments are often

considered inductive arguments because they go beyond what we know (the relevant similarities

between the object) and give a conclusion that is probably (depending on the strength of the

comparison), but not necessarily, true.

Consider this strong argument from analogy:

P1. Eastern long-beaked echidnas are similar to mammals because they have hair and are

warm-blooded.

P2. Mammals give birth to live offspring.

C. Therefore, Eastern long-beaked echidnas probably also give birth to live offspring.

This argument is strong because, as you probably learned in elementary school, some

characteristics used to identify mammals are having hair, being warm-blooded, and giving birth

to live offspring. So, if an animal has several of these characteristics, it is likely to have others

and the more it has the more likely it is to have the others. We know, however, that there are

exceptions. Not all mammals have hair or give birth to live young, and non-mammals may have

some of the same characteristics. In fact, the Eastern long-beaked echidna is a mammal, but it—

like the platypus—lays eggs (National Geographic, 2010). If you were the first to discover the

Eastern long-beaked echidnas and observed that it had many mammal qualities, you would be

justified in concluding that it also gave live birth until you discovered otherwise. This illustrates

how an argument from analogy (or any inductive argument for that matter) can be strong, but it

can still have a false conclusion.

Here’s an example of a weak argument from analogy:

P1. Apples are similar to oranges because they are both roundish and grow on trees.

P2. Oranges are citrus fruits.

C. Therefore, apples are probably also citrus fruit.

This is a weak argument from analogy because being roundish and growing on trees aren’t

relevant (i.e., they aren’t essential qualities) to a fruit being a citrus fruit (Swain, 2015). Although

many citrus fruits are roundish and most grow on trees, that’s not what makes them citrus, so

having those qualities shouldn’t be used to determine what other fruits are citrus.

When evaluating arguments from analogy, you should focus on how similar (or different) the

things being compared are. It’s easy to say that more similarities they have the stronger the

argument, but you need to be able to establish that the similarities are relevant to the quality or

feature included in the conclusion. In the two examples above, it’s not only that the things being

compared are alike in the ways stated; it’s just how relevant the identified similarities are to the

conclusion.

Appeals to authority

The key to appeal to authority being strong or weak is the relevance of the authority to the

conclusion. The basic form for appeal to authority is:

P1. [Person A] said that [some statement] is true.

P2. [Person A] is an authority on the subject.

C. Therefore, [some statement] is true.

The strength of the argument is based on premise 2, so you MUST explain the type of authority

the person is (see the examples below). In explaining and supporting an appeal to authority

argument, you need to establish that premise 2 is true—that the person is actually a relevant

authority on the topic being discussed. You would also need to explain the reason behind why

the expert or authority made the claim they did—it’s not enough just to say the authority said it.

A strong appeal to authority argument shows that not only the authority made the claim, but also

that the person is a relevant authority. An example of a strong argument from authority is:

P1. Stephen Hawking said that black holes emit radiation.

P2. Hawking was the leading cosmologist in the world.

C. Therefore, black holes emit radiation.

As an appeal to authority argument, this is strong. As the leading cosmologist (someone who

studies the physical nature of the universe), Hawking developed many theories about the

universe and particularly black holes and then proved them mathematically. Although the

radiation he predicted, now known as “Hawking radiation,” has not yet been observed, most

physicists accept his arguments for its existence because (simplified version) the mathematics

works and it helps explain observed phenomena better than other theories (Wall, 2018).

Remember, this is an inductive argument, so it doesn’t intend to prove the conclusion beyond

any doubt at all and it’s still possible for the conclusion to be false—Hawking could be proven

wrong sometime in the future. However, right now, based on everything we know and

Hawking’s work, his theories are the best we have, so based on his authority we should accept

the existence of Hawking radiation.

Here is an example of a weak argument from authority (please read the explanation before you

react emotionally):

P1. The Bible says that the Earth is flat.

P2. The Bible is the word of God.

C. Therefore, the Earth is flat.

The problem with this argument may be more subtle than some of the other examples I’ve

provided, depending on your personal religious beliefs. Christian “flat earthers” often cite

specific Bible verses to support their beliefs (e.g., Job 9:8, Isaiah 44:24, Ezekiel 1:26,

Ecclesiastes 1:5, Genesis 1:1-8, etc.—see Stallings, n.d.). When they do, they are giving an

appeal to authority argument. The authority being appealed to is the Christian God (who, if he

exists, would be the ultimate authority as an omniscient being). That’s what premise 2 is saying;

if the Bible is the word of God and God is the authority, then we should believe God said. The

problem is getting people to accept the God of the Bible as the authority. Only people who

already believe in Christianity will accept the Christian God as an authority and the Bible as true.

Even among that group, most Christians in the U.S., for example, don’t take the Bible as literal

truth (Cole, 2017). They interpret it as a metaphor, so they’d be unlikely to accept this argument.

Additionally, while Christians are a large group and may be the majority religion in the U.S.,

they are less than a third of the world population (Pew Research, 2012). That means this

argument is weak because only a very few people are likely to accept the authority being

appealed to in support of the conclusion.

Almost all religious-based arguments can be reduced to or include a weak appeal to authority in

this way. In general, unless you know your audience shares your religious beliefs, it is usually

best to avoid basing arguments on those beliefs. Anyone who doesn’t already agree with your

beliefs will likely automatically reject any premise based on a specific religion. It’s better to start

with premises that everyone is likely to accept or at least to consider as possibly true.

Inductive generalizations

Inductive generalizations are probably the most common form of inductive arguments. The basic

form for inductive generalizations stated in the text is:

P1. X% of observed Fs are Gs.

C. Therefore, X% of all Fs are Gs.

Even though this form lists statistics, many arguments of this type are more vague and use the

word “many” rather than actual percentages and conclude with a statement about “all” of the

things being discussed (you should be able to see how that weakens the argument). As with the

other inductive arguments above, the strength of the argument relies on the amount and

relevance of the evidence.

An example of a strong inductive generalization is:

P1. 95% of all observed swans have been white.

C. Therefore, 95% of all swans are white.

This is an inductive argument because it starts with a factual claim about a large portion of a

group (i.e., the sample) and draws a conclusion about all members of the group (i.e., the

population). Scientific arguments take this form because we don’t observe all possible instances

(e.g., every possible case of cancer), but we extend the observations we do make to conclusions

about cases we haven’t observed. The possibility of the observations not applying to all cases is

why scientists say things like, “The findings suggest that drug X reduces the spread of cancer”

rather than claiming drug X will always reduce the spread of cancer.

Weak inductive generalizations are based on a small number of observations. These are the basis

of most stereotypes. For stereotypes, they are not wrong because no member of the group

exhibits those behaviors; they are wrong because the attribution of the behavior to the entire

group is based on a small number of observations. Consider this weak inductive inference:

P1. My philosophy professor was a hard grader.

C. Therefore, all philosophy professors are hard graders.

Basing a claim about every single philosophy professor on your experience of one philosophy

professor isn’t anywhere near strong enough. Even if you had taken 5 philosophy classes, and

they were all hard graders, that wouldn’t be enough. Hopefully, you can see how this example

extends to any common stereotype about a group.

References

Cone, A. (2017, May 16). Gallup: Record low 24% believe Bible is literal word of God. United

Press International. Retrieved from https://www.upi.com/Gallup-Record-low-24-believe-

Bible-is-literal-word-of-God/3971494949716/

National Geographic. (2010, December 6). Pictures: 14 rarest and weirdest mammal species

named. National Geographic. Retrieved from

https://news.nationalgeographic.com/news/2010/12/photogalleries/101206-rarest-

weirdest-species-mammals-edge-list-pictures/

Pew Research Center. (2012, December 18). The global religious landscape. Pew Research

Center: Religion & Public Life. Retrieved from

http://www.pewforum.org/2012/12/18/global-religious-landscape-exec/

Stallings, R. (n.d.). The Biblical flat earth: The teaching from scripture. Retrieved from

http://www.philipstallings.com/2015/06/the-biblical-flat-earth-teaching-from.html

Swain, J. (2015, October 25). Ask Dr. Knowledge: What is a citrus? The Boston Globe.

Retrieved from

http://archive.boston.com/business/technology/articles/2010/10/25/what_is_a_citrus_fruit

/

Wall, M. (2018, March 15). How Stephen Hawking transformed our understanding of black

holes. Space.com. Retrieved from https://www.space.com/39988-black-hole-mysteries-

stephen-hawking.html