Basic Concepts 3a: Convergent and Serial Premises

Overview

Most arguments you encounter in articles and books will contain more than 2 or 3 premises. Also, in more complex arguments major premises won't obviously be true so the arguer will provide sub-premises to support those major premises. Arguments that contain sub-premises are called extended arguments. Premises can relate to the conclusion and to each other in various ways. In this lesson we will look at convergent premises and serial premises. Convergent premises are independent reasons in support of a conclusion. They don't depend on each other in any way. Serial premises function like sub-arguments: They are reasons given in support of a more basic premise.

Extended Arguments

Up until now we've been applying our analytical skills to relatively simple arguments. Now we will begin to apply those skills to extended arguments. What's an extended argument? Well, I'm glad you asked: An extended argument is one that (a) has a main conclusion supported by premises which themselves are in turn supported by sub-premises and/or (b) has premises that work together to support the conclusion and/or premises that independently support the conclusion. In this lesson we'll look at (a) which are called serial premises and (c) which are called convergent premises.

Convergent Premises

Convergent premises are more than on independent reason in support of a conclusion. Let's look at an example:

Scene: Ami comes back from a two week camping trip
Mom: (a) Ami, you need to take a shower! (b) You stink and (c) it's not healthy.

The conclusion is "Ami, you need to take a shower." It looks like the arguer has given us two independent reasons. First, Ami should take a shower because (b) he stinks. Second, because (c) it's not healthy to go without showering for two weeks when you've been sweating every day.

Both (b) and (c) are independent reasons for Ami to shower. Even if (c) were false or never mentioned it would do nothing to undermine (b) as a reason.

When we formalize an argument with convergent premises it doesn't matter what order we put them in since they function independently of each other.

Formalizing the argument would look like this (reversing P1 and P2 would also be fine):

P1 You stink.
P2 Going without a shower for a long time is unhealthy
C. You should take a shower.

Let's look at one more example:

(a) Everyday Otis Ponens waits for me at the top of the stairs and (b) he keeps me company when I'm stuck at home alone writing lessons. (c) Otis Ponens is the best dog ever. And also (d) he (almost) never pees in the house.

The conclusion is (c). Notice that each premise (a), (b), and (d) are independent reasons that support the conclusion. If I didn't list one, the remaining ones wouldn't be any less relevant to the conclusion.

If we formalize the argument it should look like this (P1-P3 could be in any order):

P1. Everyday Otis Ponens waits for me at the top of the stairs.
P2. He keeps me company when I'm stuck at home alone writing lessons.
P3. He (almost) never pees in the house.
C. Otis Ponens is the best dog ever.

Serial Premises and the "Why Should I Believe That?" Test

Serial premises are when one premise supports another premise in the same way a major premise would support a conclusion. So, when we reconstruct our arguments, the order in which we put them is going to matter. We can also think of the supported major premise as a sub-conclusion. The terminology isn't that important so long as you understand the relationship. Let's look at an example of a serial relationship between premises:


Based on the video clip and some background information we can infer the following argument:

(a) Mugatu is a fashion genius. (b) He invented the piano key necktie which became an important milestone in men's fashion.
(c) For instance, back in the 80s all the cool kids owned piano key neckties.

The conclusion of the argument is (a) Mugatu is a fashion genius. (See Basic Concepts 1 if you're unsure why). Once we've identified the main conclusion we know that whatever remains are premises which means that they should support the main conclusion. Let's see:

(b) He invented the piano key necktie is a reason to believe that he is a fashion genius only if it was also an important milestone in men's fashion. But some people might question that the piano key necktie was an important milestone in men's fashion. Did the piano key necktie become an important milestone in men's fashion? Most people will want some reason or evidence to believe it's true. That's where sub-premises come in. Sub-premises give support to what might be questionable main premises and will answer the questions "why should I believe [insert major premise]?". So, why should I believe that the piano key necktie became an important milestone in men's fashion? Well, because (c) back in the 80s all the cool kids owned piano key neckties.

Don't believe me? Just look at this cool kid from the 80s:

piano%20key%20necktie.jpg

We may or many not think (c) provides adequate support for (b) but that's beside the point for now. All we care about is figuring out the relationship between the premises to each other and to the conclusion. In this case, (c) is a serial sub-premise of the conclusion: it provides support for a major premise (b) but not for the conclusion directly. Premises that directly support the conclusion are called major premises.

Now that we're familiar with the terminology, let's put the argument into standard form.

It should look like this:

P1.ii In the 80s, all the cool kids owned piano key neckties.
P1.i Mugatu invented the pianokey necktie which became an important milestone in men's fashion.
C Mugatu is a fashion genius.

Notice something important. Instead of listing (b) and (c) as P1 and P2 I've listed them both as P1 to show that they are part of the same line of argument—one supporting the other. However, I've also used lower case roman numerals to show the order of dependance. P1.i is the major premise since it directly supports C and P1ii is a sub-premise since it directly supports P1i. The lower the value of the roman numeral of a premise, the more closely it should be related to the conclusion.

In some arguments it will sometimes be tricky to figure out which is the major premise and which is the sub-premise. To figure this out we can use the "Why should I believe that?" test again. Suppose I'm not sure which is the major premise: (b) Mugatu invented the piano key necktie which was an important milestone in men's fashion OR (c) In the 80s, all the cool kids owned piano key neckties. Let's apply the test.

A: Why should I believe that Mugatu invented the piano key neckties which became an important milestone in men's fashion?
BECAUSE in the 80s all the cool kids owned piano key neckties.

OR

B: Why should I believe that in the 80s all the cool kids owned piano key neckties?
BECAUSE Mugatu invented the piano key necktie which became an important milestone in men's fashion.

Clearly, A makes more sense. Whatever premise we put in the form of a question 'because' will be the major premise.

Let's try one more example:

(a) Students seeking a rewarding career in any field should study philosophy because (b) philosophy will give you the tools to succeed. (c) Philosophy teaches you to write and think clearly at a high level. (d) For example, philosophy undergrads score the highest of any other major on the LSAT and GRE tests.

The conclusion is (a). Now, to figure out the relationship of the other premises to each other and the conclusion we ask:

Why should I believe [(b) philosophy will give you the tools to succeed]?

The best answer is (c) philosophy teaches you to write and think clearly at a high level. That is support the claim that philosophy will give you the tools to succeed. We apply the test again to find out how the remaining premises are related:

Why should I believe [(c) philosophy teaches you to write and think clearly at a high level]?

The best answer is because (d), philosophy undergrads score the highest of any other major on the LSAT and GRE tests. This is evidence for the claim that philosophy teaches you to write and think clearly at a high level.

Now we can reconstruct the argument and show the logical relationship between the premises (and the conclusion).

P1.iii For example, philosophy undergrads score the highest of any other major on the LSAT and GRE tests.
P1.ii Philosophy teaches you to write and think clearly at a high level.
P1.i Philosophy will give you the tools to succeed.
C. Students seeking a rewarding career in any field should study philosophy.

If you start at the conclusion and ask of it "Why should I believe that?" the next line up should give you the answer, and if you repeat the process it should work all the way up. Each line should be the answer to the line below it why you ask "why should I believe that?"

This is how serial premises work. They provide additional support for a more basic premise in the argument.

Combining Convergent and Serial Premises

Extended arguments can use both convergent and serial premises. Let's take a look at an example.

(a) Drinking tea is more communal than coffee (b) since it's more likely to be brewed in a pot. (c) Tea also has health benefits that coffee doesn't. (d) For example it detoxifies the toxins and cures cancer. (e) Therefore, people should drink tea more often.

(e) is the conclusion. Now we ask, why should I believe that [(e) people should drink tea more often]? It looks like both (a) and (c) answer that question but they are unrelated to each other so they must be convergent premises.

So far my argument reconstruction looks like this:

P1. Drinking tea is more communal than coffee.
P2. Tea has health benefits that coffee doesn't.
C. Therefore, people should drink tea more often.

But someone might challenge P1 or P2, or both. The arguer has anticipated this and provided additional support for those basic premises.

I ask:

Why should I believe that [P1 drinking tea is more communal than drinking coffee]?
BECAUSE (b) it's more likely to be brewed in a pot.

Since (b) answers answers the question about P1, it's a serial sub-premise.

My argument reconstruction now looks like this:

P1.ii Since tea is more likely to be brewed in a pot
P1.i Drinking tea is more communal than coffee.
P2. Tea has health benefits that coffee doesn't.
C. Therefore, people should drink tea more often.

One more step. I ask of P2:

Why should I believe that [P2 tea has more health benefits that coffee doesn't have]?
BECAUSE (d) it detoxifies the toxins and cures cancer.

Since (d) answers the question, that is, give support to P2 we know it's a serial sub-premise of P2.

My final argument reconstruction will look like this:

P1.ii Since tea is more likely to be brewed in a pot
P1.i Drinking tea is more communal than coffee.
P2.ii Tea detoxifies the toxins and cures cancer.
P2.i Tea has health benefits that coffee doesn't.
C. Therefore, people should drink tea more often.

Looking ahead. Recall that I said critical thinking is defined as a systematic method of evaluating arguments, reasons, and evidence. Notice that now that we have systematically laid out the parts and structure of the argument it's going to be much easier to evaluate it. We can look at each component individually and evaluate both whether it's true and whether it genuinely supports the thing it's supposed to support. Laying out this argument should allow you to see that there are some weak premises as well as weak links between premises. This is the beginning of evaluating arguments. But notice that first you have to make the parts and structure explicit. Then and only then are you are much less likely to make errors in evaluating the argument. Critical thinking is the systematic evaluation of arguments, reasons, and evidence. Beat it into your head and you'll be a smarty-pants in no time!

Self Quiz

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