Argument Diagramming Part II

PHIL 121: Methods of Reasoning

February 1, 2013

Instructor:Karin Howe

Binghamton University

Some issues from last lecture …• The principle of fairness

– "We should always interpret the argument in a way that is consistent with the author's intentions. For example, we should always use language that is as close as possible to the language the author uses. We should not put words in the author's mouth, or take words out of the author's mouth."

– In other words, it is important to preserve the meaning of an author's statements.

• The principle of charity– "If there is some uncertainty, we should always

put the argument in the best possible light. If there is ambiguity, always choose the interpretation that makes the argument stronger rather than weaker."

– If there are two possible interpretations of an author's argument, we should pick whichever one makes the argument stronger.

Problem: sometimes these two principles conflict

• What do we do when they conflict? Which principle should we choose? In other words, is it better to be fair, or charitable?

Which should we choose?

• Answer according to the text:– "The convention in logic is to represent the

argument in such a way that the premises directly support the conclusion, and leave the question of whether the premises are true to the evaluation stage."

– This seems to imply that the principle of charity trumps or outweighs the principle of fairness.

Wrong answer!

• If this is the way you choose to go then any argument can be made valid! (or strong)

• We can (almost) always re-write the premises of an argument in such a way as to make the argument valid, if we are allowed to change them into other premises altogether! (e.g., change the statement from a universal affirmative to a universal negative, as they did in the previous example)

• This is carrying the principle of charity too far

Executive decision (important!)

• Yes, you should definitely employ both the principle of charity and the principle of fairness when interpreting an author's argument.

• However, when they conflict (if they really do), then the principle of fairness wins.

• In particular, you should never violate the principle of fairness in order to satisfy the principle of charity.

Luckily, in this case, we don't really have to choose …

• Moral: if you come up against a case where it feels like the argument should be valid, but only can be made so by changing the premises completely, look for an implicit premise that can fix things.

Some important definitions

• valid• invalid• strength• sound• unsound• cogency

Different types of arguments

• deductive• inductive• argument by analogy• abductive

Deductive vs. Non-deductive Arguments

• Deductive arguments are arguments that guarantee the truth of their conclusions, given that their premises are true.– In other words, if their premises are true then their

conclusion must also be true.

• Whereas, non-deductive arguments only show that their conclusions are likely, given the truth of their premises.– In other words, if their premises are true then their

conclusion is also likely to be true.

Types of Non-deductive Arguments

• Inductive arguments– An argument in which the description of some sample

is extended to items outside of the sample.

• Argument by analogy– An argument that (1) asserts that two things, call them

A and T, are similar to each other to a certain degree (this is called the analogy), (2) takes a description of A (called the analog), and (3) extends that description to T (called the target).

• Abductive arguments– An abductive argument is often called an "inference to

the best explanation."

Validity and Invalidity

• A valid argument is one having the form such that it is impossible that all of its premises are true and its conclusion false.

• An invalid argument is one having the form such that it is possible that all of its premises are true, and yet the conclusion is false.

How can an invalid argument still be a good argument?

• Inductive arguments are technically invalid (since it is possible for the premises to be true while the conclusion is false), but they can still present a strong argument.– A strong argument, then, is an invalid argument in

which is likely that the conclusion is true, given that the premises are true.

– A weak argument is an invalid argument in which it is not likely that the conclusion is true, given the truth of the premises.

Soundness and Cogency• An argument is sound if and only if: it is valid and

has all true premises.• An argument is unsound if and only if: it is either

invalid, or has one or more false premises.• A cogent argument is a strong argument in which

all the premises are actually true in our world.• Any argument that is either weak, or strong with at

least one false premise, is uncogent.– Special note: If the argument is a convergent argument,

you will need to assess the cogency of each "branch" of the argument separately. If at least one branch of the argument is cogent then the whole argument is cogent.

Evaluating arguments

All arguments have two different features that must be separately evaluated: form and content:

The evaluation of the form of anFORM argument asks whether the

conclusion follows from thepremises.

The evaluation of the content ofCONTENT an argument asks whether all of

the premises are true.

Form vs. Content

• Form:– validity

– strength

• Validity applies to what kinds of arguments?– Deductive arguments

• What kind of arguments are strong (or weak)?– Non-deductive arguments

• Content:– soundness

– cogency

• What kind of arguments can be sound?– Deductive arguments

• What kind of arguments can be cogent?– Non-deductive arguments

Consider the following pair of arguments

1. All kangaroos can fly.

2. Karin is a kangaroo.

____________________

Therefore Karin can fly.

This argument is valid.

Is it sound?

1. 90% of kangaroos can fly.

2. Karin is a kangaroo.

____________________

Therefore Karin can fly.

This argument is strong.

Is it cogent?

True fact: 97% of all questions about validity can be answered by thinking about kangaroos

The Penguin Argument

1. Everything that flies is a bird.2. Penguins can fly.________________________________Therefore, penguins are birds.

QuickTime™ and a decompressor

are needed to see this picture.

Diagramming and Analyzing Arguments

A Quick How-to Guide

Step 1: Diagram the Argument

1. Highlight the conclusion and subconclusion indicators2. Highlight the premise indicators3. Identify the conclusion (and the subconclusion(s), if

there are any)4. Identify the explicit premises5. Identify any implicit premises or subconclusions, or the

implicit conclusion if the conclusion is unstated.6. Break the argument down into separate statements7. Rewrite the statements8. Diagram the argument

Step 2: Sound (or Cogent) or Not?

• To show that an argument is unsound:– Show that either some or all of the premises are (likely)

not true, or that the argument is invalid.

• To show that an argument is sound:– Show that the argument is both valid and all the

premises are (likely) true.

• To show that an argument is cogent:– Show that the argument is both strong and all the

premises are (likely) true.

• To show that an argument is uncogent:– Show that either some or all of the premises are (likely)

not true, or that the argument is weak.

Two Methods for Showing Unsoundness/Uncogency

• Quick-and-dirty method– Pick whichever aspect (form or content) seems easiest to critique,

and do that. (See the rigorous method for specific tips for critiquing the different aspects of the argument)

– Note: If the aspect that you look at first turns out to be fine, then you must default to the rigorous method.

• Rigorous method– First look at form, and determine if the argument is valid/invalid,

strong/weak.• If argument is invalid or weak, STOP. The argument is

unsound and/or uncogent– If the argument is valid or strong, go on to look at content. Are all

of the premises (likely) true?• If at least one of the premises seems false, STOP. The

argument is unsound and/or uncogent.– If all of the premises are (likely) true, then the argument is sound

or cogent.

Determining whether the form of an argument is good or bad: some nitty gritty details

• Step 1: determine what kind of argument you are dealing with– In other words, is this a deductive argument or

some kind of non-deductive argument? If it is a non-deductive argument, which kind of non-deductive argument is it?

• Step 2: analyze the argument for validity/invalidity, strong vs. weak, depending on what kind of argument it is

Determining Validity/InvalidityThree methods for determining validity or invalidity of an

argument:1. Recognizing common valid or invalid forms2. Using the definition of validity or invalidity3. Content substitution (counter-example)

Note: the text also lists another method (truth tables). This is another method you can use to determine validity or invalidity; however, we will set this method aside until Part III (Sentential Logic) of this course.

We will talk more about the three methods above in another lecture (they are complicated and important skills that will take some time to develop)

Determining the Strength of a Non-deductive Argument

• In determining the strength of a non-deductive argument, things get a bit messier.

• Unlike validity, strength comes in degrees.

• Also, what makes a non-deductive argument strong or weak depends on what kind of argument it is.

Let's Practice!

• The Babel Fish Argument• God's argument: If there is proof that I exist then

that denies faith and without faith I don’t exist. Therefore, I refuse to prove that I exist.

• Man's argument: It is impossible that the Babel fish could have evolved by chance. If the Babel fish could not have evolved by chance then that proves that you (God) exist. Therefore, by your own argument, you don’t exist.

God's Argument: Good Argument or Not?

Man's Argument: Good Argument or Not?

Doing Well in Methods of Reasoning

Cats Are Liquids

Cats with Teapot Fetishes

Lack of Pirates Causes Global Warming

You may be interested to know that global warming, earthquakes, hurricanes, and other natural disasters are a direct effect of the shrinking numbers of Pirates since the 1800s. For your interest, I have included a graph of the approximate number of pirates versus the average global temperature over the last 200 years. As you can see, there is a statistically significant inverse relationship between pirates and global temperature.