Argument Diagramming Part II

PHIL 121: Methods of ReasoningFebruary 1, 2013

Instructor:Karin HoweBinghamton University

Some issues from last lecture …• The principle of fairness

– "We should always interpret the argument in away that is consistent with the author'sintentions. For example, we should always uselanguage that is as close as possible to thelanguage the author uses. We should not putwords in the author's mouth, or take words outof the author's mouth."

– In other words, it is important to preserve themeaning 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. Ifthere is ambiguity, always choose theinterpretation that makes the argument strongerrather than weaker."

– If there are two possible interpretations of anauthor's argument, we should pick whicheverone makes the argument stronger.

Problem: sometimes these two principles conflict

• What do we do when they conflict? Whichprinciple should we choose? In other words, is itbetter 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 premisesdirectly support the conclusion, and leave thequestion of whether the premises are true to theevaluation stage."

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

Wrong answer!

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

• We can (almost) always re-write the premises ofan argument in such a way as to make theargument valid, if we are allowed to change theminto other premises altogether! (e.g., change thestatement from a universal affirmative to auniversal negative, as they did in the previousexample)

• This is carrying the principle of charity too far

Executive decision (important!)

• Yes, you should definitely employ both theprinciple of charity and the principle of fairnesswhen 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 theprinciple of fairness in order to satisfy theprinciple of charity.

Luckily, in this case, we don'treally have to choose …

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

Some importantdefinitions

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

Different types ofarguments

• deductive• inductive• argument by analogy• abductive

Deductive vs. Non-deductive Arguments

• Deductive arguments are arguments thatguarantee the truth of their conclusions, given thattheir 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 theirpremises.– 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 sampleis 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 toT (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 formsuch that it is impossible that all of itspremises are true and its conclusion false.

• An invalid argument is one having the formsuch that it is possible that all of itspremises are true, and yet the conclusion isfalse.

How can an invalid argument stillbe a good argument?

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

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

– A weak argument is an invalid argument in which it isnot likely that the conclusion is true, given the truth ofthe 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" ofthe argument separately. If at least one branch of theargument is cogent then the whole argument is cogent.

Evaluating arguments

All arguments have two different features thatmust 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 whatkinds of arguments?– Deductive arguments

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

• Content:– soundness– cogency

• What kind of argumentscan be sound?– Deductive arguments

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

Consider the following pair of arguments

1. All kangaroos canfly.

2. Karin is a kangaroo.____________________Therefore Karin can fly.

This argument is valid.Is it sound?

1. 90% of kangarooscan fly.

2. Karin is a kangaroo.____________________Therefore Karin can fly.

This argument is strong.Is it cogent?

True fact: 97%of all questionsabout validitycan beanswered bythinking aboutkangaroos

The Penguin Argument

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

Diagramming and AnalyzingArguments

A Quick How-to Guide

Step 1: Diagram the Argument1. 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 thepremises 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 forcritiquing the different aspects of the argument)

– Note: If the aspect that you look at first turns out to be fine, thenyou 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 argumentis good or bad: some nitty gritty details

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

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

• Step 2: analyze the argument forvalidity/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 isanother 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 sometime to develop)

Determining the Strength of aNon-deductive Argument

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

• Unlike validity, strength comes in degrees.• Also, what makes a non-deductive argument

strong or weak depends on what kind ofargument 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 Babelfish could have evolved by chance. If the Babelfish could not have evolved by chance then thatproves that you (God) exist. Therefore, by yourown argument, you don’t exist.

God's Argument: GoodArgument or Not?

Man's Argument: GoodArgument 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 thatglobal warming, earthquakes,hurricanes, and other naturaldisasters are a direct effect ofthe shrinking numbers ofPirates since the 1800s. Foryour interest, I have included agraph of the approximatenumber of pirates versus theaverage global temperature overthe last 200 years. As you cansee, there is a statisticallysignificant inverse relationshipbetween pirates and globaltemperature.