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Lecture Notes Unit 1

Contents

  1. Basic Definitions
  2. Standard Form
  3. Identifying the Conclusion
  4. Distinguishing Arguments From Other Discourse
  5. Induction and Deduction
  6. Evaluating Arguments
  7. Argument Mapping
  8. Argument Reconstruction
  9. What Is and Isn’t Relevant when Evaluating Arguments

Or jump to the unit 2 lecture notes or unit 3 lecture notes.

A. Basic Definitions

These definitions are bit crude and oversimplified, but they’ll do for a start.

What is a definition anyway? Can a definition be right or wrong?

Reasoning is any form of thinking in which one makes an inference.

An inference is the process of forming a new belief on the basis of other beliefs.

My wife tells me that there are new episodes of Midsomer Murders on Acorn TV. From this, I infer (make the inference) that she will be watching TV all night.

The reasoning involved in an inference can typically be expressed as an argument. In this course, we will usually focus on arguments and statements, rather than on inferences and beliefs, because they are public things we can experience together, making them easier to discuss directly.

An argument is a collection of statements, some of which (the premises) are put forth as providing support, evidence, or reasons in favor of, another statement (the conclusion).

I have seven first cousins on my dad’s side of the family. I have nine first cousins on my mom’s side of the family. I have no other first cousins. Seven plus nine is sixteen. Hence, I have sixteen first cousins in total.

The “put forth as” here is important. An argument is an argument so long as the premises are claimed to, or suggested as, providing support for the conclusion, even if they don’t actually do so.

Obama is a Muslim. Therefore, he is a terrorist.

This is a lousy argument. Not only is the premise false, even if it were true, it would not provide a good reason for believing the conclusion. But none of that means it isn’t an argument: it just isn’t a very good one.

A statement is a declarative sentence, or part of a sentence, that is either true or false.

The En Vogue single “My Lovin’ (You’re Never Gonna Get It)” was released in 1992. (True.)
The capital of Sweden is Amsterdam. (False.)

A grammatical sentence may contain more than one statement. Consider:

The Boston Red Sox won the AL pennant in 2018, and the LA Dodgers won the NL pennant in 2018.

hodor

How many statements does the example above contain? The answer is: 3 (the whole sentence is also a statement)

Some sentences may contain no statements at all; this is typically the case with questions, commands, exclamations, etc.

Are you feeling OK?
Hold the door!
Darn!

The truth value of a statement is its status as true or false (or something in between?).

In classical logic, there are only two truth values: truth and falsity.

descartes

A single statement on its own is not an argument, and does not represent an inference. To have an argument, there must be an alleged supporting relationship.

On the other hand, since a sentence may contain multiple statements, a sentence can contain an entire argument.

I think, therefore I am. (René Descartes)

A premise is a statement in an argument that is put forth as providing support or reasons for accepting the conclusion.

The conclusion is the statement which the rest of the argument is put forth as supporting or providing reasons for.

In Descartes’s famous argument, “I think” is the premise, and “I am” is the conclusion.

Notice the same statement can be a premise in one argument, and the conclusion of another.

A proposition is what is meant by a statement: the idea or notion it expresses.

What propositions are, and whether or not they can be considered “real things”, is the kind of thing philosophers debate.

“Snow is white” expresses in English the same proposition that “Der Schnee ist weiß” expresses in German.

Logic is the systematic study of the evaluation of arguments in terms of what features they must have for the premises to support the truth of their conclusions. (A science? An art?)

Epistemology is the philosophical study of knowledge and the justification of beliefs and related cognitive states.

Rhetoric is the study of what ways of presenting arguments, or other forms of speech or writing, are most effective in convincing others or achieving other desired goals.

As a philosophy professor, I am only supposed to care about the first two, but that’s not really true.

B. Standard Form

When studying or evaluating an argument, it is convenient to have it in a form where each premise is labeled and numbered, and the conclusion is listed last, separated from the premises, and also labeled.

P1. If God exists, God created everything in the universe.
P2. If God created everything in the universe, then everything in the universe is good.
P3. Not everything in the universe is good. C. God does not exist.

img

Here it is obvious what the conclusion is, and what the premises are, but arguments are very seldomly given to us in this form. If you are reading a newspaper editorial, or listening to lecture, or reading a book, it takes some more work to separate out the premises and the conclusion.

Writing an argument in standard form presupposes each argument has only one conclusion, though it may have many premises. This is a standard assumption: we could consider a paragraph, for example, which reaches multiple conclusions as multiple arguments, not a single one. We shall later consider a broader notion of argument, however.

C. Identifying the Conclusion

In actual speech or writing, the conclusion is not always at the end. It could be at the beginning, or even somewhere in the middle.

Certain words can be helpful in separating out premises and conclusion.

A premise indicator is a word or phrase that is typically used within, or just before, a statement used as a premise.

“since”, “because”, “as”, “for”, “given that”, “inasmuch as”, “for the reason that”, etc.

A conclusion indicator is a word or phrase that is typically used within, or just before, a statement used as a conclusion.

“therefore”, “thus”, “hence”, “consequently”, “so”, “it must be that”, “as a result”, etc.

Sometimes, there are few or no indicators, and you have to use common sense to make the determination.

God is defined as the most perfect being. A perfect being must have every trait or property that it’s better to have than not to have. It is better to exist than not to exist. Therefore, God exists.

Conclusion: God exists.

Hillary Clinton must be a communist spy. She supports socialized health care, and everyone who supports socialized health care is a communist spy.

Conclusion: Hillary Clinton is a communist spy.

It has rained more than 15 inches per year in Amherst every year for the past 30 years. So you can safely bet it will rain more than 15 inches in Amherst this year.

Conclusion: It will rain more than 15 inches in Amherst this year.

Professor Chappell said that the ratio of female to male students in the class was exactly 3:1. This means that there are 112 female students in the class, because there are 148 students in the class total.

Conclusion: There are 112 female students in the class.

The Encyclopædia Britannica has an article on symbiosis. It stands to reason that the Encyclopedia Americana has an article on symbiosis as well, since the two reference works tend to cover the same topics.

Conclusion: The Encyclopedia Americana has an article on symbiosis.

vizzini

D. Distinguishing Arguments From Other Discourse

Obviously, not all language consists of arguments.

An argument must at least implicitly have a premise or premises and a conclusion: there must be reasoning from something to something else.

Non-arguments fall into many categories.

1. Simple Statements, Reports and Other Straightforward Non-Inferential Language

If passage simply makes a claim, or even a series of claims, without offering any rationale, reasons or proof, it is not an argument.

Apple makes the best computers, Toyota makes the best cars, and France makes the best wine.

A loosely associated collection of statements, even on the same topic, need not be an argument.

The GNU/Linux operating system is an open source alternative to Windows and Mac OS X. It is free, as is most of the software for it. It powers over 60% of web servers and over 95% of the world’s supercomputers. The first version was created by Linus Torvalds in 1991, who modeled its architecture on the UNIX platform.

Even if an expository passage has a “topic sentence”, and a more unified subject matter, it is not an argument unless there is an inference.

The University of Massachusetts system offers excellent higher education opportunities at its five campuses. UMass Amherst is the flagship campus, and offers a wide variety of programs. The Boston metro area is served by UMass Boston, and the Northern and Southern parts of the Commonwealth are served by UMass Lowell and UMass Dartmouth. Its Nobel-prize winning Medical School is located in Worcester.

A report of an event, such as a news story, is typically not an argument.

The number of refugees worldwide is the highest it has ever been. A recent Gallup poll suggests that over 25% of Afghans wish to leave Afghanistan. Numbers are similarly high elsewhere in the Middle East. Many European countries have put in to place more stringent immigration policies as the number of people seeking asylum grows.

A simple warning or piece of advice, by itself, is not an argument.

Never get involved in a land war in Asia.

However, if reasons are offered in favor of advice or a suggestion, it may take the form of an argument.

In an IRA account, the amount of interest you earn grows exponentially in proportion to how long you keep the money in the account. Hence, if you are in your 20s you should invest now, as the long term dividends will outweigh the temporary inconveniences.

img

This is an argument with the conclusion, “if you are in your 20s, you should invest now.”

Suppose in the above, we swap “you should invest now” for simply “invest now”: would it still be an argument?

You might have thought that the conclusion should be simply “you should invest now”, and that the “you are in your 20s” was another premise. But this is probably not right, which leads to our next topic.

2. Conditional Statements

A conditional statement is a statement that claims that one thing is true if or provided that something else is, either by using the phrase “if … then …” or a synonymous phrase or construction (such as “provided that” or “on the condition that”).

If you are in your 20s, you ought to invest in an IRA now.

The antecedent of a conditional is the if-part, or the statement, which, if true, would mean that the consequent is true.

The consequent of a conditional is the then-part, or the statement which is true if the antecedent is.

→

In the example above, “you are in your 20s” is the antecedent, and “you ought to invest in an IRA now” is the consequent.

Notice that the word is “consequent”, not “consequence”.

Conditionals are quite often used as premises in arguments, and can also be conclusions, such as in the example above.

By themselves, however, they are not entire arguments.

It is easy to get confused about this, because the relationship between antecedent and consequent seems a lot like the relationship between premises and conclusion.

However, if you simply utter a conditional, you are not actually putting forth the antecedent or consequent as true. You may do this in a separate premise, but it requires a separate premise.

If Susanna is a UMass student, she can get a free account on box.com. Susanna is a UMass student. Therefore, she can get a free account on box.com

This is an argument, but only because it includes the last two sentences. This argument form is called modus ponens.

An argument can include a conditional only to deny its consequent.

If the Bible is true, then the world was created in seven days. The world was not created in seven days. Therefore, the Bible is not true.

This argument form is called modus tollens … whence the saying, “one person’s modus ponens is another’s modus tollens.”

If a conditional is true, the condition mentioned in the antecedent is said to be a sufficient condition for the condition mentioned in the consequent.

If a conditional is true, the condition mentioned in the consequent is said to be a necessary condition for the condition mentioned in the antecedent.

The presence of water is a necessary condition for the presence of life. (Because it’s true that: “If life is present, water is present.”)

3. Explanations

An explanation is an attempt to shed light on a certain thing, event or fact—an attempt to state why it is (how it is).

Explanations can sound like arguments because they often include words like “because” or “since”.

Dinosaurs went extinct because an asteroid collided with Earth 66 million years ago.

dinos

It would be a bit odd to think of this as an argument, however.

We are not supposed to “conclude” that dinosaurs went extinct on the basis of the “premise” that an asteroid hit Earth.

Nonetheless, I think the precise difference between arguments and explanations (if there is one) is not as simple or widely agreed-upon as logic textbooks tend to suggest.

What is an explanation? What is the difference between a good explanation and a bad one? Is perhaps an explanation something that could have been an argument under different circumstances?

The explanandum of an explanation is the thing or fact being explained.

The explanans of an explanation is whatever is used to shed light on the explanandum.

You may even come across what we usually think of as a “conclusion indicator” used with an explanandum.

When light hits the Earth’s atmosphere, light with wavelengths at the lower end of the visible spectrum are more widely scattered than light with wavelengths at the higher end. Thus, the sky is blue.

4. Examples and Illustrations

An illustration is the attempt to explain something, or make it clearer, by means of an example.

An argument from example is an argument in which an example is used as a premise.

Compare:

A stimulant is any substance that increases nervous activity in the body. For example, caffeine lowers the level of adenosine released into the bloodstream, thereby preventing its usual effects of calming the body and producing fatigue.

Drinking and driving poses an unacceptable risk to society. Laura Gorman was killed in Central Florida in 2006, and her family, friends and community have still not recovered.

coffee

What’s the difference?

In the first example, the statement about stimulants in general is not a conclusion, where the example is a premise.

In the second example, at least possibly, the first statement is meant as a conclusion.

E. Induction and Deduction

1. Overview

A deductive argument is one in which the conclusion is put forth as following necessarily from the premises: i.e., with the suggestion that it is impossible that the conclusion could be false if the premises are true.

An inductive argument is one in which the conclusion is put forth as most likely following from the premises: i.e., with the suggestion that it is improbable or unlikely that the conclusion could be false if the premises are true.

img

These may not be the definitions you expected. There is an older usage of these terms, on which deduction means reasoning from the general to the specific, and induction means reasoning from the specific to the general.

The older definitions aren’t “wrong”, but they don’t reflect the way the words are now used by logicians. We’ll be using the newer definitions.

On the new definitions, the difference has to do rather with how strong the relationship between the premises and conclusion is supposed to be.

With the new definitions, a deductive argument may reason from the specific to general:

3 is prime. 5 is prime. 7 is prime. Therefore, all odd integers between 2 and 8 are prime. (Deductive)

Or vice versa for an inductive argument:

Most NRA members are conservatives. Jason isn’t a conservative, so he’s probably not an NRA member. (Inductive)

rhombus

Of course, just because a certain argument is put forth as having a certain kind of relationship, doesn’t mean it actually does. An argument can be deductive even if it is possible for the premises to be true and the conclusion to be false, so long as the form of the argument suggests that this kind of relationship is what is supposed to hold.

By definition, all squares are rhombuses.
By definition, all squares are rectangles.
Therefore, all rhombuses are rectangles.
(Deductive, but invalid.)

Most Pro Basketball Players are American.
Most Americans are out of shape.
LeBron is a Pro Basketball player.
So LeBron is probably out of shape.
(Inductive, but weak.)

2. Common Types of Deductive Arguments

Arguments whose reasoning is entirely mathematical are typically deductive. (Those involving statistical probabilities may be inductive.)

The University has a total enrollment of 28,635. Of these, 20,394 are enrolled in undergraduate degree programs. Therefore, there are 8241 students enrolled in other ways, such as in graduate programs or nondegree programs.

boyega

Arguments whose reasoning depends solely on the definitions of the words it uses are deductive.

John Boyega is a man.
He’s not married.
That makes him a bachelor!

Arguments whose reasoning only appeals to their logical forms, that is, their grammatical structures and the “semantic rules” (meaning) applying to simple topic-neutral words such as “all”, “or”, “not”, “if … then …” and so on, represent the mainstay of deductive logic.

The classical form of such arguments is the “syllogism”, some forms of which have special names in logic.

A syllogism is a deductive argument with exactly two premises.

If Harry catches the snitch, the Gryffindor team earns 150 points.
If the Gryffindor team earns 150 points, Gryffindor will win the game.
Therefore, if Harry catches the snitch, Gryffindor will win the game.
(“Hypothetical syllogism”)

Either Trump with win the election, or Clinton will win the election.
Trump will not win the election.
Therefore, Clinton will win the election.
(“Disjunctive syllogism”)

toaster All toasters are time travel devices.
All time travel devices are made of gold.
Therefore, all toasters are made of gold.
(“Categorical syllogism”)

buzz

With a deductive argument, the truth of the conclusion is thought, rightly or wrongly, to be “contained” in the truth of the premises. Not so with inductive arguments.

3. Common Types of Inductive Arguments

Inductive reasoning involves reaching a conclusion not thought to be absolutely necessary for the mere truth of the premises. It involves “going beyond” them in some way.

A good example of this is a prediction of the future on the basis of past events.

The Commonwealth of Massachusetts has held a Sales-Tax-Free holiday every year from 2009 to 2015. Thus, they will no doubt have one again in 2016.

Reasoning by analogy—pointing out that certain things have certain features in common and concluding that they (probably) would have others in common as well–is another common form of induction.

My mom’s 2012 Volvo station wagon came with a 10 year warranty. You bought your 2012 Volvo station wagon at the same dealer, so you probably have the same warranty.

Reasoning that involves applying an observed pattern to a larger class of cases, or to every member of a group based on a subset—generalization—is typically inductive.

buenoEvery dish I’ve gotten from Bueno y Sano has been delicious. I bet all their dishes are delicious.

Arguments that rely on the testimony or authority on an individual, or the accuracy of a sign, writing, or signal are inductive.

It’s going to rain today. It says so on the news.

The train crossing signal is flashing. There must be a train coming.

Arguments based on cause/effect relationships are usually inductive.

I’m hearing some very loud popping noises coming from the park. They’re having fireworks!

fireworks

Arguments that employ a mixture of types of reasoning, some of which would be deductive on their own, some of which would be inductive on their own, are typically considered inductive as a whole.

Notice in the example below, part of the reasoning involves Prof. Chappell’s testimony. This is enough to make it inductive, despite that otherwise it relies on mathematics. (The mathematics is wrong, but that alone doesn’t make it inductive.)

Professor Chappell said that the ratio of female to male students in the class was exactly 3:1. This means that there are 112 female students in the class, because there are 148 students in the class total.

F. Evaluating Arguments

1. Basic Terminology

Remember that I said that this argument was lousy for two reasons:

Obama is a Muslim. Therefore, he is a terrorist.

The premise is false, and even if it were true, the conclusion wouldn’t follow from it.

Fix one of these two things, and you still have a bad argument.

Obama is a Muslim. Therefore, he prays facing Mecca.

Obama is a Christian. Therefore, he is a terrorist.

From a logical point of view, we can evaluate an argument in two different dimensions.

The first involves whether or not the premises are true.

An argument is factually correct if all its premises are true.

basketball The Earth is round. All basketballs are round. Hence, the Earth is a basketball.

Notice this is not enough to make this a good argument. We’ll get to what is wrong with it in a bit.

Otherwise an argument is factually incorrect.

The example below is also a bad argument, but for a different reason.

toaster All toasters are time travel devices.
All time travel devices are made of gold.
Therefore, all toasters are made of gold.

In addition to factual correctness, the other feature a “good” argument needs to have is a good process of reasoning: there must the appropriate kind of link between the premises and conclusion. Whether or not the premises are in fact true, they have to provide the right kind of support for the conclusion assuming they were true.

Inductive and deductive arguments aim to provide different kinds of support for their conclusions, and so here we use different terminology.

A deductive argument is valid if it has a form that means that its conclusion actually must necessarily be true if its premises are.

A deductive argument is invalid if it has a form that allows that its premises could be true while its conclusion is false.

yoda

Validity is not about whether the premises, or even the conclusion, are in fact true.

Rather it’s about the process of reasoning: the relationship or connection between them.

The toaster example is valid, but not factually correct.

The basketball example is invalid, despite being factually correct.

There the premises are in fact true while the conclusion is false, which guarantees that it must be invalid.

However, a deductive argument is invalid if it is even possible for the premises to be true and the conclusion false.

Yoda is one with the Force. All Jedis are one with the Force. Therefore, Yoda is a Jedi.

A inductive argument is strong if its conclusion would in fact probably be true on the basis of the truth of its premises.

In the past, everyone who has ingested large quantities of cyanide has died. Therefore, if you ingest that bottle of cyanide you’ll die.

A inductive argument is weak if it is not strong.

A few people who have eaten honey have gotten sick from it. Therefore, if you eat any honey, you’ll get sick.

honey

Again, this has to do with the inferential connection, not the actual truth or falsity of the statements.

A weak argument can have true premises and a probably true conclusion.

A strong argument can have one or more false premises, with a true or false conclusion and still be strong.

Everyone who has ingested more than 100mL of water has died within an hour. Therefore, if you ingest that 500mL bottle of water you’ll die within an hour.

This argument is strong, but it isn’t factually correct.

An argument needs both true premises and a strong inferential connection to be a logically good argument.

A sound deductive argument is one that is both valid and factually correct.

A cogent inductive argument is one that is both strong and factually correct.

Sound deductive arguments necessarily have true conclusions.

All vegans are vegetarians. No vegetarians eat meat. Therefore, no vegans eat meat.

In the case of inductive arguments, however, it is possible, though unlikely, that a cogent argument could have a false conclusion.

All US Presidents have been men. Therefore, the next US President will also be a man.

While these uses for the terms “valid” and “sound” for deductive arguments have become pretty universal, the terminology for inductive arguments is not as settled; you may see a phrase such as “inductive validity” or “inductive force” used for strength and “inductive soundness” used for cogency.

Logically speaking, an argument should be evaluated positively if it is sound (if deductive) or cogent (if inductive). Recall the definitions:

A sound deductive argument is one that is both valid and factually correct.

A cogent inductive argument is one that is both strong and factually correct.

Factual correctness has to do with the truth of the premises. There is no general procedure for determining the truth of a statement. (I wish there were.)

However, if you have good reason to think a premises are false, you also have reason to think the argument is factually incorrect. (Consider, however, whether or not there are similar premises in the vicinity that might be used in a similar, but distinct, argument.)

For the moment, let us consider the other aspects of evaluation: deductive validity and inductive strength.

2. Deductive Validity

To review:

A deductive argument is valid if it has a form that means that its conclusion actually must necessarily be true if its premises are.

Another way of putting this is that the form of the argument must necessarily preserve truth, or be “truth-preserving.”

Let us begin by considering how this applies to syllogistic-style reasoning.

The logical form of an argument is determined by holding fixed the meanings of the logical words like “if”, “and”, “or” and “not”.

Since we are not concerned with the actual truth or falsity of the premises, we can ignore the actual meanings of the “content” words. Or if you like, we should consider all the possible meanings for them. (Using variables helps us to ignore the “actual” meanings.)

tattoo (Modus ponens)

If it is Thursday, then we have class today.
It is Thursday.
Therefore, we have class today.

Form:
If P then Q.
P
Therefore, Q.

tweedle

Let us focus on the form. Whatever P and Q are, in classical logic, there are four possibilities:
(1) P and Q are both true;
(2) P is true, Q is false;
(3) P is false, Q is true, and
(4) P and Q are both false.

Let us see if any of those possibilities can make both premises true but the conclusion false.

We hold fixed the semantical rule for “if … then …”: If P, then Q rules out the possibility that P is true and Q is false.

The first possibility makes both premises true, but also makes the conclusion true; the second possibility makes the first premise false; the third and fourth possibilities make the second premise false.

It is not possible for the conclusion to be false if the premises are true, whatever P and Q are in actuality. Hence, any argument of this form is valid.

Similarly:

(Disjunctive syllogism)
Either Trump will win or Clinton will win.
Clinton will not win.
Therefore, Trump will win.

Form
Either P or Q.
Not-Q
Therefore, P.

The semantic rule for “or” is that it the statement it forms is only true when at least one of the two sides is true.

The semantic rule for “not” is that what results is true when what it is applied to is false, and vice versa.

So for the same four possibilities, (1) makes the second premise false, (2) makes both premises true, but also the conclusion, (3) also makes the second premise false, and (4) makes the first premise false. No possibility makes the premises true and the conclusion false. This means it is valid.

This is all assuming “classical logic”.

Non-classical logic is logic in which it is not assumed that every statement has one and only one of the two truth-values: truth, and falsity.

pinno

As an example, let us consider what Graham Priest calls The Logic of Paradox (LP), in which statements can be either true or false, or both, or neither. According to it, disjunctive syllogism arguments are invalid.

Instead of four possibilities for P and Q together, there are sixteen. Consider the one on which “P” is false (only), and “Q” is both true and false. Then both “Either P or Q” and “not-Q” are true, but “P” is not, so the form is not truth-preserving.

Validity for other kinds of deductive arguments, such as those involving mathematics and definitions, can usually be reduced to this form. Usually, this requires taking a defined word (“definiendum”) (or mathematical operator) and substituting the phrase that defines it (“definiens”), one or more times. The details can be tricky, however.

3. Counterexamples

Since deductive validity is determined by form, if two deductive arguments have the same form, both are valid or both are invalid.

It is impossible for a valid argument to have true premises and a false conclusion. Hence, if you’re considering one argument, and you can find a different argument with the same form with true premises and a false conclusion, both are invalid.

A counterexample to the validity of an argument is another argument with the same form with true premises and a false conclusion.

(The fallacy of affirming the consequent)

Yoda is one with the force. If Yoda is a Jedi, then Yoda is one with the Force. Therefore, Yoda is a Jedi.

Form:
P.
If Q then P.
Therefore, Q.

Counterexample:

The Earth is round. If the Earth is a basketball, then the Earth is round. Therefore, the Earth is a basketball.

The counterexample method is a way of showing an argument to be invalid by providing a counterexample.

creature No rodents are reptiles.
No mice are reptiles.
Therefore, some rodents are mice.


Form:
No A are B.
No C are B.
Therefore, some A are C.

Counterexample:
No mammals are fish.
No plants are fish.
Therefore, some mammals are plants.

It is not possible to find a counterexample for a valid argument. However, one cannot use the counterexample method to prove that an argument is valid. It is not enough to find an argument with the same form that isn’t a counterexample: one would have to show that none are.

toaster All toasters are time travel devices.
All time travel devices are made of gold.
Therefore, all toasters are made of gold.
(Valid)

Unfortunately, we cannot delve further into methods for determining the validity or invalidity of deductive arguments without getting right into symbolic logic.

4. Inductive Strength

Recall our definition:

A inductive argument is strong if its conclusion would in fact probably be true on the basis of the truth of its premises.

strong

Unlike validity, strength comes in degrees. Some strong arguments are stronger than others, depending on how high the probability the premises establish for the conclusion. We could if we wish draw a sharp cut off (>50%?, 70%?, 99%?) if we wished, but there isn’t always a reason to do so.

Inductive strength basically requires two things: the relative probability of the conclusion given the premises must be high, and this high probability must be on the basis of the premises; it cannot simply be because the conclusion’s probability is high on its own.

The probability of the conclusion given the premises must be high, and it must be higher than the prior probability of the conclusion on its own.

Arnold Schwarzenegger was in California yesterday. It is likely, therefore, that multiple babies will be born in California today.

Going into a lot of detail here would require discussing the probability calculus, a part of mathematics. There are other courses here at UMass which cover this.

I’m just going to mention the barest outline of what is involved, and give an example. The main thing has to do with the conditional probability of the conclusion relative to the premises. It is commonplace to write P(A|B) for the probability of A given B. We assume that probabilities can be represented by numbers ranging from 0 (impossible) to 1 (guaranteed), where 0.5 is even chances either way.

Bayes’ theorem is a mathematical formula used to determine the probability of something conditional upon something else. It may be written:
P(A|B) = P(B|A) × P(A)(P(B|A) × P(A)) + (P(B|not-A) × P(not-A))

dice

For inductive logic, if we are interested in the probability of the conclusion relative to the premises, then A = the conclusion, and B = the premises taken together.

P(A) is the prior probability of the conclusion; how likely you would have considered it based on the other things you know.

P(B|A) is how likely the premises would be assuming the conclusion is true.

P(B|not-A) is how likely the premises would be assuming the conclusion is false.

P(not-A) is the inverse of P(A): the prior probability of the conclusion not being true.

This sounds more complicated than it is. Notice that the right side of Bayes’ theorem is of the form XX + Y. It grows as X grows and shrinks as Y grows. Aside from prior probabilities, X is determined by the likelihood of the premises when the conclusion is true, and Y is determined by the likelihood of the premises when the conclusion is false.

Satya’s pregnancy test was positive. Therefore, she’s pregnant.

pregtest

Unlike deductive arguments, inductive arguments are very sensitive to background information. We need to assign a “prior” probability to Satya being pregnant prior to the news of the test. Let us assume that is 25%. (For example, perhaps she slept with her husband exactly once in the last month, but on a fertile day in her cycle.)

We also need to have information about the accuracy of the test she takes. Let us suppose that it is 95% accurate: it will be positive for a pregnant woman 95% of the time, and positive for a non-pregnant woman only 5% of the time.

We then have:

P(Pregnant|PositiveTest) =
P(PositiveTest|Pregnant) × P(Pregnant)(P(PositiveTest|Pregnant) × P(Pregnant)) + (P(PositiveTest|not-Pregnant) × P(not-Pregnant))
= 0.95 × 0.25(0.95 × 0.25) + (0.05 × 0.75) = 0.863

So interpreted, this is a fairly strong argument. There is an 86% chance that Satya is pregnant assuming the premise is true.

But this all depends on our assumptions about the prior probabilities and so on. For all intents and purposes, these can be considered additional premises (sometimes implicit, sometimes explicit). If we lower our prior estimate of her pregnancy to 5%, then there’s only about a 50% chance that a positive test means she’s pregnant. If we are forced to revise our assumptions about the reliability of the tests, things change as well.

This relates to another difference between inductive and deductive logic (at least classical deductive logic).

An argument or system of logic is monotonic if the addition of a premise or premises cannot make its inferential connection weaker, and non-monotonic otherwise.

Deductive arguments are usually considered monotonic, but induction is non-monotonic, as seen by these examples:

Satya’s pregnancy test was positive. Therefore, she’s pregnant. [Added premise: The test was 10 years old, and she mixed her pee with vinegar.]

That man in a business suit is entering the convenience mart. Hence, he plans on buying something. [Added premise: He is wearing a ski mask and brandishing a pistol.]

interro

Additional premises which, when reasonable to believe, and added to an otherwise cogent argument, render that argument weak, are sometimes called “defeaters”.

There are a number of reasons evaluating the strength of inductive arguments is complicated.

5. A Useful Chart

argument chart

To traverse this chart, start at the top. Ask these questions in this order. Go left for “yes”, right for “no”:

  1. Does the passage represent reasoning from premises to a conclusion?
  2. Are the premises represented or suggested as providing necessary support for the conclusion, so that there is no gap between their truth and that of the conclusion?
  3. If you assume the premises were true (ignoring their actual truth value), would they provide the right kind of support for the conclusion?
  4. Are the premises in fact true? (In other words, is the argument factually correct?)

G. Argument Mapping

1. Basic Idea

It is often useful to represent the inferential patterns, or from/to relationships, in an argument with a kind of map.

To do this, we start by assigning numbers to each statement in the argument.

We use these numbers in our diagram and we use arrows to represent the inferences between them. Customarily we put the conclusion (or main conclusion) at the bottom.

If there is one premise and one conclusion, a single arrow will do the trick. The arrow points from the premise to the conclusion.

➀ I think, therefore ➁ I am.
diagram

2. Independent versus Conjoint Premises

If an argument has multiple premises, we diagram them differently depending on whether or not they support the conclusion independently from one another, or only when combined.

Two premises are independent when they each provide support for the conclusion, without presupposing the truth of each other.

Two premises are conjoint when they provide little or no support for the conclusion without presupposing the truth of each other.

➀ Having unprotected sex is a bad idea. ➁ Unprotected sex often leads to unwanted pregnancy. ➂ People who have unprotected sex are much more likely to catch STDs.
diagram

food

Here, the conclusion is ➀, and the premises are ➁ and ➂. However, ➁ provides a reason for ➀ even without presupposing ➂. Similarly, ➂ provides a reason for ➀ without ➁.

These premises are independent from one another, and so we have two distinct inferential relationships going from the premises to the conclusion. We represent these with two separate arrows, as above.

The next example is different.

➀ You won’t like Guido’s. ➁ They only serve Italian food, and ➂ you hate Italian food.
diagram

Hating Italian food—➂—wouldn’t be a reason to think someone would dislike Guido’s unless that’s what they serve—➁. Similarly, the fact that this is what they serve wouldn’t be a reason to expect someone to hate it unless you know they hate Italian food.

These premises provide support for ➀ only together or in combination. They are conjoint premises. Conjoint premises are linked to the conclusion only by a single inferential connection. So we represent that in the chart with braces joining the two premises and an arrow from that brace to the conclusion.

If the argument has more than two premises you could have both at once.

➀ Kim is a convicted felon, and ➁ convicted felons aren’t allowed to vote. ➂ Kim doesn’t care enough about politics to vote anyway. So ➃ Kim won’t be voting on Tuesday.
diagram

3. Extended Arguments

So far we have considered arguments in the narrow sense, including only those with a single conclusion for which all premises are aimed at providing support.

However, something which is a premise of one argument can be a conclusion of another, and vice versa.

Quite often, however, someone putting forth an argument will also provide arguments for their premises, or use the same premises to reach multiple conclusions. In such cases, we can consider this broader notion.

(Notice this definition still excludes a situation in which multiple arguments are given in the same passage where there are no overlapping premises/conclusions.)

An extended argument is a connected series of arguments in which arguments are also provided for premises to the main argument, or premises to them, and so on, or in which the same premises are used to support more than one conclusion.

We can map extended arguments simply by using the same numbered “node” as both premise and conclusion, with arrows pointing both to it and from it.

food ➀ Chuck D has a powerful rapping voice, and ➁ his lyrics are always politically poignant. ➂ This makes him one of the best front men in rap history. Combine that with the fact that ➃ Flavor Flav is one of the most creative hype men ever, and there can be no doubt that ➄ Public Enemy is one of the greatest rap acts of all time.
diagram

food

These kinds of maps for arguments are often called Scriven diagrams, after philosopher/logician Michael Scriven. They may also be called “argument trees” or “tree diagrams”.

Hurley uses the following symbolization for the same premise or premises being used to reach multiple conclusions:

diagram

I confess, however, that it is not obvious to me why that notation would be more appropriate than two separate arrows.

Extended arguments can become more and more complex, as can the diagrams that represent them, with chains of reasoning of any length.

food All in all, ➀ an orange makes for a very healthful snack. ➁ Oranges provide a daily dose of Vitamin C. ➂ Doctors recommend consuming at least 75mg of Vitamin C per day, and ➃ a single orange typically contains 80–100mg. ➄ The membranes of oranges contain hesperidin, and ➅ studies show that hesperidin can lower cholesterol. ➆ So eating oranges may have a positive effect on your cholesterol levels. ➇ Studies also show that smelling oranges reduces tension levels in those tested, which suggests that ➈ the mere scent of orange is calming. ➉ Staying relaxed is a very important aspect of staying healthy.
diagram

archery

Each node that has at least one arrow pointing to it is the conclusion of a sub-argument.

The conclusion at the bottom of the diagram—which has arrows pointing to but none pointing from it—can be considered the main conclusion.

Those premises which do not have any arrows pointing to them could be considered the “ultimate premises”. The others are playing the role of both conclusion and premise in the extended argument.

Hurley doesn’t do this, but once you finish a diagram, it might be helpful to renumber the “ultimate premises” as (P1), (P2), etc., and the conclusions of all subarguments as (C1), (C2), marking the main conclusion with an asterisk *.

This would make it easier to put them in standard form (see above).

Here’s what this would look like for the orange example.

All in all, (C4*) an orange makes for a very healthful snack. (C1) Oranges provide a daily dose of Vitamin C. (P1) Doctors recommend consuming at least 75mg of Vitamin C per day, and (P2) a single orange typically contains 80–100mg. (P3) The membranes of oranges contain hesperidin, and (P4) studies show that hesperidin can lower cholesterol. (C2) So eating oranges may have a positive effect on your cholesterol levels. (P5) Studies also show that smelling oranges reduces tension levels in those tested, which suggests that (C3) the mere scent of orange is calming. (P6) Staying relaxed is a very important aspect of staying healthy.
diagram

Time permitting, we’ll do some more examples on the board.

H. Argument Reconstruction

1. Why Reconstruct?

cat

So far most of the arguments we have considered have been made-up examples written by me. They were usually written deliberately in a way that makes it easy to appreciate their structure, or at least the point I was trying to make.

Most arguments you come across in your daily life, however, were not self-consciously produced as arguments. The premises and conclusions may have been left partially implicit, or intermingled with non-argumentative language. Assumptions which are taken for granted or considered to be common knowledge may be left out. The writing or speech may involve rhetorical devices and expressions of feeling that are not necessary for appreciating the core of the argument.

It is an important skill, therefore, to be able to read a argumentative piece of prose, or hear an argumentative speech, and extract from it the real gist of the argument, remove what is inessential, and reconstruct it in standard form—or, in the case of an extended argument, put all the sub-arguments in standard form, with all hidden assumptions made explicit.

Argument reconstruction is not an exact science. Often it involves some guesswork about what the author or the argument intended. You will get better results, however, if you try to interpret charitably, in the following sense.

The principle of charity asserts that when interpreting someone else, if there are multiple possible interpretations, try to choose the one that is most likely to make their beliefs true and their reasoning valid or strong.

interpret

(Of course, this is not the only meaning of “charity”, but it is what we will be using in this class.)

This can be difficult to do if you’re interpreting an argument for a conclusion you don’t accept, or a person whom you dislike, but it is all the more important then. If you can put an argument in its best form before evaluating it, your evaluation is much more likely to be worthwhile or definitive.

2. Implicit Parts of An Argument: Overview

In actual discourse, premises and conclusions are sometimes left implicit or unstated. In these cases, the author trusts that the audience will be able to figure this out. Parts might also be disguised as rhetorical questions or similar.

An implicit conclusion is an intended conclusion of argument that is not actually written or spoken.

An implicit premise is an intended premise of argument that is not actually written or spoken.

cochran You should never wear white after Labor Day, and look it’s September 22nd already. (Implicit conclusion.)

If the glove don’t fit, you must acquit. (Implicit second premise and implicit conclusion.)

The above example is arguably an exception to what we said earlier: that a conditional by itself is not an argument, but only because the rest of the argument is left implicit.

It was supposed to be obvious that the glove didn’t fit, and thus obvious that the jurors were to conclude that they must acquit.

An enthymeme is an argument with implicit premises.

3. Validity and Connecting Premises

Recognizing a certain kind of implicit premise is at the heart of argument reconstruction.

In a well-constructed argument, it should be obvious how every premise is connected to other premises and/or the conclusion, and the resulting form should nearly always be valid/strong.

Using a valid form is part of applying the principle of charity. People rarely use patently invalid or weak reasoning, and the exceptions are very obvious.

monty python sir bedevere and witch In a scene from Monty Python and the Holy Grail (watch here), villagers accuse a woman of being a witch. Since they burn witches, and also burn wood, they conclude that witches must be made of wood. They weigh her to see if she weighs the same as a duck, since both ducks and wood float in water. Consider

All things made of wood burn.
Witches burn.
Therefore, witches are made of wood.


This argument is not just unsound; it is blatantly invalid. But it also stands out as such. It would be an insult to actual people to interpret them as reasoning this poorly.

Every invalid argument (or if inductive, every weak argument) can be turned in to a valid argument (strong argument) by the addition of the right premise or premises. Therefore, the principle of charity demands that, unless we have a very good reason not to do so, we should interpret the author of the argument as intending such a premise or premises implicitly.

The Monty Python example argument above is invalid, but becomes valid if we add the premise:

If all things made of wood burn, then all things that burn are made of wood.

Of course, then the argument is still blatantly unsound (because it is factually incorrect). But that’s only because this is an unusual, extreme example.

It’s usually possible to do better.

A connecting premise for an argument is a premise that the argument can be assumed to be employing implicitly because it is needed to make the argument deductively valid or inductively strong.

Typically, a connecting premise is a premise that would go conjointly with one of the explicit premises to allow us to reach the conclusion.

fitzy Kelly’s last name is Fitzpatrick, so she must be Irish.

(Connecting premise: Most people with the last name Fitzpatrick are Irish.)

4. Connecting Conditionals and Covering Generalizations

One way that always makes an otherwise-invalid argument valid is to add a connecting conditional, which is just a connecting premise taking the form of an if-then statement with the other premise or premises as antecedent and the conclusion as consequent.

1. A.
2. B.
3. C.
4. Therefore, D.

Becomes valid like so:

1. A.
2. B.
3. C.
4. If A and B and C, then D.
5. Therefore, D.

Kelly’s last name is Fitzpatrick.
Therefore, Kelly is Irish.


Connecting conditional: If Kelly’s last name is Fitzpatrick, then Kelly is Irish.

Although it is always possible to make an argument valid in this way, this is not usually the best way to interpret an argument.

The problem is that specific if-then premises added like this seem question begging. It’s like adding the premise, “hey, my premises lead to my conclusion”. This wouldn’t convince anyone who doubted the connection. If they thought the argument was invalid before, they’d simply think the new premise is false.

So, when possible, it is better to use a covering generalization.

A generalization is a statement that makes a claim about all, every, no, or at least almost all or most members in a group.

A covering generalization for an argument is a connecting premise taking the form of a generalization, which implies the corresponding connecting conditional for the argument, but also covers all relevantly similar cases.

Ronaldo Cristiano Ronaldo is a professional soccer player. Hence, he’s an athlete.

Connecting conditional: If Cristiano Ronaldo is a professional soccer player, then he’s an athlete.
Covering generalization: All professional soccer players are athletes.

(Adding either premise would make the argument valid, but the generalization better captures the intended reasoning, as it is not arbitrarily limited to the one particular case involved in the argument.)

5. Finding the Right Generalizations

When interpreting an argument as using a covering generalization, there are often multiple options that would make the argument valid.

Apply the principle of charity when determining what covering generalization to interpret an argument as having.

Kelly’s last name is Fitzpatrick, so she must be Irish.

?? Covering generalization: Everyone whose last name is longer than two letters is Irish. ?? (Uncharitable!)

Similar considerations can arise with the difference between hard and soft generalizations.

A hard generalization is one that makes an assertion about all or every member of a group, or about what is always true. (When used as a connecting premise, a hard generalization typically makes the argument deductively valid.)

A soft generalization is one that makes an assertion about most or almost all members of a group, or about what is usually true. (When used as a connecting premise, a soft generalization typically makes the argument inductively strong.)

Kelly’s last name is Fitzpatrick, so she must be Irish.

?? Hard covering generalization: ?? Everyone with the last name Fitzpatrick is Irish. ?? (Uncharitable!)

Or:
Soft covering generalization: Most people with the last name Fitzpatrick are Irish

The cost of interpreting the argument the second way (with “most”) as opposed to the first way (with “every”) is that the argument becomes only inductive rather than deductive. Still, the inductive argument is much more likely to be cogent than the deductive one is to be sound, given what we know, so that’s the most charitable way to read it.

But sometimes a hard generalization is more appropriate.

suukyi Aung San Suu Kyi lives in Yangon. Hence, she lives in Myanmar.

Hard covering generalization: Everyone who lives in Yangon lives in Myanmar.
Soft covering generalization: Most people who live in Yangon live in Myanmar.

(Here the hard generalization seems more appropriate. Yangon is not half in Myanmar and half not.)

The scope must also be considered.

The scope of a generalization is the group or category of things it is about. Generalizations about a large group have wide scope; those about a smaller group have narrow scope.

All wild animals are dangerous. (Wider scope)
All wild adult tigers who have not been recently fed are dangerous. (Narrower scope)

Notice that the difference between wider and narrower scopes is not the same as that between hard and soft generalizations.

Most atoms are neutrally charged. (Soft generalization, very wide scope.)
All people elected President in both 2008 and 2012, and who used to live in the Whitehouse, and has two teenage daughters and a hot wife, love to play basketball. (Hard generalization, very narrow scope.)

Choosing the right scope when reconstructing often involves a trade-off between applying the principle of charity to one premise (implicit or explicit) and to another.

Oh, look, an American car. What junk!

car

It might be uncharitable to interpret the person giving this argument as committed to the wide generalization “All American cars are junk”. Perhaps they only believe the much narrower, and more plausible, generalization, “all cars made by the ‘big three’ American auto manufacturers from the 1980s and later which have not been refitted by special professionals trained to do so are junk”. But then, of course, one has to interpret the other premise as saying this car was made by the ‘big three’ American auto manufacturers in the 1980s or later and has not been refitted by special professionals trained to do so, which is harder to establish from a quick glance.

When identifying the covering generalization, consider both narrower and wider scope generalizations. If the scope restrictions needed for some particular case aren’t mentioned, they might also be playing the role of implicit premises.

bolt Usain Bolt is an Olympic athlete, so he’s probably over six feet tall.

Wider scope generalization: Most Olympic Athletes are over six feet tall.
More plausible narrower scope generalization: Most male Olympic Athletes are over six feet tall.
Additional implicit premise: Usain Bolt is male.

It’s not unlikely that the person giving this argument thinks it’s obvious from context that Bolt is male (given his name, given that the pronoun “he” was used, etc.), and this doesn’t need to be stated explicitly.

6. Other Kinds of Implicit Premise

Sometimes the implicit premise in argument is not a covering generalization. Indeed, a generalization might be an explicit premise, and what is left implicit is a premise about the particular case.

All politicians are liars. Therefore, Trump is a liar. (Here the implicit premise is “Trump is a politician.”)

Even when this is not the case, if the reasoning is all about a particular situation, it may be more appropriate to interpret the missing premises as about only the particular case.

feathers mcgraw If I don’t pay off McGraw, he’ll show those photos to Susan. So either I lose my life savings, or I lose my marriage.

Implicit premises: If I pay off McGraw, I lose my life savings. If he shows those photos to Susan, I lose my marriage.
(And not, e.g., generalizations such as: all shared photos lead to broken marriages, etc. Perhaps with a lot of work, and more details about the situation, relevant generalizations with appropriately narrow scopes can be found. But it just may not be worth doing so.)

Sometimes disjunctions (or-statements), or other logical forms, are just as good or even better than conditionals. But the logic of a reconstructed argument should always be clear.

7. Reducing Unnecessary Rhetoric and Extraneous Content

If a sentence or part of one is not functioning either as a premise or conclusion, it can simply be eliminated from a reconstruction. Even the premise/conclusion indicators can be removed, since we’re going to use standard form anyway.

This includes rhetorical flourishes, and mere expressions of feeling.

Rhetorical questions and the like which are obviously meant to convey statements should be replaced with those statements.

willie You’re damn right pot should be legal. It’s past time. Marijuana isn’t addictive, and doesn’t it have valid medical uses? Smoke ’em if you got ’em.

Reconstruction: Marijuana is not addictive and has valid medical uses.
Most things that are not addictive and have valid medical uses should be legal.
Therefore, marijuana should be legal.


Here we left out “you’re damn right”, "it’s past time”, and “smoke ’em if you got ’em”, which weren’t playing an essential role. The rhetorical question was replaced with a statement.

Even what appears to be a premise statement should be eliminated if it cannot be “connected” in the right way to the others or the conclusion in a charitable way.

soupJose was sneezing all day. I brought him some soup. He must be sick.

Here, “I brought him some soup” is not a premise, and should just be eliminated from a reconstruction.

Compare:
Jose sneezed all day long.
I brought Jose some soup.
Most people who sneeze all day and are brought soup by me on a given day are sick.
Therefore, Jose is sick.


With:
Jose sneezed all day long.
Most people who sneeze all day on a given day are sick.
Therefore, Jose is sick.

8. The Language of a Well-Reconstructed Argument

The language should be consistent.

Notice in the marijuana example earlier, I replaced “pot” with “marijuana” in the conclusion. If you use different words, even if they mean the same thing, the logical form wouldn’t be clear unless you add clearly unnecessary premises like “Pot and marijuana are the same” which aren’t the focus of the argument.

The language should be logically streamlined.

This means the statements are written in a way that makes their logical form and logical strength clear. Try to use expressions such as:

If (not-)P then (not-)Q.
Either (not-)P or (not-)Q.
(Almost) All A are B.
(Almost) No A are B.
Some A are (not-)B.
Most A are (not-)B.

This is often a natural byproduct of adding the necessary connecting premises.

If the argument is extended, it should also be clear how the subarguments are broken down, and related to one another.

The language should be free from vagueness and ambiguity.

A phrase is ambiguous if it has more than one possible meaning.

A phrase is vague if there are not clear-cut boundaries between the cases in which it applies and the cases in which it does not.

Some ambiguous terms: “bar”, “diamond”, “mad”
Some vague terms: “bald”, “tall”, “talented”, “fascist”

It is not only individual words that can be ambiguous, but certain more complex grammatical forms.

Dr. Jenkins admitted to reckless driving in the courthouse yesterday.

diamond

Someone please take away Jenkins’s license!

In our next unit, we’ll consider logical fallacies that involve illegitimately mixing up different meanings of ambiguous words or phrases. The examples given of such things are often quite silly:

The Parks Department installed a baseball diamond. Diamonds are a kind of jewel. Hence, the Parks Department installed a jewel.

Nonetheless even with real life examples, there can be a question as to whether or not subtle shifts in meaning are taking place.

Bernie Sanders is a socialist. As the history of the Soviet Union and other Eastern bloc countries teaches us, historically, nearly all socialists have made terrible leaders. Therefore, Bernie Sanders would make a terrible leader.

The word “socialist” is probably both vague and ambiguous. Do we mean democratic socialist? Marxist-style socialist? Even those phrases are not much better. The argument is probably easier to evaluate if you avoid that word altogether and use a more precise description.

bernie Bernie Sanders is someone who thinks that the government should play an active role in regulating the economy. As the history of the Soviet Union and other Eastern bloc countries teaches us, nearly all people who think that the government should play an active role in regulating the economy have made terrible leaders. Therefore, Bernie Sanders would make a terrible leader.

Or:

Bernie Sanders is someone who thinks that the government should have complete jurisdiction over every aspect of the economy. As the history of the Soviet Union and other Eastern bloc countries teaches us, historically, nearly all people who think that the government should have complete jurisdiction over every aspect of the economy have made terrible leaders. Therefore, Bernie Sanders would make a terrible leader.

Of course, it may not be obvious which possible interpretation is right. Again, apply the principle of charity to the extent possible.

This is just a first step; even these versions of the argument have vague words like “terrible”, “active role” and “economy”.

It may not be possible to completely eliminate all vague and ambiguous language, but if there is a likely chance that the evaluation of the argument will hinge on the precise interpretation, then it is important to do as much as you can.

9. Putting It All Together

In summary, a well constructed argument has these features:

kardashian family We should hire Tina not Evelyn for our position. Tina is so smart. She went to Harvard, after all. Evelyn is not intelligent at all. C’mon, now. Her favorite show is Keeping Up With the Kardashians. Yikes!

Reconstruction: Subargument 1:
P1. Tina went to Harvard. (Explicit)
P2. Most people who have gone to Harvard are intelligent. (Implicit. Covering generalization.)
C1. Tina is intelligent. (Explicit, but with “smart”.)


Subargument 2:
P4. Evelyn’s favorite show is Keeping Up With the Kardashians. (Explicit)
P5. Most people whose favorite show is Keeping Up With the Kardashians are not intelligent. (Implicit. Covering generalization.)
C2. Evelyn is not intelligent. (Explicit)


Main argument:
C1. Tina is intelligent.
C2. Evelyn is not intelligent.
P6. If Tina is intelligent and Evelyn is not intelligent, we should hire Tina. (Implicit. Connecting conditional.)
C3. We should hire Tina. (Explicit)

The above is still not perfect; we might try to eliminate the vague word “intelligent”; we might try to replace P6 with a covering generalization, etc., but there are limits to how much can be done without further information from the author.

The above, however, gives you a rough idea of what we are looking for in your homework or exam when we ask for a reconstructed argument.

I. What Is and Isn’t Relevant when Evaluating Arguments

Most of these come from the chapter assigned from Feldman’s Reason and Argument. One quick warning: Feldman uses “strong” in a different way from our other authors. By “strong” he means an argument that is either deductively sound, or inductively cogent and undefeated. This is basically the notion of an argument that it is rational to accept or find persuasive.

A quick list:

  1. Reconstruct the argument fully and charitably before evaluating it. Unless the argument is more or less crazy on its face (e.g., Bedevere examples), this reconstruction will put the argument in a valid or strong form, so your focus should be on the premises.
  2. Don’t evaluate an argument by considering its conclusion, whether you think it’s true or false.
  3. If you know about an argument for a contrary conclusion which you think is compelling, keep open minded about which is wrong. Try to find something about one which might point to a difficulty for the other.
  4. Don’t criticize intermediate conclusions of extended arguments directly; rather, take seriously the arguments for them.
  5. Criticisms and doubts should be directed at particular premises.
  6. Criticisms should be substantial, and backed up with their own arguments. Avoid “argument stoppers”.
  7. Factual premises should not be flatly denied, but investigated; if you suspect the arguer is wrong about a factual premise, consider how they might have formed the false belief.
  8. If you reach a negative evaluation of an argument, consider whether or not a modified version could fix the difficulty with the original argument.

We basically already considered the reasons for #1.

For #2, remember that unsound and uncogent arguments can have true conclusions. You needn’t accept every argument in favor of a conclusion you accept.

Donald Trump has bad hair. Therefore, he shouldn’t be President.

While it is true that a sound argument cannot have a false conclusion, remember that you might be wrong about your original assumption instead. If you antecedently thought it was false, your reason for thinking that could also be expressed as an argument. It would beg the question to assume it must be the new argument that is wrong.

thief Malik said he saw someone driving my car on Route 9. Therefore, my car is not in the parking lot now.

You cannot dismiss this because you “know” the car is in the parking lot. This knowledge is based on an argument such as:

I parked my car in the parking lot an hour ago and haven’t touched it since. If I parked it there an hour ago and haven’t touched it since, it is still there. Therefore, it is in the parking lot.

(If your car was stolen, the conditional premise of this argument is false.)

If you are still swayed by the original argument, try to consider whether or not it points to anything that undermines the other argument. (#3)

jlib (Argument 1) All Amherst residents are allowed to check out books from the Jones library. Sam is an Amherst resident. Thus, Sam can check out books from the Jones library.

(Argument 2) Sam had his regional library privileges revoked for not paying late fees. No one who had their regional library privileges revoked can check out books from the Jones library. Therefore, Sam cannot check out books from the Jones library.

Considering the second argument can help us see what is wrong with the first argument: its first premise is false. It would only be true if its scope were narrowed: All Amherst residents who haven’t had their regional library privileges revoked can check out books from the Jones library. But that would make the argument invalid without adding a false additional premise.

The importance of not directly criticizing conclusions of sub-arguments (#4) can be seen here.

I want to climb the tallest Mountain the world. Everest is over 29000 feet high, and no other mountain the world is. So, Everest is the tallest Mountain in the world, and I should climb Everest.

(Response: Everest isn’t the highest mountain. Kilimanjaro is.)

The importance of #5 can be seen here.


If gays and lesbians are not allowed to marry, then they do not have the same rights as straight people. All people should have equal rights. Therefore, gays and lesbians should be allowed to marry.

(Response: but Homosexuality is against God’s will.)

Whether or not the response is true is of course open to debate. But whatever is decided about that, it’s hard to see how it’s relevant to the argument given. Which premise does it show to be false? If neither, then it is irrelevant.

There are times, however, where a certain objection seems relevant, but it is hard to know what premise it undermines. This could be because the argument has not been reconstructed clearly enough, and the objection might work against different premises depending on how some ambiguity is resolved.

Freew If God existed, God would have created everything in the Universe. If God had created everything in the universe, then everything in the universe would be good. Not everything in the universe is good. Therefore, God does not exist.

(Response: humans are responsible for their own free choices.)

Which premise this is relevant to may depend on what we understand “created” and “everything” to mean. Does everything include choices? Situations? Or just matter? Here are a couple possible clarifications.

If God existed, God would have made every choice ever made about the state of the universe. If God made every choice ever made about the state of the universe, then everything in the universe would be good. Not everything in the universe is good. Therefore, God does not exist.

On this interpretation, someone believing in free will would probably reject the first premise. However, we might put it instead as:

If God existed, God would be the ultimate cause of all the matter in the universe. If God was the ultimate cause of all the matter in the universe, then every arrangement of that matter would be good. Not every arrangement of matter in the universe is good. Therefore, God does not exist.

On this interpretation, a believer in free will might reject the second premise instead.

When criticizing premises, try to provide a substantial reason to think the premise might really be false (#6). Don’t simply point out that the premise might be false or that it hasn’t been proven beyond a doubt.

Avoid unspecific criticisms that could be used to call into question nearly any premise on this or similar topics.

An argument stopper is a rhetorical device which calls into question all rational discussion or standards of argument evaluation on a certain topic, or even in general.

Burning the flag shows disrespect for the men and women who have died fighting for this country, and therefore, it is morally wrong to burn the flag.

(Response: who’s to say what’s right or what’s wrong?)

Jesus said that the laws of Moses would not pass away until the end of time. According to the laws of Moses, blasphemers should be stoned to death. Clearly, this law hasn’t survived until the end of time, nor should it have. Therefore, Jesus was wrong.

(Response: when it comes to religion, everyone is entitled to their own beliefs.)

cork

Some other argument stoppers:

I’m not saying these sayings aren’t true: I’m saying that they do not provide a substantial reason to reject a particular argument. If they worked against one argument on a topic, they’d work against all of them. They don’t reflect any serious engagement with the argument they’re directed towards. They represent an attempt just to ignore it.

There might be good reasons to stop arguing in situations, and maybe saying one of these things might even be worthwhile. But deciding not to consider arguments in a certain context for whatever reason is not itself a form of evaluating arguments.

For #7, consider:

You should avoid using the phrase “rule of thumb” because it has a sexist origin: the law in Britain used to be that husbands were allowed to beat their wives with any stick narrower than their thumbs.

(Response: That story seems made up.)
(Better response: It is understandable that you believe that, because CNN, Time and the Washington Post all ran stories in the 1980s suggesting that etymology, and it made its way into certain textbooks. However, in fact no such law ever existed in Britain, and researchers have recently traced the origins of the phrase to a method 17th century brewers once used to test the temperature of their beer.)

#8 isn’t so much a tip about evaluating an argument as it is a tip about making your time spent evaluating arguments worthwhile. If you evaluate an argument, and find it flawed, you may be right, but even so, it’s worth considering other arguments in the vicinity of that argument which are not so flawed.

good If God existed, God would be the ultimate cause of all the matter the universe. If God was the ultimate cause of all the matter in the universe, then every arrangement of that matter would be good. Not every arrangement of matter in the universe is good. Therefore, God does not exist.

Perhaps you find the second premise false for reasons already mentioned. Does the same rationale undermine a tweaked version?

If God existed, God would be the ultimate cause of all the matter the universe and the laws of nature governing how it is arranged. If God was the ultimate cause of all the matter in the universe and the laws of nature governing how it is arranged, then every arrangement of that matter that was not affected by human free will is good. Not every arrangement of matter that was not affected by human free will is good. Therefore, God does not exist.

Do you have your own tips for evaluating arguments?


© 2024 Kevin C. Klement