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A valid argument is a logical structure where, if the premises are true, the conclusion must also be true. Validity focuses solely on the form of the argument rather than the actual truth of the premises. Understanding validity is crucial because it helps to distinguish between arguments that are logically sound and those that may lead to false conclusions, regardless of the truthfulness of their premises.

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5 Must Know Facts For Your Next Test

An argument can be valid even if its premises are actually false; validity is about the relationship between premises and conclusion.
In a valid argument, the conclusion logically follows from the premises, meaning that there is no possible situation where the premises are true and the conclusion is false.
Testing validity often involves using tools like truth tables or syllogistic forms to ensure that the logical structure holds up.
Understanding whether an argument is valid helps in assessing its strength and reliability in deductive reasoning scenarios.
Validity is different from soundness; while all sound arguments are valid, not all valid arguments are sound since soundness requires true premises.

Review Questions

To determine if an argument is valid, one can analyze its structure to see if the conclusion logically follows from the premises. Syllogisms are particularly useful in this context because they provide a clear format for testing validity. By examining whether a syllogistic form leads to a conclusion that must be true given true premises, one can easily assess the validity of various arguments.
Understanding the distinction between validity and soundness significantly enhances critical thinking skills. Validity ensures that an argument's structure allows for true conclusions if premises are correct, while soundness confirms that those premises are indeed true. This comprehension enables individuals to evaluate arguments more effectively and avoid being misled by seemingly persuasive arguments that lack soundness despite being valid.
Logical connectives play a crucial role in shaping complex arguments by defining how individual statements relate to each other. For instance, using connectives like 'and' or 'or' can influence whether an argument remains valid based on how they combine premises. Analyzing these relationships requires careful consideration of how changes in logical connectives can alter the overall validity of an argument, making it essential for advanced reasoning skills.

Related terms

A sound argument is a valid argument with all true premises, guaranteeing the truth of the conclusion.

A syllogism is a form of deductive reasoning that consists of two premises followed by a conclusion, often used to test validity.

Logical connectives are symbols or words used to connect statements in logic, such as 'and', 'or', 'not', and 'if...then', which help in forming valid arguments.

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Subjects ( 7 ).

AP Psychology
Discrete Mathematics
Formal Logic I
Foundations of Lower Division Mathematics
Incompleteness and Undecidability
Logic and Formal Reasoning
Mathematical Logic

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For the rest of this chapter we are going to be talking specifically about evaluating deductive arguments – non-deductive arguments will come later, in Chapter 4.

A deductive argument is one which is intended to guarantee the truth of its conclusion. The terms we use in evaluating deductive arguments are validity/invalidity and soundness/unsoundness .

First, validity. A valid argument is one in which if its premises were all true, its conclusion would have to be true as well. It doesn’t matter (for validity) whether in fact the premises are true. All that matters for validity is that there should be a connection between the premises and the conclusion such that if the premises were true, the conclusion would also have to be true. A valid argument is an argument in which it is impossible for the premises to be true and the conclusion false.

The validity of an argument is independent of whether the premises are in fact true. Thus you don’t need to know anything about the subject that the argument is about in order to judge whether or not it is valid. To say that an argument is valid is to say something about its structure , not to say anything about its content. When we talk about validity, we are talking about the first of the two argument evaluation tasks above: we are talking about what the connection is between the premises and the conclusion.

A valid deductive argument is one in which if all the premises were true, the conclusion would also have to be true.

For example

P1. No men are mothers. P2. Some students are men. C. Some students are not mothers.

P1. All rugby players sing opera. P2. Kiri Te Kanawa is a rugby player. C. Kiri Te Kanawa sings opera.

Remember that when what you are considering is an argument’s validity, it doesn’t matter whether the premises are actually true. So it doesn’t matter, for the moment, whether it’s true that no men are mothers or that all rugby players sing opera. What matters is what connection (if any) there is between the premises and the conclusion. A valid argument has the strongest possible connection between premises and conclusion – so strong that if the premises were all true, the truth of the conclusion would be guaranteed.

So in the first example above, to see why the argument is valid, think: suppose it’s true that no men are mothers and that some students are men. Then, must it also be true (on that supposition) that some students are not mothers?

The answer is that supposing those premises to be true, it must also be true that some students are not mothers. So the argument is valid.

Doing the same for the Kiri Te Kanawa example: Suppose that it was true that all rugby players sang opera and that Kiri was a rugby player. Then the conclusion would have to be true as well: it would have to be true that Kiri sings opera. The argument is valid.

You may be thinking at this point, “But that’s stupid! We all know that it’s not true that all rugby players sing opera! So how can the argument be valid?”

Bear in mind that validity is not the only thing you have to take into consideration in deciding whether an argument is a good argument or not: it also matters whether the premises are true. The Kiri argument is valid, but it is still not a good argument. We will get onto this issue in a bit.

In everyday language, the word ‘valid’ is often used to mean ‘true’ or ‘reasonable’. In philosophy generally, and in this course, ‘valid’ has a technical meaning. An argument which is valid is one where it is impossible for the premises to all be true and the conclusion false.

Here are a number of different ways of saying what a valid argument is. They all amount to the same thing – you can use whichever one or ones help you to understand validity.

A valid argument is one in which:

it is impossible to have all the premises true and the conclusion false at the same time.
the conclusion logically follows from the premises.
if the premises were all true, the truth of the conclusion would be guaranteed.
if the premises were all true, the conclusion would also have to be true.

When you ask whether or not a particular argument is valid, you are talking about its structure, not about its content. Consider the following argument.

P1. All adlers are bobkins. P2. All bobkins are crockers. C. All adlers are crockers.

You can tell it’s valid even if you don’t know what adlers, bobkins or crockers are. I don’t know what they are, so I have no idea whether it’s true that all adlers are bobkins or that all bobkins or crockers. Nevertheless, I know the argument is valid: because of its structure, if the premises were true, the conclusion would have to be true too.

You cannot usually tell, from the truth or falsity of the premises and conclusion of an argument, whether it is valid or invalid. A valid argument can have false premises and a false conclusion, or false premises and a true conclusion, or true premises and a true conclusion. An invalid argument can too. There’s just one kind of case in which you can tell about an argument’s validity or invalidity from the truth or falsity of its premises and conclusion, and that is when you have an argument which has true premises and a false conclusion. A deductive argument with true premises and a false conclusion has to be invalid, because a valid argument by definition can never have true premises and a false conclusion.

So when you are deciding whether or not an argument is valid, don’t think about whether the premises and conclusion are true. Instead, imagine or suppose that the premises are true, and then think about whether that would mean that the conclusion also had to be true.

You might be wondering at this point why we should care about validity. Since validity has nothing to do with whether or not the premises are true, what’s the point of it? We shouldn’t accept the conclusion of an argument on the basis of its premises if its premises are obviously false, as they are in the Kiri Te Kanawa argument or in the “sisters and brothers” argument above. So why bother pointing out that the argument is valid, since it’s obviously a really bad argument?

In those cases, perhaps in real life contexts you wouldn’t need to. There are two conditions a deductive argument needs to satisfy in order to be any good: it has to be valid, and it has to have true premises. Once we notice that this one has false premises, we can already tell it’s a bad argument, whether or not it’s valid.

But it is important to be able to tell whether an argument is valid in other cases. One kind of case in which it matters is when a deductive argument has all true premises. That’s not enough to make it a good argument: you need to check whether or not it’s valid as well. For example, suppose someone argued like this:

P1. February is the next month after January. P2. Grass is green C. Snow is white.

Although the premises are true, they don’t connect properly to the conclusion – in fact they don’t connect to the conclusion at all. So they provide no reason whatsoever why you should believe the conclusion. This shows that just having true premises is not enough (not nearly enough!) to make an argument a good argument.

Another kind of case in which being able to assess validity is of practical importance is when others disagree with you about the falsity of the premises. In some contexts it is useful to be able to point out that, even though you think the premises are false, that even if they were true the argument would be no good.

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Pursuing Truth: A Guide to Critical Thinking

Chapter 2 arguments.

The fundamental tool of the critical thinker is the argument. For a good example of what we are not talking about, consider a bit from a famous sketch by Monty Python’s Flying Circus : 3

2.1 Identifying Arguments

People often use “argument” to refer to a dispute or quarrel between people. In critical thinking, an argument is defined as

A set of statements, one of which is the conclusion and the others are the premises.

There are three important things to remember here:

Arguments contain statements.
They have a conclusion.
They have at least one premise

Arguments contain statements, or declarative sentences. Statements, unlike questions or commands, have a truth value. Statements assert that the world is a particular way; questions do not. For example, if someone asked you what you did after dinner yesterday evening, you wouldn’t accuse them of lying. When the world is the way that the statement says that it is, we say that the statement is true. If the statement is not true, it is false.

One of the statements in the argument is called the conclusion. The conclusion is the statement that is intended to be proved. Consider the following argument:

Calculus II will be no harder than Calculus I. Susan did well in Calculus I. So, Susan should do well in Calculus II.

Here the conclusion is that Susan should do well in Calculus II. The other two sentences are premises. Premises are the reasons offered for believing that the conclusion is true.

2.1.1 Standard Form

Now, to make the argument easier to evaluate, we will put it into what is called “standard form.” To put an argument in standard form, write each premise on a separate, numbered line. Draw a line underneath the last premise, the write the conclusion underneath the line.

Calculus II will be no harder than Calculus I.
Susan did well in Calculus I.
Susan should do well in Calculus II.

Now that we have the argument in standard form, we can talk about premise 1, premise 2, and all clearly be referring to the same thing.

2.1.2 Indicator Words

Unfortunately, when people present arguments, they rarely put them in standard form. So, we have to decide which statement is intended to be the conclusion, and which are the premises. Don’t make the mistake of assuming that the conclusion comes at the end. The conclusion is often at the beginning of the passage, but could even be in the middle. A better way to identify premises and conclusions is to look for indicator words. Indicator words are words that signal that statement following the indicator is a premise or conclusion. The example above used a common indicator word for a conclusion, ‘so.’ The other common conclusion indicator, as you can probably guess, is ‘therefore.’ This table lists the indicator words you might encounter.

Each argument will likely use only one indicator word or phrase. When the conlusion is at the end, it will generally be preceded by a conclusion indicator. Everything else, then, is a premise. When the conclusion comes at the beginning, the next sentence will usually be introduced by a premise indicator. All of the following sentences will also be premises.

For example, here’s our previous argument rewritten to use a premise indicator:

Susan should do well in Calculus II, because Calculus II will be no harder than Calculus I, and Susan did well in Calculus I.

Sometimes, an argument will contain no indicator words at all. In that case, the best thing to do is to determine which of the premises would logically follow from the others. If there is one, then it is the conclusion. Here is an example:

Spot is a mammal. All dogs are mammals, and Spot is a dog.

The first sentence logically follows from the others, so it is the conclusion. When using this method, we are forced to assume that the person giving the argument is rational and logical, which might not be true.

2.1.3 Non-Arguments

One thing that complicates our task of identifying arguments is that there are many passages that, although they look like arguments, are not arguments. The most common types are:

Explanations
Mere asssertions
Conditional statements
Loosely connected statements

Explanations can be tricky, because they often use one of our indicator words. Consider this passage:

Abraham Lincoln died because he was shot.

If this were an argument, then the conclusion would be that Abraham Lincoln died, since the other statement is introduced by a premise indicator. If this is an argument, though, it’s a strange one. Do you really think that someone would be trying to prove that Abraham Lincoln died? Surely everyone knows that he is dead. On the other hand, there might be people who don’t know how he died. This passage does not attempt to prove that something is true, but instead attempts to explain why it is true. To determine if a passage is an explanation or an argument, first find the statement that looks like the conclusion. Next, ask yourself if everyone likely already believes that statement to be true. If the answer to that question is yes, then the passage is an explanation.

Mere assertions are obviously not arguments. If a professor tells you simply that you will not get an A in her course this semester, she has not given you an argument. This is because she hasn’t given you any reasons to believe that the statement is true. If there are no premises, then there is no argument.

Conditional statements are sentences that have the form “If…, then….” A conditional statement asserts that if something is true, then something else would be true also. For example, imagine you are told, “If you have the winning lottery ticket, then you will win ten million dollars.” What is being claimed to be true, that you have the winning lottery ticket, or that you will win ten million dollars? Neither. The only thing claimed is the entire conditional. Conditionals can be premises, and they can be conclusions. They can be parts of arguments, but that cannot, on their own, be arguments themselves.

Finally, consider this passage:

I woke up this morning, then took a shower and got dressed. After breakfast, I worked on chapter 2 of the critical thinking text. I then took a break and drank some more coffee….

This might be a description of my day, but it’s not an argument. There’s nothing in the passage that plays the role of a premise or a conclusion. The passage doesn’t attempt to prove anything. Remember that arguments need a conclusion, there must be something that is the statement to be proved. Lacking that, it simply isn’t an argument, no matter how much it looks like one.

2.2 Evaluating Arguments

The first step in evaluating an argument is to determine what kind of argument it is. We initially categorize arguments as either deductive or inductive, defined roughly in terms of their goals. In deductive arguments, the truth of the premises is intended to absolutely establish the truth of the conclusion. For inductive arguments, the truth of the premises is only intended to establish the probable truth of the conclusion. We’ll focus on deductive arguments first, then examine inductive arguments in later chapters.

Once we have established that an argument is deductive, we then ask if it is valid. To say that an argument is valid is to claim that there is a very special logical relationship between the premises and the conclusion, such that if the premises are true, then the conclusion must also be true. Another way to state this is

An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.

An argument is invalid if and only if it is not valid.

Note that claiming that an argument is valid is not the same as claiming that it has a true conclusion, nor is it to claim that the argument has true premises. Claiming that an argument is valid is claiming nothing more that the premises, if they were true , would be enough to make the conclusion true. For example, is the following argument valid or not?

If pigs fly, then an increase in the minimum wage will be approved next term.
An increase in the minimum wage will be approved next term.

The argument is indeed valid. If the two premises were true, then the conclusion would have to be true also. What about this argument?

All dogs are mammals
Spot is a mammal.
Spot is a dog.

In this case, both of the premises are true and the conclusion is true. The question to ask, though, is whether the premises absolutely guarantee that the conclusion is true. The answer here is no. The two premises could be true and the conclusion false if Spot were a cat, whale, etc.

Neither of these arguments are good. The second fails because it is invalid. The two premises don’t prove that the conclusion is true. The first argument is valid, however. So, the premises would prove that the conclusion is true, if those premises were themselves true. Unfortunately, (or fortunately, I guess, considering what would be dropping from the sky) pigs don’t fly.

These examples give us two important ways that deductive arguments can fail. The can fail because they are invalid, or because they have at least one false premise. Of course, these are not mutually exclusive, an argument can be both invalid and have a false premise.

If the argument is valid, and has all true premises, then it is a sound argument. Sound arguments always have true conclusions.

A deductively valid argument with all true premises.

Inductive arguments are never valid, since the premises only establish the probable truth of the conclusion. So, we evaluate inductive arguments according to their strength. A strong inductive argument is one in which the truth of the premises really do make the conclusion probably true. An argument is weak if the truth of the premises fail to establish the probable truth of the conclusion.

There is a significant difference between valid/invalid and strong/weak. If an argument is not valid, then it is invalid. The two categories are mutually exclusive and exhaustive. There can be no such thing as an argument being more valid than another valid argument. Validity is all or nothing. Inductive strength, however, is on a continuum. A strong inductive argument can be made stronger with the addition of another premise. More evidence can raise the probability of the conclusion. A valid argument cannot be made more valid with an additional premise. Why not? If the argument is valid, then the premises were enough to absolutely guarantee the truth of the conclusion. Adding another premise won’t give any more guarantee of truth than was already there. If it could, then the guarantee wasn’t absolute before, and the original argument wasn’t valid in the first place.

2.3 Counterexamples

One way to prove an argument to be invalid is to use a counterexample. A counterexample is a consistent story in which the premises are true and the conclusion false. Consider the argument above:

By pointing out that Spot could have been a cat, I have told a story in which the premises are true, but the conclusion is false.

Here’s another one:

If it is raining, then the sidewalks are wet.
The sidewalks are wet.
It is raining.

The sprinklers might have been on. If so, then the sidewalks would be wet, even if it weren’t raining.

Counterexamples can be very useful for demonstrating invalidity. Keep in mind, though, that validity can never be proved with the counterexample method. If the argument is valid, then it will be impossible to give a counterexample to it. If you can’t come up with a counterexample, however, that does not prove the argument to be valid. It may only mean that you’re not creative enough.

An argument is a set of statements; one is the conclusion, the rest are premises.
The conclusion is the statement that the argument is trying to prove.
The premises are the reasons offered for believing the conclusion to be true.
Explanations, conditional sentences, and mere assertions are not arguments.
Deductive reasoning attempts to absolutely guarantee the truth of the conclusion.
Inductive reasoning attempts to show that the conclusion is probably true.
In a valid argument, it is impossible for the premises to be true and the conclusion false.
In an invalid argument, it is possible for the premises to be true and the conclusion false.
A sound argument is valid and has all true premises.
An inductively strong argument is one in which the truth of the premises makes the the truth of the conclusion probable.
An inductively weak argument is one in which the truth of the premises do not make the conclusion probably true.
A counterexample is a consistent story in which the premises of an argument are true and the conclusion is false. Counterexamples can be used to prove that arguments are deductively invalid.

( Cleese and Chapman 1980 ) . ↩︎